Temperature field reconstruction method and system based on digital twinning and application of temperature field reconstruction method and system

Abstract

The invention provides a temperature field reconstruction method and system based on digital twinning and application thereof, and the method comprises the steps: obtaining multi-moment temperature field data of target equipment, and carrying out the spatial dimension reduction processing, and obtaining K dominant modes; based on the multi-moment temperature field data and the K dominant modes, calculating modal coefficients of the temperature field at each moment in each dominant mode, and forming modal coefficient time sequences in one-to-one correspondence with the dominant modes; training a time sequence prediction model based on the modal coefficient time sequence and the operation condition physical parameters of the target equipment in time alignment with the modal coefficient time sequence, and predicting an initial modal coefficient at a future moment by using the time sequence prediction model; performing feedback correction on the initial modal coefficient based on a correction mechanism to obtain a corrected modal coefficient; and reconstructing the temperature field of the target equipment by using the corrected modal coefficient and the K dominant modals. According to the method, through a technical chain of space dimension reduction, working condition fusion, feedback correction and modal superposition, high calculation efficiency and high full-field reconstruction precision are both considered.

Description

Technical Field

[0001] This application relates to the field of thermal management technology for industrial equipment, and in particular to a method, system and application of temperature field reconstruction based on digital twins. Background Technology

[0002] In the thermal management and health monitoring of industrial equipment, accurately grasping the temperature distribution (i.e., temperature field) inside or on the surface of the equipment is crucial. The temperature field directly affects the thermal stress distribution, fatigue life, and electrical insulation performance of materials, and is a core basis for assessing the safety and reliability of equipment operation. Localized overheating can easily induce serious failures such as winding burnout, bearing jamming, and magnetic degradation. Especially in high-power-density equipment such as motors, high-speed rotating machinery, and power electronic devices, the ability to sense temperature in real time and across the entire range is a key prerequisite for achieving active thermal protection and long-term stable system operation.

[0003] In existing technologies, temperature field prediction for target equipment mainly relies on two methods: one is through finite element simulation, which can obtain high-precision temperature field distribution, but the computation is large, the solution is time-consuming, and the real-time performance is poor, making it difficult to apply to online inference and dynamic monitoring in industrial scenarios; the other is a pure data-driven method (such as relying solely on neural networks or traditional machine learning models), which has high computational efficiency, but when the number of sensors is limited, measurement deviations exist, or operating conditions change (such as speed or load switching), the generalization ability is weak and the prediction accuracy drops significantly.

[0004] Therefore, there is an urgent need for a temperature field reconstruction method that can balance high computational efficiency and high full-field reconstruction accuracy in industrial scenarios where sensors are sparse and measurement biases exist. Summary of the Invention

[0005] The purpose of this application is to provide a temperature field reconstruction method, system and application based on digital twins, so as to achieve both high computational efficiency and high full-field reconstruction accuracy in industrial scenarios where sensors are sparse and measurement bias exists.

[0006] To address the aforementioned technical problems, the embodiments of this application provide the following technical solutions: The first aspect of this application provides a temperature field reconstruction method based on digital twins, characterized in that it includes: S1 acquires multi-moment temperature field data of the target device and performs spatial dimensionality reduction processing to obtain K dominant modes; S2 calculates the modal coefficients of the temperature field at each time step under each dominant mode based on the multi-time temperature field data and the K dominant modes, forming a modal coefficient time series that corresponds one-to-one with each dominant mode; S3 trains a time-series prediction model based on the modal coefficient time series and the operating condition physical parameters of the target device that are time-aligned with it, and uses the time-series prediction model to predict the initial modal coefficients at future times. S4 performs feedback correction on the initial modal coefficients based on the correction mechanism to obtain the corrected modal coefficients; S5 uses the corrected modal coefficients and the K dominant modes to reconstruct the temperature field of the target device.

[0007] In some modified embodiments of the first aspect of this application, step S4 includes: S401 acquires temperature data measured by sensors arranged on the target device; S402 performs feedback correction on the initial modal coefficients based on the temperature data to obtain the corrected modal coefficients.

