A server liquid cooling heat dissipation control method based on phase change material

Abstract

The application discloses a server liquid cooling heat dissipation control method based on a phase change material, belongs to the field of new materials, data centers and intelligent control, and realizes accurate perception of a real-time phase change state of the phase change material by directly fusing multi-source sensing data, and dynamically adjusts a prediction model structure based on the real-time phase change state, thereby solving the problem of control precision degradation caused by indirect perception in a traditional scheme. Through double-target verification and gradual smoothing of model parameter replacement, the accuracy and stability of prediction are ensured. Cross-domain joint optimization is carried out in combination with computing load scheduling information, accurate regulation and control of liquid cooling flow are realized under the premise of guaranteeing the computing performance of the server, and the adaptability and operation efficiency of the liquid cooling heat dissipation system of the data center are improved.

Description

Technical Field

[0001] This application relates to the fields of new materials, data centers, and intelligent control, and in particular to a server liquid cooling heat dissipation control method based on phase change materials. Background Technology

[0002] With the explosive growth of cloud computing and AI big data technologies, the power density of single data center racks continues to rise. Traditional air cooling methods can no longer meet the heat dissipation requirements, and liquid cooling has become the mainstream technology. Introducing phase change materials (PCMs) into liquid cooling can utilize their latent heat of phase change to absorb a large amount of heat energy under near-isothermal conditions, offering advantages such as high energy storage density and small temperature fluctuations.

[0003] In related technologies, PCM-based server liquid cooling control schemes typically assess the server's thermal response level by collecting thermal parameters such as temperature and temperature rise rate, and then generate cooling adjustment strategies accordingly. This scheme, through closed-loop regulation, alleviates the cooling response lag problem to some extent under instantaneous high load scenarios.

[0004] However, the control strategy adjustments in the above scheme are based on indirect indicators of the server's thermal parameters, rather than a direct perception of the PCM's own phase transition state. The thermal response characteristics of the PCM undergo qualitative changes during its phase transition lifecycle, and relying solely on thermal parameters cannot distinguish which kinetic mode the PCM is currently in. This results in an inability to perform structural updates based on fundamental changes in the PCM's kinetic characteristics, leading to a continuous degradation in control accuracy throughout the entire phase transition lifecycle. Summary of the Invention

[0005] This application provides a server liquid cooling heat dissipation control method based on phase change materials, the technical solution of which is as follows: On the one hand, a server liquid cooling heat dissipation control method based on phase change materials is provided, the method comprising: The impedance spectrum sweep data, ultrasonic echo signal, thermal sampling data and calculated load scheduling information of the synchronously acquired phase change material layer are time-stamped and fused in a dual-mode manner to obtain the solid-liquid ratio estimate and the phase change stage discrimination result. Based on the phase transition stage discrimination result, the matching basis function set is called from the stage index basis function library for the global linear prediction model, and the structural order is matched for the local nonlinear correction model, so that the configuration of the basis function set and the structural order are both controlled by the same phase transition stage discrimination result, so as to collaboratively output multi-step temperature prediction values. Based on the estimated solid-liquid ratio and the thermal sampling data, the reference temperature trajectory is deduced, and the multi-step temperature prediction value is verified with dual objectives. After the verification is passed, the parameters of the global linear prediction model and the local nonlinear correction model are gradually and smoothly replaced to obtain the updated current effective prediction model. Based on the multi-step temperature predictions output by the currently effective prediction model, the computational load scheduling information, and the solid-liquid ratio estimate, cross-domain joint optimization with computational performance preservation constraints is performed to obtain the liquid cooling flow allocation sequence for each server node, so as to regulate the liquid cooling pumps and valves. Attached Figure Description

[0006] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0007] Figure 1 This is a flowchart of a server liquid cooling heat dissipation control method based on phase change materials provided in an embodiment of this application; Figure 2 This is a flowchart of another server liquid cooling heat dissipation control method based on phase change materials provided in the embodiments of this application; Figure 3 This is a flowchart of another server liquid cooling heat dissipation control method based on phase change materials provided in the embodiments of this application. Detailed Implementation

[0008] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0009] In this application, the terms "first," "second," etc., are used to distinguish identical or similar items with essentially the same function. It should be understood that there is no logical or temporal dependency between "first," "second," and "nth," nor are there any restrictions on quantity or execution order.

[0010] It should be noted that the information (including but not limited to user device information, user personal information, etc.), data (including but not limited to data used for analysis, data stored, data displayed, etc.) and signals involved in this application are all authorized by the user or fully authorized by all parties, and the collection, use and processing of related data must comply with the relevant laws, regulations and standards of the relevant countries and regions.

[0011] In related technologies, server liquid cooling heat dissipation control schemes, when facing the challenge of continuously increasing power density in single racks of data centers, mainly rely on thermal parameters to indirectly assess the server's thermal response and adjust the cooling strategy accordingly. However, this approach cannot directly perceive the actual phase change state and kinetic mode of the phase change material (PCM), making it difficult for the control strategy to adapt to the changes in the thermal response characteristics of the PCM at different phase change stages. Consequently, the control accuracy degrades over time, failing to effectively maintain the server's stable operation and heat dissipation efficiency.

[0012] To address this issue, this application proposes a server liquid cooling heat dissipation control method based on phase change materials, see [link to relevant documentation]. Figure 1 The method includes: 101. The impedance spectrum sweep frequency data, ultrasonic echo signal, thermal sampling data and calculated load scheduling information of the synchronously acquired phase change material layer are time-stamped and fused in a dual-mode manner to obtain the solid-liquid ratio estimate and the phase change stage discrimination result.

[0013] 102. Based on the phase transition stage discrimination result, the matching basis function set is called from the stage index basis function library for the global linear prediction model, and the structure order is matched for the local nonlinear correction model, so that the configuration of the basis function set and the structure order are both controlled by the same phase transition stage discrimination result, so as to collaboratively output multi-step temperature prediction values.

[0014] 103. Based on the estimated solid-liquid ratio and thermal sampling data, the reference temperature trajectory is deduced. The multi-step temperature prediction is then validated using a dual-objective method. After successful validation, the parameters of the global linear prediction model and the local nonlinear correction model are replaced with progressively smoothed parameters to obtain the updated current effective prediction model.

[0015] 104. Based on the multi-step temperature prediction value output by the currently effective prediction model, the computational load scheduling information, and the solid-liquid ratio estimate, perform cross-domain joint optimization with computational performance preservation constraints to obtain the liquid cooling flow allocation sequence for each server node, so as to regulate the liquid cooling pump and valve.

[0016] For ease of understanding, the following explains some key terms in this embodiment: Impedance spectrum sweep data: refers to electrical data obtained by applying AC signals of different frequencies and measuring complex impedance values, which reflects the changes in the electrical properties of phase change materials with the phase change state.

[0017] Ultrasonic echo signal: refers to acoustic data obtained by emitting ultrasonic waves and receiving the echoes. Its propagation speed and attenuation characteristics reflect the changes in the acoustic properties of phase change materials with the phase change state.

[0018] Thermal sampling data refers to data such as temperature and heat flow obtained through thermal measurement equipment such as temperature sensors, which provides direct thermal state information of phase change materials.

[0019] Computational load scheduling information refers to load data related to server computing tasks, such as CPU utilization, task queue length, and power consumption, which is used to characterize the server's heat generation.

[0020] Solid-liquid ratio estimate: refers to the quantitative estimate of the ratio of liquid phase to solid phase in phase change material, which directly indicates the energy storage state of phase change material.

[0021] Phase transition stage determination result: refers to the determination of the current phase transition stage of the phase change material, such as the solid sensible heat conduction stage, the latent heat absorption stage, or the liquid convection stage, which is used to guide the adjustment of control strategies.

[0022] Global linear prediction model: refers to a prediction model used to capture the main linear dynamic behavior of a system. It typically uses a set of basis functions to map the input data to a high-dimensional linear space.

[0023] Local nonlinear correction model: refers to a correction model used to compensate for residual nonlinear components that the global linear prediction model fails to capture, providing fine-tuning of the predicted values.

[0024] Phase Index Basis Function Library: This refers to a pre-stored set of basis functions optimized for different phase transition stages, which is used to dynamically configure the global linear prediction model.

[0025] Structural order: refers to a parameter that defines the complexity of a model, such as the order of an autoregressive model or the number of layers in a neural network, which affects the model's fitting ability.

[0026] Multi-step temperature predictions refer to a sequence of predicted temperatures for multiple future time steps, providing a basis for forward-looking control.

[0027] Reference temperature trajectory: refers to the temperature change sequence obtained through independent thermodynamic model deduction or simulation, which serves as a benchmark for verifying predicted values.

[0028] Dual-objective validation: refers to the validation process that simultaneously evaluates prediction accuracy and model robustness, ensuring the reliability of prediction results.

[0029] Gradual and smooth replacement: refers to an update strategy that introduces model parameter updates step by step rather than replacing them all at once, in order to maintain system stability.

[0030] Current effective prediction model: refers to the latest prediction model that has been validated and put into use, and whose parameters have been updated.

[0031] Computing performance maintenance constraints: These are the limitations set to ensure that the computing performance of a server is not compromised during the operation of a liquid cooling system.

[0032] Cross-domain joint optimization: refers to the optimization process that considers factors from multiple domains, such as thermal management and computational load, in order to achieve globally optimal control.

[0033] Liquid cooling flow distribution sequence: refers to the specific scheme of liquid cooling flow distribution to each server node over time, obtained through optimized calculation.

[0034] Liquid cooling pumps and valves: These refer to the actuators used in liquid cooling systems to drive and regulate the flow of coolant.

[0035] The technical features of this embodiment will be described in detail below: Data acquisition, alignment, and fusion yielded estimated solid-liquid ratio values ​​and phase transition stage discrimination results.

[0036] To accurately perceive the real-time state of phase change materials (PCMs), impedance spectrum sweep data, ultrasonic echo signals, thermal sampling data, and computational load scheduling information of the PCM layer can be collected simultaneously. Impedance spectrum sweep data can be obtained by embedding electrodes in the PCM layer and applying alternating current signals of different frequencies; its complex impedance value varies with the solid-liquid ratio of the PCM. Ultrasonic echo signals can be obtained by placing an ultrasonic transmitter / receiver on one side of the PCM layer, emitting ultrasonic waves and receiving the echoes; its propagation speed and attenuation characteristics vary with the acoustic properties of the PCM. Thermal sampling data can be obtained using temperature sensors placed inside or on the surface of the PCM layer. Computational load scheduling information can be obtained from the server's operating system or virtualization platform. After acquisition, these multi-source data can be aligned by simple linear interpolation or nearest neighbor matching based on their respective timestamps. The aligned impedance spectrum sweep data and ultrasonic echo signals undergo preliminary processing, such as extracting amplitude or time delay features, and are then fused using a simple arithmetic mean or fixed-weighted method to obtain an estimated solid-liquid ratio. The phase transition stage determination result can be determined by comparing the estimated solid-liquid ratio with a preset fixed threshold, or by comparing the temperature change rate in the thermal sampling data with a fixed threshold.

[0037] In some embodiments, representative configurations for each sensing channel are given below; these configurations are conventional in the art, and specific values ​​can be adjusted according to the characteristics of the phase change material and the server rack structure. For impedance spectrum sweep data, one or more pairs of electrodes can be embedded in the phase change material layer. A weak AC signal sweeping from the lower limit to the upper limit of the frequency is applied using electrochemical impedance spectroscopy, and the complex impedance is measured. The number of sweep points, the step size, and the single-point integration time are determined according to the required complex impedance spectrum resolution. For ultrasonic echo signals, an ultrasonic transducer can be arranged on one side of the phase change material layer to emit and receive ultrasonic waves passing through the phase change material layer. Acoustic response characteristics are extracted based on round-trip time delay and attenuation. Thermal sampling data is acquired by temperature sensors and flow meters arranged inside or on the surface of the phase change material layer. The computational load scheduling information is provided by the server's operating system or virtualization platform. All the above multi-source data are timestamped, and the alignment of the acquisition time is completed through their respective timestamps. When the sampling rates of different channels are inconsistent, they are first recorded according to their respective timestamps, and then interpolated and aligned using a unified target time grid to align the data of each channel on a unified time reference. The specific installation location of each sensor should be determined based on the principle of being able to reflect the phase changes of the entire phase change material layer and key areas. Those skilled in the art can reasonably determine this based on the structure of the cabinet and cold plate.

[0038] Based on the phase transition stage discrimination results, the prediction model is dynamically configured.

[0039] After obtaining the phase transition stage discrimination result, the structure of the prediction model can be dynamically configured using this result. Specifically, a stage index basis function library can be pre-built, containing several sets of predefined basis functions (e.g., polynomial basis functions of different orders or simple trigonometric basis functions) for different phase transition stages (e.g., solid, liquid, phase transition region). When the discrimination result indicates that the current phase transition stage is reached, the basis function set corresponding to that stage is called from the library and used as the input feature space of the global linear prediction model. The structural order can be matched for the local nonlinear correction model. For example, based on the type of phase transition stage, an order can be selected from a pre-set fixed order set (e.g., a lower order for the solid stage and a higher order for the phase transition stage). In this process, the configuration of the basis function set and the structural order are both controlled by the discrimination result of the same phase transition stage, ensuring that the model structure matches the current phase transition dynamics mode. The global linear prediction model and the local nonlinear correction model work together to output temperature prediction values ​​for multiple future time steps. For example, a global linear prediction model can provide a basic linear prediction, while a local nonlinear correction model adds a fixed-form nonlinear correction term on top of this.

[0040] The construction of the phase index basis function library was completed offline before implementation and loaded once during system deployment. The construction process included: for each phase transition stage, collecting representative sample data of the temperature response of the phase transition material at that stage. This sample data included temperature time series obtained from digital twins or experimental rigs under different heat loads and boundary conditions, along with their corresponding driving inputs. For the sample data of each phase transition stage, a set of basis functions capable of fully linearly expressing the temperature dynamics within that stage was selected, forming the basis function set corresponding to that stage. Each basis function in the basis function set served as the observation function of the global linear prediction model, and their combination formed the observation function space for that stage. The specific form of the basis functions varies depending on the stage: In the solid-state sensible heat conduction stage, the temperature changes approximately linearly or quasi-linearly with the heat load, so low-order polynomial or exponential functions can be used as basis functions; in the latent heat absorption stage, the temperature is approximately isothermal within the phase transition range while the solid-liquid ratio changes rapidly, so a combination of a function with the solid-liquid ratio or phase transition fraction as the independent variable and a time term can be used as the basis function; in the liquid convection stage, the temperature rises rapidly again with sensible heat, so higher-order polynomials or functions containing convection terms can be used as basis functions. The dimension of the basis function set (i.e., the number of observed functions) is determined based on the fitting residuals of the sample data for that stage after expansion in the basis function space, aiming to achieve sufficient expression with the fewest basis functions within a set residual threshold. An index relationship is established with the phase transition stage discrimination result as the index key and the corresponding basis function set as the index value, so that the matching basis function set can be directly retrieved based on the current phase transition stage discrimination result during runtime. The above construction process can be repeated offline to update as the phase change material ages.

[0041] The specific structures and parameter update methods of the global linear prediction model and the local nonlinear correction model are explained below.

[0042] The global linear prediction model uses the observation function space provided by the basis function set as input features. It maps multi-source data, after timestamp alignment and dual-model fusion, to this observation function space to obtain observation vectors. The global linear prediction model establishes a multivariate linear regression relationship on this observation function space, outputting multi-step temperature predictions. The local nonlinear correction model defines its structure using the autoregressive order and the input order, and compensates for the nonlinear residuals of the global linear prediction model's output. Both models work together to output multi-step temperature predictions. The parameters of both models are initialized with a small segment of historical operating data or offline calibration data during deployment, and then updated online during operation.

[0043] The specific method for online parameter updates is as follows: With the goal of minimizing the multi-step prediction error between the predicted temperature values ​​for several future control cycles and the corresponding measured temperature values, the regression parameters of the global linear prediction model and the parameters of the local nonlinear correction model are recursively updated. Specifically, after obtaining the measured temperature value in each control cycle, the prediction error between the current output of the global linear prediction model and the measured value is calculated. Based on this prediction error, the model parameters are further recursively corrected, gradually approximating the values ​​that minimize the prediction error. To prevent parameters from forgetting historical valid information under time-varying conditions, a forgetting factor can be introduced in the recursion, making the influence of recent data on parameter updates relatively greater. The set of parameters obtained through online updates serves as the candidate "updated parameters."

[0044] The updated candidate parameters do not take effect immediately but must first undergo the aforementioned dual-objective verification: when both the accuracy verification quantity and the robustness verification quantity meet their respective thresholds, the dual-objective verification is considered successful. Subsequently, the candidate parameters are gradually replaced with the currently effective parameters over several transition steps using a progressive and smooth replacement method, resulting in the updated currently effective prediction model. If the dual-objective verification fails, the candidate parameters are discarded, the currently effective prediction model continues to run, and candidate parameters can be regenerated with new measured data in the next control cycle. Through this method, the generation, verification, and activation of the "updated parameters" form a complete closed loop, enabling the prediction model to continuously and adaptively update as the kinetic properties of the phase change material change.

[0045] The model parameters were gradually and smoothly replaced by extrapolating the reference temperature trajectory and verifying the dual objectives.

[0046] To ensure the accuracy and reliability of multi-step temperature predictions, a reference temperature trajectory can be extrapolated based on the solid-liquid ratio estimate and thermal sampling data. The extrapolation process can employ a simplified thermodynamic model of the phase change material, such as a lumped-parameter model based on the principle of energy conservation. In this model, the solid-liquid ratio estimate can be used to adjust the equivalent specific heat capacity of the phase change material, while the thermal sampling data serves as the boundary condition input for the model. Iterative calculations within the prediction time domain using this simplified model yield a series of reference temperature values, constituting the reference temperature trajectory. A dual-objective verification is then performed on the multi-step temperature predictions. The predicted values ​​are compared point-by-point with the reference temperature trajectory, and the mean absolute error is calculated as the accuracy verification measure. A pre-set perturbation with a fixed amplitude and direction is applied to the current parameters of the global linear prediction model and the local nonlinear correction model. The model is then rerun, and the maximum deviation between the predicted values ​​and the unperturbed predicted values ​​is observed as the robustness verification measure. The dual-objective verification is considered successful when both the accuracy verification measure and the robustness verification measure are below a pre-set fixed robustness threshold. After successful verification, a gradual and smooth replacement is performed on the parameters of the global linear prediction model and the local nonlinear correction model. For example, the difference between the updated parameters and the current parameters is gradually and linearly replaced with the current parameters at fixed step sizes and fixed number of periods until all replacements are completed, thus obtaining the updated and currently effective prediction model.

[0047] The following is a specific implementation of a phase change material (PCM) thermodynamic model to facilitate the reproduction of the reference temperature trajectory in a digital twin. This PCM thermodynamic model describes transient heat transfer within the PCM layer based on the energy conservation equation. The left side of the equation represents the rate of change of energy over time within each spatial discrete unit, and the right side represents the difference between the heat flux density introduced into that unit (caused by conduction and convection) and the internal heat source term (such as the heat generation power transferred from a server chip via a cold plate). The latent heat of phase change is handled using the effective heat capacity method: the equivalent specific heat capacity of the PCM in the solid-liquid two-phase region is taken as the increasing value with the change in the local solid-liquid ratio, allowing the latent heat to be absorbed or released in the form of equivalent heat capacity within a temperature range where the temperature remains approximately constant; alternatively, the enthalpy method is used, directly solving for the latent heat with enthalpy as the variable, with the latent heat included in the enthalpy-temperature relationship. The equivalent thermophysical parameters (equivalent thermal conductivity, equivalent specific heat capacity) of each spatial discrete unit are determined based on the local solid-liquid ratio of that unit and are assigned differentiated values ​​for each unit as the solid-liquid ratio changes.

[0048] During the solution process, the predicted time domain is used as the time range, and a preset time step is used. The process iterates forward step by step from the current moment. At each time step, the current phase distribution parameters and thermal boundary conditions are substituted into the equations to obtain the temperature values ​​of each spatial discrete unit at that time step, thus obtaining the temperature field distribution for that time step. The current phase distribution parameters are obtained by mapping the estimated solid-liquid ratio. The mapping relationship is as follows: the estimated solid-liquid ratio is used as the solid fraction or liquid fraction of each discrete unit within the phase change material region, or the equivalent thermophysical parameters of each unit are determined based on the calibration relationship between the solid-liquid ratio and the phase distribution. The thermal boundary conditions are obtained by converting thermal sampling data, including the convective heat transfer boundary determined by the coolant inlet temperature and flow rate, and the heat source term or heat flux density boundary corresponding to the server's heating power. From the temperature field distribution at each time step, the temperature values ​​at the corresponding measurement locations and time steps corresponding to the multi-step temperature predictions are extracted and arranged in chronological order to form a reference temperature trajectory. The control equations, latent heat treatment, boundary conditions, and initial value settings of the above model together constitute an feasible reference temperature trajectory extrapolation scheme.

[0049] Cross-domain joint optimization yields the liquid cooling flow distribution sequence.

[0050] After obtaining the updated multi-step temperature predictions from the currently active prediction model, a cross-domain joint optimization, including computational performance preservation constraints, is performed, combining computational load scheduling information and solid-liquid ratio estimates. The urgency of cooling requirements for each server node in the future prediction time domain can be determined using a simple lookup table or empirical formula based on the multi-step temperature predictions and solid-liquid ratio estimates. For example, when the predicted temperature is close to the upper limit and the solid-liquid ratio estimate is low, the cooling requirement is more urgent. Then, a cross-domain joint optimization objective function is constructed, incorporating the computational performance requirements of the scheduled tasks on the server nodes from the computational load scheduling information. This objective function can be a simple weighted sum, including a temperature control deviation term, a flow rate adjustment cost term, and a computational performance deviation cost term, where the weights of each term can be preset to fixed values. During the optimization process, computational performance preservation constraints must be met, for example, setting a fixed minimum flow rate guarantee for server nodes assigned to critical tasks. Physical constraints of the liquid cooling system must also be met, such as the upper limit of total flow rate and the upper limit of flow rate change rate. Under these fixed constraints, the optimization objective is solved using standard optimization algorithms (e.g., linear programming or quadratic programming) to obtain the liquid cooling flow distribution sequence for each server node. This sequence is used to regulate the liquid cooling pumps and valves to achieve accurate cooling of the server nodes.

[0051] This application achieves accurate real-time perception of the phase change state of phase change materials by directly fusing multi-source sensor data, and dynamically adjusts the prediction model structure accordingly, solving the problem of control accuracy degradation caused by indirect perception in traditional solutions. Dual-objective verification and progressively smooth model parameter replacement ensure the accuracy and stability of the prediction. Cross-domain joint optimization, combined with computational load scheduling information, achieves accurate control of liquid cooling flow while ensuring server computing performance, improving the adaptability and operational efficiency of data center liquid cooling systems.

