A data center electromechanical system model identification method and system

Abstract

The application discloses a data center electromechanical system model identification method and system, and particularly relates to the technical field of data center electromechanical system operation management. The residual error between the preset model output and the actual output is subjected to nonlinear mapping to generate a compensation signal, and the fine residual error is obtained after superposition. The degradation index is extracted from the fine residual error and the compensation signal. The decoupling matrix is constructed according to the causal relationship between the degradation index and the variable, and the control instruction is decoupled. The frequency spectrum of the residual deviation after decoupling is monitored, and the damping signal is injected when periodic oscillation is detected. The model error is continuously evaluated, and the re-identification is triggered when the threshold value is exceeded and the time is continuous, the model is updated with real-time data, and iteration is performed. The application improves the model accuracy through nonlinear compensation and degradation tracking, eliminates oscillation through decoupling and damping, and realizes adaptive tracking through online model updating, thereby reducing local overheating, reducing energy consumption and equipment wear.

Description

Technical Field

[0001] This invention relates to the field of data center electromechanical system operation and management technology, and more specifically, to a data center electromechanical system model identification method and system. Background Technology

[0002] Data center electromechanical systems typically employ physical mechanism-based or data-driven models to predict cooling demand and control equipment such as chillers, pumps, and fans. A common model building approach involves offline collection of operational data over a period of time during the system design or commissioning phase to identify a set of fixed model parameters. For example, the least squares method can be used to fit the transfer function between chilled water temperature and server load, or neural networks can be used to learn energy consumption characteristics under historical operating conditions. These offline identification models achieve good control performance when the data center load is stable and the outdoor climate is stable.

[0003] In actual operation, data centers frequently experience various dynamic changes. On the one hand, with continuous server upgrades or fluctuating business loads, the heat generated by IT equipment can fluctuate dramatically by more than 50% within minutes. On the other hand, the performance of the electromechanical equipment itself slowly degrades over time; for example, scaling on the inner wall of heat exchangers increases thermal resistance, or zero-point drift of temperature sensors causes systematic deviations in measurements. When these dynamic changes accumulate to a certain extent, a significant mismatch will appear between the pre-established static model and the actual physical system.

[0004] The residual between the model's predicted output and actual sensor readings gradually increases, making it difficult for control algorithms based on the model to accurately predict future temperature trends. While some improved solutions attempt to correct the model online, most only address linear models or assume constant coupling, making it difficult to handle variations across different time scales, such as rapid load shocks, slow equipment degradation, and multivariable nonlinear coupling. Therefore, this invention proposes a model identification method and system for data center electromechanical systems to solve the aforementioned problems. Summary of the Invention

[0005] To achieve the above objectives, the present invention provides the following technical solution: A method for identifying a data center electromechanical system model includes the following steps: The residual sequence between the predicted output and the actual output of the preset model is input into a pre-built nonlinear mapper to generate a nonlinear compensation signal. The nonlinear compensation signal is then superimposed on the output of the preset model to obtain a refined residual. The preset model is either the initial model of the data center electromechanical system or the model after the last update. Based on the time-series variation trend of refined residuals and nonlinear compensation signals, trace features reflecting equipment performance degradation or sensor drift are extracted, and degradation indices are calculated. Based on the degradation index and the strength of the causal relationship between multiple operating variables collected in real time, a decoupling control matrix is ​​constructed. The decoupling control matrix is ​​used to decouple the control commands and output the decoupled control commands and residual dynamic deviations. Among them, the control commands refer to the original control commands for the actuators of the electromechanical system. Monitor the spectral characteristics of residual dynamic deviation. When periodic oscillations are detected in multiple actuators, activate active disturbance rejection control to inject damping signals to eliminate the oscillations. The model error of the current preset model is continuously evaluated. When the model error exceeds the preset model error threshold and the duration exceeds the preset duration threshold, a re-identification trigger signal is generated. In response to the re-identification trigger signal, the parameters or structure of the preset model are updated online using the real-time operating data of the data center electromechanical system. The updated preset model is then used as the preset model for the next iteration.

[0006] In a preferred embodiment, the pre-built nonlinear mapper is a deep residual shrinking network, which sequentially includes an input layer, a first convolutional layer, a first batch normalization layer, a first activation function layer, a soft thresholding layer, a second convolutional layer, a second batch normalization layer, a second activation function layer, a global average pooling layer, and an output layer. The input layer receives the residual sequence. The first convolutional layer uses a convolutional kernel of a preset size and a preset stride to extract features. The first batch normalization layer converts the extracted features into a distribution with zero mean and unit variance. The first activation function layer uses a linear rectified function to perform a nonlinear transformation. The soft thresholding layer calculates an adaptive threshold based on the mean absolute value of the output features of the first activation function layer, and sets features within the adaptive threshold range to zero, while features outside the range shrink towards zero. The second convolutional layer uses a convolutional kernel of another preset size to perform deep convolution, and the second batch normalization layer and the second activation function layer perform normalization and linear rectification transformation again. Global average pooling layers compress multidimensional feature maps into one-dimensional feature vectors; The output layer maps a one-dimensional feature vector into a single numerical value as a nonlinear compensation signal through fully connected neurons. The range of values ​​for the nonlinear compensation signal is constrained to a preset multiple of the standard deviation of the residual sequence.

[0007] In a preferred embodiment, extracting trace features reflecting device performance degradation or sensor drift includes: Construct a sliding time window with a fixed time window, where each time window contains continuous refined residual data points and corresponding nonlinear compensation signal data points; Empirical mode decomposition is performed on the refined residual sequence within each time window to obtain several intrinsic mode function components and one residual component. The few intrinsic mode function components with the lowest frequency are selected as low-frequency trend terms. The cumulative compensation energy value is obtained by summing the nonlinear compensation signal sequences within each time window. The trace features are composed of the slope change rate of the low-frequency trend term, the year-on-year growth rate of the cumulative compensation energy value, and the root mean square offset of the refined residual sequence. The calculated degradation index also includes: Each component in the trace features is input into a pre-trained fuzzy inference system. The fuzzy inference system uses a triangular membership function to map the value of each component to several fuzzy levels and outputs the corresponding continuous values ​​as a comprehensive degradation index. When the overall degradation index exceeds the preset threshold, it is determined that there is significant equipment performance degradation or sensor drift.

[0008] In a preferred embodiment, the multiple runtime variables collected in real time include: Chilled water supply temperature, chilled water return temperature, cooling water supply temperature, cooling water return temperature, chiller evaporation pressure, chiller condensation pressure, refrigerant flow rate, outdoor dry bulb temperature, outdoor wet bulb temperature, cold aisle supply air static pressure, hot aisle return air temperature, and total server load power. The strength of causal relationship is calculated using the transfer entropy method: for any two running variables, time series data of a preset length are selected, the transfer entropy value from the first variable to the second variable and the reverse transfer entropy value are calculated, and the larger value is taken as the strength of the original causal relationship between the two variables. When the degradation index exceeds the preset amplification threshold, the original causal relationship strength is multiplied by an amplification factor greater than one. Constructing the decoupling control matrix includes: taking the control commands of all actuators as the set of output variables and all controlled parameters as the set of input variables, normalizing the causal relationship strength and filling it into the off-diagonal positions of the decoupling control matrix, while fixing the diagonal positions to one. The decoupling compensation matrix is ​​obtained by inverting the decoupling control matrix. The control commands are decoupled using a decoupling control matrix. Specifically, the original control command vector is multiplied by the decoupling compensation matrix to obtain the decoupled control command vector.

[0009] In a preferred embodiment, the spectral characteristics for monitoring residual dynamic deviation include: The residual dynamic deviation is subjected to discrete Fourier transform at a fixed sampling frequency to calculate the power spectral density in the preset low-frequency to preset high-frequency band range, and the dominant frequency corresponding to the peak power spectral density is identified. When the main frequency remains constant for several consecutive sampling periods and its corresponding power spectral density exceeds the preset power multiple of the baseline power spectral density, it is determined that multiple actuators are experiencing periodic oscillations. Initiating active disturbance rejection control by injecting damping signals includes: constructing an extended state observer based on residual dynamic deviations to estimate the total system disturbance in real time; The dynamic damping coefficient is calculated based on the main frequency, and the dynamic damping coefficient is positively correlated with the square of the main frequency. A nonlinear state error feedback control law is used to combine the residual dynamic deviation with the total disturbance estimated by the extended state observer to generate a preliminary damping control quantity. The initial damping control quantity is multiplied by the dynamic damping coefficient to obtain the final injected damping signal, which is then superimposed on the decoupled control command. After each injection of damping signal, the spectral characteristics of the residual dynamic deviation are recalculated until the peak power spectral density drops below the preset power ratio of the baseline power spectral density, at which point the injection stops.