[0008] In some modified embodiments of the first aspect of this application, the physical mounting position of the sensor on the target device is fixed, and its mapping position in the spatial sampling point set representing the multi-time temperature field data is determined in the following manner: A discrete search space is constructed using the index of the spatial sampling points. A local search strategy is used to optimize the mapping position of the sensor in the search space so that the evaluation index between the measurement data and the temperature value of the multi-time temperature field data at the mapping position is minimized.

[0009] In some modified embodiments of the first aspect of this application, step S402 includes: S4021 calculates the residual between the temperature data and the predicted temperature at the mapped location reconstructed from the initial mode coefficients and the K dominant modes; S4022 uses a gradient enhancement tree model to model the residual, and corrects the initial modal coefficients based on the output of the gradient enhancement tree model to obtain the corrected modal coefficients.

[0010] In some modified embodiments of the first aspect of this application, steps S401 and S402 are performed during the target device initialization phase; and / or, During the operation of the target device, steps S401 and S402 are repeated.

[0011] In some modified embodiments of the first aspect of this application, the method for training the time series prediction model includes: A physical constraint term is introduced into the loss function of the training time-series prediction model. The physical constraint term is constructed based on the physical laws followed by the target device. The physical laws mentioned include at least one of the following: the heat conduction equation, the law of conservation of energy, or thermal boundary conditions.

[0012] In some modified embodiments of the first aspect of this application, the method for training the time series prediction model includes: An initial time series prediction model is trained based on the modal coefficient time series under multiple operating conditions and the time-aligned physical parameters of the operating conditions. In the target application scenario, the initial time series prediction model is fine-tuned using small sample measured data to obtain the time series prediction model.

[0013] In some modified embodiments of the first aspect of this application, the K dominant modes satisfy: The cumulative energy retention rate of the first K dominant modes is not less than 99%, where K is a positive integer not exceeding 5.

[0014] A second aspect of this application provides a temperature field reconstruction system based on digital twins, used in the temperature field reconstruction method based on digital twins described in the first aspect, comprising: The spatial dimensionality reduction module is used to acquire multi-moment temperature field data of the target device and perform spatial dimensionality reduction processing to obtain K dominant modes; The modal coefficient calculation module is used to calculate the modal coefficients of the temperature field at each time step under each of the dominant modes based on the multi-time temperature field data and the K dominant modes, forming a modal coefficient time series that corresponds one-to-one with each of the dominant modes; The time series prediction module is used to train a time series prediction model based on the modal coefficient time series and the operating condition physical parameters of the target device that are time-aligned with it, and to use the time series prediction model to predict the initial modal coefficients at future times. The feedback correction module is used to perform feedback correction on the initial modal coefficients based on the correction mechanism to obtain the corrected modal coefficients; The temperature field reconstruction module is used to reconstruct the temperature field of the target device using the corrected modal coefficients and the K dominant modes.

[0015] A third aspect of this application provides an application method for a temperature field reconstruction system based on digital twins as described in the second aspect, comprising: The temperature value of the reconstructed temperature field of the target device is compared with a preset temperature threshold. Based on the comparison results, it was determined whether there were any localized high-temperature areas. When the local high-temperature region exists, a cooling control command corresponding to the location of the local high-temperature region is generated. The cooling system is adjusted based on the cooling control command to cool the local high-temperature area.

[0016] The temperature field reconstruction method based on digital twins provided in the first aspect of this application extracts K dominant modes by performing spatial dimensionality reduction processing on high-dimensional, multi-time temperature field data. This compresses the original space, such as tens of thousands of degrees of freedom, into a low-dimensional modal space (such as 5 dimensions). This fundamental compression constructs a compact spatial basis for the digital twin model, enabling all subsequent modeling, prediction, and correction processes to be carried out in the low-dimensional coefficient space. This significantly reduces computational complexity and memory usage, meeting the millisecond-level response requirements of real-time inference of digital twins in industrial scenarios.