[0052] This application further proposes steps for time-stamp alignment and dual-mode fusion of synchronously acquired impedance spectrum sweep data, ultrasonic echo signals, thermal sampling data, and calculated load scheduling information of the phase change material layer to obtain the estimated solid-liquid ratio and the phase change stage discrimination result. (See [link to relevant documentation]). Figure 2 ,include: 201. Extract electrical response features and acoustic response features from the impedance spectrum sweep data and the ultrasonic echo signal, respectively. Perform cross-validation based on the electrical response features and the acoustic response features to obtain the cross-validation results. The cross-validation results are used to represent the consistency and deviation of the solid-liquid ratio characterization under the two sensing modes.

[0053] 202. Based on the results of the cross-validation, the confidence weights of the impedance spectrum sweep data and the ultrasonic echo signal are determined. Based on the confidence weights, the solid-liquid ratio characterization of the two sensing modes is adaptively weighted and fused to obtain the estimated solid-liquid ratio value.

[0054] 203. Based on the rate of change of the estimated solid-liquid ratio, the temperature of the phase change material in the thermal sampling data, and the cross-validation results, determine the phase change stage discrimination result.

[0055] For example, the steps of extracting electrical and acoustic response features from the impedance spectrum sweep data and the ultrasonic echo signal, respectively, aim to extract key information directly related to the solid-liquid phase change of the phase change material from the raw sensor data. The impedance spectrum sweep data, by measuring the electrical response of the phase change material at different frequencies, reflects the changes in its internal ionic conductivity and dielectric constant, which differ between the solid and liquid states. Electrical response features can be the complex impedance amplitude and phase angle at a specific frequency, or parameters such as resistance and capacitance obtained by fitting an equivalent circuit model. The ultrasonic echo signal utilizes the differences in the propagation speed and attenuation characteristics of ultrasound in different phase media to characterize the physical state of the phase change material. Acoustic response features can be the round-trip time delay, attenuation coefficient, sound velocity, or reflection coefficient of the ultrasound. By extracting these features, the complex raw signal can be transformed into more physically meaningful and easily analyzed indicators, providing a foundation for subsequent solid-liquid ratio characterization.

[0056] Based on this, cross-validation is performed using the electrical and acoustic response characteristics to obtain cross-validation results. These results represent the consistency and deviation of the solid-liquid ratio characterization under the two sensing modes. The purpose of cross-validation is to evaluate the consistency and differences between two sensing modes (electrical and acoustic) based on different physical principles in characterizing the solid-liquid ratio of phase change materials. Since the two sensing modes may be affected by different noise sources, environmental factors, or sensor drift, their output solid-liquid ratio characterizations may have deviations. Cross-validation quantifies the deviation amount and direction of change by comparing the solid-liquid ratio characterization values ​​obtained independently from the two modes, for example, through time-series consistency analysis. For example, the mean square error, correlation coefficient, or whether their trends over time are synchronized can be calculated between the two characterization values. The cross-validation result can be a comprehensive index, including, for example, the degree of consistency (e.g., high, medium, low) and the direction of deviation (e.g., high for electrical mode, high for acoustic mode, irregular fluctuations, etc.), thus providing a basis for subsequent confidence weight adjustment.

[0057] Based on the results of this cross-validation, the confidence weights of the impedance spectrum sweep data and the ultrasonic echo signal are determined. This step aims to dynamically adjust the contribution of the two sensing modes in the solid-liquid ratio estimation according to the cross-validation results. When the cross-validation results show that the two modes are highly consistent, they can be assigned higher weights. When deviations occur, the weights need to be adjusted according to the nature of the deviation. For example, if the cross-validation results indicate that the signal quality of a certain sensing mode has decreased or is abnormal, its confidence weight will be reduced to decrease its impact on the solid-liquid ratio estimate. The determination of the confidence weights can be based on preset rules or adaptive algorithms. For example, when the deviation direction is unidirectional and continuous, the confidence weight of the sensing mode identified as the source of deviation is reduced. When the deviation direction is bidirectional and alternating, the confidence weights of both sensing modes are reduced simultaneously, and sensor state verification is triggered. When the deviation direction is irregular and fluctuating, the confidence weight of the previous cycle is maintained unchanged, and the value of the filtering smoothing coefficient in the adaptive weighted fusion is increased. This dynamic weight adjustment mechanism can effectively cope with data uncertainties caused by sensor failure, environmental interference, or changes in the properties of phase change materials.

[0058] Based on the confidence weight, an adaptive weighted fusion is performed on the solid-liquid ratio representations from the two sensing modes to obtain the estimated solid-liquid ratio. Adaptive weighted fusion combines the solid-liquid ratio representations from the two sensing modes according to their corresponding confidence weights to obtain a more accurate and robust estimate. For example, a weighted average method can be used, multiplying the solid-liquid ratio representations from both modes by their respective confidence weights, then summing and normalizing. Alternatively, more complex fusion algorithms, such as Kalman filtering or particle filtering, can be used, with the confidence weights serving as adjustment factors for the observation noise covariance. This fusion method fully utilizes the complementary advantages of the two sensing modes while suppressing the influence of unreliable data through the confidence weight mechanism, thus providing a stable and high-precision solid-liquid ratio estimate under various operating conditions.

[0059] Based on the rate of change of the estimated solid-liquid ratio, the phase change material temperature in the thermal sampling data, and the cross-validation results, the phase change stage is determined. This step aims to integrate multi-source information to accurately determine the specific phase change stage the phase change material is currently in. The rate of change of the estimated solid-liquid ratio directly reflects the speed of the phase change process; for example, the rate of change of the solid-liquid ratio is usually high during the latent heat absorption stage. The temperature of the phase change material is a direct reflection of its thermodynamic state; for example, the temperature may remain relatively stable during the latent heat absorption stage. The cross-validation results provide an assessment of the reliability of the estimated solid-liquid ratio and can be used to verify the preliminary stage determination results. For example, when the rate of change of the solid-liquid ratio is low and the temperature rises rapidly, it may be in the solid-state sensible heat conduction stage. When the rate of change of the solid-liquid ratio is high and the temperature is relatively stable, it may be in the latent heat absorption stage. By combining this information and using the cross-validation results to verify the preliminary determination, the accuracy and robustness of the phase change stage determination can be improved, avoiding misjudgments caused by fluctuations in a single indicator or sensor anomalies. The phase transition stage determination results can include the solid-state sensible heat conduction stage, the latent heat absorption stage, or the liquid convection stage, etc.

[0060] By introducing a mechanism for cross-validation of the electrical and acoustic response characteristics of impedance spectrum sweep data and ultrasonic echo signals, this application can effectively identify and quantify the consistency and deviation of solid-liquid ratio characterization under two sensing modes. Therefore, this application can dynamically determine the confidence weights of the two sensing modes based on the cross-validation results, and use these weights to adaptively weight and fuse the solid-liquid ratio characterization, thereby improving the accuracy and robustness of the solid-liquid ratio estimate even in the presence of noise, bias, or inconsistency in multi-source data. Furthermore, by comprehensively considering the rate of change of the solid-liquid ratio estimate, the phase change material temperature, and the cross-validation results, this application can more accurately determine the specific phase change stage of the phase change material, avoiding the limitations of single-index judgment. This multi-dimensional, adaptive fusion and discrimination mechanism ensures the reliability of the phase change material state information, providing a more accurate and robust decision-making basis for subsequent server liquid cooling heat dissipation control, thus effectively avoiding the problem of decreased control accuracy caused by inaccurate phase change state information.

[0061] This application further proposes a cross-validation method based on electrical and acoustic response characteristics to obtain cross-validation results, including: A first solid-liquid ratio characterization value is generated based on the electrical response characteristics, and a second solid-liquid ratio characterization value is generated based on the acoustic response characteristics.

[0062] A time-series consistency analysis was performed on the first and second solid-liquid ratio characterization values ​​to obtain the trend of the deviation amount and direction of the deviation.

[0063] Based on the deviation amount and the trend of the deviation direction, the cross-validation result is generated, which includes the consistency and deviation direction of the solid-liquid ratio characterization of the two sensing modes.

[0064] For example, in this application, a first solid-liquid ratio characterization value is generated based on the electrical response characteristics. This step aims to convert the extracted electrical response characteristics into a quantitative representation of the solid-liquid ratio of the phase change material. One implementation is to directly convert the real-time acquired electrical response characteristics into the first solid-liquid ratio characterization value using a pre-established mapping model between electrical characteristics and the solid-liquid ratio (e.g., a regression model or lookup table trained based on calibration data). Another implementation is to construct a physical electrical model based on the differences in electrical properties (such as conductivity and dielectric constant) between the solid and liquid states of the phase change material, and then calculate the solid-liquid ratio by measuring electrical parameters and combining them with the material's geometry.

[0065] A second solid-liquid ratio characterization value is generated based on the acoustic response characteristics. This step aims to convert the extracted acoustic response characteristics into a quantitative representation of the solid-liquid ratio of the phase change material. One approach is to pre-calibrate an empirical relationship curve or mathematical model between the acoustic response characteristics (e.g., ultrasonic wave propagation speed or attenuation) and the solid-liquid ratio, and then input the real-time acoustic characteristics into the model to obtain the second solid-liquid ratio characterization value. Another approach is to utilize the differences in the propagation characteristics of acoustic waves in different phase media, and calculate the solid-liquid ratio of the phase change material by measuring the time of flight, frequency shift, or waveform distortion of the ultrasonic waves, combined with acoustic physics principles.

[0066] A temporal consistency analysis was performed on the first and second solid-liquid ratio characterization values. This analysis aimed to assess the degree and trend of synchronous changes in the solid-liquid ratio characterization values ​​over time under two different sensing modes. One approach is to calculate the dynamic correlation coefficient or cross-correlation function between the first and second solid-liquid ratio characterization value sequences within a sliding time window to quantify their temporal synchronicity. Another approach is to employ a Dynamic Time Warping (DTW) algorithm to compare the similarity of the two time series, thereby assessing their consistency in the temporal dimension and identifying potential temporal misalignments or phase differences.

[0067] Obtaining the magnitude and trend of deviation is crucial for quantifying the degree of difference between two solid-liquid ratio values ​​and their evolution over time. One approach is to calculate the instantaneous difference between the first and second solid-liquid ratio values ​​and then apply a moving average or exponential smoothing to this difference sequence to obtain the magnitude of deviation. The trend of the deviation direction (e.g., continuous increase, continuous decrease, or fluctuation) is determined by analyzing the first derivative or the slope of the trend line. Another approach is to employ statistical methods, such as calculating the root mean square error (RMSE) of the two value sequences as the magnitude of deviation, and identifying the persistence or alternation of the deviation direction by comparing the change in the sign of the difference over consecutive time steps.

[0068] Based on the deviation amount and the trend of the deviation direction, the cross-validation result is generated. This step integrates the aforementioned quantified deviation information to form the cross-validation result. One implementation is to combine and judge the deviation amount (e.g., comparison with a preset threshold) and the trend of the deviation direction (e.g., unidirectional continuity, bidirectional alternation, or irregular fluctuation) using preset logical rules or decision trees, thereby generating a cross-validation result that includes the degree of consistency and the direction of deviation. Another implementation is to use a fuzzy logic system, taking the deviation amount and the trend of the deviation direction as input, and outputting the degree of consistency and the direction of deviation of the solid-liquid ratio representation of the two sensing modes through a fuzzy inference mechanism.

[0069] The cross-validation result includes the solid-liquid ratio of the two sensing modes, representing the degree of consistency and the direction of deviation. The cross-validation result is a structured output used to guide subsequent decision-making. One implementation is that the cross-validation result can be a data structure with two fields: one field represents the degree of consistency (e.g., a floating-point number between 0 and 1, or a discrete level such as "high," "medium," or "low"), and the other field represents the direction of deviation (e.g., an enumerated value such as "high for electrical mode," "high for acoustic mode," or "no deviation"). Another implementation is to represent the degree of consistency as a confidence score and the direction of deviation as a flag indicating which sensing mode is more likely to have a deviation, or a vector representing the relative trend of deviation.

[0070] The above technical solution generates a first solid-liquid ratio characterization value based on electrical response characteristics. This leverages the sensitivity of electrical sensors to the difference in ionic conductivity between the solid and liquid phases of phase change materials, directly quantifying the phase change state from an electrical perspective. This avoids indirect inference based on thermal parameters, ensuring the characterization value accurately reflects the phase change dynamics under electrical modes. A second solid-liquid ratio characterization value is generated based on acoustic response characteristics. This utilizes the correspondence between acoustic sensors and the sound velocity differences between the solid and liquid phases of phase change materials, providing independent and complementary quantitative information from an acoustic perspective. This enhances the diversity of overall perception and reduces the impact of single-sensor bias. A time-series consistency analysis is performed on the first and second solid-liquid ratio characterization values. By examining the coordinated changes of the two characterization values ​​over time, dynamic trends are captured rather than single-point data, effectively distinguishing the actual phase change process from noise interference and preventing short-term fluctuations from misleading judgments. The trend of the deviation amount and direction of deviation is obtained, quantifying the degree and directional evolution of the difference between the two sensing modes. This provides objective indicators to identify systematic biases or drifts, providing data support for subsequent decision-making. Cross-validation results are generated based on the variation trend of the deviation and the direction of deviation. The consistency level and deviation direction are dynamically generated by integrating the deviation and trend information, making the cross-validation results more interpretable and adaptable, ensuring reliable output even under complex operating conditions. The cross-validation results include the consistency level and deviation direction of the solid-liquid ratio representation for both sensing modes, directly outputting key evaluation parameters. This facilitates accurate adjustment of confidence weights in subsequent adaptive weighted fusion, thereby improving the overall accuracy of the solid-liquid ratio estimation. By providing more accurate and reliable cross-validation results, this application can effectively improve the accuracy of subsequent solid-liquid ratio estimates and phase transition stage discrimination results, thereby optimizing the formulation of liquid cooling heat dissipation control strategies and ensuring stable and efficient operation of the server under different phase transition stages.

[0071] This application further proposes generating a first solid-liquid ratio characterization value based on electrical response characteristics and a second solid-liquid ratio characterization value based on acoustic response characteristics, including: screening the complex impedance amplitude and phase angle of different frequency bands in the electrical response characteristics to extract frequency band response characteristic parameters sensitive to the difference in ionic conductivity between the solid and liquid phases of the phase change material; generating the first solid-liquid ratio characterization value based on these frequency band response characteristic parameters; extracting the ultrasonic round-trip time delay from the acoustic response characteristics; and generating the second solid-liquid ratio characterization value based on the correspondence between the ultrasonic round-trip time delay and the difference in sound velocity between the solid and liquid phases of the phase change material.

[0072] For example, screening the amplitude and phase angle of complex impedance in different frequency bands of the electrical response characteristics to extract frequency response characteristic parameters sensitive to the difference in ionic conductivity between the solid and liquid phases of a phase change material (PCM) refers to analyzing the variation of the electrical response (such as the amplitude and phase angle of complex impedance) of the PCM in different solid-liquid phase states within a specific frequency range. For instance, a comprehensive electrochemical impedance spectroscopy (EIS) test can be performed on the PCM beforehand, and its solid-liquid ratio can be determined using methods such as differential scanning calorimetry (DSC), thereby identifying the frequency bands where the amplitude and phase angle of complex impedance change the most during the phase transition and are highly correlated with the change in ionic conductivity. Another approach is to predict, based on the compositional characteristics and electrochemical model of the PCM, which frequency bands can effectively capture the difference in ionic conductivity between the solid and liquid phases through theoretical calculations or simulations, and then screen these frequency bands as sensitive bands. This step aims to focus on the electrical signals that best reflect the solid-liquid phase change of the PCM, eliminating the influence of irrelevant or interfering frequency bands.

[0073] Generating the first solid-liquid ratio characterization value based on the frequency band response characteristic parameters refers to using the frequency band response characteristic parameters obtained above, which are sensitive to differences in ionic conductivity, and transforming them into a quantified solid-liquid ratio characterization value through a specific algorithm or model. For example, an empirical mapping function can be established, which takes the complex impedance amplitude, phase angle, or a combination thereof in a specific frequency band as input and outputs the corresponding solid-liquid ratio. This mapping function can be trained and calibrated using offline experimental data. Another approach is to construct an electrical model based on physical principles, which uses the solid-liquid ratio of the phase change material as an internal parameter. By solving this model, the measured frequency band response characteristic parameters can be inverted into the solid-liquid ratio.

[0074] Extracting the ultrasonic round-trip time delay (RTD) from the acoustic response characteristics involves emitting ultrasonic pulses into a phase change material (PCM) layer using an ultrasonic sensor and receiving the ultrasonic signals reflected back from the PCM interior or boundary, measuring the time delay from emission to reception. For example, the pulse-echo method can be used, employing a single ultrasonic transducer as both transmitter and receiver to measure the time it takes for the ultrasonic wave to propagate through the PCM layer and reflect back from the other side. Another approach is the penetration method, where a transmitter and a receiver are placed on opposite sides of the PCM layer to measure the time required for the ultrasonic wave to penetrate the entire PCM layer. Since ultrasonic waves propagate at different speeds in materials of different phases, variations in the RTD directly reflect the phase changes of the PCM material.

[0075] Based on the correspondence between the ultrasonic round-trip time delay and the difference in sound velocity between the solid and liquid phases of the phase change material, the second solid-liquid ratio characterization value is generated. This refers to utilizing the physical characteristic that the propagation speed of ultrasound differs in the solid and liquid states of the phase change material to convert the measured ultrasonic round-trip time delay into a quantitative characterization of the solid-liquid ratio. For example, based on the known sound velocities of ultrasound in pure solid and pure liquid phase change materials, as well as the path length of ultrasound propagation, a hybrid model or interpolation relationship between the solid-liquid ratio and the effective sound velocity can be established. By converting the measured round-trip time delay into the effective sound velocity of the current phase change material, the solid-liquid ratio can be derived using this hybrid model. Another approach is to establish a direct mapping relationship between the ultrasonic round-trip time delay and different solid-liquid ratios through experimental calibration, forming a lookup table or fitting curve, thereby directly obtaining the solid-liquid ratio characterization value based on the real-time measured round-trip time delay.

[0076] Through the above technical solutions, regarding electrical response characteristics, by screening frequency band response characteristic parameters sensitive to the difference in ionic conductivity between the solid and liquid phases of the phase change material, it is ensured that the extracted electrical features can accurately capture the change in the essential physical quantity of ionic conductivity during the solid-liquid phase transition of the phase change material, thereby avoiding interference from irrelevant frequency bands and improving the relevance and accuracy of electrical characterization. Regarding acoustic response characteristics, by extracting the ultrasonic round-trip time delay and generating a second solid-liquid ratio characterization value based on its correspondence with the difference in sound velocity between the solid and liquid phases of the phase change material, the high sensitivity of ultrasonic wave propagation speed to material phase state is utilized, ensuring that the acoustic characterization can accurately reflect the difference in sound velocity between the solid and liquid phases of the phase change material, thereby enhancing the reliability of the acoustic characterization. This targeted feature extraction and characterization value generation method based on physical correspondence enables the first and second solid-liquid ratio characterization values ​​to more accurately and reliably reflect the true solid-liquid ratio of the phase change material. This not only improves the effectiveness of subsequent cross-validation, but also lays a solid foundation for the accuracy of the solid-liquid ratio estimation and phase transition stage discrimination results, thereby improving the accuracy and robustness of the entire server liquid cooling heat dissipation control method.

[0077] This application further proposes a method for determining the confidence weights of impedance spectrum sweep data and ultrasonic echo signals based on the results of the above cross-validation, the method comprising: The first signal quality characterization of impedance spectrum sweep data and the second signal quality characterization of ultrasonic echo signal are obtained.

[0078] When the cross-validation results indicate that the consistency of the solid-liquid ratio characterization of the two sensing modes is lower than the preset consistency threshold, the confidence weights of the impedance spectrum sweep data and the ultrasonic echo signal are determined based on the deviation direction in the cross-validation results.

[0079] Specifically, when the deviation is unidirectional and continuous, the confidence weight of the sensing mode identified as the deviation source is reduced. When the deviation is bidirectional and alternating, the confidence weights of both sensing modes are reduced simultaneously, and a sensor state verification is triggered. When the deviation is irregular and fluctuating, the confidence weight of the previous cycle is maintained, and the value of the filtering smoothing coefficient in the adaptive weighted fusion is increased.

[0080] For example, when determining confidence weights, a first signal quality characterization of the impedance spectrum sweep data and a second signal quality characterization of the ultrasonic echo signal are obtained. These first and second signal quality characterizations are used to evaluate the reliability and validity of the raw sensor data. For instance, these signal quality characterizations may include, but are not limited to, signal-to-noise ratio (SNR), signal strength, data integrity (such as the sweep point missing rate or the degree of ultrasonic distortion), or they may be measured based on sensor self-diagnosis results, packet loss rate, sampling frequency stability, and other indicators. These signal quality characterizations provide a basis for data reliability in subsequent weight adjustments, ensuring that weight adjustments not only rely on cross-validation results but also incorporate the signal quality information itself, thereby avoiding misjudgments caused by signal quality issues.

[0081] When the cross-validation result indicates that the consistency of the solid-liquid ratio characterization of the two sensing modes is lower than a preset consistency threshold, the system will determine the confidence weights of the impedance spectrum sweep data and the ultrasonic echo signal based on the deviation direction in the cross-validation result. This deviation direction is a crucial component of the cross-validation result, indicating the trend of difference between the characterization values ​​of the two sensing modes. For example, a rule base can be preset to find corresponding weight adjustment strategies based on the deviation direction (unidirectional continuous, bidirectional alternating, random jumps). Alternatively, based on fuzzy logic or an expert system, the deviation direction and degree can be used as input to dynamically output weight adjustment factors. This deviation-direction-based weight determination method allows for dynamic customization of strategies for different deviation modes, rather than using fixed rules, thereby enhancing the system's adaptability.

[0082] This application employs a differentiated weight adjustment strategy for different deviation directions. When the deviation is unidirectional and continuous, the system will reduce the confidence weight of the sensing mode identified as the deviation source. For example, an attenuation factor (such as 0.8 or 0.5) can be set, and the weight of the deviation source can be multiplied by this factor, or a fixed value can be directly subtracted from its weight. Alternatively, the attenuation factor can be dynamically calculated based on historical data analysis, making it proportional to the duration or magnitude of the deviation. This approach effectively isolates the influence of potential fault sources, preventing them from erroneously dominating the fusion process, thereby improving the accuracy of solid-liquid ratio estimation.

[0083] When the deviation direction alternates bidirectionally, the system will simultaneously reduce the confidence weights of both sensing modes and trigger a sensor status review. For example, the weights of both sensing modes can be multiplied by a small attenuation factor (e.g., 0.6), and a sensor review request can be sent to the system maintenance module. Alternatively, the weight adjustment magnitude can be related to the alternation frequency or amplitude, while simultaneously initiating deeper sensor diagnostic procedures, such as self-calibration or fault warnings. This strategy can respond promptly to system anomalies or complex interferences, avoid error accumulation, and ensure the system remains robust when facing more complex sensor problems.

[0084] When the deviation direction is irregular and fluctuates randomly, the system will maintain the confidence weights from the previous cycle and increase the value of the smoothing coefficient in the adaptive weighted fusion. For example, the current weights can be kept unchanged while the exponential smoothing coefficient or the noise covariance parameter of the Kalman filter in the fusion algorithm can be increased to enhance the smoothing effect. Alternatively, median filtering or moving average filtering can be introduced, and the data can be preprocessed before fusion while keeping the weights unchanged. This approach aims to suppress noise interference, ensure the stability of the fusion process, and avoid over-adjusting weights due to short-term, irregular fluctuations, thereby improving the robustness of the solid-liquid ratio estimation.