[0010] In a preferred embodiment, continuously evaluating the model error of the current preset model includes: The predicted output value of the preset model and the actual sensor measurement value are collected at a preset frequency. The absolute percentage error is calculated and smoothed by the exponential weighted moving average method to obtain the smoothed model error. The smoothing factor is taken within a preset range. The preset model error threshold is a dynamically adjusted threshold. Its initial value is set to an initial preset percentage. Whenever the preset model is successfully updated online, the preset model error threshold is automatically reset to the update reset multiple of the average smoothed model error of the preset model in the first preset time period after the update. The preset duration threshold is set to a preset number of seconds. When the smoothed model error exceeds the preset model error threshold after dynamic adjustment and the over-limit state is continuously maintained for more than the preset duration threshold, a re-identification trigger signal is generated. Additional monitoring will be conducted if the chiller load rate changes by more than a first preset percentage of load change within a preset first time period, or if the cooling fan speed changes by more than a preset percentage of speed change within a preset second time period. If either of these conditions occurs, a re-identification trigger signal will be generated immediately. In response to the re-identification trigger signal, the preset model is updated online. The linear parameter part is updated by recursive least squares method, and the nonlinear parameter part is updated by long short-term memory network. The process is carried out in parallel and parameter cross-validation is performed at the end of each iteration. The parameter combination that minimizes the model prediction error is retained.

[0011] In a preferred embodiment, the generation of the nonlinear compensation signal further includes the following post-processing steps: After obtaining the initial compensation value through fully connected neurons in the output layer, adaptive amplitude adjustment is performed on the initial compensation value. The adaptive amplitude adjustment process first calculates the local standard deviation of the residual sequence within the current time window, and then determines an amplitude compression factor based on the ratio of the local standard deviation to the global standard deviation of the residual sequence. When the ratio is less than the preset lower limit, the amplitude compression factor is set to the first preset value; when the ratio is greater than the preset upper limit, the amplitude compression factor is set to the second preset value; when the ratio is between the preset lower limit and the preset upper limit, the amplitude compression factor is linearly inversely proportional to the ratio. Multiply the initial compensation value by the amplitude compression factor to obtain the final nonlinear compensation signal; The final nonlinear compensation signal is further constrained within a preset local multiple of the local standard deviation of the residual sequence.

[0012] In a preferred embodiment, the process of calculating the degradation index further includes a dynamic correction step: After the fuzzy inference system outputs the comprehensive degradation index, the refined residual value at the next time step is predicted using an autoregressive moving average model based on the most recent sampling points of the refined residual sequence, and the predicted residual is calculated. When the absolute value of the prediction residual exceeds the preset prediction error threshold, a positive correction coefficient is generated. The value of the positive correction coefficient is proportional to the absolute value of the prediction residual and is limited to a preset correction coefficient range. Multiply the comprehensive degradation index output by the fuzzy inference system by the positive correction coefficient to obtain the corrected comprehensive degradation index; When the corrected overall degradation index exceeds the preset degradation threshold, it is determined that there is significant equipment performance degradation or sensor drift. The revised comprehensive degradation index is also used to replace the original comprehensive degradation index in the construction of the subsequent decoupling control matrix.

[0013] In a preferred embodiment, a data center electromechanical system model recognition system includes: The residual compensation module is used to input the residual sequence between the predicted output and the actual output of the preset model into a pre-built nonlinear mapper to generate a nonlinear compensation signal, and then superimpose the nonlinear compensation signal onto the output of the preset model to obtain a refined residual; wherein, the preset model is the initial model of the data center electromechanical system or the model after the last update; The degradation assessment module is used to extract trace features reflecting equipment performance degradation or sensor drift based on the time-series variation trend of refined residuals and nonlinear compensation signals, and to calculate degradation indices. The decoupling control module is used to construct a decoupling control matrix based on degradation indicators and the strength of causal relationships between multiple real-time collected operating variables. The decoupling control matrix is ​​used to decouple control commands and output the decoupled control commands and residual dynamic deviations. The control commands refer to the original control commands for the actuators of the electromechanical system. The oscillation suppression module is used to monitor the spectral characteristics of residual dynamic deviation. When periodic oscillations are detected in multiple actuators, the active disturbance rejection control is activated to inject a damping signal to eliminate the oscillations. The model update module is used to continuously evaluate the model error of the current preset model. When the model error exceeds the preset model error threshold and the duration exceeds the preset duration threshold, a re-identification trigger signal is generated. In response to the re-identification trigger signal, the parameters or structure of the preset model are updated online using the real-time operating data of the data center electromechanical system. The updated preset model is then used as the preset model for the next iteration.

[0014] The technical effects and advantages of this invention are as follows: This invention generates a refined residual by inputting the residual sequence between the predicted output and the actual output of a preset model into a nonlinear mapper to generate a nonlinear compensation signal, which is then superimposed. This allows for online compensation of prediction errors in the operating point drift and nonlinear regions, ensuring that the preset model maintains high prediction accuracy even after significant load fluctuations or equipment aging, thereby reducing the risk of localized overheating due to model mismatch. Furthermore, by constructing a decoupled control matrix based on the causal relationship strength between degradation indices and operating variables, control commands are decoupled, and the spectral characteristics of residual dynamic deviations are monitored. When periodic oscillations are detected in multiple actuators, active disturbance rejection control (ADRC) is activated to inject damping signals, effectively eliminating chain-coupled oscillations in the electromechanical system, improving system stability, and reducing mechanical wear of actuators. Finally, by continuously evaluating the model error of the current preset model, a re-identification trigger signal is generated when the model error exceeds a dynamic adjustment threshold and persists for a certain period. Real-time operating data is used to update the parameters or structure of the preset model online, enabling the model to adaptively track the time-varying characteristics of the system. This reduces overcooling or undercooling caused by model mismatch, achieving continuous optimization of data center energy efficiency and extending equipment lifespan. Attached Figure Description

[0015] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to the accompanying drawings; Figure 1 This is a schematic diagram of a data center electromechanical system model identification method according to the present invention.

[0016] Figure 2 This is a schematic diagram of a data center electromechanical system model recognition system according to the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] Reference Figure 1 - Figure 2 The following examples were obtained: Example 1: A method for identifying a data center electromechanical system model, comprising the following steps: The residual sequence between the predicted output and the actual output of the preset model is input into a pre-built nonlinear mapper to generate a nonlinear compensation signal. The nonlinear compensation signal is then superimposed on the output of the preset model to obtain a refined residual. The preset model is either the initial model of the data center electromechanical system or the model after the last update. Based on the time-series variation trend of refined residuals and nonlinear compensation signals, trace features reflecting equipment performance degradation or sensor drift are extracted, and degradation indices are calculated. Based on the degradation index and the strength of the causal relationship between multiple operating variables collected in real time, a decoupling control matrix is ​​constructed. The decoupling control matrix is ​​used to decouple the control commands and output the decoupled control commands and residual dynamic deviations. Among them, the control commands refer to the original control commands for the actuators of the electromechanical system. Monitor the spectral characteristics of residual dynamic deviation. When periodic oscillations are detected in multiple actuators, activate active disturbance rejection control to inject damping signals to eliminate the oscillations. The model error of the current preset model is continuously evaluated. When the model error exceeds the preset model error threshold and the duration exceeds the preset duration threshold, a re-identification trigger signal is generated. In response to the re-identification trigger signal, the parameters or structure of the preset model are updated online using the real-time operating data of the data center electromechanical system. The updated preset model is then used as the preset model for the next iteration.

[0019] The pre-constructed nonlinear mapper is a deep residual shrinking network, which sequentially includes an input layer, a first convolutional layer, a first batch normalization layer, a first activation function layer, a soft thresholding layer, a second convolutional layer, a second batch normalization layer, a second activation function layer, a global average pooling layer, and an output layer. The input layer receives the residual sequence, and the first convolutional layer extracts features using a pre-defined kernel size and a pre-defined stride. The pre-defined kernel size is typically a kernel of length three or five, and the pre-defined stride is one, determined based on the local correlation and sampling frequency of the residual signal in the data center electromechanical system. For example, if the residual sequence is sampled once per second, a kernel of length three can capture the residual change pattern over three adjacent time steps.

[0020] The first batch normalization layer transforms the extracted features into a distribution with zero mean and unit variance, based on the overall statistical characteristics of the training dataset. The first activation function layer uses a linear rectified function for nonlinear transformation. This function retains the original value for positive inputs and outputs zero for negative inputs. This is based on the fact that there are alternating positive and negative errors in the residual sequence, and the linear rectified function can effectively suppress meaningless negative fluctuations.

[0021] The soft thresholding layer calculates an adaptive threshold based on the mean absolute value of the output features of the first activation function layer, sets features within the adaptive threshold range to zero, and shrinks features outside the range towards zero. The adaptive threshold is calculated as follows: First, calculate the absolute values ​​of all elements of the current batch output features. Then, calculate the arithmetic mean of these absolute values. Multiply this mean by a preset coefficient (usually between 0.3 and 0.5) to obtain the final threshold. The threshold setting is based on the theory of deep residual shrinkage networks, namely, the feature amplitude corresponding to noise is small, while the feature amplitude corresponding to useful signals is large. Soft thresholding can remove noise redundancy. For example, the first activation function layer outputs five feature values: -2.0, -0.1, +0.3, +1.5, and +0.05. Their absolute average is 0.79, which, multiplied by a coefficient of 0.4, yields a threshold of 0.316. Then, -0.1, +0.3, and +0.05, whose absolute values ​​are less than 0.316, are set to zero. -2.0 shrinks to -1.684, and +1.5 shrinks to +1.184. After this processing, small random fluctuations in the residual sequence are completely eliminated, while larger systematic biases are retained.