[0017] By accurately projecting the original temperature field onto the dominant mode space, a time series of mode coefficients corresponding one-to-one with each mode is generated. This effectively characterizes the complex full-field thermal evolution process as a low-dimensional time-series signal. This representation inherits the high fidelity of physical simulation, preserving the main physical characteristics of the temperature field while achieving extreme compression, providing reliable input for high-precision dynamic prediction. Using the target equipment's operating condition physical parameters, aligned with the mode coefficient time, as auxiliary input to the time-series prediction model enables the digital twin model to proactively sense changes in operating conditions and adaptively adjust its prediction behavior, significantly enhancing the model's adaptability and generalization ability under changing operating conditions.

[0018] The initial modal coefficients are corrected by feedback based on the correction mechanism. This closed-loop correction link effectively compensates for system errors caused by sensor bias, unmodeled thermal effects, or local nonlinearity, ensuring that the reconstructed temperature field can still maintain a high degree of consistency with the physical entity under actual deployment conditions where sensors are sparse and measurement noise exists.

[0019] By linearly superimposing the corrected low-dimensional modal coefficients with the dominant modes characterizing the spatial distribution, the real-time temperature field of the entire surface of the target device is reconstructed with high fidelity. This digital twin method can not only accurately reproduce the temperature at the locations of deployed sensors, but also reliably infer the thermal state of unmeasured areas, achieving a leap from point monitoring to field sensing, and breaking through the limitation of traditional methods that can only predict local measurement points.

[0020] This method employs a technical chain that includes spatial dimensionality reduction to construct a twin substrate, operating condition fusion to drive dynamic evolution, feedback correction to ensure consistency between virtual and real data, and modal superposition to achieve full-field reconstruction. It achieves synergistic optimization in four dimensions: computational efficiency, operating condition adaptability, anti-interference robustness, and full-domain perception capability. This results in high-precision, low-latency, and robust temperature field reconstruction, providing reliable and feasible core technical support for constructing a high-fidelity digital twin of the temperature rise field. Attached Figure Description

[0021] The above and other objects, features, and advantages of exemplary embodiments of this application will become readily understood by reading the following detailed description with reference to the accompanying drawings. In the drawings, several embodiments of this application are illustrated by way of example and not limitation, with the same or corresponding reference numerals denoteing the same or corresponding parts, wherein: Figure 1 The energy distribution spectra of the five dominant POD modes in Example 1 are schematically shown; Figure 2 A schematic diagram showing the comparison of degrees of freedom before and after dimensionality reduction in Example 1 is provided. Figure 3 The dimensionality reduction rate and energy retention rate of Example 1 are schematically shown. Figure 4 The diagram schematically illustrates a comparison of the actual, predicted, and simulated values ​​at the sensor mapping locations of four key thermally sensitive areas of the electric spindle in the digital twin system constructed at 12000 RPM in Example 1. Figure 5 The diagram schematically illustrates the comparison of representative node temperature responses at 12000 RPM in Example 1 (simulation and reconstruction). Detailed Implementation

[0022] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0023] It should be noted that, unless otherwise stated, the technical or scientific terms used in this application shall have the ordinary meaning as understood by one of ordinary skill in the art to which this application pertains.

[0024] The first aspect of this application provides a temperature field reconstruction method based on digital twins, including: S1 acquires multi-moment temperature field data of the target device and performs spatial dimensionality reduction processing to obtain K dominant modes.

[0025] Specifically, the target equipment refers to an industrial device or electromechanical system that generates a non-uniform temperature distribution during operation and whose thermal behavior exhibits dynamic evolution characteristics. For example, the target equipment could be an electric spindle, a turbine shaft, or a compressor rotor.

[0026] Multi-moment temperature field data refers to complete temperature distribution information collected at multiple points in time, covering the entire physical surface or internal space of a target device. The temperature field data at each moment contains temperature values ​​at a large number of spatial locations on the target device, forming a high-dimensional snapshot; the data from multiple moments are combined to form a dataset reflecting the spatiotemporal evolution of the temperature field.