[0085] The above technical solution, by comprehensively considering signal quality information and the specific processing mechanism of deviation direction, solves the problem of difficulty in guaranteeing the accuracy of solid-liquid ratio estimation in complex scenarios. For example, obtaining signal quality characterization provides a reliable basis for weight determination, ensuring that weight adjustment not only depends on cross-validation results but also incorporates the quality information of the signal itself, thereby avoiding misjudgments caused by signal quality issues. When the cross-validation results indicate a consistency level lower than a preset consistency threshold, weights are determined based on the deviation direction. This allows for dynamic customization of strategies for different deviation modes, rather than using fixed rules, enhancing adaptability. When the deviation direction is unidirectional and continuous, the confidence weight of the sensing mode identified as the deviation source is reduced, effectively isolating the influence of potential fault sources and preventing them from erroneously dominating the fusion process. When the deviation direction is bidirectional and alternating, the weights are simultaneously reduced and sensor status verification is triggered to respond promptly to systemic anomalies and avoid error accumulation. When the deviation direction is irregularly fluctuating, the weights of the previous cycle are maintained unchanged and the filtering smoothing coefficient is increased to suppress noise interference and ensure the stability of the fusion process. These measures work together to improve the robustness and accuracy of weight determination in complex deviation scenarios, providing reliable input for subsequent adaptive weighted fusion, thereby making the solid-liquid ratio estimate more accurate and providing a solid foundation for the discrimination of phase transition stages.

[0086] This application further proposes a method for determining the phase transition stage discrimination result based on the rate of change of the solid-liquid ratio estimate, the phase change material temperature in the thermal sampling data, and cross-validation results. The method includes: determining the dominant kinetic mode currently in which the phase change material layer is located based on the rate of change of the solid-liquid ratio estimate and the phase change material temperature in the thermal sampling data; determining a preliminary stage discrimination result based on the dominant kinetic mode and the solid-liquid ratio estimate; verifying the preliminary stage discrimination result based on the consistency of the solid-liquid ratio characterization of the two sensing modes in the cross-validation results to obtain a verification conclusion, which indicates whether the preliminary stage discrimination result is reliable; when the verification conclusion indicates that the preliminary stage discrimination result is unreliable, shifting the preliminary stage discrimination result to the phase transition stage discrimination result of the previous cycle to obtain the phase transition stage discrimination result, which includes a solid-state sensible heat conduction stage, a latent heat absorption stage, or a liquid convection stage; and when the verification conclusion indicates that the preliminary stage discrimination result is reliable, directly using the preliminary stage discrimination result as the phase transition stage discrimination result.

[0087] In this step, based on the rate of change of the estimated solid-liquid ratio and the phase change material temperature in the thermal sampling data, the dominant kinetic mode of the phase change material layer is determined. This step aims to identify the current physical state and heat transfer mechanism of the phase change material by analyzing its macroscopic thermodynamic behavior. The rate of change of the estimated solid-liquid ratio reflects the speed of the phase change process, while the phase change material temperature directly indicates its thermal state. Specifically, an expert system based on physical laws can be constructed. This system, based on the combined characteristics of the solid-liquid ratio change rate and the phase change material temperature, and combined with preset physical rules, infers the most suitable dominant kinetic mode, such as the solid-state sensible heat conduction mode, the latent heat absorption mode, or the liquid convection mode. Alternatively, a data-driven approach can be used, such as using clustering algorithms (e.g., K-means) to cluster historical solid-liquid ratio change rate and phase change material temperature data, mapping different clusters to different dominant kinetic modes, thereby achieving mode identification.

[0088] Based on the dominant kinetic model and the estimated solid-liquid ratio, a preliminary stage discrimination result is determined. This step, after determining the dominant kinetic model of the phase change material layer, further combines the actual solid-liquid ratio value to perform a more detailed stage division of the phase change process. The dominant kinetic model provides the macroscopic background, while the estimated solid-liquid ratio provides microscopic phase information. In specific implementation, a multidimensional lookup table can be constructed, whose index includes the discrete intervals of the dominant kinetic model and the estimated solid-liquid ratio. The values ​​in the lookup table are the corresponding preliminary stage discrimination results, which can indicate the specific sub-stage position of the phase change material under the current kinetic model. Alternatively, a fuzzy inference system can be used, taking the dominant kinetic model and the estimated solid-liquid ratio as fuzzy inputs, and outputting a fuzzy set representing the sub-stages of the phase change through preset fuzzy rules and membership functions. Then, defuzzification is performed to obtain the preliminary stage discrimination result.

[0089] Based on the consistency of the solid-liquid ratio representations of the two sensing modes in the cross-validation results, the preliminary discrimination result is reviewed to obtain a review conclusion. This review conclusion indicates whether the preliminary discrimination result is reliable. This step introduces a multi-sensor data cross-validation mechanism to assess the confidence level of the preliminary discrimination result. The consistency of the cross-validation results reflects the degree of mutual corroboration of the solid-liquid ratio representations under different sensing modes and is an important basis for judging data reliability. In specific implementation, the consistency of the cross-validation results can be compared with a preset consistency threshold. If the consistency is higher than the threshold, the preliminary discrimination result is considered reliable; otherwise, it is considered unreliable. Alternatively, the consistency can be used as input, and a continuous reliability score can be output through a fuzzy logic system or probabilistic model. This score is then matched with a preset reliability level to obtain the review conclusion.

[0090] When the review conclusion indicates that the preliminary stage judgment result is unreliable, the preliminary stage judgment result is shifted to the phase transition stage judgment result of the previous cycle to obtain the phase transition stage judgment result. This phase transition stage judgment result includes the solid-state sensible heat conduction stage, the latent heat absorption stage, or the liquid convection stage. This step aims to smooth the process by introducing historical information when the reliability of the preliminary judgment result is questionable, avoiding misjudgments caused by instantaneous data fluctuations or sensor anomalies. Shifting to the result of the previous cycle is a strategy to maintain temporal continuity. In specific implementation, a weighted average method can be used to weight and fuse the current unreliable preliminary judgment result with the phase transition stage judgment result of the previous cycle, with the previous cycle result having a higher weight, to achieve the shift towards historical results. Alternatively, the phase transition stage judgment result of the previous cycle can be directly used as the current phase transition stage judgment result, or the range of variation of the current preliminary result can be limited to a certain extent so that it does not deviate too far from the result of the previous cycle.

[0091] When the verification conclusion indicates that the preliminary stage discrimination result is reliable, this preliminary stage discrimination result is directly used as the discrimination result for the phase transition stage. This step means that when cross-validation of multi-sensor data confirms that the preliminary discrimination result has high reliability, the system can trust and directly adopt the result, thereby ensuring that the control strategy can respond promptly to the real state changes of the phase change material. In specific implementation, the system directly outputs the preliminary stage discrimination result determined by the dominant kinetic model and the solid-liquid ratio estimate as the phase transition stage discrimination result. Alternatively, a simple logical verification can be performed before direct adoption, such as checking whether the preliminary discrimination result is within a reasonable physical range, to further enhance its robustness.

[0092] The above technical solution determines the dominant kinetic mode of the phase change material layer based on the rate of change of the solid-liquid ratio estimate and the phase change material temperature in the thermal sampling data. This dynamically captures the thermodynamic state of the phase change material, providing a macroscopic and real-time physical background for subsequent stage discrimination. Based on this, the preliminary stage discrimination result is determined by combining the dominant kinetic mode and the solid-liquid ratio estimate. This ensures that the division of phase change stages considers not only macroscopic kinetic characteristics but also microscopic phase information, thereby improving the precision and accuracy of the discrimination. Furthermore, this application introduces a mechanism to verify the preliminary stage discrimination result based on the consistency of the solid-liquid ratio characterization of the two sensing modes in the cross-validation results. This mechanism utilizes the mutual verification capability between multi-sensor data to effectively identify and evaluate the reliability of the preliminary discrimination result. When the verification conclusion indicates that the preliminary stage discrimination result is unreliable, the preliminary stage discrimination result is shifted to the phase change stage discrimination result of the previous cycle. This effectively avoids misjudgments and frequent, erroneous adjustments to the control strategy caused by instantaneous data anomalies or sensor noise, ensuring the stability and continuity of the phase change stage discrimination. When the verification conclusion indicates that the preliminary discrimination result is reliable, the preliminary discrimination result is directly adopted, ensuring the system's rapid response to changes in the actual phase transition state. Through this strategy combining reliability verification and smoothing, this application can output more accurate and robust phase transition stage discrimination results, including the solid-state sensible heat conduction stage, the latent heat absorption stage, or the liquid convection stage. This provides high-quality input for the subsequent basis function set calls and structural order matching of the global linear prediction model and the local nonlinear correction model, thereby improving the overall accuracy and stability of the server liquid cooling heat dissipation control method. Especially at the critical stage where the thermal response characteristics of the phase change material undergo a qualitative change, it enables more precise adjustment of the control strategy, avoiding the problem of continuous degradation of control accuracy.

[0093] This application further proposes a method for determining the dominant kinetic mode of a phase change material (PCM) layer based on the rate of change of the estimated solid-liquid ratio and the temperature of the PCM in thermal sampling data. The method includes: comparing the rate of change of the estimated solid-liquid ratio with a preset rate of change threshold; if the rate of change is lower than the preset rate of change threshold, the PCM layer is determined to be in a state of slow solid-liquid ratio change; otherwise, it is determined to be in a state of rapid solid-liquid ratio change. The method also includes comparing the heating rate of the PCM temperature in the thermal sampling data with a preset heating rate threshold; if the heating rate is lower than the preset heating rate threshold, the PCM layer is determined to be in a state of slow temperature increase; otherwise, it is determined to be in a state of rapid temperature increase. When both the solid-liquid ratio and temperature are in a state of slow solid-liquid ratio change and rapid temperature increase, the dominant kinetic mode is determined to be the solid-state sensible heat conduction mode. When both the solid-liquid ratio and temperature are in a state of rapid solid-liquid ratio change and slow temperature increase, the dominant kinetic mode is determined to be the latent heat absorption mode. When both the solid-liquid ratio and temperature are in a state of slow solid-liquid ratio change and the dominant kinetic mode determined in the previous cycle was a latent heat absorption mode or a liquid convection mode, the dominant kinetic mode is determined to be the liquid convection mode. When the solid-liquid ratio changes rapidly and the temperature rises rapidly, the dominant dynamic mode is determined to be a transition mode from the latent heat absorption stage to liquid convection, and the transition mode is mapped to the latent heat absorption mode.

[0094] For example, the rate of change of the estimated solid-liquid ratio is compared with a preset rate of change threshold. If the rate of change is lower than the preset rate of change threshold, the phase change material layer is determined to be in a state of slow solid-liquid ratio change; otherwise, it is determined to be in a state of rapid solid-liquid ratio change. This technical feature aims to preliminarily distinguish the physical state of the phase change material by quantifying the rate of change of the solid-liquid ratio over time. The rate of change of the estimated solid-liquid ratio reflects the speed of the phase change material's transformation from solid to liquid or from liquid to solid phase. The preset rate of change threshold is a key parameter used to define the boundary between "slow change" and "rapid change". For example, the rate of change can be obtained by calculating the ratio of the difference between the estimated solid-liquid ratios of adjacent time steps to the time step length, and then compared with the preset threshold. This threshold can be calibrated according to the physical properties of the phase change material, the application scenario, and experimental data. For example, the rate of change of the solid-liquid ratio is usually higher in the latent heat absorption stage of phase change and lower in the sensible heat conduction stage. Alternatively, the sliding window averaging method can be used to calculate the trend of solid-liquid ratio change over a period of time and compare it with a dynamically adjusted threshold. Dynamic thresholds can be adaptively adjusted based on historical data of system operation or current environmental conditions to improve the flexibility and accuracy of judgment.

[0095] This technique compares the heating rate of the phase change material (PCM) temperature in thermal sampling data with a preset heating threshold. If the heating rate is lower than the preset threshold, the PCM layer is considered to be in a slow-rise temperature state; otherwise, it is considered to be in a rapid-rise temperature state. This feature helps determine the thermodynamic behavior of the PCM by analyzing the rate of temperature change over time. The heating rate is an important indicator reflecting the heat absorption or release process of the PCM. The preset heating threshold is used to distinguish between "slow-rise" and "rapid-rise" temperature changes. For example, the heating rate can be obtained by performing a first-order difference or fitting on the PCM temperature in the thermal sampling data. The preset heating threshold can be set according to the PCM's phase change temperature range, sensible heat capacity, latent heat value, and the system's allowable temperature fluctuation range. For example, during the latent heat absorption stage, although heat absorption continues, the temperature may remain relatively stable, exhibiting a slow-rise state. Alternatively, methods such as Kalman filtering can be used to smooth the temperature data before calculating the heating rate to reduce the impact of measurement noise. The preset temperature threshold can be designed as a piecewise function, using different thresholds for different temperature ranges or solid-liquid ratio ranges to capture the temperature dynamics of phase change materials more precisely.

[0096] Based on this, when the solid-liquid ratio changes slowly and the temperature rises rapidly, the dominant kinetic mode is determined to be the solid-state sensible heat conduction mode. This determination logic aims to identify that the phase change material is in the solid stage, mainly absorbing heat through sensible heat. At this time, the phase change material has not yet begun large-scale melting, the solid-liquid ratio changes slowly, but its temperature rises rapidly due to continuous heat absorption. For example, after the system receives signals of a slow change in the solid-liquid ratio and a rapid temperature rise, it directly triggers the determination of the solid-state sensible heat conduction mode. This usually occurs in the early stage of the phase change process, that is, the phase change material begins to heat up from a solid state below the phase change temperature. Alternatively, a time window mechanism can be introduced, that is, the solid-state sensible heat conduction mode is only confirmed when the conditions of a slow change in the solid-liquid ratio and a rapid temperature rise are met for several consecutive control cycles, in order to avoid misjudgments caused by instantaneous fluctuations.

[0097] When the phase change material (PCM) is in a state of rapid solid-liquid ratio change and slow temperature rise, the dominant kinetic mode is determined to be the latent heat absorption mode. This determination logic aims to identify when the PCM is undergoing a phase change process, primarily absorbing heat through latent heat. At this stage, the PCM undergoes large-scale melting, and the solid-liquid ratio changes rapidly. However, due to the isothermal characteristics of latent heat absorption, the rate of temperature rise slows down. For example, when the rate of change of the solid-liquid ratio exceeds a preset threshold and the rate of temperature rise is lower than a preset threshold, the system determines it to be in the latent heat absorption mode. This is the core heat storage stage of the PCM. Alternatively, the absolute value range of the solid-liquid ratio can be used for auxiliary judgment. For example, only when the estimated solid-liquid ratio is between 0.1 and 0.9 is it considered to be in the latent heat absorption mode to avoid misjudgment when the material is completely solid or completely liquid.

[0098] When the phase change material is in a state of gradual solid-liquid ratio change and rapid temperature rise, and the dominant kinetic mode determined in the previous cycle was either latent heat absorption or liquid convection, the dominant kinetic mode is determined to be liquid convection. This determination logic aims to identify that the phase change material has completely melted and is in the liquid stage, absorbing heat mainly through convection. At this time, the solid-liquid ratio is close to 1, changing slowly, and the temperature will rise rapidly again due to continuous heat absorption. The "dominant kinetic mode determined in the previous cycle" is introduced to resolve the ambiguity of the transition from the end of latent heat absorption to liquid convection and avoid confusion with the solid-state sensible heat conduction mode. For example, under the conditions of gradual solid-liquid ratio change and rapid temperature rise, the system will query historical mode records. If the previous cycle was a latent heat absorption mode or a liquid convection mode, then the current mode is confirmed to be liquid convection. This effectively utilizes time series information to enhance the accuracy of the determination. Alternatively, a "mode transition counter" can be set, which increments when the current conditions are met and the previous cycle mode was latent heat absorption or liquid convection. The system is only identified as being in liquid convection mode when the counter reaches a preset value (e.g., three consecutive cycles) to improve the stability of the determination.

[0099] When the solid-liquid ratio changes rapidly and the temperature rises rapidly, the dominant kinetic mode is determined to be a transition mode from the latent heat absorption stage to liquid convection, and this transition mode is mapped to the latent heat absorption mode. This determination logic specifically handles the complex situation of phase change materials transitioning from the latent heat absorption stage to the liquid convection stage. During this transition period, the solid-liquid ratio may still be changing rapidly (a small amount of solid phase is still melting), while the temperature also begins to rise rapidly (most of the melted part begins to sensible heat). Mapping this to the latent heat absorption mode is to maintain a certain degree of conservatism in the control strategy, ensuring that the system can still fully utilize the remaining latent heat absorption capacity before fully entering liquid convection. For example, when both rapid solid-liquid ratio change and rapid temperature rise are detected simultaneously, the system identifies it as a special transition state. To simplify subsequent control logic and ensure safety, it is temporarily classified as a latent heat absorption mode. Alternatively, a more detailed internal evaluation of the transition mode can be performed before mapping, for example, judging the degree of transition based on the absolute value of the solid-liquid ratio (whether it is close to 1). If the solid-liquid ratio is already very close to 1, then you can consider adjusting the control parameters in the latent heat absorption mode, which is mapped to the latent heat absorption mode, to make it more inclined to the response characteristics of the liquid convection mode, so as to achieve a smooth transition.

[0100] By comparing the solid-liquid ratio change rate with a preset change rate threshold and the heating rate with a preset heating threshold, the dynamic thermal behavior of phase change materials can be quantified, thereby accurately identifying the solid-state sensible heat conduction mode and typical latent heat absorption mode. More importantly, by introducing the dominant kinetic mode determined in the previous cycle as a condition for judging the liquid convection mode, the confusion between the liquid convection mode and the solid-state sensible heat conduction mode in terms of apparent characteristics is effectively avoided, improving the robustness of the judgment. In addition, for the complex state of transitioning from latent heat absorption to liquid convection at the end of the latent heat absorption stage, this solution identifies it as a transition mode and maps it to the latent heat absorption mode. This not only simplifies the mode discrimination logic but also ensures that the latent heat characteristics of the phase change material can still be fully utilized during the transition stage, avoiding premature or inappropriate switching of control strategies due to misjudgment. Through the above accurate identification of the dominant kinetic mode, a more reliable basis can be provided for the subsequent phase change stage discrimination, thereby improving the configuration accuracy of the global linear prediction model and the local nonlinear correction model, and optimizing the overall performance of server liquid cooling heat dissipation control.

[0101] This application further proposes a method for determining preliminary stage discrimination results based on the dominant kinetic mode and the estimated solid-liquid ratio. The method includes: determining a solid-liquid ratio threshold division method corresponding to the dominant kinetic mode, wherein different solid-liquid ratio threshold ranges are used for the solid-state sensible heat conduction mode, the latent heat absorption mode, and the liquid convection mode. The estimated solid-liquid ratio is matched with the solid-liquid ratio threshold range corresponding to the dominant kinetic mode to obtain the preliminary stage discrimination result. This preliminary stage discrimination result is used to indicate the subdivided stage position of the phase change material layer under the current dominant kinetic mode.

[0102] The dominant kinetic mode refers to the primary heat transfer and phase change mechanism of the phase change material at a specific moment, categorizing the phase change material's state into different thermal behavior modes. This mode serves as a crucial contextual input for subsequent processing steps, ensuring that the system response remains consistent with the current physical state of the phase change material. For example, classification can be performed using a pre-defined set of rules, based on experimental observations or theoretical models, mapping sensor data (such as temperature, solid-liquid ratio change rate) to specific modes. Alternatively, a machine learning classifier can be employed, learning from historical data patterns to distinguish different modes. The solid-liquid ratio threshold segmentation refers to a set of predefined or dynamically adjusted solid-liquid ratio ranges or boundary values ​​used to delineate different sub-stages within each dominant kinetic mode. This segmentation provides a structured framework for interpreting continuous solid-liquid ratio estimates as discrete and meaningful phase change sub-stages, crucial for fine-grained control. For example, a fixed solid-liquid ratio range can be assigned to each mode's sub-stage based on material properties and typical operating conditions. Alternatively, the threshold can be adaptively adjusted based on the phase change material's aging state, historical performance, or other contextual information to achieve more flexible and robust stage identification. These distinct solid-liquid ratio threshold ranges refer to unique numerical ranges of the solid-liquid ratio used for the three dominant kinetic modes: sensible heat conduction, latent heat absorption, and liquid convection. This differentiation is crucial because the relationship between the solid-liquid ratio and thermal behavior varies across different modes. For example, in the latent heat absorption mode, a small change in the solid-liquid ratio may represent a significant energy absorption, while in the sensible heat heating mode, the same change may indicate a different thermal state. These ranges can be empirically determined through extensive experimental testing and observation of the behavior of phase change materials under various thermal loads. Alternatively, detailed thermal models of phase change materials can be used for numerical simulations to predict the evolution of the solid-liquid ratio under different conditions, thereby accurately defining the threshold ranges corresponding to different thermonic stages within each mode. The matching process involves comparing the current solid-liquid ratio estimate with the solid-liquid ratio threshold ranges corresponding to the identified dominant kinetic modes. This operation converts the quantitative solid-liquid ratio estimate into a qualitative phase change sub-stage, providing actionable information for control. For example, the solid-liquid ratio estimate can be directly compared with the upper and lower limits of each interval in the current mode's threshold set. Alternatively, fuzzy logic rules can be used to assign membership degrees to multiple sub-stages as the solid-liquid ratio estimate approaches the boundary, thereby achieving a more refined and robust classification. This preliminary stage discrimination result refers to the initial output indicating a specific sub-stage within the currently identified dominant kinetic mode of the phase change material. It provides more refined information on the phase change material state classification than a simple dominant kinetic mode. This result is "preliminary" because it may require further validation. For example, it could be a simple text label or numerical identifier (e.g., "Sensible heat conduction in the solid state – initial stage," "Latent heat absorption in the late stage of melting," "Liquid convection in the liquid state – later stage").Alternatively, when matching is fuzzy or based on fuzzy logic, a probability distribution of possible sub-stages can be output. The location of this sub-stage refers to a finer classification of the phase change material state within a broader dominant kinetic mode. For example, in a "latent heat absorption mode," it can distinguish between "initial melting," "intermediate melting," and "late melting." This provides a higher-resolution understanding of the thermal state of the phase change material, enabling more accurate and adaptive control strategies. For instance, ordered numerical values ​​(such as 1, 2, 3) can be used to represent the progress of sub-stages within a mode. Alternatively, specific descriptive terms can be used to clearly indicate the location in the phase change (e.g., "initial stage of solid-state sensible heat conduction," "intermediate stage of latent heat absorption," "late stage of liquid convection").