[0022] The second convolutional layer uses a kernel of a different preset size for deep convolution. This preset size is typically seven or nine units in length, because deep convolution requires a larger receptive field to extract higher-order features. The second batch normalization layer and the second activation function layer perform normalization and linear rectification transformations again, serving the same purpose as the first group: stabilizing the training process of the deep network. The global average pooling layer compresses the multidimensional feature map into a one-dimensional feature vector. Specifically, it calculates the arithmetic mean of all values ​​within each two-dimensional feature channel, forming a vector with a length equal to the number of channels. This operation reduces the number of parameters and enhances the network's resistance to overfitting.

[0023] The output layer maps a one-dimensional feature vector into a single numerical value as a nonlinear compensation signal through fully connected neurons. These neurons employ linear transformations, and their weight parameters are obtained through network training. The range of the nonlinear compensation signal is constrained to a preset multiple of the standard deviation of the residual sequence. This preset multiple is typically two or three, based on the fact that the residual distribution of the data center electromechanical system approximates a Gaussian distribution, and three times the standard deviation encompasses over 99% of the residual amplitude. For example, if the standard deviation of the current residual sequence is 0.5 degrees, and the preset multiple is two, the nonlinear compensation signal is limited to between -1.0 and +1.0 degrees. If the original value output by the network is 1.5 degrees, the actual compensation signal used is truncated to 1.0 degrees, thus avoiding excessive compensation that could cause system oscillations.

[0024] The generation of the nonlinear compensation signal also includes the following post-processing steps. After obtaining the preliminary compensation value through fully connected neuron mapping in the output layer, adaptive amplitude adjustment processing is performed on this preliminary compensation value. The preliminary compensation value refers to the original value directly calculated by the output layer of the deep residual shrinkage network. This value has not yet undergone amplitude limiting and dynamic adjustment. The adaptive amplitude adjustment processing first calculates the local standard deviation of the residual sequence within the current time window. The current time window refers to the most recent continuous sampling time interval. The window length is set according to the response speed of the data center's electromechanical system, typically ranging from 30 to 120 seconds. The local standard deviation reflects the degree of fluctuation in the residual sequence within this time window. For example, if the current time window length is 60 seconds, with sampling once per second, resulting in 60 residual values, the local standard deviation of these residual values ​​is calculated to be 0.3 degrees.

[0025] The global standard deviation refers to the standard deviation of the residual sequence during the entire operation period from system startup or the last model update to the present. The global standard deviation is 0.5 degrees. Then, an amplitude compression factor is determined based on the ratio of the local standard deviation to the global standard deviation of the residual sequence. This ratio is equal to the local standard deviation divided by the global standard deviation. The purpose of the amplitude compression factor is to: compress the compensation amplitude to avoid overshoot when local fluctuations are small; and allow larger compensation to quickly correct errors when local fluctuations are large.

[0026] When the ratio is less than the preset lower limit, the amplitude compression factor is set to the first preset value. The preset lower limit is set based on the normal range of residual fluctuations under normal data center operating conditions, typically 0.5. The first preset value is set to 0.3 based on experience, meaning that the compensation amplitude can be compressed to a maximum of 30% of the original. When the ratio is greater than the preset upper limit, the amplitude compression factor is set to the second preset value. The preset upper limit is set based on the critical value when the residual exhibits abnormally large fluctuations, typically 1.5. The second preset value is set to 1.2 based on experience, meaning that the compensation amplitude is allowed to be amplified to a maximum of 120% of the original.

[0027] When the ratio falls between the preset lower limit and the preset upper limit, the amplitude compression factor is linearly inversely proportional to the ratio. This linear inverse relationship means the amplitude compression factor equals a constant minus another constant multiplied by the ratio; the specific form is obtained by fitting experimental data. For example, if the preset lower limit is 0.5, the corresponding compression factor is 0.3; if the preset upper limit is 1.5, the corresponding compression factor is 1.2; and when the ratio is 1.0, the compression factor obtained through linear interpolation is 0.75.

[0028] If the current local standard deviation is 0.3 degrees and the global standard deviation is 0.5 degrees, the ratio is 0.6, falling between 0.5 and 1.5. Then the compression factor is (0.3 plus (0.6 minus 0.5) multiplied by (1.2 minus 0.3) divided by (1.5 minus 0.5)) equals 0.39. Multiplying the initial compensation value by the amplitude compression factor yields the final nonlinear compensation signal. For example, if the initial compensation value is 1.0 degrees and the amplitude compression factor is 0.39, then the final nonlinear compensation signal is 0.39 degrees.

[0029] The final nonlinear compensation signal is further constrained within a preset local multiple of the local standard deviation of the residual sequence. This preset local multiple is set according to the data center's electromechanical system's safety amplitude limit requirements for the compensation signal, typically two or three. The basis for this is that the local standard deviation reflects the amplitude of current short-term fluctuations, and three times the local standard deviation can cover 99% of short-term fluctuations. For example, if the current local standard deviation is 0.3 degrees and the preset local multiple is two, the final nonlinear compensation signal is limited to between -0.6 degrees and +0.6 degrees. If the final nonlinear compensation signal calculated in the previous step is 0.7 degrees, the actual signal truncation used is 0.6 degrees. This post-processing step ensures that the nonlinear compensation signal can adaptively adjust its amplitude according to local fluctuations without exceeding the safety range.

[0030] The training process of the deep residual shrinkage network is as follows: First, a training dataset is collected, consisting of input residual sequence samples and corresponding target compensation values. The input residual sequence samples are taken from the difference between the predicted output and the actual output in the historical operating data of the data center electromechanical system. The corresponding target compensation values ​​are constructed as follows: while collecting historical operating data, the predicted output value of the preset model and the actual sensor measurement value are recorded. The ideal compensation amount is defined as the theoretical correction value that makes the output of the preset model equal to the actual output. For each sampling time, the ideal compensation amount is equal to the actual sensor measurement value minus the predicted output value of the preset model. This value can be directly calculated from the historical data without additional experiments.

[0031] For example, at a certain sampling moment, the preset model predicts the chilled water supply temperature to be 7.0 degrees Celsius, while the actual sensor measures 7.3 degrees Celsius. The ideal compensation is +0.3 degrees Celsius. The residual sequence is used as the input sample, and the corresponding ideal compensation is used as the output label, forming a training data pair. If the preset model's predicted value in historical data is close to the actual value, the residual sequence is smaller, and the corresponding ideal compensation is also smaller. To ensure that the training data covers various operating conditions, it is necessary to collect operating data under steady-state conditions, load increase conditions, load decrease conditions, and the initial stage of equipment aging. At least one thousand continuous sampling points should be collected for each condition. After data collection, all data pairs are randomly shuffled and divided into training, validation, and test sets in a 6:2:2 ratio.

[0032] The network parameters were initialized randomly, with the weights of each layer initialized to a Gaussian distribution with a mean of zero and a variance of 0.01, and the biases initialized to zero. The loss function was the mean squared error, calculated as the average of the squared difference between the nonlinear compensation signal output by the network and the target compensation value. The optimizer was the adaptive moment estimation algorithm, with the learning rate initially set to 0.001 and the batch size set to 32.

[0033] The training process is as follows: Input residual sequence samples from the training set are batch-wise fed into the network, the loss function value is calculated, then backpropagation is used to calculate the gradient of each layer's parameters, and finally, the optimizer is used to update the network parameters. After each training epoch, the network performance is evaluated using a validation set. If the validation set loss no longer decreases for five consecutive epochs, training stops. The network parameters with the minimum validation set loss are selected as the trained model, and its generalization ability is verified using a test set. This training process is completed offline. After training, the network parameters are fixed and deployed to the controller of the data center electromechanical system.

[0034] Extracting trace features that reflect equipment performance degradation or sensor drift includes the following operations: Construct a sliding time window with a fixed time window. A fixed time window refers to a continuous time interval of constant length, such as five minutes, ten minutes, or thirty minutes. The sliding time window moves forward continuously over time, shifting by one sampling period each time. Each time window contains continuous refined residual data points and corresponding nonlinear compensation signal data points. The refined residual data points are the specific values ​​of the refined residual sequence obtained in the previous step at each sampling time. The nonlinear compensation signal data points are the specific values ​​of the nonlinear compensation signal generated in the previous step at each sampling time. For example, if the sampling period is one second and the fixed time window is ten minutes, then each window contains six hundred refined residual data points and six hundred nonlinear compensation signal data points. Every second the window slides, the oldest data point is removed and the newest data point is added.

[0035] A refined residual data point refers to each specific value in the sequence of differences between the preset model output and the actual output obtained after superimposing nonlinear compensation signals. The physical unit of this data point is the same as the actual output; for example, when the actual output is temperature, the unit of the refined residual is degrees Celsius; when the actual output is pressure, the unit is kilopascals. For example, if the preset model predicts the chilled water supply temperature at a certain moment to be 7.0 degrees Celsius, and the actual sensor measures 7.3 degrees Celsius, then the original residual is -0.3 degrees Celsius. The nonlinear compensation signal generated by the nonlinear mapper is +0.1 degrees Celsius, and after superposition, the refined residual is -0.2 degrees Celsius. This -0.2 degrees Celsius is a refined residual data point, its data type is floating-point, and its unit is degrees Celsius.