[0027] Temperature field data at multiple moments can be obtained through numerical simulation, such as using simulation software like finite element analysis (FEA) or computational fluid dynamics (CFD) to simulate and calculate the complete thermal field distribution of the target device at different moments based on its geometric model, material properties, boundary conditions, and operating conditions.

[0028] In practical applications, this data can be collected offline in advance and stored in a database as the basic input data for subsequent spatial dimensionality reduction processing and training of time series prediction models.

[0029] The multi-time temperature field data can be spatially reduced using methods such as intrinsic orthogonal decomposition (POD), principal component analysis, and autoencoders to extract a small number of representative dominant modes, significantly reducing the computational complexity of subsequent modeling. Among these methods, POD, which offers advantages in energy optimality and physical interpretability, is preferred.

[0030] The dominant mode is a typical spatial temperature distribution pattern with high energy contribution extracted from multi-time temperature field data. Each mode characterizes a basic physical feature of the thermal behavior of the target equipment, such as overall temperature rise, local hot spots, axial gradient, etc. Among them, the axial temperature distribution gradient refers to the spatial distribution feature of systematic increase, decrease or non-uniform change of temperature along the main axis of the target equipment (from one end to the other).

[0031] Furthermore, the K dominant modes satisfy: The cumulative energy retention rate of the first K dominant modes is not less than 99%, where K is a positive integer not exceeding 5.

[0032] Multi-time temperature field data can contain tens of thousands to hundreds of thousands of degrees of freedom (i.e., grid nodes). By using K dominant modes, over 99% of the energy information in the multi-time temperature field data can be captured, significantly reducing the input-output size of subsequent time-series prediction models and substantially improving training efficiency and inference speed. Furthermore, because most of the energy information is retained, the temperature field reconstructed using these K dominant modes is highly consistent with the original field, with minimal errors in key regions (such as hotspot locations and temperature gradients), providing a reliable basis for subsequent precise thermal management (such as localized cooling control). K can be 3, 4, or 5.

[0033] Based on the multi-time temperature field data and the K dominant modes, S2 calculates the modal coefficients of the temperature field at each time under each dominant mode, forming a time series of modal coefficients that correspond one-to-one with each dominant mode.

[0034] Specifically, the modal coefficients are the projection weights of the temperature field at each moment onto the corresponding dominant mode, reflecting the activity level of that mode at the current moment; the linear superposition of multiple modal coefficients with their corresponding dominant modes can reconstruct the overall temperature distribution at that moment.

[0035] For example, suppose there are three dominant modes extracted, namely... At time t, The corresponding modal coefficients are The corresponding modal coefficients are The corresponding modal coefficients are Then the temperature field at time t It can be approximated as:

[0036] S3 trains a time-series prediction model based on the modal coefficient time series and the operating physical parameters of the target device that are time-aligned with it, and uses the time-series prediction model to predict the initial modal coefficients at future times.

[0037] Specifically, operating condition physical parameters refer to the time-varying operating conditions preset during the numerical simulation process that generates multi-time temperature field data. These operating condition physical parameters can serve as input loads or boundary conditions for the simulation model, directly driving the dynamic evolution of the thermal field.

[0038] The physical parameters of the operating conditions include any one or more of the following: rotational speed, load torque or cutting force, drive current, input power, cooling system parameters (such as coolant flow rate and inlet temperature), and dynamic control signals (such as start / stop commands and acceleration). All of the above parameters are provided in time series form, with the same time step as the temperature field output by the simulation.

[0039] Temporal prediction models for predicting modal coefficients can be trained using time-series models such as Gated Recurrent Units (GRUs), Long Short-Term Memory Networks (LSTMs), or Temporal Convolutional Networks (TCNs). Among them, GRUs maintain good modeling ability for time dependencies while having a simpler structure, fewer parameters, and higher training and inference efficiency, making them suitable for deployment in industrial equipment thermal prediction scenarios with high real-time requirements.

[0040] To improve the physical consistency and generality of the time series prediction model, the method for training the time series prediction model further includes: A physical constraint term is introduced into the loss function of the training time-series prediction model. The physical constraint term is constructed based on the physical laws followed by the target device. The physical laws mentioned include at least one of the following: the heat conduction equation, the law of conservation of energy, or thermal boundary conditions.