[0103] The above technical solution, by dynamically determining the corresponding solid-liquid ratio threshold based on the dominant kinetic mode, ensures that the threshold setting is highly consistent with the current thermodynamic state of the phase change material, avoiding discrimination bias caused by mode differences. Different solid-liquid ratio threshold ranges are used in the solid-state sensible heat conduction mode, latent heat absorption mode, and liquid convection mode, fully considering the uniqueness of the solid-liquid ratio change rate in each mode. For example, in the latent heat absorption mode, the solid-liquid ratio changes rapidly while the temperature rises slowly. The differentiated range design eliminates interference between modes and enhances the specificity of the threshold division. Accurately matching the real-time acquired solid-liquid ratio estimate with the solid-liquid ratio threshold range corresponding to the current dominant kinetic mode, combined with real-time measurement data and mode-specific thresholds, achieves precise positioning of the phase change material layer subdivision stage, significantly reducing the risk of misjudgment. The preliminary stage discrimination results can accurately indicate the sub-stage position of the phase change material layer under the current dominant dynamic mode, such as the initial, middle or final stage of latent heat absorption. This provides a more granular and reliable basis for subsequent liquid cooling heat dissipation control, thereby improving the adaptability and accuracy of the overall control system and ensuring that the server can obtain the best heat dissipation effect in different phase change stages.

[0104] This application further proposes a server liquid cooling heat dissipation control method based on phase change materials, which includes: based on the phase change stage discrimination result, calling a matching basis function set from the stage index basis function library for the global linear prediction model, and matching the structural order for the local nonlinear correction model. The configuration of the basis function set and the structural order are both controlled by the same phase change stage discrimination result, so as to collaboratively output multi-step temperature prediction values. For example, see Figure 3 The method includes the following steps: 301. Based on the phase transition stage discrimination result, retrieve the basis function set corresponding to the phase transition stage discrimination result from the index basis function library of the stage, and use the observation function in the basis function set as the observation function space of the global linear prediction model.

[0105] 302. Based on the nonlinear intensity of the dominant dynamic mode captured by the basis function set, determine the structural order of the local nonlinear correction model. The nonlinear intensity is determined based on the dynamic mode type indicated by the phase transition stage discrimination result.

[0106] 303. The basis function set and the structural order are combined as a co-configuration combination and synchronously loaded into the global linear prediction model and the local nonlinear correction model.

[0107] In this process, based on the phase transition stage determination result, a set of basis functions corresponding to the phase transition stage determination result is retrieved from the stage index basis function library. The observed functions in this basis function set are then used as the observation function space of the global linear prediction model. This step aims to select the set of mathematical functions that best characterizes the thermodynamic behavior of the phase transition material at its current specific phase transition stage for the global linear prediction model. This stage index basis function library can be pre-constructed, storing basis function sets optimized for different phase transition stages (e.g., solid-state sensible heat conduction stage, latent heat absorption stage, liquid convection stage). For example, in the solid-state sensible heat conduction stage, polynomial or exponential functions might be chosen as basis functions to capture the linear or quasi-linear changes in temperature with time or heat flow. In the latent heat absorption stage, specific function forms that reflect isothermal phase transition characteristics, or functions containing phase transition fractions as variables, might be selected. The retrieval process can be a direct lookup table mapping, i.e., directly indexing to the corresponding basis function set based on the phase transition stage determination result. Alternatively, it can be rule-based matching, which dynamically selects the most suitable set of basis functions based on the characteristics of the phase transition stage (such as temperature range, solid-liquid ratio change rate, etc.). The observation function space is the input feature space composed of these selected basis functions. The global linear prediction model will perform linear regression or state estimation in this space to predict the temperature of the phase change material.

[0108] Based on the nonlinear intensity of the dominant kinetic modes captured by the basis function set, the structural order of the local nonlinear correction model is determined. This nonlinear intensity is determined based on the type of kinetic mode indicated by the phase transition stage discrimination result. This step aims to adaptively adjust the complexity of the local nonlinear correction model according to the inherent nonlinearity of the current phase transition stage. This nonlinear intensity can be a quantitative assessment of the nonlinearity of the thermodynamic behavior of the current phase transition stage; for example, the latent heat absorption stage typically has a high nonlinear intensity, while the solid-state sensible heat conduction stage has a relatively low nonlinear intensity. This intensity can be obtained in advance through experimental data analysis or physical model simulation and correlated with the phase transition stage discrimination result. The determination of the structural order can include: one approach is to map the nonlinear intensity to a pre-defined order hierarchy table; for example, low nonlinear intensity corresponds to lower autoregressive and input orders, and high nonlinear intensity corresponds to higher orders, ensuring that the correction model can capture more complex nonlinear relationships. Another approach is to dynamically calculate the required number of model parameters or network layers based on the nonlinear intensity; for example, for a local nonlinear correction model with a neural network structure, higher nonlinear intensity may require more hidden layers or neurons. The structural order can be the autoregressive order, the input order, or a more generalized model complexity parameter.

[0109] Based on this, the basis function set and the structural order are combined as a co-configuration combination and synchronously loaded into the global linear prediction model and the local nonlinear correction model. This step ensures the consistency of the configuration between the global linear prediction model and the local nonlinear correction model. This co-configuration combination means that the selection of the basis function set and the determination of the structural order are not independent, but interrelated and jointly serve to accurately predict the current phase transition stage. Synchronous loading can be achieved in several ways. For example, through a unified configuration management module, when the phase transition stage discrimination result changes, this module will update the corresponding parameters of the two models simultaneously. Alternatively, atomic operations can be used to ensure that the basis function set and the structural order are loaded into their respective models within the same control cycle, avoiding model mismatch or prediction instability caused by asynchronous loading.

[0110] The above technical solution retrieves matching basis function sets from the stage index basis function library based on the phase transition stage discrimination results. This allows the global linear prediction model to select the most suitable observation function space for the dominant linear behavior of the current phase transition stage, providing a more accurate basis for linear prediction and avoiding the mismatch problem that may arise from general basis functions in specific phase transition stages. The structural order of the local nonlinear correction model is determined based on the nonlinear intensity of the dominant dynamic mode captured by the basis function set. This ensures that the correction model can adaptively adjust its complexity to accurately capture the nonlinear components that the global linear model fails to fully represent in the current phase transition stage. For example, in stages with strong nonlinearity, such as latent heat absorption, the correction model will correspondingly increase its order to enhance its correction capability. In stages with weak nonlinearity, such as sensible heat conduction, the correction model will reduce its complexity to avoid overfitting. This mechanism of coordinating and synchronously loading the basis function set and structural order based on the phase transition stage discrimination results solves the problem of prediction bias accumulation and accuracy degradation caused by the model configuration's inability to accurately capture the nonlinear characteristics of the current phase transition behavior. By ensuring that the global linear model and the local nonlinear correction model are always in optimal matching state, this application improves the accuracy and stability of multi-step temperature prediction, provides a more reliable input for subsequent liquid cooling flow distribution optimization, and thus improves the overall performance and efficiency of server liquid cooling heat dissipation control.

[0111] This application further proposes a method for determining the structural order of a local nonlinear correction model based on the nonlinear intensity of the dominant dynamic modes captured by the basis function set. The method includes: determining the magnitude of the linearized residual deviation of the global linear prediction model for the system's nonlinear behavior at the current phase transition stage, based on the nonlinear intensity. This magnitude of the linearized residual deviation characterizes the amplitude range of nonlinear components that the global linear prediction model failed to capture in the increased-dimensional linear space. Based on this magnitude of the linearized residual deviation, determining the required compensation level for the local nonlinear correction model. Based on this compensation requirement level, determining the autoregressive order and input order of the local nonlinear correction model, whereby the autoregressive order and the input order together constitute the structural order.

[0112] The nonlinear intensity refers to the degree or magnitude of nonlinear characteristics in the system's behavior. In phase change material liquid cooling systems, the phase change process itself is highly nonlinear, and the kinetic characteristics of different phase change stages (such as solid-state sensible heat conduction, latent heat absorption, and liquid convection) differ significantly, leading to varying degrees of nonlinearity in the system's response to external stimuli. It is a key indicator for evaluating the ability of a global linear prediction model to capture the system's nonlinear behavior at the current phase change stage, directly influencing the configuration of subsequent local nonlinear correction models. This nonlinear intensity can be determined in several ways. For example, it can be determined by analyzing the kinetic mode type indicated by the phase change stage discrimination results, where the latent heat absorption stage typically has a higher nonlinear intensity, while the nonlinear intensity of the solid-state sensible heat conduction stage is relatively lower. Alternatively, it can be determined through statistical analysis of the system response characteristics (such as temperature change rate, solid-liquid ratio change rate, etc.) at different phase change stages in historical data, quantifying the degree of nonlinearity at different stages and mapping it to a nonlinear intensity value.

[0113] The magnitude of the linearization residual bias refers to the range of amplitudes of nonlinear components that the global linear prediction model fails to fully capture when attempting to describe the system behavior using linear methods. Even if the global linear prediction model makes predictions in an upgraded linear space, there will still be deviations from the actual system behavior. These deviations mainly originate from the inherent nonlinear characteristics of the system. This magnitude directly quantifies the inadequacy of the global linear prediction model in the current phase transition stage, providing a clear compensation target for the local nonlinear correction model. The magnitude of the linearization residual bias can be determined by analyzing the statistical characteristics (such as root mean square error, maximum absolute error, etc.) of the historical prediction residual sequence of the global linear prediction model in the current phase transition stage, and then corrected in conjunction with the nonlinearity intensity. Alternatively, based on system identification techniques, a local linearization analysis can be performed on the global linear prediction model in the current phase transition stage, and the magnitude of the residual bias can be estimated by calculating the difference between the linearized model and the actual system response.

[0114] This compensation requirement level is a quantitative classification of the compensation capability required by the local nonlinear correction model based on the magnitude of the linearized residual deviation. It reflects the complexity and correction capability that the local nonlinear correction model needs to effectively compensate for the shortcomings of the global linear prediction model. Multiple levels can be set for this compensation requirement level, such as "low," "medium," and "high," with a preset range for the magnitude of the linearized residual deviation for each level. When the calculated magnitude of the linearized residual deviation falls within a certain range, the corresponding compensation requirement level is determined. Alternatively, a fuzzy logic system can be used, taking the magnitude of the linearized residual deviation as input, outputting continuous compensation requirement level values ​​through fuzzy inference rules, and then discretizing them into several preset levels.

[0115] The autoregressive order and input order are key parameters describing the structural complexity of a locally nonlinear correction model. The autoregressive order determines the model's dependence on its own historical outputs, i.e., how many past output values ​​the model considers when predicting the current output. The input order determines the model's dependence on the historical values ​​of external input signals, i.e., how many past input values ​​the model considers. Together, they constitute the structural order of the locally nonlinear correction model, directly affecting the model's fitting ability and computational complexity. They need to be dynamically adjusted according to the compensation requirement level to avoid overfitting while ensuring the correction effect. The autoregressive order and input order can be determined by pre-establishing a mapping table between the compensation requirement level and the autoregressive and input orders. Once the compensation requirement level is determined, the corresponding order combination can be directly looked up from the mapping table. Alternatively, model selection criteria (such as AIC and BIC criteria) combined with cross-validation can be used to search for the optimal combination of autoregressive and input orders under different compensation requirement levels and store it as empirical rules or a lookup table.

[0116] Through the above technical solution, based on the nonlinear intensity, the magnitude of the linearized residual error of the global linear prediction model in the current phase transition stage is determined. This step directly assesses the amplitude range of the nonlinear components that the global linear prediction model failed to capture in the current phase transition stage, providing an accurate basis for subsequent adjustments and ensuring that the assessment avoids ambiguity regarding the dynamic characteristics of the phase transition. Based on this linearized residual error magnitude, the required compensation level for the local nonlinear correction model is determined, converting the residual error magnitude into a quantified compensation requirement, making model adjustment more systematic and avoiding inefficiencies caused by subjective judgment. Based on the compensation requirement level, the autoregressive order and input order of the local nonlinear correction model are determined, and specific structural parameters are set to ensure that the local model can effectively capture residual nonlinear behavior. By matching the compensation requirement, the complexity and accuracy of the model are balanced. The entire process is interconnected, from the assessment of nonlinear intensity to the implementation of structural order. It achieves adaptive and accurate matching of the structural order of the local nonlinear correction model, thereby improving the accuracy and reliability of multi-step temperature predictions. Especially in the scenario of complex and variable phase change material dynamics, it can better adapt to changes in system behavior and provide a more solid foundation for subsequent liquid cooling flow distribution optimization.

[0117] This application further proposes a method for determining the magnitude of the linearization residual error of a global linear prediction model in the current phase transition stage based on nonlinear intensity. This process includes: determining a linearization capability attenuation factor of the global linear prediction model in the current phase transition stage based on nonlinear intensity. This linearization capability attenuation factor reflects the amplification of prediction error caused by the increased nonlinearity of the global linear prediction model during the phase transition stage. Obtaining the historical prediction residual sequence output by the global linear prediction model within a recent time window, this historical prediction residual sequence is obtained by subtracting the historical temperature multi-step prediction values ​​output by the global linear prediction model from the corresponding historical temperature measured values ​​point by point. Based on the linearization capability attenuation factor and the statistical characteristics of the historical prediction residual sequence, determining the magnitude of the linearization residual error, such that the magnitude of the linearization residual error shifts towards the upper envelope direction of the historical prediction residual sequence as the nonlinear intensity increases.

[0118] The nonlinear intensity refers to the degree to which the system behavior deviates from the linear model, and it can be determined based on the type of kinetic mode indicated by the phase transition stage discrimination results. For example, in the latent heat absorption stage of a phase change material, the nonlinear intensity of the system is usually high due to the complexity of the solid-liquid phase transition process. In contrast, the nonlinear intensity is relatively low in the solid-state sensible heat conduction stage or the liquid-state convection stage. This nonlinear intensity can be quantified in various ways, such as based on the weights of the nonlinear terms in the system's kinetic model, the significance index of nonlinear features in historical data, or by classifying or regressing the degree of nonlinearity using machine learning models. Another approach is to analyze the correlation between the system's input and output data, such as calculating the nonlinear correlation coefficient or using kernel function methods to assess its nonlinearity.

[0119] This global linear prediction model is a mathematical model used to predict the future state of a system, primarily based on the assumption of linearity to model the system's behavior. This model typically takes the form of an autoregressive moving average (ARMA) model, a state-space model, or a linear regression model. For example, it could be a multivariate linear regression model based on least squares, trained using historical input and output data. Alternatively, it could be a Kalman filter used to estimate and predict the system state.

[0120] The magnitude of the linearized residual bias refers to the range of amplitudes of the nonlinear components that the global linear prediction model fails to fully capture after linearizing the nonlinear behavior of the system. This magnitude characterizes the potential maximum deviation between the linear model's prediction and the actual system behavior. It can be expressed as the width of the confidence interval for the prediction error, the maximum possible error value, or the upper limit of the error variance. For example, it can be defined as the upper limit of the absolute value of the prediction residual at a specific confidence level.

[0121] The linearization capability attenuation factor is a coefficient reflecting the amplification of prediction bias caused by the increased nonlinearity during the phase transition stage of the global linear prediction model. As the nonlinearity of the system increases, the predictive ability of the linear model decreases, and the prediction bias is correspondingly amplified. This attenuation factor quantifies this amplification effect. For example, this factor can be a value between 0 and 1; the higher the nonlinearity, the smaller the factor, indicating a more severe attenuation of the linear model's predictive ability. Alternatively, the factor can be a multiplier greater than 1, directly amplifying the estimated value of the prediction residual to reflect the increased uncertainty caused by nonlinearity.

[0122] This historical prediction residual sequence is a series of error values ​​obtained by subtracting the historical temperature predictions from the global linear prediction model point by point from the corresponding historical measured temperatures. This sequence records the model's prediction accuracy over a past period. For example, it could be an array containing the differences between the predicted and actual values ​​for each of the past N control periods.

[0123] These statistical characteristics refer to the properties obtained from statistical analysis of historical forecast residual sequences, such as mean, variance, standard deviation, maximum value, minimum value, skewness, and kurtosis. These characteristics can reflect the distribution, fluctuation range, and trend of the residuals. For example, the 95% confidence interval of the residual sequence, or the mean and maximum value of its absolute values, can be calculated.

[0124] The upper envelope offset refers to adjusting the magnitude of the linearized residual bias towards the upper limit or maximum value of the historical predicted residual sequence when the nonlinearity increases. This means that with higher nonlinearity, the estimation of prediction bias will be more conservative to cover a larger potential error range. For example, if the 95% upper envelope of the historical residual sequence is X, when the nonlinearity increases, the magnitude of the linearized residual bias can be adjusted to a value greater than X, or the maximum absolute value of the historical residual sequence can be directly used as a reference.

[0125] The above technical solution enables a more accurate quantification of the linearization residual error magnitude of the global linear prediction model in the current phase transition stage, reflecting the nonlinear behavior of the system. By introducing a linearization capability attenuation factor, the degree of prediction deviation amplification caused by the increased nonlinearity during the phase transition stage can be dynamically reflected, avoiding ignoring the impact of dynamic changes while relying solely on static nonlinearity intensity values. This allows for a more accurate capture of the impact of nonlinearity on prediction accuracy. Combining the statistical characteristics of historical prediction residual sequences and using historical error data from actual model operation as an objective basis ensures the authenticity and reliability of the deviation magnitude estimation. As nonlinearity intensity increases, the linearization residual error magnitude is shifted towards the upper envelope direction of the historical prediction residual sequence. This conservative estimation strategy effectively prevents underestimation of actual deviation risk in the high nonlinearity stage, providing a more reliable and secure basis for determining the compensation requirement level for subsequent local nonlinearity correction models, thereby improving the accuracy and robustness of the entire temperature prediction model.

[0126] This application further proposes a method to determine the target values ​​of the autoregressive order and the input order for the local nonlinear correction model based on the compensation requirement level and from a preset mapping relationship between compensation level and order. The current values ​​of the autoregressive order and the input order currently used by the local nonlinear correction model are obtained. The target values ​​of the autoregressive order and the input order are compared with the current values ​​of the autoregressive order and the input order, respectively. When the deviation exceeds a preset order adjustment threshold, the target values ​​of the autoregressive order and the input order are used as the updated autoregressive order and input order.

[0127] For example, the compensation requirement level is an indicator that measures the strength or degree to which the local nonlinear correction model needs to compensate for the nonlinear behavior of the system. This level can be comprehensively evaluated based on factors such as the strength of the system's nonlinearity and the magnitude of the linearization residual error of the global linear prediction model. The preset compensation level and order mapping relationship is a pre-established lookup table or function stored in the system, which associates different compensation requirement levels with specific autoregressive order target values ​​and input order target values ​​required by the local nonlinear correction model. For example, this mapping relationship can be a discrete lookup table, mapping a low compensation requirement level to a lower autoregressive order and input order. A medium compensation requirement level maps to a medium order. A high compensation requirement level maps to a higher order. These order values ​​are predetermined based on historical data analysis, expert experience, or model identification experiments. Alternatively, the mapping relationship can also be a continuous function, for example, using a piecewise linear or nonlinear function to continuously map the compensation requirement level to the autoregressive order target value and the input order target value. Function parameters can be trained and optimized using machine learning methods based on a large amount of simulation or actual operating data to ensure that the optimal order configuration can be provided under different compensation requirements.

[0128] After determining the target order, the system needs to obtain the current values ​​of the autoregressive order and input order currently used by the local nonlinear correction model. The local nonlinear correction model has a currently effective autoregressive order and input order configuration for each control cycle or update cycle. Obtaining these current values ​​is to compare them with the target values ​​determined based on the latest compensation requirements, thereby determining whether order adjustment is needed. The system can directly read the currently used autoregressive order and input order from the configuration register or memory of the local nonlinear correction model. These values ​​are typically stored after model initialization or the last successful update. Alternatively, in a distributed control system, the current order value can be obtained by communicating with the model management module to request the order parameters for its current operating state.

[0129] The target value of the autoregressive order and the target value of the input order are compared with the current values ​​of the autoregressive order and the input order, respectively. This comparison is to assess the difference between the current model order and the ideal target order. This difference is a key basis for determining whether the model structure needs adjustment. Direct numerical comparisons can be performed, such as calculating the absolute or relative difference between the target value and the current value. Alternatively, vector distance or similarity metrics can be used to compare the autoregressive order and the input order as a vector to comprehensively assess their differences.

[0130] When the deviation exceeds a preset order adjustment threshold, the target value of the autoregressive order and the target value of the input order are used as the updated autoregressive order and input order, respectively. This preset order adjustment threshold is a key parameter that defines the allowable range of order deviation. The system will only trigger an order update operation when the difference between the target order and the current order is sufficiently large, exceeding this threshold. This helps avoid frequent fluctuations in the model order and improves system stability. The updated order will replace the current order and become the structural parameter used by the locally nonlinear correction model in subsequent runs. For example, a fixed integer threshold can be set, and an update will only be performed when the difference between the target value of the autoregressive order and the current value is greater than or equal to 2. A similar threshold can be set for the input order. Alternatively, the threshold can be dynamically adjusted according to the system's operating state or phase transition stage. For example, during the rapid phase transition stage of a phase change material, the system's nonlinearity changes drastically, and the order adjustment threshold can be appropriately lowered to allow the model to respond faster. During stable operation, the threshold can be increased to reduce unnecessary adjustments.

[0131] The above technical solution determines the target values ​​of the autoregressive order and the input order based on the compensation demand level from a preset mapping relationship. This directly links the order selection to the system's nonlinear compensation needs, avoiding biases from subjective experience and ensuring a high degree of matching between the local nonlinear correction model structure and the nonlinear characteristics of the current phase transition stage. By obtaining the current order and comparing it with the target order, and introducing a preset order adjustment threshold, updates are only triggered when there is a deviation. This effectively avoids frequent fluctuations in the model order, enhancing the robustness and stability of model updates. This mechanism ensures that the model order can respond to compensation demands promptly and accurately when the phase transition state changes rapidly, thereby effectively suppressing the accumulation of prediction errors, improving the accuracy of multi-step temperature predictions and the overall stability of the system, and avoiding prediction accuracy degradation and system instability problems caused by order mismatch. By combining the aforementioned global linear prediction model and local nonlinear correction model, this dynamic and intelligent order adjustment mechanism further optimizes the adaptability and accuracy of the prediction model. Especially in the liquid cooling heat dissipation scenario where the thermodynamic behavior of phase change materials is complex and variable, it can more accurately capture and correct nonlinear dynamics, providing a more reliable temperature prediction basis for server liquid cooling heat dissipation control.

[0132] This application further proposes a method for performing dual-objective verification of multi-step temperature predictions based on solid-liquid ratio estimates and thermal sampling data to extrapolate a reference temperature trajectory. This method includes: Using the estimated solid-liquid ratio and thermal sampling data as inputs, a phase change material thermodynamic model is independently extrapolated within a digital twin to obtain a reference temperature trajectory. The multi-step temperature predictions are compared with the reference temperature trajectory to obtain an accuracy verification quantity characterizing the degree of prediction deviation. Simultaneously, perturbations are applied to the parameters of the global linear prediction model and the local nonlinear correction model to test prediction stability, obtaining a robustness verification quantity characterizing the prediction's disturbance rejection capability. The accuracy verification quantity and the robustness verification quantity are jointly evaluated. If both the accuracy verification quantity and the robustness verification quantity meet a preset accuracy threshold, the dual-objective verification is considered successful. Otherwise, the dual-objective verification is considered unsuccessful.