[0036] Nonlinear compensation signal data points refer to the compensation values ​​output by the nonlinear mapper at any given time. Their units are consistent with the residuals, such as degrees Celsius, kilopascals, or percentages. These data points are not control commands but rather correction values ​​used to adjust the model's predicted values. Their range is typically limited to a preset multiple of the residual standard deviation. For example, if the nonlinear compensation signal output by the nonlinear mapper at any given time is positive zero (one degree), this value is used as a data point in subsequent cumulative summation calculations.

[0037] Empirical Mode Decomposition (EMD) is performed on the refined residual sequence within each time window, yielding several intrinsic mode function (EMF) components and one residual component. EMD is an adaptive signal decomposition method that decomposes nonlinear, non-stationary signals into multiple EMF components arranged from high to low frequency and a monotonic residual component. Each EMF component represents an oscillation mode at a different time scale in the original signal. The lowest-frequency EMF components are selected as the low-frequency trend term. "Lowest frequency" means that the center frequency of these components is closest to zero, reflecting long-term, slow changes in the signal. The number of selected components is typically one to three, determined based on the time-varying characteristics of the degradation process of the data center's electromechanical system. For example, after performing EMD on the refined residual sequence, five EMF components and one residual component are obtained. The first component has the highest frequency, corresponding to second-level noise. The fifth component has the lowest frequency, corresponding to hour-level baseline drift; the fifth component is selected as the low-frequency trend term. If the fifth component still contains relatively fast fluctuations, the superposition of the fourth and fifth components can be selected as the low-frequency trend term.

[0038] The cumulative compensation energy value is obtained by summing the nonlinear compensation signal sequences within each time window. Summation involves adding the values ​​of all nonlinear compensation signal data points within the window. Since nonlinear compensation signals can be positive or negative, their signs are preserved during summation. The cumulative compensation energy value reflects the total compensation magnitude paid by the nonlinear mapper to correct model errors within that time window. For example, if there are three nonlinear compensation signal data points within a window: positive 0.2 degrees, negative 0.1 degrees, and positive 0.3 degrees, the summation result is positive 0.4 degrees.

[0039] The trace features are composed of the slope change rate of the low-frequency trend term, the year-on-year growth rate of the cumulative compensation energy value, and the root mean square offset of the refined residual sequence. The slope change rate refers to the slope of the fitted straight line of the low-frequency trend term within the time window. The year-on-year growth rate is calculated by subtracting the cumulative compensation energy value of the previous window from the current window's cumulative compensation energy value, and then dividing by the cumulative compensation energy value of the previous window. The root mean square offset is the square root of the average of the squares of all data points in the refined residual sequence. For example, if the low-frequency trend term linearly rises from 0.5 degrees to 0.7 degrees within the window, with a time span of ten minutes, then the slope is 0.02 degrees per minute. The cumulative compensation energy value is positive 0.4 degrees in the current window and positive 0.3 degrees in the previous window. The month-on-month growth rate is 0.33. The three values ​​of the refined residual sequence are negative 0.1 degrees, positive 0.2 degrees, and positive 0.3 degrees, with squares of 0.01, 0.04, and 0.09 respectively. The average is 0.047, and the root mean square offset after taking the square root is approximately 0.22 degrees.

[0040] The calculation of the degradation index also includes the following operations: Each component of the trace features is input into a pre-trained fuzzy inference system. The fuzzy inference system is a computational model based on fuzzy logic; its input is precise numerical values, and its output is continuous numerical values ​​obtained after fuzzification, rule-based inference, and defuzzification. This fuzzy inference system uses a triangular membership function to map the numerical value of each component to several fuzzy levels. The triangular membership function is a commonly used fuzzification tool; its shape is an isosceles triangle, determined by three parameters: the left endpoint, the vertex, and the right endpoint. Fuzzy levels are typically divided into three levels: low, medium, and high, or further subdivided into five levels: very low, low, normal, high, and very high. The fuzzy inference system outputs the corresponding continuous numerical values ​​as a comprehensive degradation index; the comprehensive degradation index is a dimensionless number between zero and one, where zero represents no degradation and one represents severe degradation. For example, suppose the slope change rate is 0.02 degrees per minute. After this value is input into the fuzzy inference system, the triangular membership function determines that the membership degree for the "moderate degradation" level is 0.7, for the "high degradation" level it is 0.3, and for all other levels it is 0. The fuzzy rule base contains a rule: if the slope is moderately degraded and the cumulative compensation energy value's year-on-year growth rate is normal, then the comprehensive degradation index is 0.5. Through a weighted average of multiple rules, the final output comprehensive degradation index is 0.55.

[0041] The rule base of the fuzzy inference system is constructed as follows: First, the three components of the trace features are divided into three fuzzy levels: the slope change rate of the low-frequency trend term is divided into three levels: "low slope," "medium slope," and "high slope"; the month-on-month growth rate of the cumulative compensation energy value is divided into three levels: "negative growth," "stable," and "positive growth"; and the root mean square offset of the refined residual sequence is divided into three levels: "small offset," "medium offset," and "large offset." The comprehensive degradation index is used as the output and is divided into four levels: "no degradation," "mild degradation," "moderate degradation," and "severe degradation." Based on data center operating experience and expert knowledge, the following nine fuzzy rules are formulated: Rule 1: If the slope is low, the month-on-month growth rate is negative, and the offset is small, then the comprehensive degradation index is no degradation. Rule 2: If the slope is low, the month-on-month growth rate is stable, and the offset is medium, then the comprehensive degradation index is mildly degraded. Rule 3: If the slope is low, the month-on-month growth rate is positive, and the offset is large, then the comprehensive degradation index is moderate degradation. Rule 4: If the slope is moderate, the month-on-month growth rate is negative, and the offset is moderate, then the comprehensive degradation index is mild degradation. Rule 5: If the slope is moderate, the month-on-month growth rate is stable, and the offset is large, then the comprehensive degradation index is moderately degraded. Rule 6: If the slope is moderate, the month-on-month growth rate is positive, and the offset is large, then the comprehensive degradation index is severely degraded. Rule 7: If the slope is high, the month-on-month growth rate is negative, and the offset is large, then the comprehensive degradation index is moderate degradation. Rule 8: If the slope is high, the month-on-month growth rate is stable, and the offset is large, then the comprehensive degradation index is severely degraded. Rule 9: If the slope is high, the month-on-month growth rate is positive, and the offset is large, then the comprehensive degradation index is severely degraded. Each rule uses an AND logic to connect the antecedent conditions. Fuzzy inference employs the Maddani minimum operation rule, meaning the trigger strength of each rule is the minimum value of the membership degrees of the three antecedents. The final output comprehensive degradation index is defuzzified using the centroid method. The formula is: the comprehensive degradation index equals the centroid-weighted sum of the membership functions of all rules divided by the total trigger strength. The above rule base is set offline before system deployment and remains fixed during operation. If the actual data center operating characteristics deviate from the preset rules, the rule parameters can be refitted by collecting new data, but the rule logic structure remains unchanged.

[0042] When the overall degradation index exceeds a preset threshold, significant equipment performance degradation or sensor drift is determined. The preset threshold is set based on the tolerance of the data center's electromechanical system to degradation, typically 0.6. This threshold is based on statistical analysis of a large amount of historical operating data: when the overall degradation index is below 0.6, the system can still maintain normal control performance; when it is above 0.6, the model error increases significantly and the control effect decreases. For example, if the overall degradation index output by the fuzzy inference system is 0.75, exceeding the preset threshold of 0.6, then significant equipment performance degradation or sensor drift is determined. This determination result is used to adjust the amplification factor of the causal relationship strength in subsequent steps and to trigger more frequent model error assessments. If the overall degradation index is 0.4, then it is determined that no significant degradation has been reached, and the causal relationship strength is not further amplified.

[0043] After the fuzzy inference system outputs the comprehensive degradation index, based on the most recent sampling points of the refined residual sequence, an autoregressive moving average model is used to predict the refined residual value at the next time step, and the predicted residual is calculated. The autoregressive moving average model is a time series forecasting model, abbreviated as AMA model. This model consists of an autoregressive component and a moving average component. The autoregressive component uses a linear combination of the refined residual values ​​from the past several time steps to predict the current value, while the moving average component uses a linear combination of the prediction errors from the past several time steps to correct the predicted value. The model order is determined based on the dynamic characteristics of the data center's electromechanical system; typically, the autoregressive order is two, and the moving average order is one.

[0044] The recent sampling points refer to a continuous period of time preceding the current moment. The number of sampling points is determined based on the model order and computational resources, typically ranging from ten to thirty points. Predicting the refined residual value for the next moment involves substituting the refined residual data from the current moment and previous moments into the model to calculate the estimated residual value for the next sampling period. The predicted residual equals the actual measured refined residual value at the next moment minus the model's predicted value. For example: the sampling period is one second, the model uses an autoregressive order of two and a moving average order of one, and the current moment is second t; using the refined residual values ​​from second t and second t-1, along with the prediction error at second t, the predicted refined residual value for second t+1 is 0.3 degrees; the actual measured refined residual value at second t+1 is 0.5 degrees, therefore the predicted residual is +0.2 degrees.

[0045] When the absolute value of the predicted residual exceeds a preset prediction error threshold, a positive correction coefficient is generated. This preset prediction error threshold is set based on the allowable prediction deviation of the data center's electromechanical system, typically taking 0.1 degrees Celsius or 0.1 times the actual output range. This threshold is based on a statistical evaluation of the model's predictive capability: under normal operating conditions, the absolute value of the predicted residual has a 95% probability of being less than this threshold. The positive correction coefficient is a value greater than or equal to one, and its function is to amplify the comprehensive degradation index of the fuzzy inference system's output. For example, if the preset prediction error threshold is 0.1 degrees, and the current absolute value of the predicted residual is 0.2 degrees, exceeding the threshold, a positive correction coefficient is generated.

[0046] The positive correction coefficient is proportional to the absolute value of the prediction residual and is limited to a preset correction coefficient range. Proportionality means the positive correction coefficient equals one plus a proportionality constant multiplied by the difference between the absolute value of the prediction residual and the threshold. The proportionality constant is set empirically, typically ranging from five to ten. The lower limit of the preset correction coefficient range is one, and the upper limit is set based on the maximum allowable correction margin, typically ranging from 1.5 to 2.0. For example, if the proportionality constant is eight, the preset prediction error threshold is 0.1 degrees, and the absolute value of the prediction residual is 0.2 degrees, then the deviation is 0.1 degrees. The positive correction coefficient equals one plus eight multiplied by 0.1, which equals 1.8. If the preset upper limit of the correction coefficient is 1.5, then the actual positive correction coefficient used is limited to 1.5.

[0047] Multiply the comprehensive degradation index output by the fuzzy inference system by the positive correction coefficient to obtain the corrected comprehensive degradation index. For example, if the comprehensive degradation index output by the fuzzy inference system is 0.5 and the positive correction coefficient is 1.5, then the corrected comprehensive degradation index is 0.75.

[0048] When the corrected overall degradation index exceeds a preset degradation threshold, significant equipment performance degradation or sensor drift is determined. The preset degradation threshold is typically set to 0.6, and this threshold is based on statistical analysis of a large amount of historical operating data: when the corrected overall degradation index is below 0.6, the system's false alarm rate is below 5%; when it is above 0.6, the occurrence rate of actual degradation events exceeds 90%. For example, if the corrected overall degradation index is 0.75, exceeding 0.6, significant equipment performance degradation or sensor drift is determined.

[0049] The revised comprehensive degradation index is also used to replace the original comprehensive degradation index in the construction of the subsequent decoupling control matrix. The subsequent construction of the decoupling control matrix requires the degradation index to calculate the amplification factor of the causal relationship strength. Because the revised comprehensive degradation index considers the influence of prediction residuals, it reflects the true degradation state of the current system better than the original comprehensive degradation index, and therefore replaces the original value in subsequent calculations. For example: the original comprehensive degradation index is 0.5, which does not trigger a degradation judgment, and the causal relationship strength in the decoupling control matrix is ​​not amplified. The revised comprehensive degradation index is 0.75, which triggers a degradation judgment, and the causal relationship strength is multiplied by an amplification factor greater than one, thereby enhancing the decoupling effect.

[0050] The real-time collected runtime variables include the following twelve specific parameters: Chilled water supply temperature refers to the temperature of the water output from the chiller unit to the chilled water pipeline, and the unit is degrees Celsius. Chilled water return temperature refers to the water temperature returning from the terminal air conditioner to the chiller unit, and the unit is degrees Celsius. Cooling water supply temperature refers to the water temperature output from the cooling tower to the condenser of the chiller unit, and is expressed in degrees Celsius. Cooling water return temperature refers to the temperature of the water returning from the chiller unit's condenser to the cooling tower, measured in degrees Celsius. The evaporation pressure of a chiller unit refers to the saturation pressure of the refrigerant in the evaporator, and the unit is kilopascals (kPa). The condensing pressure of a chiller unit refers to the saturation pressure of the refrigerant in the condenser, and the unit is kilopascal (kPa). Refrigerant flow rate refers to the mass flow rate of refrigerant flowing through a chiller unit or terminal air conditioner, measured in kilograms per second. Outdoor dry-bulb temperature refers to the ordinary temperature of the air, measured by an outdoor weather station, and is expressed in degrees Celsius. Outdoor wet-bulb temperature refers to the temperature at which air becomes saturated after water evaporates and cools, reflecting air humidity; the unit is degrees Celsius. Cold aisle air static pressure refers to the static pressure of the air inside the cold aisle of the server rack, measured in Pascals. Hot aisle return air temperature refers to the temperature of the air exhausted from the hot aisle of the server rack, measured in degrees Celsius. The total load power of the server refers to the total electrical power consumed by all servers in the data center, measured in kilowatts. The sampling frequency of the above twelve variables is once per second, and all data is collected synchronously and stored in the controller's memory.

[0051] The calculation of the causal relationship strength adopts the transfer entropy method. Transfer entropy is used to quantify the predictive ability of one time series to another. For any two operating variables, time series data of a preset length are first selected. The preset length is set according to the response time of the data center electromechanical system and the data stationarity. Usually, three hundred to one thousand sampling points are selected, corresponding to five to fifteen minutes of historical data.

[0052] The process of calculating the transfer entropy from the first variable to the second variable is as follows: Using the historical values ​​of both the first and second variables as conditions, calculate the reduction in uncertainty of the current value of the second variable. Then, calculate the reverse transfer entropy from the second variable to the first variable. The larger of the two transfer entropy values ​​is taken as the strength of the original causal relationship between the two variables. The strength of the original causal relationship is a value between zero and one, where zero indicates no causal relationship and one indicates complete causality. For example, taking the chilled water supply temperature and chilled water return temperature as two variables, with a preset length of 300 points, the transfer entropy from the supply temperature to the return temperature is calculated to be 0.7, and the reverse transfer entropy is 0.2. Therefore, the strength of the original causal relationship is taken as 0.7, indicating that the supply temperature has a strong influence on the return temperature.

[0053] When the degradation index exceeds a preset amplification threshold, the original causal relationship strength is multiplied by an amplification factor greater than one. The preset amplification threshold is set based on the degradation sensitivity requirements of the data center's electromechanical system, typically 0.4 or 0.5. The amplification factor is set according to the severity of degradation, typically ranging from 1.2 to 2.0. The specific value of the amplification factor is directly proportional to the degradation index: the more the degradation index exceeds the threshold, the larger the amplification factor. For example, if the preset amplification threshold is 0.5 and the current degradation index is 0.7, exceeding the threshold, the original causal relationship strength of 0.7 is multiplied by the amplification factor of 1.5, resulting in an amplified causal relationship strength of 1.05. If the multiplication result exceeds one, it is truncated to one.

[0054] Constructing the decoupled control matrix involves the following operations: The decoupling control matrix uses the control commands of all actuators as the set of output variables. Actuators include chillers, chilled water pumps, cooling water pumps, cooling tower fans, terminal air conditioning fans, electronic expansion valves, etc. Control commands refer to the opening degree, frequency, or start / stop commands of these actuators. The input variables are all controlled parameters, including cold aisle supply air static pressure, hot aisle return air temperature, and chilled water supply temperature. The normalized causal relationship strengths are filled into the off-diagonal positions of the decoupling control matrix. Normalization means dividing all causal relationship strengths by their maximum possible value, making the result fall between zero and one. Rows in the decoupling control matrix correspond to output variables, and columns correspond to input variables. The off-diagonal rows and columns represent different variable pairs, and the diagonal position is fixed at one. For example, with three actuators, the decoupling control matrix is ​​a 3x3 matrix. The first row and second column contain the normalized causal relationship strength of 0.6 from the control command of the first actuator to the second controlled parameter; the second row and first column contain the reverse 0.3; and the first row and first column on the diagonal contain one.

[0055] The decoupling compensation matrix is ​​obtained by inverting the decoupling control matrix. The inversion operation can be performed using Gaussian elimination or Newton's iteration method, and is calculated in real time in the controller. The product of the decoupling compensation matrix and the original matrix is ​​an identity matrix. The control commands are decoupled using the decoupling control matrix. Specifically, the original control command vector is multiplied on the left by the decoupling compensation matrix to obtain the decoupled control command vector. The original control command vector is a column vector composed of the command values ​​of each actuator directly output by the proportional-integral-derivative controller or model predictive controller.