[0133] For example, in the step of extrapolating the reference temperature trajectory, the estimated solid-liquid ratio and thermal sampling data are used as inputs to drive the phase change material thermodynamic model independently within the digital twin, resulting in the reference temperature trajectory. The estimated solid-liquid ratio and thermal sampling data are key operating parameters acquired by the system in real time, accurately reflecting the current state of the phase change material and the external thermal environment. This digital twin is a high-fidelity mapping of the physical system in digital space, capable of simulating the complex thermodynamic behavior of phase change materials. Driving the phase change material thermodynamic model independently means using the physical model within the digital twin, based on the current estimated solid-liquid ratio and thermal sampling data, to independently calculate the temperature change trend of the phase change material over a future period, thereby generating an objective and independent reference temperature trajectory. This independent simulation can be achieved in several ways. For example, it can be based on a finite element analysis (FEA) model to perform a detailed simulation of the heat transfer process of phase change materials, or it can be achieved by using a numerical simulation method based on the control volume method to solve the energy conservation equation under the condition of latent heat release / absorption of phase change, so as to obtain an accurate temperature distribution and change.

[0134] In the steps of obtaining the accuracy verification quantity and the robustness verification quantity, the multi-step temperature prediction value is compared with the reference temperature trajectory to obtain the accuracy verification quantity, which characterizes the degree of prediction deviation. This multi-step temperature prediction value is the collaborative output of the global linear prediction model and the local nonlinear correction model, while the reference temperature trajectory is derived from an independent digital twin. The comparison between the two can directly quantify the accuracy of the prediction model. The accuracy verification quantity can be expressed as statistical indicators such as the root mean square error (RMSE), mean absolute error (MAE), or maximum absolute deviation between the predicted value and the reference trajectory, used to measure the accuracy of the prediction. Simultaneously, perturbations are applied to the parameters of the global linear prediction model and the local nonlinear correction model to test the prediction stability, obtaining the robustness verification quantity, which characterizes the prediction's ability to withstand disturbances. Applying perturbations to the model parameters aims to simulate situations such as parameter uncertainty, sensor noise, or model drift that may occur in actual operation. This perturbation can be a random, small change, such as superimposing Gaussian white noise on the current parameter value, or a systematic change in boundary conditions, to test the model's performance under different operating conditions. By observing the changes in the model's predicted output under perturbation, its robustness can be assessed. Robustness validation metrics can be reflected in indicators such as the maximum deviation between the perturbed and unperturbed predicted sequences, the variance of the prediction error, or the convergence of the predicted trajectory.

[0135] In the joint judgment step, the accuracy verification quantity and the robustness verification quantity are jointly judged. If both the accuracy verification quantity and the robustness verification quantity meet a preset accuracy threshold and a preset robustness threshold, the dual-objective verification is deemed successful. Otherwise, the dual-objective verification is deemed unsuccessful. The preset accuracy threshold and preset robustness threshold are thresholds set based on system performance requirements and actual operating experience. For example, the accuracy threshold can be set as the RMSE of the prediction error being less than a certain specific value, while the robustness threshold can be set as the maximum deviation of the predicted value from the reference trajectory not exceeding a certain safe range under a specific disturbance. Only when the prediction model simultaneously meets the requirements of both dimensions is its prediction result considered reliable and usable, thus allowing subsequent model parameter updates. This joint judgment mechanism ensures that the model not only predicts accurately but also remains stable in the face of uncertainty.

[0136] Through the above technical solution, this application introduces a dual-objective verification mechanism to comprehensively evaluate the accuracy and stability of the prediction model, ensuring that model updates are based on reliable verification, thereby improving the robustness and accuracy of the overall control system. Specifically, using the estimated solid-liquid ratio and thermal sampling data as inference inputs, the phase change material thermodynamic model is driven to independently perform inferences within a digital twin to obtain a reference temperature trajectory. This step utilizes an independent thermodynamic model to generate an objective benchmark, avoiding potential biases introduced by relying solely on the prediction model itself, and providing a reliable reference for subsequent verification. The multi-step temperature prediction values ​​are compared with the reference temperature trajectory to obtain an accuracy verification quantity characterizing the degree of prediction deviation. This directly quantifies the prediction accuracy, ensuring that the model output is consistent with the actual thermodynamic behavior. Simultaneously, perturbations are applied to the parameters of the global linear prediction model and the local nonlinear correction model to test the prediction stability, obtaining a robustness verification quantity characterizing the prediction's disturbance resistance capability. This assesses the model's sensitivity to parameter changes and prevents prediction failure due to noise or disturbances. The accuracy verification quantity and the robustness verification quantity are jointly judged. When the accuracy verification quantity meets the preset accuracy threshold and the robustness verification quantity meets the preset robustness threshold, the dual-objective verification is determined to be passed; otherwise, it is not passed. This joint judgment mechanism forces the prediction to meet the standards in both accuracy and stability before the model can be updated. This solves the stability problem that may be ignored by a single verification index and ensures the reliability of subsequent control optimization.

[0137] This application proposes a method that uses the estimated solid-liquid ratio and the thermal sampling data as inputs to drive the thermodynamic model of the phase change material to perform independent deduction in a digital twin, thereby obtaining a reference temperature trajectory.

[0138] For example, the method includes the following steps: converting the estimated solid-liquid ratio into the current phase state distribution parameters of the phase change material region in the phase change material thermodynamic model; and converting the thermal sampling data into the thermal boundary conditions of the phase change material thermodynamic model. Based on the current phase state distribution parameters and the thermal boundary conditions, the phase change material thermodynamic model is driven to iteratively solve forward along the prediction time domain in the digital twin to obtain the temperature field distribution at each time step. From the temperature field distribution at each time step, the temperature measurement location and the temperature value at the corresponding time step are extracted to form the reference temperature trajectory.

[0139] The solid-liquid ratio estimate refers to the proportion of solid to liquid substances in a phase change material (PCM), a key parameter directly reflecting the current phase change state of the PCM. Its function is to provide direct perception of the internal state of the PCM, avoiding the limitations of relying solely on indirect thermal parameters for inference. This solid-liquid ratio estimate can be obtained in various ways, such as through dual-mode fusion of electrical response characteristics (e.g., impedance spectrum sweep data) and acoustic response characteristics (e.g., ultrasonic echo signals). Alternatively, it can be estimated using optical sensing technology, utilizing the difference in transmittance or reflectance of the PCM in its solid and liquid states. The thermal sampling data refers to real-time operational data related to heat transfer collected from the server liquid cooling system, such as the temperature of the PCM, inlet and outlet coolant temperatures, and flow rate. Its function is to provide real-time information on the system's external thermal environment and operating conditions, providing accurate boundary conditions for the derivation of thermodynamic models. This thermal sampling data can be directly collected by temperature sensors, flow sensors, etc., placed inside or on the surface of the PCM layer. Alternatively, it can be obtained by scanning the surface of the PCM layer with an infrared thermal imager to acquire temperature distribution data. Using the above-mentioned solid-liquid ratio estimates and thermal sampling data as inputs, the initial and boundary conditions for driving the thermodynamic model of phase change materials to perform simulation calculations are intended to ensure that the model inference in the digital twin can be based on the real system state and external environment, thereby improving the accuracy and reliability of the inference results.

[0140] A digital twin is a virtual mapping of a physical entity in digital space, capable of reflecting the state, behavior, and performance of the physical entity in real time. Here, the digital twin carries a thermodynamic model of a phase change material (PCM) and can receive real-time data for simulation. Its function is to provide a high-fidelity simulation environment that runs in parallel with the actual physical system, independently deduce the thermodynamic behavior of PCM, and serve as an independent reference benchmark for verifying predictive models. This digital twin can be based on a detailed physical model constructed using finite element analysis (FEA) or the finite volume method (FVM) and run on a high-performance computing platform. Alternatively, it can be based on a lightweight model constructed using reduced-order models (ROM) or data-driven models (such as neural networks) and run on edge computing devices or cloud platforms. The PCM thermodynamic model is a mathematical model describing the thermophysical properties (such as specific heat capacity, thermal conductivity, density, etc.) of PCM in different phase states and their changes with temperature and phase change processes. Its function is to accurately simulate the heat storage, heat release, and temperature field evolution during the phase change process of PCM. The phase change material thermodynamic model can be based on a phase change heat transfer model established using the enthalpy method or the effective heat capacity method. It can also be combined with a phase field model or Stefan problem solution method to describe the solid-liquid interface evolution in greater detail. This independent derivation means that the derivation process is independent of the multi-step temperature prediction model in the server liquid cooling heat dissipation control method, and does not share parameters or structures. Its purpose is to provide an objective and independent reference trajectory, avoiding coupling with the prediction model to be verified, thereby ensuring the fairness and validity of the verification results. This reference temperature trajectory refers to the sequence of temperature changes over time at each temperature measurement point of the phase change material within the future prediction time domain, derived from the phase change material thermodynamic model in the digital twin. Its purpose is to serve as a benchmark for comparison with the multi-step temperature prediction values, thereby evaluating the accuracy and robustness of the prediction model.

[0141] Converting the estimated solid-liquid ratio into the current phase distribution parameters of the phase change material region in the phase change material thermodynamic model refers to mapping the macroscopic solid-liquid ratio estimate to the phase distribution information of the microscopic or local regions in the phase change material thermodynamic model. Its purpose is to ensure that the model accurately reflects the actual distribution of solid and liquid phases within the phase change material, thereby accurately simulating its thermodynamic behavior. This conversion can be performed using a pre-calibrated solid-liquid ratio-phase distribution lookup table or functional relationship. Alternatively, the estimated solid-liquid ratio can be used as the initial solid-liquid phase fraction for each discrete unit within the phase change material region, thereby determining its equivalent thermophysical parameters. The current phase distribution parameters refer to the parameters in the phase change material thermodynamic model used to describe the current solid-liquid phase distribution of the phase change material, such as the solid fraction, liquid fraction, or equivalent thermophysical parameters of each spatial discrete unit. Their purpose is to provide an accurate initial state for the iterative solution of the thermodynamic model. Converting the thermal sampling data into thermal boundary conditions for the phase change material (PCM) thermodynamic model refers to transforming real-time collected thermal sampling data (such as coolant temperature, flow rate, server heat generation power, etc.) into the boundary condition form required by the PCM thermodynamic model. Its purpose is to ensure that the model can accurately simulate the influence of the external thermal environment on the PCM. This conversion can directly use the coolant temperature as the fluid temperature in the convective heat transfer boundary condition, and convert the flow rate into the convective heat transfer coefficient. Alternatively, the server heat generation power can be used as a heat source term within the PCM layer or as a heat flux density boundary condition at the interface with the PCM. These thermal boundary conditions, such as temperature boundary conditions, heat flux density boundary conditions, or convective heat transfer boundary conditions, describe the heat transfer at the model boundary in the PCM thermodynamic model. Their function is to drive the model to simulate heat transfer within the prediction time domain.

[0142] Based on the current phase distribution parameters and thermal boundary conditions, the thermodynamic model of the phase change material is driven to iteratively solve forward along the predicted time domain in the digital twin. This refers to starting and running the thermodynamic model of the phase change material for calculation using the transformed parameters and conditions. Its function is to enable the model to dynamically simulate the thermal response of the phase change material over a future period based on the initial state and external environment. The predicted time domain refers to the length of the future period, such as the next few minutes or hours. Its function is to determine the time range for model extrapolation. The iterative solution forward refers to the model calculating the temperature field distribution at each future time point step by step, starting from the current moment, with a preset time step. Its function is to simulate the dynamic process of heat transfer and capture the temperature change over time. This solution process can use numerical methods such as explicit or implicit finite difference methods and finite element methods to solve partial differential equations. It can also use ordinary differential equation solvers such as the Runge-Kutta method for time stepping. The temperature field distribution obtained at each time step refers to the set of temperature values ​​of all spatial discrete units within the phase change material layer at each time step within the predicted time domain. Its function is to provide complete thermal state information of phase change materials at different times.

[0143] Extracting the temperature values ​​at the corresponding measurement locations and time steps from the temperature field distribution at each time step refers to filtering the temperature data corresponding to the multi-step temperature prediction in terms of spatial location and time point from the complete temperature field distribution data output by the model. Its purpose is to ensure comparability between the reference trajectory and the predicted value. This extraction can be done directly from the temperature field distribution data based on preset measurement point coordinates and prediction time steps. Alternatively, an interpolation algorithm can be used to obtain accurate measurement point temperatures from discrete temperature field data. The corresponding measurement location refers to the spatial location of the actual temperature sensor or virtual measurement point corresponding to the multi-step temperature prediction. The corresponding time step refers to the future time point corresponding to the multi-step temperature prediction. Forming the reference temperature trajectory involves arranging the extracted temperature values ​​at corresponding measurement locations at different time steps in chronological order to form a continuous temperature sequence. Its purpose is to construct a reference benchmark consistent with the output format of the prediction model for dual-objective validation.

[0144] By converting the estimated solid-liquid ratio into the current phase state distribution parameters of the phase change material region in the phase change material thermodynamic model, and combining this with thermal sampling data to convert it into thermal boundary conditions, this scheme can accurately map the actual solid-liquid state of the phase change material and the external thermal environment to the thermodynamic model in the digital twin. This allows the phase change material thermodynamic model to iteratively solve forward along the prediction time domain in the digital twin based on initial and boundary conditions that are closest to the real physical state, thereby obtaining the temperature field distribution at each time step. This extrapolation method based on direct phase change state perception and real-time thermal environment data improves the accuracy of the reference temperature trajectory and overcomes the errors caused by traditional methods that rely solely on indirect thermal parameters to infer the phase change state. The reference temperature trajectory is formed by extracting the temperature measurement location and temperature value corresponding to the multi-step temperature prediction from the temperature field distribution at each time step, ensuring the consistency between the reference trajectory and the multi-step temperature prediction to be verified in both spatial and temporal dimensions. This allows subsequent dual-objective verification to be performed based on a highly matched benchmark. This accurate and independent reference trajectory extrapolation mechanism provides a solid foundation for the accuracy and robustness verification of multi-step temperature predictions, effectively avoiding the problem of unreliable verification results caused by inaccurate reference trajectories, thereby improving the reliability and control accuracy of the entire liquid cooling heat dissipation control method.

[0145] This application further proposes a method to drive a phase change material (PCM) thermodynamic model to iteratively solve forward along the predicted time domain in a digital twin based on the current phase state distribution parameters and thermal boundary conditions, obtaining the temperature field distribution at each time step. This process includes: determining the equivalent thermophysical parameters of each spatial discrete element in the PCM thermodynamic model at the current time step based on the current phase state distribution parameters. These equivalent thermophysical parameters are assigned differentiated values ​​to each element based on local variations in the solid-liquid ratio. The equivalent thermophysical parameters and thermal boundary conditions are then substituted into the heat conduction equation of the PCM thermodynamic model, and the model is advanced forward along the predicted time domain with a preset time step, solving for the temperature value of each spatial discrete element step by step. After all time steps are solved, the set of temperature values ​​of all spatial discrete elements corresponding to each time step is taken as the temperature field distribution for that time step.

[0146] The current phase distribution parameter refers to the spatial distribution of solid and liquid substances in the phase change material at a certain moment. It can be obtained from the solid-liquid ratio estimate through mapping or interpolation algorithms. For example, the solid-liquid ratio estimate can be discretized into multiple intervals, each corresponding to a phase distribution pattern. Alternatively, a continuous mapping can be established by creating a functional relationship between the solid-liquid ratio and the phase distribution. The thermal boundary condition refers to the conditions under which the phase change material system exchanges heat with the external environment, such as the heat output of a server chip, the inlet temperature and flow rate of the coolant, etc. These conditions can be extracted from thermal sampling data, for example, by directly using temperature and flow rate data measured by sensors as boundary inputs. Alternatively, the thermal boundary conditions for a future period can be obtained by fitting or predicting the thermal sampling data. The phase change material thermodynamic model is a mathematical model describing the changes in physical quantities such as temperature, phase state, and heat flow of the phase change material under thermal influence. This model can be constructed based on the law of conservation of energy and the principles of heat transfer. For example, the enthalpy method can be used to handle the latent heat of phase change. Alternatively, the effective heat capacity method can be used to simplify the simulation of the phase change process. The digital twin is a virtual mapping of a physical entity in digital space, capable of reflecting the state and behavior of the physical entity in real time. In this application, the digital twin can be a simulation platform containing a thermodynamic model of the phase change material, such as a simulation environment built using finite element analysis (FEA) software, or a virtual system implemented using computational fluid dynamics (CFD) tools. The prediction time domain refers to a time range extending into the future from the current moment. For example, it can be set to several minutes or hours in the future, the specific length depending on the response requirements of the control strategy and the limitations of computational resources. The iterative solution is a numerical method that gradually approximates the accurate solution through repeated calculations. For example, the heat conduction equation can be discretized using explicit or implicit finite difference methods and iterated using time steps. Alternatively, the continuous domain can be divided into discrete elements using the finite element method, and iterative solutions can be obtained by solving a system of linear equations. The spatial discrete element refers to dividing the continuous phase change material region into several small, independent computational units. For example, the phase change material layer can be divided into regular cubic or tetrahedral elements using mesh generation techniques. Alternatively, an unstructured mesh can be used to divide the material based on its geometry and thermal flux characteristics. The equivalent thermal property parameters refer to the parameters obtained by weighted averaging or equivalent processing of the solid and liquid thermal property parameters of the phase change material during the phase change process to simplify calculations; examples include equivalent thermal conductivity and equivalent specific heat capacity. These parameters can be determined by linear interpolation based on the solid-liquid ratio, or by consulting a pre-established nonlinear mapping table between the solid-liquid ratio and thermal property parameters. The element-by-element differential assignment based on local variations in the solid-liquid ratio means that the equivalent thermal property parameters of each spatial discrete element are determined independently based on its own solid-liquid ratio, rather than using the average solid-liquid ratio of the entire phase change material layer.For example, each cell can be assigned an independent solid-liquid ratio value, and its corresponding equivalent thermal properties can be calculated based on this value. Alternatively, an interpolation algorithm can be used to infer the solid-liquid ratio of the current cell based on the solid-liquid ratio distribution of adjacent cells, thereby determining its thermal properties. The heat conduction equation describes the physical laws governing heat transfer within an object. For example, a transient heat conduction equation can be established using Fourier's law of heat conduction combined with the principle of energy conservation. Alternatively, when considering convective heat transfer, an energy equation including convection terms can be used. The preset time step refers to dividing the prediction time domain into several discrete time intervals during the iterative solution process. For example, it can be set to milliseconds or seconds based on the model's stability requirements and computational accuracy needs. Alternatively, an adaptive time step strategy can be used to dynamically adjust the step size according to the rate of temperature change. Solving for the temperature values ​​of each spatial discrete cell step-by-step means calculating the temperature values ​​of all spatial discrete cells within each time step, based on the boundary conditions of the current time step and the temperature field distribution of the previous time step. For example, the finite difference method or finite volume method can be used to discretize the heat conduction equation into a system of algebraic equations, which can then be solved numerically. Alternatively, parallel computing techniques can be used to solve for the temperature values ​​of multiple units simultaneously to improve efficiency. This temperature field distribution refers to the set of temperature values ​​for all spatially discrete units within the phase change material layer at a given moment. For example, the temperature values ​​of each unit can be stored in the form of a three-dimensional matrix. Alternatively, the temperature distribution can be displayed as a heatmap using visualization software.

[0147] The above technical solution determines the equivalent thermophysical parameters of each spatial discrete unit based on the current phase distribution parameters, ensuring that the thermophysical property assignments are directly related to the actual distribution of the solid-liquid ratio of the phase change material, thus avoiding spatial errors caused by global averaging. The equivalent thermophysical parameters are assigned differentiated values ​​to each unit according to the local changes in the solid-liquid ratio, enabling the model to accurately reflect the differences in thermal characteristics of the phase change material at the micro-unit level and solving the heat conduction distortion under non-uniform phase change conditions. Substituting the equivalent thermophysical parameters and thermal boundary conditions into the heat conduction equation, combined with dynamic thermophysical properties and external heat input, makes the thermodynamic model more closely resemble the actual physical process. Advancing along the prediction time domain with a preset time step, the temperature values ​​of each spatial discrete unit are solved step by step, ensuring continuous iteration in the time dimension and accurately capturing the transient evolution of thermal behavior. After all time steps are solved, the set of temperature values ​​is used as the temperature field distribution, providing complete space-time thermal data and laying a high-precision foundation for the subsequent extraction of reference temperature trajectories. These technologies work together to improve the accuracy of the temperature field distribution, ensuring that the reference temperature trajectory truly reflects the thermal dynamics of the phase change material. This, in turn, improves the accuracy and reliability of dual-objective verification, makes the parameter replacement of the prediction model more robust, and optimizes the liquid cooling heat dissipation control effect.

[0148] This application further proposes a method to test the prediction stability by applying perturbations to the parameters of a global linear prediction model and a local nonlinear correction model, thereby obtaining a robustness verification quantity characterizing the prediction's disturbance resistance capability. Specifically, this method includes: determining the perturbation amplitude based on the parameter change amplitudes of the global linear prediction model and the local nonlinear correction model within a historical update cycle, and determining the perturbation direction based on the directional distribution of the parameter change amplitudes. Based on the perturbation amplitude and direction, multiple perturbations are applied to the current parameters of the global linear prediction model and the local nonlinear correction model. After each perturbation, the global linear prediction model and the local nonlinear correction model are driven to collaboratively output a set of perturbation prediction sequences. The deviation between the multiple sets of perturbation prediction sequences and the unperturbed multi-step temperature prediction values ​​is calculated, and the divergence trend of the deviation as the number of prediction steps increases is extracted. The deviation and the divergence trend are used together as a robustness verification quantity.

[0149] For example, in determining the perturbation magnitude, this application bases it on the parameter change magnitudes of the global linear prediction model and the local nonlinear correction model within historical update cycles. Here, the parameter change magnitude refers to the order of magnitude of change in the model's internal parameters (e.g., coefficients of the linear model, weights of the nonlinear correction model, etc.) during past update iterations. Its purpose is to ensure that the applied perturbation magnitude accurately reflects the range of parameter fluctuations in actual model operation, avoiding evaluation distortion caused by setting fixed or random perturbation magnitudes. For example, the perturbation magnitude can be determined by statistically analyzing the maximum absolute change or root mean square change of model parameters within historical update cycles. Alternatively, an adaptive method can be used to dynamically adjust the calculation strategy for the perturbation magnitude based on the parameter change activity at different stages of model operation (e.g., early, middle, and late phases of phase transition). For instance, in stages with frequent parameter changes, a larger historical window or more sensitive statistical indicators can be used to determine the magnitude.

[0150] This application also determines the perturbation direction based on the directional distribution of parameter change amplitudes. The directional distribution of parameter change amplitudes reveals the tendency of model parameters to increase or decrease during the update process. The purpose of determining the perturbation direction is to make the applied perturbation more closely resemble the evolution trend of model parameters during the actual update process, thereby improving the realism of the robustness assessment. For example, the perturbation direction can be determined by analyzing the sign (positive or negative) of parameter changes and their frequency distribution within historical update cycles. If a parameter tends to increase in historical updates, the perturbation direction can be biased towards the positive direction. Another approach is to use principal component analysis (PCA) or other dimensionality reduction techniques to extract the main change directions from the historical parameter change vectors and use this as a reference for the perturbation direction.

[0151] After determining the perturbation amplitude and direction, this application applies multiple perturbations to the current parameters of the global linear prediction model and the local nonlinear correction model. The purpose of applying multiple perturbations is to simulate various possible disturbance scenarios, comprehensively evaluate the model's stability under different perturbations, and improve the comprehensiveness and reliability of the robustness assessment. For example, the Monte Carlo method can be used to randomly generate multiple sets of perturbation vectors within a defined perturbation amplitude range and directional distribution, and apply them to the model's current parameters respectively. Alternatively, more uniform sampling methods such as Latin hypercube sampling can be used to select representative perturbation points in the parameter space to ensure sufficient coverage of the parameter space.

[0152] After each perturbation, the global linear prediction model and the local nonlinear correction model are driven to collaboratively output a set of perturbation prediction sequences. The purpose of collaboratively outputting perturbation prediction sequences is to observe the model's predictive performance under simulated actual operating conditions after the parameters are perturbed, thereby assessing its sensitivity to parameter fluctuations. For example, after each perturbation, the perturbed model parameters are loaded into the global linear prediction model and the local nonlinear correction model, and the current input data (such as impedance spectrum sweep data, ultrasonic echo signals, thermal sampling data, and calculated load scheduling information) are used to drive these two models to collaboratively generate a sequence of temperature prediction values ​​for multiple future time steps. Another approach is to update the model parameters to the model's internal state after the perturbation, and then use the model's own prediction mechanism, combined with historical observation data and future preset operating condition data, to generate a perturbed prediction sequence.

[0153] The deviation between multiple perturbation-based predicted sequences and the unperturbed multi-step temperature predictions is calculated. The purpose of calculating this deviation is to quantify the difference between the model's predictions under parameter perturbations and the baseline predictions (i.e., the unperturbed predictions), thus intuitively reflecting the model's sensitivity. For example, statistical indicators such as mean squared error (MSE), mean absolute error (MAE), or maximum absolute error can be used to calculate the difference between each perturbation-based and unperturbed predicted sequence at each time step, and then aggregated. Furthermore, the correlation coefficient or dynamic time warping (DTW) distance between two sequences can also be calculated to assess their similarity in shape and trend.

[0154] Based on this, the divergence trend of the deviation degree as the number of prediction steps increases is extracted. The purpose of extracting the divergence trend is to assess the stability decay characteristics of the model in long-term prediction, that is, whether the prediction error increases as the prediction time window lengthens. For example, regression analysis (such as linear regression or exponential regression) can be performed on the deviation degree at different prediction steps to fit a functional relationship between the deviation degree and the number of prediction steps, and its slope or growth rate can be extracted as a quantitative indicator of the divergence trend. Another approach is to calculate the variance or standard deviation of the deviation degree in different prediction step intervals and observe its change pattern as the number of prediction steps increases to determine the degree of divergence.

[0155] Deviation and divergence trend are used together as robustness validation metrics. Using both together provides a multi-dimensional, comprehensive indicator to fully evaluate the model's resilience, considering both short-term prediction accuracy and long-term prediction stability. For example, deviation and divergence trend can be weighted and summed to form a single comprehensive robustness index, with weights set according to the emphasis on short-term accuracy and long-term stability in practical applications. Alternatively, deviation and divergence trend can be treated as two independent indicators, compared separately with preset robustness thresholds; only when both requirements are met is the model considered to have passed robustness validation.

[0156] Through the above technical solution, this application addresses the problem of lacking a perturbation method based on the dynamic changes of historical parameters to accurately simulate the actual fluctuations during model updates when verifying prediction stability. This lack of a perturbation method can lead to robustness assessments deviating from real-world scenarios, potentially introducing false stability judgments, and thus affecting the control reliability after model updates. Specifically, the perturbation amplitude is determined based on the parameter change magnitude within the historical update cycle, ensuring that the perturbation amplitude directly reflects the fluctuation range of the model in real iterations and avoiding evaluation distortion caused by arbitrary perturbations. The perturbation direction is determined based on the directional distribution of parameter change amplitudes, capturing the trend characteristics of parameter evolution and ensuring that the perturbation direction aligns with the actual parameter update path. By applying multiple perturbations to the current model parameters and driving a collaborative output perturbation prediction sequence, diverse disturbance environments are simulated, comprehensively covering potential unstable scenarios. The deviation degree between the perturbation prediction sequence and the unperturbed prediction value is calculated to quantify the model's bias sensitivity in short-term predictions. The long-term prediction stability decay characteristics of the model are evaluated by extracting the divergence trend of the deviation degree as the number of prediction steps increases. By combining the degree of deviation and divergence trend as robustness verification metrics, multi-dimensional indicators are provided to comprehensively assess the model's disturbance resistance, thereby ensuring the control robustness after model updates and improving the reliability of the heat dissipation system. This disturbance method based on the dynamic changes of historical parameters makes the robustness assessment closer to actual operating conditions, ensuring the stability and reliability of the prediction model after parameter updates, and thus improving the performance and robustness of the entire liquid cooling heat dissipation control system.

[0157] This application further proposes to perform asymptotic smooth replacement of the parameters of the global linear prediction model and the local nonlinear correction model after successful verification, in order to obtain an updated, currently effective prediction model. In some of the schemes described above in this application, updating the prediction model after successful verification is proposed to improve control accuracy; however, directly replacing parameters in this process may lead to system instability and jumps in predicted values.

[0158] The gradual, smooth replacement process includes: Determine the number of transition steps required for both the global linear prediction model and the local nonlinear correction model to transition from the current parameters to the updated parameters.

[0159] The transition step count is the number of control cycles required for the model parameters to smoothly adjust from old to new values. Its core function is to avoid abrupt parameter changes, thereby maintaining system stability. This transition step count can be dynamically determined based on the magnitude of the deviation between the current and updated parameters. For example, the deviation magnitude can be quantified by calculating the Euclidean distance, Manhattan distance, or other norms between the current and updated parameters, and then mapped to a suitable transition step count based on a preset mapping function or lookup table. Generally, the larger the deviation, the more transition steps are needed, and vice versa. Furthermore, the mapping function or lookup table can be dynamically adjusted based on historical update effects (such as fluctuations in prediction residuals) with each parameter update, making the determination of the transition step count more adaptive.

[0160] Within this transition step, the parameters of the global linear prediction model are increased from the current parameters to the updated parameters in each control cycle according to the transition ratio coefficient, while the parameters of the local nonlinear correction model are increased from the current parameters to the updated parameters in each control cycle according to the same transition ratio coefficient.

[0161] The transition proportionality coefficient is a factor used to control the rate at which the parameter approaches the updated value from the current value in each control cycle. Its function is to ensure smooth, gradual changes in the parameter, avoiding large jumps within a single control cycle. One implementation method is to use a linear incremental strategy. For example, with a total number of transition steps of N, the parameter update amount in each control cycle is (updated parameter - current parameter) / N. Therefore, the parameter in the k-th control cycle (k from 1 to N) is the current parameter + k × (updated parameter - current parameter) / N. Another implementation method is to use a non-linear incremental strategy, such as an S-shaped curve or an exponential curve, so that the change is slower in the early and late stages of the transition and faster in the middle stage, or vice versa, to adapt to different system dynamic characteristics.

[0162] After all transitions are completed according to the specified number of transition steps, the updated parameters are replaced with the currently effective parameters of the global linear prediction model and the currently effective parameters of the local nonlinear correction model, respectively, to obtain the updated currently effective prediction model.

[0163] This section describes the steps of the gradual and smooth parameter replacement process. It indicates that after a series of smooth transitions, the new, validated parameters are officially put into use, becoming the benchmark parameters for the model in subsequent control cycles. Its purpose is to ensure that the model always uses the latest and stable parameters for prediction, thereby maintaining the accuracy of predictions and the effectiveness of control. One implementation method is to directly assign the validated "updated parameters" to the "currently effective parameters" variable after all transition steps are completed, ensuring that the model switches to a fully updated state after the transition is complete. Another implementation method is to set a status flag to indicate the completion of parameter updates. When the transition is complete, the flag is set to "updated," and when the model loads parameters, the parameter set marked "updated" is loaded first.

[0164] By dynamically determining the transition steps through the above technical solutions, the model update process can adaptively adjust the transition time according to the deviation between the old and new parameters, avoiding excessively fast or slow switching. Parameters are increased incrementally according to the transition ratio coefficient over each control cycle, ensuring gradual changes rather than instantaneous jumps, thereby reducing the impact on system output and improving the stability of the control system. The synchronous and gradual updating of parameters in the global linear prediction model and the local nonlinear correction model maintains their synergistic effect, ensuring the accuracy and robustness of the overall prediction model. In the liquid cooling heat dissipation control method for servers based on phase change materials, this smooth update mechanism is crucial for maintaining the accuracy and stability of the prediction model, especially in scenarios where the thermodynamic properties of phase change materials are complex and dynamically changing. It effectively avoids cooling strategy errors caused by sudden changes in model parameters, thus better ensuring the stable operation and computing performance of the server, and ensuring the continuity of the predicted output, making control decisions based on predicted values ​​more reliable.

[0165] This application further proposes a method for obtaining the liquid cooling flow allocation sequence for each server node by performing cross-domain joint optimization with computational performance preservation constraints, based on the multi-step temperature predictions, computational load scheduling information, and solid-liquid ratio estimates output by the currently effective prediction model. The method includes: determining the cooling demand urgency of each server node in the future prediction time domain based on the multi-step temperature predictions and solid-liquid ratio estimates; the cooling demand urgency reflects the time window during which the server node can still sustain its current reliance on phase change material heat storage; constructing a cross-domain joint optimization objective based on the cooling demand urgency and the computational performance requirements of the scheduled tasks on the server nodes in the computational load scheduling information; the cross-domain joint optimization objective includes temperature control deviation cost, flow regulation cost, and computational performance deviation cost; and solving the cross-domain joint optimization objective under the conditions of satisfying the computational performance preservation constraints and the physical constraints of the liquid cooling system to obtain the liquid cooling flow allocation sequence for each server node.

[0166] For example, cross-domain joint optimization refers to the process of collaborative decision-making across multiple interrelated domains (such as thermal management and computational resource management) to achieve optimal overall system performance. Its purpose is to overcome the limitations of traditional single-domain optimization by comprehensively considering the objectives and constraints of different domains to seek a globally optimal solution. For instance, multi-objective optimization algorithms, such as weighted sum methods, ε-constraint methods, or Pareto optimization methods, can be used to integrate the optimization objectives of different domains. Alternatively, a hierarchical optimization strategy can be adopted to decompose complex problems into multiple sub-problems and achieve joint optimization through iterative coordination. The computational performance maintenance constraint refers to ensuring that server nodes maintain their expected or minimum required computational performance levels during the operation of the liquid cooling system. This constraint aims to prevent a decrease in server computing power due to adjustments in cooling strategies, thereby affecting the overall system service quality. For example, it can be set to ensure that server CPU utilization does not fall below a certain threshold, or that task processing latency does not exceed a certain upper limit. It can also be to ensure that the completion time of specific critical tasks is within a specified range. The liquid cooling flow allocation sequence refers to a series of pre-planned values ​​of the liquid coolant flow rate over time for each server node over a future period. This sequence of commands directly controls the liquid cooling pumps and valves, precisely regulating the heat dissipation of each server node. For example, this sequence could be a series of flow rate setpoints at discrete time steps, or a continuous flow function, which the control system converts into actual pump speeds and valve openings.

[0167] The cooling demand urgency is an indicator that measures the urgency of the current heat dissipation needs of a server node. It reflects the time window within which the server node can maintain normal operation relying on the heat storage capacity of the phase change material without taking additional cooling measures. The higher the indicator, the more urgent the heat dissipation demand. For example, it can be comprehensively assessed based on how close the server core temperature is to the safety threshold, the rate of change of the solid-liquid ratio of the phase change material, or the predicted temperature rise trend. The future prediction time domain refers to a future period of time considered by the optimization algorithm when making decisions. Within this time domain, the system will estimate future temperature, load, and other states based on the prediction model and formulate corresponding control strategies accordingly. For example, this time domain can be set to 5 minutes, 10 minutes, or longer in the future, depending on the dynamic response characteristics of the system and the accuracy of the prediction model.

[0168] The cross-domain joint optimization objective is a mathematical function used to quantify the overall performance of the liquid cooling system. It comprehensively considers multiple indicators such as temperature control effectiveness, flow regulation cost, and computational performance maintenance. This objective function is typically composed of a weighted sum of multiple sub-objective terms, and the optimization process aims to minimize or maximize its value. For example, it could be a weighted sum function including temperature over-limit penalties, flow change penalties, and computational performance degradation penalties. The temperature control deviation cost refers to the "cost" or "penalty" incurred by the difference between the actual temperature of the server node and the target temperature. The greater the deviation of the server temperature from the target value, the higher the cost, prompting the optimization algorithm to maintain the temperature within the ideal range. For example, the sum of squares of temperature deviations can be used as the cost function, or a step function can be set to incur a large penalty when the temperature exceeds a certain threshold. The flow regulation cost refers to the "cost" incurred by changing the liquid cooling flow rate, including energy consumption, equipment wear, and the impact on system stability. Introducing this cost aims to avoid frequent or large flow fluctuations to improve system stability and energy efficiency. For example, the absolute value or square of the flow rate change can be used as the cost function, or the number of pump start-ups and shutdowns and the valve adjustment frequency can be considered. The performance deviation cost refers to the "cost" or "penalty" incurred when the actual computing performance of a server node fails to meet expectations or minimum requirements. This cost is designed to ensure that server computing power is not sacrificed for thermal optimization. For example, it can be calculated based on the degree to which CPU utilization is lower than expected, the degree to which task completion time exceeds expectations, or a hard penalty can be set, incurring a very high cost once performance falls below a certain threshold.

[0169] Solving the cross-domain joint optimization objective involves finding a set of liquid cooling flow distribution sequences using mathematical algorithms or computational methods, such that the cross-domain joint optimization objective function is optimal (usually minimized) while satisfying all constraints. Numerical optimization techniques such as Sequential Quadratic Programming (SQP), interior-point methods, genetic algorithms, or particle swarm optimization can be employed. The physical constraints of the liquid cooling system refer to the inherent physical limitations of the liquid cooling system hardware itself, such as the maximum head and flow rate of the liquid cooling pump, the minimum / maximum valve opening, the maximum pressure capacity of the piping, and the upper limit of the total flow rate of the entire liquid cooling loop. These constraints define the practically operable range of the liquid cooling system, ensuring that the optimization result is physically achievable. For example, the total flow rate cannot exceed the maximum pump capacity, and the flow rate of a single server node cannot be lower than the minimum controllable flow rate of the valve.

[0170] By employing the aforementioned technical solution, the urgency of cooling requirements for each server node is dynamically determined based on multi-step temperature predictions and solid-liquid ratio estimates. This allows for real-time and accurate assessment of the time window during which each server node can sustain its heat storage capacity using phase change materials, providing a refined basis for subsequent optimization decisions. Furthermore, by combining the urgency of cooling requirements with the computational performance requirements of scheduled tasks on server nodes from the computational load scheduling information, a cross-domain joint optimization objective is constructed, incorporating costs for temperature control deviation, flow regulation, and computational performance deviation. This enables the optimization process to flexibly adjust the weights of various costs based on the actual urgency of cooling and computational performance requirements. This prioritizes heat dissipation efficiency when cooling needs are urgent, and rationally allocates flow when computational performance requirements are high. This avoids the reduced control accuracy and system response lag caused by rigid optimization objective weights in traditional solutions. Solving this optimization objective while satisfying computational performance maintenance constraints and liquid cooling system physical constraints, the resulting liquid cooling flow allocation sequence not only ensures a precise balance between heat dissipation efficiency and computational performance but also guarantees the feasibility of the flow allocation scheme and the stable operation of the system by considering the physical constraints of the liquid cooling system. This dynamic and collaborative optimization strategy enhances the intelligence and adaptability of liquid cooling heat dissipation control, enabling servers to maintain efficient and stable operation under different loads and phase change material conditions.

[0171] This application further proposes a method for determining the urgency of cooling requirements for each server node in the future prediction time domain based on multi-step temperature predictions and solid-liquid ratio estimates. This method includes: Based on the solid-liquid ratio estimate, the remaining latent heat capacity of the phase change material layer corresponding to each server node is determined. In the future prediction time domain, the heating rate of the multi-step temperature prediction value is correlated with the decay rate of the remaining latent heat capacity to obtain the heat dissipation pressure index of each server node.

[0172] Based on the remaining latent heat capacity and the temperature prediction value at the end of the prediction time domain in the multi-step temperature prediction value, it is determined whether each server node will experience a dual critical state of latent heat depletion and temperature exceeding the limit in the future prediction time domain.

[0173] The cooling demand urgency is obtained by combining the heat dissipation pressure index with the evaluation results of the dual critical state. The cooling demand urgency is taken as the highest value when the heat dissipation pressure index increases and a dual critical state is determined to occur.

[0174] For example, when determining the remaining latent heat capacity of the phase change material layer corresponding to each server node, the total latent heat capacity that the current solid portion can provide can be calculated by pre-calibrating the unit mass latent heat value of the phase change material and combining it with the estimated solid-liquid ratio and the total mass of the phase change material. For example, if the estimated solid-liquid ratio is 0.7 (i.e., 70% solid), then the remaining latent heat capacity is 70% of the total latent heat capacity. Alternatively, the remaining latent heat capacity can be obtained by establishing an enthalpy-temperature curve model of the phase change material, combining it with the estimated solid-liquid ratio, looking up a table or calculating it through interpolation to obtain the enthalpy value of the phase change material under the current solid-liquid ratio state, and then subtracting the enthalpy value when it is completely liquid.

[0175] Several methods can be used to correlate the heating rate of multi-step temperature predictions with the decay rate of remaining latent heat capacity to obtain the heat dissipation pressure index for each server node. For example, the average heating rate of multi-step temperature predictions over the future prediction time domain can be compared to the predicted decay rate of remaining latent heat capacity (e.g., latent heat consumption per unit time) or weighted summed to quantify the heat dissipation pressure. The heat dissipation pressure index increases when both the heating rate and latent heat decay rate are high. Another approach is to construct a dynamic model that takes the heating rate and latent heat decay rate as input and outputs the heat dissipation pressure index through a nonlinear function or lookup table. For example, when the heating rate exceeds a certain threshold and the remaining latent heat capacity falls below a certain threshold, the heat dissipation pressure index will rise sharply and nonlinearly.

[0176] To determine whether each server node will experience a dual critical state of latent heat depletion and temperature exceedance within the future prediction time domain, a latent heat depletion threshold and a temperature exceedance threshold can be set. Within the future prediction time domain, if the predicted remaining latent heat capacity is lower than the latent heat depletion threshold, and the predicted temperature at the end of the prediction time domain is higher than the temperature exceedance threshold, a dual critical state is determined to have occurred. Alternatively, the time points of latent heat depletion and temperature exceedance can be predicted separately. If both time points fall within the future prediction time domain and are close to each other (e.g., within a preset time window), a dual critical state is determined to have occurred.

[0177] When integrating the thermal stress index with the assessment results of dual-criticality states to determine the urgency of cooling demand, a weighted summation or hierarchical logic can be employed. For example, the thermal stress index can be used as a base value and adjusted based on the assessment results of dual-criticality states. If a dual-criticality state is determined to occur, the thermal stress index is either elevated to the highest level or multiplied by a larger weighting factor, regardless of its current value. Alternatively, a hierarchical logic can be used: if the dual-criticality state assessment is "yes," the cooling demand urgency is directly set to a high level. If it is "no," the cooling demand urgency is primarily determined by the thermal stress index and can be categorized into different levels based on its value.

[0178] By linking the heating rate with the latent heat decay rate, the heat dissipation pressure index is no longer a single function of temperature or solid-liquid ratio, but rather captures the dynamic matching relationship between the "rate of temperature rise" and the "rate of heat storage capacity consumption." When the temperature rises rapidly and the latent heat is consumed rapidly, the heat dissipation pressure index rises sharply, reflecting the magnitude of the heat dissipation pressure at the current moment. When the temperature rises rapidly but the latent heat is consumed slowly, the heat dissipation pressure index remains at a moderate level, reflecting that although there is thermal shock, the heat storage buffer is still sufficient. Based on this, by linking the remaining latent heat capacity with the predicted temperature value at the end of the prediction time domain, it is possible to predict in advance whether latent heat depletion and temperature exceeding the limit will occur in the same prediction time domain, capturing the impending heat dissipation capacity gap. By integrating the heat dissipation pressure index with the prediction results of dual critical states, the urgency of cooling demand simultaneously includes information from two time dimensions: "current heat dissipation pressure" and "future critical risk." This allows for an earlier increase in the urgency rating when latent heat is about to be depleted but the current temperature has not yet exceeded the limit, providing a forward-looking decision-making basis for the pre-allocation of cooling capacity in subsequent cross-domain joint optimization, avoiding cooling lag caused by waiting for the temperature to exceed the limit before responding.

[0179] This application further proposes a method for determining whether each server node will experience a dual critical state of latent heat depletion and temperature exceeding the limit within the future prediction time domain, based on the temperature prediction value at the end of the prediction time domain from the remaining latent heat capacity and multi-step temperature prediction values. This method includes: determining whether there is a temperature rise rate jump point caused by latent heat depletion within the future prediction time domain based on the temperature rise amplitude between adjacent time steps in the remaining latent heat capacity and multi-step temperature prediction values; determining the jump time step corresponding to the temperature rise rate jump point; determining the expected occurrence time step of temperature exceeding the limit based on the difference between the temperature prediction value after the jump time step and the preset upper temperature threshold, and the temperature rise rate after the jump time step; and determining the expected occurrence time step of temperature exceeding the limit based on the temperature prediction value after the jump time step and the expected occurrence time step. If the jump time step falls within the future prediction time domain and the expected occurrence time step is not later than the corresponding time step at the end of the prediction time domain, it is determined that a dual critical state will occur. Otherwise, it is determined that a dual critical state will not occur.

[0180] For example, to determine whether there is a temperature rise rate jump point caused by latent heat depletion within the future prediction time domain, and to determine the jump time step corresponding to the temperature rise rate jump point, it is necessary to obtain the remaining latent heat capacity of the phase change material layer corresponding to each server node. This capacity reflects the total amount of latent heat that the phase change material can still absorb in its current state. The temperature rise amplitude between adjacent time steps in the multi-step temperature prediction values ​​is obtained; this amplitude directly characterizes the rate of temperature change over time within the prediction time domain. The physical characteristic of latent heat depletion is that when the latent heat of the phase change material is completely absorbed, its temperature will change from an approximately isothermal state to a rapidly heating state, leading to an increase in the temperature rise rate. Therefore, this turning point can be identified by analyzing the trend of the temperature rise amplitude. For example, the second derivative of the temperature rise amplitude or its rate of change can be calculated. When this value exceeds a preset threshold, it is determined to be a temperature rise rate jump point, and the corresponding prediction time step is recorded as the jump time step. Another approach is to set a dynamic threshold; when the ratio or difference of the temperature rise amplitudes of adjacent time steps exceeds this dynamic threshold, a temperature rise rate jump is considered to have occurred.