[0056] Left multiplication refers to placing the decoupling compensation matrix on the left and the command vector on the right, performing a matrix-vector multiplication operation. Each component in the decoupled control command vector includes compensation for the influence of other variables, thus reducing the coupling effect. For example, the original control command vector is a chilled water pump frequency of 40 Hz and a cooling tower fan speed of 800 rpm. The decoupling compensation matrix is ​​a 2x2 square matrix, with the first row and first column at 0.9, the first row and second column at -0.2, the second row and first column at -0.1, and the second row and second column at 1.1. After left multiplication, the decoupled chilled water pump frequency is 40 x 0.9 plus 800 x -0.2 equals 36 minus 16 equals 20 Hz, and the decoupled cooling tower fan speed is 40 x -0.1 plus 800 x 1.1 equals -4 plus 880 equals 876 rpm. This result replaces the original command and is sent to the actuator.

[0057] The spectral characteristics of residual dynamic deviation monitoring include: A Discrete Fourier Transform (DFT) is performed on the residual dynamic deviation at a fixed sampling frequency. The DFT converts the time-domain signal into a frequency-domain representation, outputting the amplitude and phase corresponding to different frequencies. The power spectral density is calculated within a preset low-frequency to preset high-frequency band. The preset low-frequency band is typically 0.01 Hz, corresponding to a long-period fluctuation of 100 seconds. The preset high-frequency band is typically 0.5 Hz, corresponding to a short-period fluctuation of 2 seconds. Power spectral density represents the energy magnitude of each frequency component. The dominant frequency corresponding to the peak power spectral density is identified, i.e., the frequency value with the highest power spectral density within the preset frequency band. For example, if the sampling frequency is once per second, and residual dynamic deviation data for the most recent 60 seconds is collected, totaling 60 points, after the DFT, the maximum power spectral density value of 0.5 Hz appears at 0.1 Hz; therefore, 0.1 Hz is the dominant frequency.

[0058] When the main frequency remains constant for several consecutive sampling periods and its corresponding power spectral density exceeds a preset power multiple of the baseline power spectral density, it is determined that multiple actuators are experiencing periodic oscillations. The "several consecutive sampling periods" are typically five to ten periods, based on the premise that a brief, single fluctuation is insufficient to determine continuous oscillation; multiple periods need to be observed to confirm stability. The baseline power spectral density refers to the average power spectral density when the system is operating normally without oscillations, usually obtained through historical data statistics. The preset power multiple is set according to the oscillation significance requirement, typically three to five times. For example: If the main frequency remains unchanged at 0.1 Hz for five consecutive sampling periods, and the current power spectral density is 0.5, while the baseline power spectral density is 0.1, the ratio is 5, exceeding the preset power multiple of 3. Therefore, it is determined that multiple actuators are experiencing periodic oscillations.

[0059] Initiating active disturbance rejection control (ADRC) by injecting a damping signal involves the following operations. ADRC is a control method that does not rely on an exact mathematical model. Its core is to estimate and compensate for the total system disturbance in real time. An extended state observer is constructed based on the residual dynamic deviation. The extended state observer is used to estimate the residual dynamic deviation, its derivative, and the total system disturbance in real time. The observer adopts a third-order structure, with three state variables defined as follows: the first state variable equals the residual dynamic deviation; the second state variable equals the first derivative of the residual dynamic deviation; and the third state variable equals the total system disturbance. The observer has two inputs: the first input is the actuator command value corresponding to the current residual dynamic deviation in the decoupled control command; and the second input is the actual value of the residual dynamic deviation measured at the current moment. The observer has three outputs: an estimate of the residual dynamic deviation, an estimate of its first derivative, and an estimate of the total system disturbance.

[0060] The observer is implemented using a discrete-time recursive approach, with a sampling period of ten times per second, meaning the sampling interval δ equals 0.1 seconds. The observer parameters are configured using the bandwidth method: the observer bandwidth ωo is set to five times the control system bandwidth ωc. If the control system bandwidth ωc is 2 radians per second, then ωo is 10 radians per second. The three gain parameters of the observer are calculated using the following formulas: The formula for calculating the first observer gain β1 is: β1 equals one minus the cube root of the sampling interval multiplied by the observer bandwidth. Substituting the values: the sampling interval is 0.1 seconds, the observer bandwidth is 10, then one minus 0.1 multiplied by 10 equals zero, zero cubed is zero, the cube root is zero, one minus zero equals one, that is, β1 equals one. In actual implementation, β1 is taken as one.

[0061] The formula for calculating the second observer gain β2 is: β2 equals (one minus the sampling interval multiplied by the square of the observer bandwidth) multiplied by three divided by the sampling interval. Substituting the values: one minus zero multiplied by ten equals zero, the square of zero is zero, one minus zero equals one, multiplied by three equals three, divided by zero gives thirty, that is, β2 equals thirty.

[0062] The formula for calculating the gain β3 of the third observer is: β3 equals (one minus the cube of the sampling interval multiplied by the observer bandwidth) multiplied by one divided by the square of the sampling interval. Substituting the values: one minus zero equals ten, zero cubed equals zero, one minus zero equals one, divided by the square of zero and zero, we get one hundred, that is, β3 equals one hundred.

[0063] Substituting the gains of the three observers into the standard third-order extended state observer recursive formula, the recursive calculation is performed once every 0.1 seconds. For example, at a certain sampling moment, the measured residual dynamic deviation is +0.3 degrees, and the fan speed command in the decoupled control command is 800 revolutions per minute. Using the state estimate from the previous moment and combining it with the current input, the observer recursively calculates: the residual dynamic deviation estimate is +0.29 degrees, its first derivative estimate is 0.02 degrees per second, and the total system disturbance estimate is -0.03 degrees. This total disturbance estimate is used for subsequent compensation. It is fed into the nonlinear state error feedback control law to counteract the impact of the disturbance on the system. The entire observer performs a recursive calculation once every 0.1 seconds, requiring no knowledge of the precise mathematical model of the motor or fan; it can operate solely based on the input and output data.

[0064] The extended state observer is used to estimate the total system disturbance in real time. The total system disturbance includes the overall effects of unmodeled internal dynamics, parameter variations, nonlinear coupling, and external disturbances. The estimated value is output in numerical form and updated once per sampling period. The dynamic damping coefficient is calculated based on the dominant frequency, and it is positively correlated with the square of the dominant frequency. Its expression is: the dynamic damping coefficient equals the proportionality constant multiplied by the square of the dominant frequency. The proportionality constant is set according to the system inertia and actuator capability, typically ranging from 0.5 to 2.0. The positive correlation is based on the fact that the higher the frequency, the faster the oscillation, requiring stronger damping to suppress it. For example, if the dominant frequency is 0.1 Hz and the proportionality constant is 1, the dynamic damping coefficient is 0.01; if the dominant frequency is 0.2 Hz, the dynamic damping coefficient is 0.04.

[0065] The nonlinear state error feedback control law is used to generate an initial control quantity based on the residual dynamic deviation and its derivative, without including total disturbance compensation. The control law has two inputs: the current estimate of the residual dynamic deviation (from the first output of the observer) and the estimate of its first derivative (from the second output of the observer). The output is the initial control quantity u0.

[0066] The control law employs a nonlinear combination approach, calculated as follows: u0 equals the first control gain multiplied by the exponential factor of the deviation estimate, plus the second control gain multiplied by the derivative estimate. The exponential factor α is set to 0.5, which is less than 1, resulting in a relatively larger gain when the deviation is small, thus enhancing sensitivity to small oscillations. The first control gain Kp is set to twice the control system bandwidth ωc, i.e., 4.0. The second control gain Kd is set to 1.5 times the control system bandwidth ωc, i.e., 3.0. All gains and exponential factors are set during system initialization and remain unchanged during operation.

[0067] For example: The current deviation estimate is +0.3 degrees, the exponential factor to the power of 0.5 is +0.548, the first term is 4.0 multiplied by 0.548 equals 2.192, the derivative estimate is 0.02 degrees per second, the second term is 3.0 multiplied by 0.02 equals 0.06; the two terms are added together to get 2.252, which is the initial control quantity u0, in dimensionless percentage, with the maximum value limited to between plus and minus 100%.

[0068] The initial damping control value is multiplied by the dynamic damping coefficient to obtain the final injected damping signal, which is then superimposed on the decoupled control command. Superposition means adding the damping signal to the corresponding component of the decoupled control command without changing the basic structure of the original command. For example, if the initial damping control value is 0.4, the dynamic damping coefficient is 0.01, and the final damping signal is 0.004, the fan speed in the decoupled control command is 800 revolutions per minute. After superimposing the damping signal, it becomes 800.004 revolutions per minute, a minimal change that still effectively suppresses oscillations.

[0069] After each injection of a damped signal, the spectral characteristics of the residual dynamic deviation are recalculated until the peak power spectral density drops below a preset power ratio of the baseline power spectral density. Injection then stops, and the newly acquired residual dynamic deviation data after the damped signal injection is recalculated. The time window length is the same as the initial analysis. The preset power ratio is typically 1.5 or 2, indicating that the allowed residual oscillation power does not exceed 1.5 times the baseline. For example, after injecting a damped signal, if the recalculated peak power spectral density is 0.15 and the baseline is 0.1, the ratio is 1.5, which equals the preset power ratio of 1.5. Injection then stops. If the ratio is still greater than 1.5, injection continues, and a re-detection is performed after each injection.

[0070] Continuous evaluation of the model error of the current preset model includes: The system collects predicted output values ​​from a preset model and actual sensor measurements at a preset frequency. This preset frequency is typically once per second or ten times per second, consistent with the sampling period of the control system. The predicted output value refers to the result calculated by the preset model based on the current input variables, such as the predicted static pressure of the cold aisle supply air or the return air temperature of the hot aisle. The actual sensor measurements refer to the values ​​directly read from temperature sensors, pressure sensors, or flow meters deployed within the data center. The absolute percentage error is calculated using the formula: Absolute percentage error equals the predicted output value minus the absolute value of the actual sensor measurement, divided by the actual sensor measurement, and then multiplied by 100%. If the actual sensor measurement is zero, the predicted output value is used as the denominator.

[0071] The smoothed model error is obtained by smoothing using the exponentially weighted moving average method: The exponentially weighted moving average (ERM) is a recursive smoothing algorithm. Its formula is: the current smoothing error equals the smoothing factor multiplied by the current absolute percentage error plus (one minus the smoothing factor) multiplied by the smoothing error at the previous time step. The smoothing factor is set within a preset range, typically between 0.1 and 0.3. A smaller smoothing factor results in a stronger smoothing effect but a slower response to short-term fluctuations; a larger smoothing factor results in a faster response but a lower smoothness. This value is based on statistical analysis of data center noise characteristics: second-level noise amplitude is approximately 1% to 3%, and a smoothing factor of 0.2 can attenuate noise to over 80% within two periods. For example: if the current absolute percentage error is 5%, the previous smoothing error is 4%, and the smoothing factor is 0.2, then the current smoothing error equals 0.2 multiplied by 5 plus 0.8 multiplied by 4 equals 1 plus 3.2 equals 4.2%.

[0072] The preset model error threshold is a dynamically adjusted threshold, and its initial value is set as an initial preset percentage, which is usually five percent. This value is based on the fact that under normal operating conditions, the model error of the data center electromechanical system is generally less than three percent, and setting five percent as the initial tolerance limit can avoid frequent triggering. Whenever the preset model is successfully updated online, the preset model error threshold is automatically reset to the update reset multiple of the average smoothed model error of the preset model in the first preset time period after the update. The first preset time period is usually one hour or half an hour. This length is based on the fact that the model needs a period of time to complete convergence and evaluate the steady-state accuracy of the new model after the update.

[0073] The update reset factor is typically set to two or three, meaning that a new model is allowed to fluctuate by twice the average error after stable operation before triggering re-identification. For example, if the average smoothed model error is 2% in the first hour after a successful online update, setting the update reset factor to two would reset the preset model error threshold to 4%. The preset duration threshold is set to a preset number of seconds, typically 30 or 60 seconds. This value is based on the fact that data center electromechanical systems have high thermal inertia; brief exceedances will not cause substantial problems, while a risk may arise only if the duration exceeds 30 seconds.

[0074] When the smoothed model error exceeds the dynamically adjusted preset model error threshold and this over-limit state continues for more than the preset duration threshold, a re-identification trigger signal is generated. For example: the current smoothed model error is 4.5%, and the preset model error threshold is 4%. If the over-limit state starts at second p and continues until second p plus 30, a re-identification trigger signal is generated. If the error falls below 4% during the duration, the timer is reset to zero.

[0075] Additional monitoring is conducted to detect if the chiller unit load rate changes by more than a first preset percentage within a preset first time period, or if the cooling fan speed changes by more than a preset percentage within a preset second time period. In either case, a re-identification trigger signal is immediately generated. The preset first time period is typically ten or fifteen seconds, based on the rapid response of the chiller unit load rate; a change exceeding the threshold within ten seconds indicates a significant load fluctuation. The first preset percentage of load change is typically 20%, based on the fact that the chiller unit load rate can change by 20% to 50% during server load fluctuations. The preset second time period is typically five or ten seconds, based on the rapid adjustment speed of the cooling fan speed. The preset percentage of speed change is typically 50%, based on the fact that rapid changes in fan speed can significantly alter airflow distribution and heat exchange efficiency.

[0076] For example: If the chiller unit load rate increases from 30% to 55% within ten seconds, a change of 25%, exceeding 20%, a re-identification trigger signal is immediately generated without waiting for the model error to exceed the limit. Similarly, if the cooling fan speed decreases from 800 rpm to 380 rpm within five seconds, a change of 52.5%, exceeding 50%, it will also trigger immediately.

[0077] In response to the re-identification trigger signal, the preset model is updated online. The linear parameter part is updated using recursive least squares (RLS), an online parameter estimation algorithm that updates the parameter estimate each time a new data point is received, without needing to store all historical data. Its forgetting factor is typically set to 0.95 to 0.99 to gradually discard the influence of old data. The nonlinear parameter part is updated using a long short-term memory (LSM) network. LSM is a recurrent neural network with the ability to remember long-term dependencies. Its structure includes an input gate, a forget gate, an output gate, and memory units, with one to three layers and ten to fifty hidden units per layer. The two methods are executed in parallel, meaning that RLS and LSM network training are run simultaneously on the same set of real-time data.

[0078] At the end of each iteration, parameter cross-validation is performed. Cross-validation involves testing the updated models using a small, recently unused segment of data (e.g., the last ten sampling points) and calculating the prediction errors for each. The parameter combination that minimizes the model's prediction error is retained as the preset model. For example, after a re-identification trigger, recursive least squares updates the linear parameter set A, while long short-term memory updates the nonlinear parameter set B. Using the test data from the last ten seconds, if the average prediction error of parameter set A is 2.1%, and the average prediction error of parameter set B is 1.8%, then parameter set B is selected as the new model parameters. If the difference between the two errors is less than 0.2%, then both sets of parameters are used together.

[0079] Example 2: A data center electromechanical system model recognition system, comprising: The residual compensation module is used to input the residual sequence between the predicted output and the actual output of the preset model into a pre-built nonlinear mapper to generate a nonlinear compensation signal, and then superimpose the nonlinear compensation signal onto the output of the preset model to obtain a refined residual; wherein, the preset model is the initial model of the data center electromechanical system or the model after the last update; The degradation assessment module is used to extract trace features reflecting equipment performance degradation or sensor drift based on the time-series variation trend of refined residuals and nonlinear compensation signals, and to calculate degradation indices. The decoupling control module is used to construct a decoupling control matrix based on degradation indicators and the strength of causal relationships between multiple real-time collected operating variables. The decoupling control matrix is ​​used to decouple control commands and output the decoupled control commands and residual dynamic deviations. The control commands refer to the original control commands for the actuators of the electromechanical system. The oscillation suppression module is used to monitor the spectral characteristics of residual dynamic deviation. When periodic oscillations are detected in multiple actuators, the active disturbance rejection control is activated to inject a damping signal to eliminate the oscillations. The model update module is used to continuously evaluate the model error of the current preset model. When the model error exceeds the preset model error threshold and the duration exceeds the preset duration threshold, a re-identification trigger signal is generated. In response to the re-identification trigger signal, the parameters or structure of the preset model are updated online using the real-time operating data of the data center electromechanical system. The updated preset model is then used as the preset model for the next iteration.

[0080] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0081] It should be understood that in the various embodiments of this application, the order of the above-mentioned processes does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0082] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0083] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0084] The above are merely specific embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for identifying a data center electromechanical system model, characterized in that, Includes the following steps: The residual sequence between the predicted output and the actual output of the preset model is input into a pre-built nonlinear mapper to generate a nonlinear compensation signal. The nonlinear compensation signal is then superimposed on the output of the preset model to obtain a refined residual. The preset model is either the initial model of the data center electromechanical system or the model after the last update. Based on the time-series variation trend of refined residuals and nonlinear compensation signals, trace features reflecting equipment performance degradation or sensor drift are extracted, and degradation indices are calculated. Based on the degradation index and the strength of the causal relationship between multiple operating variables collected in real time, a decoupling control matrix is ​​constructed. The decoupling control matrix is ​​used to decouple the control commands and output the decoupled control commands and residual dynamic deviations. Among them, the control commands refer to the original control commands for the actuators of the electromechanical system. Monitor the spectral characteristics of residual dynamic deviation. When periodic oscillations are detected in multiple actuators, activate active disturbance rejection control to inject damping signals to eliminate the oscillations. The model error of the current preset model is continuously evaluated. When the model error exceeds the preset model error threshold and the duration exceeds the preset duration threshold, a re-identification trigger signal is generated. In response to the re-identification trigger signal, the parameters or structure of the preset model are updated online using the real-time operating data of the data center electromechanical system. The updated preset model is then used as the preset model for the next iteration.