[0181] When determining the expected time step for a temperature exceedance, the difference between the predicted temperature after the jump time step and the preset upper temperature threshold is obtained. This difference indicates the margin between the current predicted temperature and the safe upper limit. The heating rate after the jump time step is obtained, reflecting the upward trend of temperature after latent heat depletion. Since the temperature rise accelerates after latent heat depletion, this accelerating trend needs to be considered to predict when the upper temperature limit will be reached. For example, starting from the jump time step, subsequent temperature predictions can be iterated to find the first time step that exceeds the preset upper temperature threshold, which is the expected time step for a temperature exceedance. Alternatively, based on the predicted temperature after the jump time step and the heating rate, linear or nonlinear extrapolation methods can be used to calculate the time required for the temperature to reach the preset upper temperature threshold, thereby determining the expected time step.

[0182] In determining whether a double critical state will occur, logical judgment is required. First, it is determined whether the identified jump time step falls within the future prediction time domain. If the jump time step is outside the prediction time domain, it means that latent heat depletion will not occur within the current timeframe of interest, thus not constituting a double critical state. Second, it is determined whether the identified expected occurrence time step of temperature exceeding the limit is no later than the corresponding time step at the end of the prediction time domain. If the expected occurrence time step of temperature exceeding the limit is later than the end of the prediction time domain, it means that even if latent heat is depleted, the temperature will not exceed the upper limit within the current prediction time domain, again not constituting a double critical state. Only when both conditions are simultaneously met—that is, both latent heat depletion and temperature exceeding the limit will occur within the future prediction time domain—is a double critical state determined to occur. Otherwise, a double critical state is determined not to occur.

[0183] The above technical solution accurately captures the temperature rise rate jump point caused by latent heat depletion and accurately predicts the time when the temperature exceeds the limit, thus avoiding deviations in the assessment of cooling demand urgency due to inaccurate judgment. This step-by-step and refined judgment mechanism utilizes the physical law that the thermal response characteristics of phase change materials undergo a qualitative change after latent heat depletion. By analyzing the dynamic changes in the predicted temperature value rather than a static threshold, it improves the accuracy of identifying the critical point of the thermal state of server nodes. This allows for a more accurate identification of server nodes facing the dual risks of latent heat depletion and temperature exceeding the limit when assessing the urgency of cooling demand, thus providing more reliable input for subsequent cross-domain joint optimization. When combined with the aforementioned cooling demand urgency assessment method, it ensures that the liquid cooling flow allocation strategy can respond promptly and effectively mitigate potential thermal risks, thereby improving the control effect of the entire liquid cooling system and the operational stability of the server.

[0184] This application further proposes a cross-domain joint optimization objective based on the urgency of cooling demand and the computational performance requirements of the scheduled tasks on server nodes in the computational load scheduling information. For example, the method includes determining a temperature control deviation cost coefficient and a flow regulation cost coefficient for each server node based on the urgency of its cooling demand. The temperature control deviation cost coefficient increases with increasing cooling demand urgency, while the flow regulation cost coefficient decreases. Based on the computational performance requirements of the scheduled tasks on each server node, a computational performance deviation cost coefficient is determined for each server node. This computational performance deviation cost coefficient increases with increasing computational performance requirements. The cross-domain joint optimization objective is then constructed by multiplying the temperature control deviation cost by the temperature control deviation cost coefficient, the flow regulation cost by the flow regulation cost coefficient, and the computational performance deviation cost by the computational performance deviation cost coefficient.

[0185] The cooling demand urgency is an indicator that measures the urgency of each server node's cooling resource needs in the future prediction time domain. It comprehensively reflects the server node's current heat load, the heat storage state of the phase change material, and the potential overheating risk. Its role is to serve as a key basis for dynamically adjusting various cost coefficients in the optimization objective, ensuring that cooling resources are prioritized for allocation to the server nodes that need them most. The cooling demand urgency can be determined by comprehensively assessing the remaining latent heat capacity of the corresponding phase change material layer of the server node, the temperature rise rate in the prediction time domain, and whether a dual critical state of latent heat depletion and temperature exceeding the limit will occur. Alternatively, it can be comprehensively evaluated using fuzzy logic or machine learning models by combining the server node's historical temperature trend, current computing load, and preset safe temperature threshold.

[0186] The temperature control deviation cost coefficient is a weighting factor used to quantify the degree of "penalty" incurred when a server node's temperature deviates from the target temperature. In the optimization objective, this coefficient is multiplied by the temperature control deviation cost; a larger value indicates a lower tolerance for temperature control deviation, and the optimizer will be more inclined to reduce the node's temperature deviation. This coefficient can be designed as a monotonically increasing function of cooling demand urgency, such as a linear, exponential, or piecewise function, ensuring that the coefficient increases when cooling demand urgency is high. Alternatively, it can be implemented using a lookup table, pre-setting different temperature control deviation cost coefficient values ​​based on different cooling demand urgency levels.

[0187] The flow regulation cost coefficient is a weighting factor used to quantify the "cost" or "penalty" of liquid cooling flow regulation operations. In the optimization objective, this coefficient is multiplied by the flow regulation cost; a larger value indicates a stricter restriction on flow regulation, and the optimizer will be more inclined to maintain flow stability or reduce flow variations. This coefficient can be designed as a monotonically decreasing function of cooling demand urgency, such as an inverse proportional function or a negative exponential function, ensuring that the coefficient decreases when cooling demand urgency is high, thus allowing for larger flow regulation to meet cooling requirements. Alternatively, different flow regulation cost coefficient values ​​can be assigned based on different intervals of cooling demand urgency using a pre-defined step function or lookup table.

[0188] The computing performance requirement refers to the minimum or expected standard that the scheduled task imposes on each server node in terms of processing power, response time, throughput, etc. Its purpose is to determine the cost factor for computing performance deviation, ensuring that liquid cooling control does not impair the execution efficiency of critical computing tasks. This computing performance requirement can be directly obtained from computing load scheduling information, such as task priority, SLA (Service Level Agreement) requirements, and CPU / GPU utilization targets. Alternatively, it can be indirectly inferred by analyzing the task type (such as AI training, data analysis, real-time services, etc.) and its sensitivity to computing resources.

[0189] The computational performance deviation cost coefficient is a weighting factor used to quantify the degree of "penalty" incurred when the actual computational performance of a server node deviates from its requirements. In the optimization objective, this coefficient is multiplied by the computational performance deviation cost; the larger the value, the lower the tolerance for performance degradation, and the more the optimizer will tend to protect the node's computational performance. This coefficient can be designed as a monotonically increasing function of the computational performance requirement; for example, the higher the computational performance requirement (such as a high-priority task), the larger the coefficient. Alternatively, the coefficient can be determined based on the task's priority or importance level through a pre-defined mapping relationship.

[0190] This cross-domain joint optimization objective is a comprehensive objective function that integrates the optimization objectives from three different domains—temperature control deviation cost, flow regulation cost, and computational performance deviation cost—through a weighted summation method. Its purpose is to ensure that the liquid cooling flow allocation decision simultaneously considers the heat dissipation requirements of server nodes, the operating efficiency of the liquid cooling system, and the performance guarantee of the computational task, achieving global optimum. This optimization objective can be expressed as: J = C_ temp ×E_temp+C_flow×E_flow+C_perf×E_perf, where C represents the cost coefficient and E represents the corresponding cost term (such as the square of the temperature deviation, the absolute value of the flow rate change, the percentage of performance degradation, etc.). In practical solutions, optimization algorithms such as linear programming, quadratic programming, and nonlinear programming can be used to find the liquid cooling flow rate allocation sequence that minimizes the objective function through iterative solutions.

[0191] The above technical solution dynamically adjusts the weights of various costs in the optimization objective based on the urgency of cooling needs for each server node and the computational performance requirements of the tasks to be scheduled. When the cooling needs of a server node are high, the temperature control deviation cost coefficient is increased and the flow regulation cost coefficient is decreased. This makes the optimization process focus more on the temperature control of that node and allows for more flexible flow regulation to quickly respond to heat dissipation needs. When the tasks to be scheduled have high computational performance requirements for the server node, the computational performance deviation cost coefficient is increased, thus more strictly penalizing any flow allocation scheme that may lead to a decrease in computational performance during the optimization process. This dynamic and adaptive cost coefficient adjustment mechanism enables the constructed cross-domain joint optimization objective to more accurately reflect the real-time priorities and constraints of different server nodes and different tasks, thereby avoiding the problems of uneven resource allocation or performance degradation of critical tasks that may be caused by traditional fixed-weight optimization objectives. By solving this dynamic optimization objective, a more reasonable and efficient liquid cooling flow allocation sequence can be obtained, maximizing the maintenance of computational performance while ensuring server heat dissipation, thus improving the operational efficiency and stability of the entire data center.

[0192] This application further proposes a method for solving a cross-domain joint optimization objective to obtain a liquid cooling flow allocation sequence for each server node, under the conditions of satisfying both computational performance preservation constraints and liquid cooling system physical constraints. The method includes: differentially relaxing the upper limit of the flow rate change rate in the liquid cooling system physical constraints based on the cooling demand urgency of each server node, obtaining a dynamic flow rate change rate constraint for each server node, which relaxes as the cooling demand urgency increases; analyzing the computational performance preservation constraint, transforming the computational performance requirements of the scheduled task for each server node into a minimum flow guarantee lower limit for each server node; and solving the cross-domain joint optimization objective within the feasible region jointly defined by the dynamic flow rate change rate constraint, the minimum flow guarantee lower limit, and the total flow upper limit in the liquid cooling system physical constraints to obtain the liquid cooling flow allocation sequence for each server node.

[0193] For example, based on the urgency of cooling demand for each server node, the upper limit of the flow rate change rate in the physical constraints of the liquid cooling system is differentially relaxed to obtain the dynamic flow rate change rate constraint for each server node. This dynamic flow rate change rate constraint relaxes as the urgency of cooling demand increases, aiming to enable the liquid cooling system to flexibly adjust its upper limit of the flow rate change rate according to the actual cooling needs of each server node. The urgency of cooling demand is a comprehensive indicator reflecting the severity of the current thermal state of the server node and its required cooling response speed. For example, it can be comprehensively evaluated through factors such as the remaining latent heat capacity of the phase change material layer, the predicted temperature rise rate, and the proximity to the temperature threshold. The upper limit of the flow rate change rate in the physical constraints of the liquid cooling system is usually a preset, global maximum flow rate change rate used to ensure the stable operation of the hydraulic system. Through differential relaxation, different upper limits of the flow rate change rate can be set for nodes with different urgency levels. For example, a function or lookup table positively correlated with the urgency of cooling demand can be used to map the urgency to a relaxation coefficient, and then this relaxation coefficient can be multiplied by the original upper limit of the flow rate change rate to obtain the dynamic flow rate change rate constraint. Another approach is to preset different upper limits for flow rate changes based on different levels of urgency of cooling demand (such as low, medium, and high). When a node is at a certain urgency level, the corresponding upper limit is used.

[0194] This paper analyzes the performance maintenance constraints, transforming the performance requirements of scheduled tasks on each server node into a minimum flow guarantee limit for each server node. The aim is to convert abstract performance requirements into quantifiable liquid cooling flow rates. These performance maintenance constraints refer to the minimum performance level that a server node needs to maintain when executing a specific computational task, such as CPU clock speed, throughput, or response latency. When server temperatures are too high, the system may reduce performance to protect the hardware, i.e., thermal throttling occurs. To avoid this, sufficient cooling flow rate needs to be ensured. This analysis can be achieved by establishing a thermal-performance model of the server, which can predict the heat generated by the server based on a given computational load and performance requirements, and further calculate the minimum cooling flow rate required to maintain that performance. Another approach is to establish an empirical mapping relationship or lookup table between computational performance requirements and the required minimum cooling flow rate through extensive experimental or historical data, thereby directly converting performance requirements into a minimum flow guarantee limit.

[0195] Within the feasible region jointly defined by the dynamic flow rate change constraint, the minimum flow guarantee lower bound, and the total flow upper bound in the liquid cooling system physical constraints, a cross-domain joint optimization objective is solved to obtain the liquid cooling flow allocation sequence for each server node, aiming to find the optimal flow allocation scheme. This feasible region is the set of all possible flow allocation schemes defined by the aforementioned constraints. The dynamic flow rate change constraint limits the speed of flow adjustment for each node, the minimum flow guarantee lower bound ensures the computational performance of each node, and the total flow upper bound in the liquid cooling system physical constraints represents the maximum total flow resource that the entire liquid cooling system can provide. This cross-domain joint optimization objective is typically a comprehensive objective function, which may include multiple sub-objectives such as temperature control deviation cost, flow adjustment cost, and computational performance deviation cost, aiming to optimize the overall system performance while satisfying all constraints. Various optimization algorithms can be used to solve this optimization objective. For example, when the objective function and constraints can be expressed in linear or quadratic form, convex optimization methods such as linear programming or quadratic programming can be used for accurate solution. For more complex nonlinear or nonconvex problems, heuristic algorithms, such as genetic algorithms, particle swarm optimization algorithms, or simulated annealing algorithms, can be used to find approximate optimal solutions in a reasonable time.

[0196] By employing the aforementioned technical solutions, and through differentiated relaxation of the upper limit of the flow rate change based on the urgency of cooling demand, the liquid cooling system can dynamically adjust its flow response speed according to the actual heat load and cooling requirements of each server node. This avoids the risk of thermal runaway or performance degradation caused by high-urgency nodes failing to receive sufficient cooling in time due to limited flow adjustment under uniform rigid constraints. By resolving the abstract computational performance maintenance constraint into a specific minimum flow guarantee lower limit, the optimization model can be directly quantified and meet the server's performance requirements, ensuring that computational performance is not compromised during cooling regulation. Solving the cross-domain joint optimization objective within the flexible feasible domain defined by these dynamic and quantified constraints allows the optimization process to more accurately balance cooling efficiency, energy consumption, and computational performance, thereby generating a liquid cooling flow allocation sequence that is more adaptable to actual operating conditions and more robust and efficient. This improves the precision and intelligence of liquid cooling heat dissipation control, especially in complex data center environments where cooling demands vary greatly among server nodes and loads change dynamically. It can effectively avoid flow allocation conflicts and improve the overall stability and energy efficiency of the system.

[0197] This application further proposes a differentiated relaxation of the upper limit of the flow rate change rate in the physical constraints of the liquid cooling system based on the urgency of the cooling demand of each server node, resulting in a dynamic flow rate change rate constraint for each server node. This process includes: determining a relaxation coefficient for each server node based on the urgency of its cooling demand, where the relaxation coefficient monotonically increases with the urgency of the cooling demand; multiplying the upper limit of the flow rate change rate in the physical constraints of the liquid cooling system by the relaxation coefficient of each server node to obtain the upper limit of the dynamic flow rate change rate for each server node; and using the upper limit of the dynamic flow rate change rate for each server node as the flow rate change rate constraint for each server node when solving the cross-domain joint optimization objective.

[0198] The system determines a relaxation coefficient for each server node based on its cooling demand urgency. This relaxation coefficient monotonically increases with increasing cooling demand urgency. The relaxation coefficient is a dynamic factor used to adjust the upper limit of the traffic change rate, quantifying the flexibility allowed for traffic adjustment. Its core function is to differentiate the relaxation or tightening of traffic change rate restrictions based on the server's cooling demand urgency, ensuring that servers with high urgency receive faster and larger traffic adjustments to prioritize their cooling needs. The monotonically increasing characteristic ensures that the higher the urgency, the greater the relaxation coefficient, thus achieving reasonable resource allocation. For example, this can be implemented using a pre-defined lookup table or piecewise function. For instance, the cooling demand urgency can be divided into several discrete levels, each pre-configured with a corresponding relaxation coefficient value, and these values ​​increase with increasing urgency level. During system runtime, the system consults this table or function to obtain the corresponding relaxation coefficient based on the currently calculated server cooling demand urgency. Alternatively, the relaxation coefficient can be dynamically calculated using a continuous mathematical mapping function. This function takes the urgency of cooling demand as input and outputs a monotonically increasing relaxation coefficient. For example, a linear, exponential, or sigmoid function can be used, and its specific parameters can be adjusted through offline calibration or online learning to ensure that the growth trend of the relaxation coefficient matches the actual system response requirements.

[0199] The upper limit of the flow rate change rate in the physical constraints of the liquid cooling system is multiplied by the relaxation coefficient of each server node to obtain the upper limit of the dynamic flow rate change rate for each server node. The upper limit of the flow rate change rate is the maximum allowable flow adjustment range of the liquid cooling system per unit time, reflecting the physical response capability of the liquid cooling pumps and valves, as well as the system stability requirements. By multiplying with the relaxation coefficient, a global or static physical constraint is transformed into a dynamic, adaptive constraint for each server node. This multiplication operation directly quantifies the degree of relaxation, allowing servers with high urgency to have a higher upper limit of the flow rate change rate, thus allowing for a faster cooling response, while servers with low urgency maintain a relatively conservative flow adjustment strategy to avoid unnecessary system disturbances. For example, in each control cycle, the preset upper limit of the basic flow rate change rate applicable to all server nodes in the physical constraints of the liquid cooling system is obtained. For each server node, its relaxation coefficient, determined according to its own cooling demand urgency, is multiplied by this basic upper limit of the flow rate change rate to directly calculate the upper limit of the dynamic flow rate change rate allowed for that server node in the current cycle. Alternatively, considering that the overall operating status of the liquid cooling system may affect the upper limit of the flow rate change, a global, basic upper limit of the flow rate change can be dynamically adjusted based on macroscopic parameters such as the overall load and pump pressure of the liquid cooling system. On this basis, this dynamically adjusted basic upper limit is multiplied by the relaxation coefficient of each server node to further refine and personalize the dynamic flow rate change upper limit of each node, achieving multi-level adaptive adjustment.

[0200] The upper limit of the dynamic flow rate change rate for each server node is used as a constraint on the flow rate change rate when solving the cross-domain joint optimization objective. The cross-domain joint optimization objective aims to comprehensively consider multiple dimensions of optimization objectives, including temperature control deviation costs, flow regulation costs, and computational performance deviation costs. Using the upper limit of the dynamic flow rate change rate as a constraint in the optimization process ensures that the flow adjustment scheme generated by the optimization algorithm when searching for the optimal liquid cooling flow allocation sequence does not exceed the actual physical response capability of the liquid cooling system, and can be differentiated according to the urgency of the actual cooling needs of each server node. This makes the optimization results both physically realistic and highly adaptable and flexible, avoiding suboptimal solutions or situations where urgent cooling needs cannot be met due to rigid constraints. For example, in solvers based on model predictive control (MPC) or linear / quadratic programming optimization algorithms, the upper limit of the dynamic flow rate change rate calculated by each server node is directly used as a constraint on the change in its corresponding flow variable between adjacent control cycles. For example, in the constraint set of an optimization problem, it can be represented as flow(t) - flow(t-1) <= upper limit of dynamic flow rate change, ensuring that the optimization result satisfies this dynamic boundary. Alternatively, for scenarios using heuristic or intelligent optimization algorithms (such as genetic algorithms, particle swarm optimization, etc.) to solve cross-domain joint optimization objectives, the upper limit of dynamic flow rate change can be included as part of the feasible solution space. During the algorithm iteration process, any generated candidate flow allocation sequence must pass the verification of this upper limit of dynamic flow rate change. Candidate solutions that do not meet the constraints will be eliminated or corrected, thereby guiding the optimization search process to converge to a valid solution that meets the dynamic constraints.

[0201] Through the above technical solution, this application provides a refined and adaptive liquid cooling flow rate constraint mechanism. Given that in some of the above embodiments, the upper limit of the flow rate change rate in the physical constraints of the liquid cooling system may lead to rigid flow allocation or response delays due to its fixed nature, making it impossible to accurately match changes in server urgency, this application introduces a relaxation coefficient that is monotonically increased with the urgency of cooling demand for each server node, thereby achieving differentiated adjustment of the upper limit of the flow rate change rate. For example, when the urgency of cooling demand for a server node increases, its corresponding relaxation coefficient increases accordingly, thus widening the upper limit of the dynamic flow rate change rate for that server node. This allows the liquid cooling system to adjust the liquid cooling flow of that node more quickly and significantly to prioritize its urgent cooling needs. Conversely, for server nodes with lower cooling demand urgency, the relaxation coefficient is smaller, and the upper limit of the dynamic flow rate change rate is relatively conservative, avoiding unnecessary drastic flow fluctuations and maintaining system stability. This dynamic and differentiated constraint mechanism enables the optimization algorithm to generate a more adaptive and responsive liquid cooling flow distribution sequence when solving cross-domain joint optimization objectives. This effectively avoids the problem of optimization results being out of touch with actual needs due to fixed constraints, improves the response speed and control accuracy of the liquid cooling heat dissipation control system under complex and variable loads, and ensures the stable operation of server computing performance.

[0202] This application further proposes a method to solve a cross-domain joint optimization objective within a feasible region jointly constrained by dynamic flow rate change constraints, a minimum flow guarantee lower limit, and a total flow upper limit in the physical constraints of the liquid cooling system. This results in a liquid cooling flow allocation sequence for each server node. The solution process includes: determining the search priority of each server node based on its cooling demand urgency, with the search priority increasing as the cooling demand urgency increases; determining the initial flow allocation value for each server node in descending order of search priority within the feasible region, ensuring that the server node with the higher search priority occupies the flow allocation space first; and using this initial flow allocation value as the search starting point, performing joint iterative adjustments to the flow allocation of each server node within the feasible region until the cross-domain joint optimization objective meets the convergence condition, thus obtaining the liquid cooling flow allocation sequence for each server node.

[0203] For example, when determining the search priority of each server node during the solution process, this search priority is an indicator that guides the optimization algorithm to prioritize which server nodes to consider when allocating resources. The cooling demand urgency is a quantitative value that measures the urgency of a server node's current cooling needs; a higher value indicates a more urgent cooling demand. Associating the search priority with this cooling demand urgency, and increasing it as the urgency increases, aims to ensure that, with limited resources, the cooling needs of server nodes with high heat loads and the risk of overheating are prioritized. For example, a preset mapping function, such as a piecewise linear function or an exponential function, can be used to map continuous cooling demand urgency values ​​to discrete priority levels (e.g., levels 1 to 5), or the urgency values ​​can be directly normalized and used as continuous priority weights. Another approach is to set a series of urgency thresholds; when a node's cooling demand urgency exceeds a certain threshold, its search priority is increased to the corresponding higher level.

[0204] Within this feasible region, the initial flow allocation value for each server node is determined node by node in descending order of search priority, ensuring that server nodes with higher search priority occupy flow allocation space within this feasible region first. This initial flow allocation value is the initial liquid cooling flow rate set for each server node before the optimization algorithm begins iterations. This feasible region is jointly defined by dynamic flow rate change constraints, minimum flow guarantee lower limit, and the total flow upper limit in the physical constraints of the liquid cooling system, representing the set of all possible liquid cooling flow allocation schemes. By determining the initial value according to descending search priority, it ensures that server nodes with high cooling urgency can obtain sufficient flow allocation space first, avoiding a disadvantageous situation due to insufficient resources in the early stages of optimization. For example, a proportional allocation strategy can be adopted, that is, a portion of the flow is reserved from the total flow upper limit for allocation based on the proportion of the cooling urgency of high-priority nodes to the total urgency of all high-priority nodes. Alternatively, a simplified predictive model can be used, combining historical operating data and current load conditions, to quickly estimate the initial flow value that meets the basic cooling requirements of high-priority nodes, ensuring that this initial value is within the feasible region.