2. The data center electromechanical system model identification method according to claim 1, characterized in that, The pre-built nonlinear mapper is a deep residual shrinking network, which includes, in sequence, an input layer, a first convolutional layer, a first batch normalization layer, a first activation function layer, a soft thresholding layer, a second convolutional layer, a second batch normalization layer, a second activation function layer, a global average pooling layer, and an output layer. The input layer receives the residual sequence. The first convolutional layer uses a convolutional kernel of a preset size and a preset stride to extract features. The first batch normalization layer converts the extracted features into a distribution with zero mean and unit variance. The first activation function layer uses a linear rectified function to perform a nonlinear transformation. The soft thresholding layer calculates an adaptive threshold based on the mean absolute value of the output features of the first activation function layer, and sets features within the adaptive threshold range to zero, while features outside the range shrink towards zero. The second convolutional layer uses a convolutional kernel of another preset size to perform deep convolution, and the second batch normalization layer and the second activation function layer perform normalization and linear rectification transformation again. Global average pooling layers compress multidimensional feature maps into one-dimensional feature vectors; The output layer maps a one-dimensional feature vector into a single numerical value as a nonlinear compensation signal through fully connected neurons. The range of values ​​for the nonlinear compensation signal is constrained to a preset multiple of the standard deviation of the residual sequence.

3. The data center electromechanical system model identification method according to claim 2, characterized in that, Extracting trace features that reflect equipment performance degradation or sensor drift includes: Construct a sliding time window with a fixed time window, where each time window contains continuous refined residual data points and corresponding nonlinear compensation signal data points; Empirical mode decomposition is performed on the refined residual sequence within each time window to obtain several intrinsic mode function components and one residual component. The few intrinsic mode function components with the lowest frequency are selected as low-frequency trend terms. The cumulative compensation energy value is obtained by summing the nonlinear compensation signal sequences within each time window. The trace features are composed of the slope change rate of the low-frequency trend term, the year-on-year growth rate of the cumulative compensation energy value, and the root mean square offset of the refined residual sequence. The calculated degradation index also includes: Each component in the trace features is input into a pre-trained fuzzy inference system. The fuzzy inference system uses a triangular membership function to map the value of each component to several fuzzy levels and outputs the corresponding continuous values ​​as a comprehensive degradation index. When the overall degradation index exceeds the preset threshold, it is determined that there is significant equipment performance degradation or sensor drift.

4. The data center electromechanical system model identification method according to claim 3, characterized in that, The real-time collected operating variables include: chilled water supply temperature, chilled water return temperature, cooling water supply temperature, cooling water return temperature, chiller evaporation pressure, chiller condensation pressure, refrigerant flow rate, outdoor dry bulb temperature, outdoor wet bulb temperature, cold aisle supply air static pressure, hot aisle return air temperature, and total server load power. The strength of causal relationship is calculated using the transfer entropy method: for any two running variables, time series data of a preset length are selected, the transfer entropy value from the first variable to the second variable and the reverse transfer entropy value are calculated, and the larger value is taken as the strength of the original causal relationship between the two variables. When the degradation index exceeds the preset amplification threshold, the original causal relationship strength is multiplied by an amplification factor greater than one. Constructing the decoupling control matrix includes: taking the control commands of all actuators as the set of output variables and all controlled parameters as the set of input variables, normalizing the causal relationship strength and filling it into the off-diagonal positions of the decoupling control matrix, while fixing the diagonal positions to one. The decoupling compensation matrix is ​​obtained by inverting the decoupling control matrix. The control commands are decoupled using a decoupling control matrix. Specifically, the original control command vector is multiplied by the decoupling compensation matrix to obtain the decoupled control command vector.

5. The data center electromechanical system model identification method according to claim 4, characterized in that, The spectral characteristics of residual dynamic deviation monitoring include: The residual dynamic deviation is subjected to discrete Fourier transform at a fixed sampling frequency to calculate the power spectral density in the preset low-frequency to preset high-frequency band range, and the dominant frequency corresponding to the peak power spectral density is identified. When the main frequency remains constant for several consecutive sampling periods and its corresponding power spectral density exceeds the preset power multiple of the baseline power spectral density, it is determined that multiple actuators are experiencing periodic oscillations. Initiating active disturbance rejection control by injecting damping signals includes: constructing an extended state observer based on residual dynamic deviations to estimate the total system disturbance in real time; The dynamic damping coefficient is calculated based on the main frequency, and the dynamic damping coefficient is positively correlated with the square of the main frequency. A nonlinear state error feedback control law is used to combine the residual dynamic deviation with the total disturbance estimated by the extended state observer to generate a preliminary damping control quantity. The initial damping control quantity is multiplied by the dynamic damping coefficient to obtain the final injected damping signal, which is then superimposed on the decoupled control command. After each injection of damping signal, the spectral characteristics of the residual dynamic deviation are recalculated until the peak power spectral density drops below the preset power ratio of the baseline power spectral density, at which point the injection stops.

6. The data center electromechanical system model identification method according to claim 5, characterized in that, Continuous evaluation of the model error of the current preset model includes: The predicted output value of the preset model and the actual sensor measurement value are collected at a preset frequency. The absolute percentage error is calculated and smoothed by the exponential weighted moving average method to obtain the smoothed model error. The smoothing factor is taken within a preset range. The preset model error threshold is a dynamically adjusted threshold. Its initial value is set to an initial preset percentage. Whenever the preset model is successfully updated online, the preset model error threshold is automatically reset to the update reset multiple of the average smoothed model error of the preset model in the first preset time period after the update. The preset duration threshold is set to a preset number of seconds. When the smoothed model error exceeds the preset model error threshold after dynamic adjustment and the over-limit state is continuously maintained for more than the preset duration threshold, a re-identification trigger signal is generated. Additional monitoring will be conducted if the chiller load rate changes by more than a first preset percentage of load change within a preset first time period, or if the cooling fan speed changes by more than a preset percentage of speed change within a preset second time period. If either of these conditions occurs, a re-identification trigger signal will be generated immediately. In response to the re-identification trigger signal, the preset model is updated online. The linear parameter part is updated by recursive least squares method, and the nonlinear parameter part is updated by long short-term memory network. The process is carried out in parallel and parameter cross-validation is performed at the end of each iteration. The parameter combination that minimizes the model prediction error is retained.

7. The data center electromechanical system model identification method according to claim 2, characterized in that, The generation of the nonlinear compensation signal also includes the following post-processing steps: After obtaining the initial compensation value through fully connected neurons in the output layer, adaptive amplitude adjustment is performed on the initial compensation value. The adaptive amplitude adjustment process first calculates the local standard deviation of the residual sequence within the current time window, and then determines an amplitude compression factor based on the ratio of the local standard deviation to the global standard deviation of the residual sequence. When the ratio is less than the preset lower limit, the amplitude compression factor is set to the first preset value; when the ratio is greater than the preset upper limit, the amplitude compression factor is set to the second preset value; when the ratio is between the preset lower limit and the preset upper limit, the amplitude compression factor is linearly inversely proportional to the ratio. Multiply the initial compensation value by the amplitude compression factor to obtain the final nonlinear compensation signal; The final nonlinear compensation signal is further constrained within a preset local multiple of the local standard deviation of the residual sequence.

8. The data center electromechanical system model identification method according to claim 3, characterized in that, The process of calculating the degradation index also includes a dynamic correction step: After the fuzzy inference system outputs the comprehensive degradation index, the refined residual value at the next time step is predicted using an autoregressive moving average model based on the most recent sampling points of the refined residual sequence, and the predicted residual is calculated. When the absolute value of the prediction residual exceeds the preset prediction error threshold, a positive correction coefficient is generated. The value of the positive correction coefficient is proportional to the absolute value of the prediction residual and is limited to a preset correction coefficient range. Multiply the comprehensive degradation index output by the fuzzy inference system by the positive correction coefficient to obtain the corrected comprehensive degradation index; When the corrected overall degradation index exceeds the preset degradation threshold, it is determined that there is significant equipment performance degradation or sensor drift. The revised comprehensive degradation index is also used to replace the original comprehensive degradation index in the construction of the subsequent decoupling control matrix.

9. A data center electromechanical system model recognition system, used to implement the data center electromechanical system model recognition method as described in any one of claims 1-8, characterized in that, include: The residual compensation module is used to input the residual sequence between the predicted output and the actual output of the preset model into a pre-built nonlinear mapper to generate a nonlinear compensation signal, and then superimpose the nonlinear compensation signal onto the output of the preset model to obtain a refined residual; wherein, the preset model is the initial model of the data center electromechanical system or the model after the last update; The degradation assessment module is used to extract trace features reflecting equipment performance degradation or sensor drift based on the time-series variation trend of refined residuals and nonlinear compensation signals, and to calculate degradation indices. The decoupling control module is used to construct a decoupling control matrix based on degradation indicators and the strength of causal relationships between multiple real-time collected operating variables. The decoupling control matrix is ​​used to decouple control commands and output the decoupled control commands and residual dynamic deviations. The control commands refer to the original control commands for the actuators of the electromechanical system. The oscillation suppression module is used to monitor the spectral characteristics of residual dynamic deviation. When periodic oscillations are detected in multiple actuators, the active disturbance rejection control is activated to inject a damping signal to eliminate the oscillations. The model update module is used to continuously evaluate the model error of the current preset model. When the model error exceeds the preset model error threshold and the duration exceeds the preset duration threshold, a re-identification trigger signal is generated. In response to the re-identification trigger signal, the parameters or structure of the preset model are updated online using the real-time operating data of the data center electromechanical system. The updated preset model is then used as the preset model for the next iteration.

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