[0205] Starting with this initial flow allocation value, the flow allocation of each server node is jointly and iteratively adjusted within the feasible region until the value of the cross-domain joint optimization objective satisfies the convergence condition, resulting in the liquid cooling flow allocation sequence for each server node. This initial flow allocation value serves as the starting point for the optimization algorithm, providing a good initial state for subsequent iterations. The joint iterative adjustment refers to the optimization algorithm simultaneously adjusting the liquid cooling flow allocation of all server nodes within the feasible region to find the optimal solution for the cross-domain joint optimization objective function. The convergence condition typically includes the objective function value changing less than a preset threshold, the number of iterations reaching an upper limit, or the solution achieving the required stability. For example, gradient descent-based optimization algorithms, such as the conjugate gradient method or quasi-Newton method, can be used to iteratively adjust the flow allocation of each server node along the negative gradient direction of the cross-domain joint optimization objective, starting from the initial flow allocation value. Alternatively, heuristic or metaheuristic algorithms, such as genetic algorithms or particle swarm optimization, can be used to search for the optimal solution by simulating natural processes, starting from the initial flow allocation value, and evaluating the objective function in each iteration until the convergence condition is met.

[0206] By employing the aforementioned technical solution, search priorities are determined based on the urgency of cooling needs. This allows the optimization algorithm to intelligently identify and prioritize server nodes with the most urgent cooling requirements, preventing resource preemption by low-urgency nodes and ensuring timely response to critical cooling demands. Within the feasible region, initial traffic allocation values ​​are determined node by node in descending search priority order. This allows high-priority nodes to occupy traffic allocation space first, providing a better starting point for subsequent iterative optimization and improving the efficiency and convergence speed of the optimization solution. Using these optimized initial traffic allocation values ​​as the search starting point, joint iterative adjustments not only ensure that the cooling needs of high-urgency nodes are prioritized but also achieve global optimization and balanced allocation of liquid cooling traffic across all server nodes while satisfying all constraints. This effectively improves the timeliness of heat dissipation control and the stability of computational performance. This priority-guided optimization strategy enables the liquid cooling system to respond more intelligently and efficiently to the dynamically changing heat dissipation demands of the data center, especially in high power density and instantaneous high-load scenarios, better maintaining stable server operation and computational performance.

[0207] To facilitate implementation, the following provides methods for determining the various thresholds, limits, and coefficients involved in this invention, and provides representative value ranges for calibration reference; these value ranges are examples and not limitations, and specific values ​​should be determined by calibration in conjunction with the characteristics of the phase change material used, sensor performance, and system hardware constraints.

[0208] (1) Dual-objective verification thresholds: The accuracy verification threshold (preset accuracy threshold) and the robustness verification threshold (preset robustness threshold) can be determined based on the statistical analysis of the model's prediction errors during its historical operation period. Specifically, the distribution characteristics of the error between the predicted and measured values ​​of temperature over a historical window (such as the upper limit of error at a certain confidence level) can be used as the calibration benchmark for the accuracy verification threshold; the distribution characteristics of the model's prediction deviation under small parameter perturbations over a historical window can be used as the calibration benchmark for the robustness verification threshold. Representatively, the accuracy verification threshold can be set to a root mean square error of predicted temperature not exceeding a certain number of temperature units, and the robustness verification threshold can be set to a maximum deviation between the perturbed and unperturbed predicted sequences not exceeding a certain number of temperature units; the specific values ​​are determined according to the system's accuracy requirements and the thermal inertia of the phase change material.

[0209] (2) Cross-validation consistency threshold (preset consistency threshold): It can be determined based on the historical distribution of the consistency of the solid-liquid ratio characterization of the two sensing modes during the normal and stable working period of the sensor. The lower tail quantile of the distribution is taken as the consistency threshold. When the consistency is lower than the threshold, it is determined that the two modes have a significant deviation.

[0210] (3) Dominant kinetic mode discrimination threshold: The preset change rate threshold and preset heating threshold can be determined based on the statistical range of the solid-liquid ratio change rate and heating rate of the phase change material in a typical phase change process. For example, two thresholds can be set based on the upper edge of the solid-liquid ratio change rate in the latent heat absorption stage and the lower edge of the heating rate in the sensible heat stage, so that the three modes of solid sensible heat conduction, latent heat absorption and liquid convection can be distinguished; the specific values ​​are adjusted according to the phase change temperature range of the material and the magnitude of sensible heat / latent heat.

[0211] (4) Order adjustment threshold (preset order adjustment threshold): The typical fluctuation range of the autoregressive order and the input order in the historical update of the local nonlinear correction model can be taken as the benchmark. When the difference between the target order and the current order exceeds the typical fluctuation range, the order update is triggered to avoid frequent order fluctuations.

[0212] (5) Gradual smooth replacement of parameters: The number of transition steps is determined based on the deviation amplitude between the current parameter and the updated parameter. The larger the deviation, the more transition steps there are. The transition ratio coefficient controls the rate at which the parameter approaches the updated value in each control cycle. It can be linearly increasing or S-shaped increasing. Both the number of transition steps and the transition ratio coefficient can be calibrated based on the parameter deviation amplitude and the system's requirements for stability. Representatively, the number of transition steps can be taken from several control cycles.

[0213] (6) Cross-domain optimization relaxation coefficient: This coefficient increases monotonically with the urgency of cooling demand. Its specific form can be a piecewise function or a monotonically increasing continuous function (such as a linear or S-shaped function), and each level of cooling demand urgency is mapped to the corresponding relaxation coefficient value. For example, low urgency corresponds to a smaller relaxation coefficient, and high urgency corresponds to a larger relaxation coefficient. The specific value is determined by the physical response capability of the liquid cooling pump and valve.

[0214] All the above thresholds, limits, and coefficients can be continuously updated through offline calibration before system deployment and online statistics during operation, thereby enabling the present invention to be stably implemented without additional creative effort.

[0215] The following example will provide a more detailed explanation of the above technical solution: Within a large data center, multiple server racks are deployed, each containing server nodes that utilize a liquid cooling system based on phase change materials (PCMs). The challenge for this data center is how to efficiently and precisely regulate the liquid cooling system to maintain stable server operating temperatures during dynamic changes in computing load, while simultaneously preventing the thermal performance of the PCMs from deteriorating over long-term use and ensuring that the performance of critical computing tasks remains unaffected. Current technical solutions typically rely on indirect thermal parameters such as server temperature and temperature rise rate to adjust cooling strategies, but they cannot directly perceive the solid-liquid phase transition state of the PCMs, leading to a continuous degradation in control precision throughout the PCM's lifespan.

[0216] This method solves the above problems through the following steps: For a server node in a data center, such as server node A, its liquid cooling system simultaneously collects data from multiple sources. For example, sensors embedded in the phase change material (PCM) layer periodically perform impedance spectrum sweeps to acquire electrical response characteristic data of the PCM. Ultrasonic sensors emit and receive ultrasonic echo signals to acquire acoustic response characteristic data of the PCM. In addition, thermal sensors such as thermocouples monitor the temperature, heat flux density, and other thermal sampling data of the PCM in real time. The data center's computing load scheduling system also provides server node A's current computing load information and scheduling predictions for a future period. All this data is timestamped after collection to ensure consistency across different data types over time.

[0217] The system performs dual-mode fusion processing on impedance spectrum sweep data and ultrasonic echo signals. Specifically, it extracts electrical response features such as complex impedance amplitude and phase angle at different frequency bands from the impedance spectrum sweep data and generates a first solid-liquid ratio characterization value based on these features. It also extracts acoustic response features such as ultrasonic round-trip time delay from the ultrasonic echo signal and generates a second solid-liquid ratio characterization value based on these features. The system performs time-series consistency analysis on these two solid-liquid ratio characterization values ​​to obtain the trend of deviation amount and direction, forming a cross-validation result. This result indicates the degree of consistency and direction of deviation of the solid-liquid ratio characterization under the two sensing modes. For example, if the ultrasonic signal exhibits a continuous unidirectional deviation due to bubble interference, the cross-validation result will indicate this deviation. Based on this cross-validation result, the system dynamically determines the confidence weights of the impedance spectrum sweep data and the ultrasonic echo signal. For example, when the cross-validation result indicates a deviation in the ultrasonic signal, the confidence weight of the ultrasonic echo signal is reduced. Then, the system uses these confidence weights to adaptively weight and fuse the solid-liquid ratio representations of the two sensing modes, thereby obtaining a more robust and accurate solid-liquid ratio estimate.

[0218] After obtaining the estimated solid-liquid ratio, the system combines the rate of change of this estimate, the phase change material temperature in the thermal sampling data, and the cross-validation results to determine the current phase change stage of the phase change material layer. For example, if the rate of change of the estimated solid-liquid ratio is low but the phase change material temperature rises rapidly, the phase change material layer is determined to be in the solid-state sensible heat conduction stage. If the estimated solid-liquid ratio changes rapidly but the phase change material temperature rises slowly, it is determined to be in the latent heat absorption stage. If the rate of change of the estimated solid-liquid ratio is low and the phase change material temperature rises rapidly, and the previous cycle was determined to be in the latent heat absorption or liquid convection mode, it is determined to be in the liquid convection stage. This judgment, directly based on the physical state of the phase change material, avoids the limitations of related technologies that rely solely on temperature for indirect inference, and can more accurately reflect the actual working state of the phase change material.

[0219] Based on the phase transition stage determination results, the system dynamically adjusts its temperature prediction model. This prediction model consists of a global linear prediction model and a local nonlinear correction model working together. For example, if the determination result is "latent heat absorption stage," the system will call a set of basis functions specifically optimized for the latent heat absorption stage from a preset stage index basis function library, using it as the observation function space of the global linear prediction model. The system will determine the required structural order (e.g., autoregressive order and input order) of the local nonlinear correction model based on the high nonlinearity characteristic of the latent heat absorption stage. This collaborative configuration ensures that the prediction model can be structurally updated according to the current dominant kinetic mode of the phase change material, improving prediction accuracy. Compared to the fixed prediction models in related technologies, this method can adapt to the changes in the thermal response characteristics of phase change materials at different phase transition stages, avoiding the problem of prediction accuracy continuously degrading over time.

[0220] After the prediction model outputs multi-step temperature predictions, the system performs dual-objective verification. Specifically, the system takes the current solid-liquid ratio estimate and thermal sampling data as input, and drives the phase change material thermodynamic model to independently deduce the data within a high-fidelity digital twin, thus obtaining a reference temperature trajectory. This reference trajectory is an independently calculated result based on physical principles and can serve as the "gold standard" for the predictions. Then, the system compares the multi-step temperature predictions output by the prediction model with this reference temperature trajectory to obtain an accuracy verification quantity characterizing the degree of prediction deviation. The system also applies small perturbations to the parameters of the global linear prediction model and the local nonlinear correction model, and observes the degree of deviation and divergence trend between the perturbed and unperturbed predictions to test the prediction model's robustness verification quantity. Only when both the accuracy verification quantity and the robustness verification quantity meet preset thresholds is the dual-objective verification considered successful. If the verification is successful, the system replaces the prediction model parameters in a progressively smooth manner to ensure the stability of the model update process and avoid control oscillations caused by parameter mutations. This dual-objective verification and progressive smooth replacement mechanism ensures the continuous reliability and high accuracy of the prediction model throughout the entire life cycle of the phase change material, overcoming the drawback of model accuracy degrading over time in related technologies.

[0221] Based on the multi-step temperature predictions, computational load scheduling information, and solid-liquid ratio estimates from the currently effective prediction model, the system performs a cross-domain joint optimization with computational performance preservation constraints. The system determines the remaining latent heat capacity of the phase change material layer of server node A based on the solid-liquid ratio estimate and, combined with the heating rate of the multi-step temperature predictions, assesses the urgency of server node A's cooling demand in the future prediction time domain. For example, it determines whether a dual critical state of latent heat depletion and temperature exceeding limits is imminent. Then, the system constructs a cross-domain joint optimization objective by combining the urgency of the cooling demand with the computational performance requirements of the scheduled tasks for server node A in the computational load scheduling information. This objective comprehensively considers the costs of temperature control deviation, liquid cooling flow rate adjustment, and computational performance deviation. For example, for server nodes with high cooling demand urgency, the temperature control deviation cost coefficient increases, while the flow rate adjustment cost coefficient decreases. For server nodes running critical tasks, the computational performance deviation cost coefficient increases. Under the conditions of satisfying computational performance maintenance constraints (e.g., translating the computational performance requirements of mission-critical tasks into a minimum guaranteed flow rate for server nodes) and liquid cooling system physical constraints (e.g., total flow rate cap and flow rate change rate cap, where the flow rate change rate cap is differentiated and relaxed based on the urgency of cooling demand), the system solves for the optimization objective, obtaining a liquid cooling flow rate allocation sequence for server node A and other server nodes. For example, the system determines the search priority based on the urgency of each server node's cooling demand, prioritizing flow rate allocation to nodes with higher urgency. This flow rate allocation sequence is used to accurately regulate the liquid cooling pumps and liquid cooling valves of each server node, thereby achieving precise temperature control of server nodes while ensuring computational performance and efficiently utilizing the heat dissipation potential of phase change materials. This cross-domain joint optimization deeply integrates thermal management and computational resource management, solving the problem of the disconnect between cooling strategies and computational performance in related technologies, and achieving optimal overall data center operational efficiency.

[0222] All of the above-mentioned optional technical solutions can be combined in any way to form the optional embodiments of this application, and will not be described in detail here.

[0223] The above are merely optional embodiments of this application and are not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A server liquid cooling heat dissipation control method based on phase change materials, characterized in that, The method includes: The impedance spectrum sweep data, ultrasonic echo signal, thermal sampling data and calculated load scheduling information of the synchronously acquired phase change material layer are time-stamped and fused in a dual-mode manner to obtain the solid-liquid ratio estimate and the phase change stage discrimination result. Based on the phase transition stage discrimination result, the matching basis function set is called from the stage index basis function library for the global linear prediction model, and the structural order is matched for the local nonlinear correction model, so that the configuration of the basis function set and the structural order are both controlled by the same phase transition stage discrimination result, so as to collaboratively output multi-step temperature prediction values. Based on the estimated solid-liquid ratio and the thermal sampling data, the reference temperature trajectory is deduced, and the multi-step temperature prediction value is verified with dual objectives. After the verification is passed, the parameters of the global linear prediction model and the local nonlinear correction model are gradually and smoothly replaced to obtain the updated current effective prediction model. Based on the multi-step temperature predictions output by the currently effective prediction model, the computational load scheduling information, and the solid-liquid ratio estimate, cross-domain joint optimization with computational performance preservation constraints is performed to obtain the liquid cooling flow allocation sequence for each server node, so as to regulate the liquid cooling pumps and valves.

2. The method according to claim 1, characterized in that, The impedance spectrum sweep data, ultrasonic echo signal, thermal sampling data, and calculated load scheduling information of the synchronously acquired phase change material layer are time-stamped and fused using dual-mode methods to obtain the solid-liquid ratio estimate and phase change stage discrimination result, including: Electrical response features and acoustic response features are extracted from the impedance spectrum sweep data and the ultrasonic echo signal, respectively. Cross-validation is performed based on the electrical response features and the acoustic response features to obtain cross-validation results. The cross-validation results are used to represent the consistency and deviation of the solid-liquid ratio characterization under the two sensing modes. Based on the results of the cross-validation, the confidence weights of the impedance spectrum sweep data and the ultrasonic echo signal are determined respectively. Based on the confidence weights, the solid-liquid ratio characterization of the two sensing modes is adaptively weighted and fused to obtain the estimated solid-liquid ratio value. Based on the rate of change of the estimated solid-liquid ratio, the temperature of the phase change material in the thermal sampling data, and the cross-validation results, the phase change stage discrimination result is determined.

3. The method according to claim 2, characterized in that, The determination of the phase transition stage discrimination result based on the rate of change of the estimated solid-liquid ratio, the phase change material temperature in the thermal sampling data, and the cross-validation results includes: Based on the rate of change of the estimated solid-liquid ratio and the phase change material temperature in the thermal sampling data, the dominant dynamic mode of the phase change material layer is determined; based on the dominant dynamic mode and the estimated solid-liquid ratio, a preliminary stage discrimination result is determined; Based on the consistency of the solid-liquid ratio characterization of the two sensing modes in the cross-validation results, the preliminary stage discrimination results are reviewed to obtain a review conclusion, which is used to indicate whether the preliminary stage discrimination results are reliable. When the verification conclusion indicates that the preliminary stage judgment result is unreliable, the preliminary stage judgment result is shifted to the phase change stage judgment result of the previous cycle to obtain the phase change stage judgment result, which includes the solid sensible heat conduction stage, the latent heat absorption stage, or the liquid convection stage. When the verification conclusion indicates that the preliminary stage discrimination result is reliable, the preliminary stage discrimination result shall be directly used as the phase transition stage discrimination result.

4. The method according to claim 1, characterized in that, The step of calling a matching basis function set for the global linear prediction model from the stage index basis function library based on the phase transition stage discrimination result, and matching the structure order for the local nonlinear correction model, includes: Based on the phase transition stage discrimination result, the basis function group corresponding to the phase transition stage discrimination result is retrieved from the stage index basis function library, and the observation function in the basis function group is used as the observation function space of the global linear prediction model; Based on the nonlinear intensity of the dominant dynamic modes captured by the basis function set, the structural order of the local nonlinear correction model is determined, wherein the nonlinear intensity is determined based on the dynamic mode type indicated by the phase transition stage discrimination result. The basis function set and the structural order are combined as a co-configuration and synchronously loaded into the global linear prediction model and the local nonlinear correction model.

5. The method according to claim 4, characterized in that, The determination of the structural order of the local nonlinear correction model based on the nonlinear intensity of the dominant dynamic modes captured by the basis function set includes: Based on the nonlinear intensity, the linearized residual deviation magnitude of the global linear prediction model for the nonlinear behavior of the system at the current phase transition stage is determined. The linearized residual deviation magnitude is used to characterize the amplitude range of the nonlinear components that the global linear prediction model failed to capture in the upgraded linear space. Based on the magnitude of the linearized residual deviation, the required compensation level for the local nonlinear correction model is determined. Based on the compensation requirement level, the autoregressive order and input order of the local nonlinear correction model are determined, and the autoregressive order and the input order together constitute the structural order.

6. The method according to claim 1, characterized in that, The step of extrapolating a reference temperature trajectory based on the estimated solid-liquid ratio and the thermal sampling data, and performing dual-objective verification on the multi-step temperature prediction, includes: Using the estimated solid-liquid ratio and the thermal sampling data as inputs, the phase change material thermodynamic model is driven to perform independent deduction in the digital twin to obtain the reference temperature trajectory; The multi-step temperature prediction value is compared with the reference temperature trajectory to obtain an accuracy verification quantity that characterizes the degree of prediction deviation. At the same time, the parameters of the global linear prediction model and the local nonlinear correction model are perturbed to test the prediction stability and obtain a robustness verification quantity that characterizes the prediction's ability to resist disturbances. The accuracy verification quantity and the robustness verification quantity are jointly determined. When the accuracy verification quantity meets the preset accuracy threshold and the robustness verification quantity meets the preset robustness threshold, the dual-target verification is determined to be successful; otherwise, the dual-target verification is determined to be unsuccessful.

7. The method according to claim 6, characterized in that, The process of using the estimated solid-liquid ratio and the thermal sampling data as inputs to drive the phase change material thermodynamic model in the digital twin for independent deduction, and obtaining the reference temperature trajectory, includes: The estimated solid-liquid ratio is converted into the current phase state distribution parameters of the phase change material region in the phase change material thermodynamic model, and the thermal sampling data is converted into the thermal boundary conditions of the phase change material thermodynamic model. Based on the current phase distribution parameters and the thermal boundary conditions, the phase change material thermodynamic model is driven to iteratively solve forward along the predicted time domain in the digital twin to obtain the temperature field distribution at each time step; The reference temperature trajectory is formed by extracting the temperature measurement location and the temperature value of the corresponding time step from the temperature field distribution at each time step, which correspond to the multi-step temperature prediction value.

8. The method according to claim 1, characterized in that, After the verification is passed, the parameters of the global linear prediction model and the local nonlinear correction model are progressively smoothed and replaced to obtain the updated current effective prediction model, including: The number of transition steps required for the global linear prediction model and the local nonlinear correction model to transition from the current parameters to the updated parameters is determined dynamically based on the magnitude of the deviation between the current parameters and the updated parameters. Within the transition steps, the parameters of the global linear prediction model are increased periodically from the current parameters to the updated parameters according to the transition ratio coefficient, while the parameters of the local nonlinear correction model are increased periodically from the current parameters to the updated parameters according to the transition ratio coefficient. After all transitions are completed according to the specified number of transition steps, the updated parameters are replaced with the currently effective parameters of the global linear prediction model and the currently effective parameters of the local nonlinear correction model, respectively, to obtain the updated currently effective prediction model.

9. The method according to claim 1, characterized in that, Based on the multi-step temperature predictions output by the currently effective prediction model, the computational load scheduling information, and the estimated solid-liquid ratio, a cross-domain joint optimization with computational performance preservation constraints is performed to obtain the liquid cooling flow allocation sequence for each server node, including: Based on the multi-step temperature prediction and the solid-liquid ratio estimate, the urgency of cooling demand for each server node in the future prediction time domain is determined. The urgency of cooling demand reflects the time window in which the server node can still maintain its current heat storage capacity using phase change materials. Based on the urgency of the cooling demand and the computing performance requirements of the scheduled tasks on the server nodes in the computing load scheduling information, a cross-domain joint optimization objective is constructed. The cross-domain joint optimization objective includes temperature control deviation cost, flow regulation cost, and computing performance deviation cost. Under the conditions of maintaining the computing performance and the physical constraints of the liquid cooling system, the cross-domain joint optimization objective is solved to obtain the liquid cooling flow allocation sequence for each server node.

10. The method according to claim 9, characterized in that, The determination of the cooling urgency of each server node in the future prediction time domain based on the multi-step temperature prediction and the solid-liquid ratio estimate includes: Based on the estimated solid-liquid ratio, the remaining latent heat capacity of the phase change material layer corresponding to each server node is determined. In the future prediction time domain, the heating rate of the multi-step temperature prediction value is correlated with the decay rate of the remaining latent heat capacity to obtain the heat dissipation pressure index of each server node. Based on the remaining latent heat capacity and the temperature prediction value at the end of the prediction time domain in the multi-step temperature prediction value, it is determined whether each server node will experience a dual critical state of latent heat depletion and temperature exceeding the limit within the future prediction time domain. The cooling demand urgency is obtained by fusing the heat dissipation pressure index with the evaluation results of the dual critical state. The cooling demand urgency is the highest value when the heat dissipation pressure index increases and it is determined that the dual critical state will occur.

Images