[0041] Specifically, thermal boundary conditions include, but are not limited to: convective heat transfer boundary, thermal radiation boundary, fixed temperature boundary, or fixed heat flux boundary.

[0042] In the process of training the time series prediction model, firstly, the modal coefficients output by the time series prediction model are linearly superimposed with the known dominant modes to reconstruct the corresponding full-field temperature distribution; then, the reconstructed temperature field is substituted into the physical laws followed by the target device to evaluate the degree of deviation between it and the ideal physical behavior.

[0043] For example, it can be used to verify whether the reconstructed temperature field during training satisfies energy conservation (i.e., whether the input power is balanced with temperature rise and heat dissipation) during time evolution, or whether the device surface conforms to the preset convective heat transfer relationship. This degree of deviation is quantified as a physical residual value and added as a physical regularization term (i.e., a physical constraint term) to the model's total loss function, participating in model optimization together with the prediction error of the modal coefficients.

[0044] By introducing physical constraints, the model learns from historical data statistical patterns while adhering to physical laws, effectively suppressing overfitting and significantly improving generalization ability in unseen conditions, noisy environments, or extrapolation scenarios. The final prediction output not only shows good data fit but also follows physical laws.

[0045] Furthermore, the dominant mode can be a condition-specific mode; The operating condition-specific modes are independently extracted from the temperature field data at multiple times under each operating condition; at this time, the modal coefficient time series is obtained by projecting the operating condition-specific modes that match the current operating condition.

[0046] Specifically, operating conditions can be divided into several categories (such as start-up, steady-state, and variable-speed conditions). For each category, the multi-time temperature field data generated under each condition undergoes separate POD decomposition to obtain a set of dominant modes applicable to that category. In this approach, obtaining the modal coefficient time series requires first identifying the current operating condition category, and then projecting it using the corresponding operating condition-specific modal basis. Correspondingly, the time series prediction model can be designed with a multi-branch structure, where each branch corresponds to a specific operating condition and the evolution of its specific modal coefficients, thereby achieving higher local reconstruction accuracy under specific operating conditions.

[0047] During model training, the physical parameters of the operating conditions and the corresponding modal coefficient time series under each operating condition category are used to train their respective branches. Each branch is optimized independently, thereby achieving refined modeling of the thermal dynamic characteristics of different operating conditions.

[0048] Furthermore, the method for training the time series prediction model includes: An initial time series prediction model is trained based on the modal coefficient time series under multiple operating conditions and the time-aligned physical parameters of the operating conditions. In the target application scenario, the initial time series prediction model is fine-tuned using small sample measured data to obtain the time series prediction model.

[0049] Specifically, the dominant mode can be a shared dominant mode; The shared dominant modes are a set of high-energy contributing spatial modes uniformly extracted from multi-moment temperature field simulation data sets under multiple operating conditions (such as startup, steady state, variable speed, and emergency stop) using a Point-of-Depth (POD) approach. This mode base characterizes the common physical features of the target equipment's thermal behavior (such as overall temperature rise pattern, axial gradient distribution, and local hot spot morphology), possessing cross-condition universality. The temperature field at any moment under any operating condition can be approximately reconstructed by a linear combination of this same set of shared dominant modes. All subsequent modal coefficient time series are obtained by projecting from this shared mode base, ensuring the comparability and consistency of modal coefficients under different operating conditions.

[0050] Based on this, an initial time series prediction model is trained using multi-condition simulation data (including the physical parameters of the operating conditions under each condition and their corresponding modal coefficient time series), so that it learns the general mapping relationship between the operating condition input and the evolution of the shared modal coefficients.

[0051] Subsequently, small-sample measured data is collected for the target application scenario. Small-sample measured data refers to synchronous observation data collected within a short period of time during the actual operation of the target equipment using a limited number of temperature sensors (e.g., 1 to 10 key locations) and operating condition monitoring devices, covering a small number of typical operating conditions (e.g., equipment start-up, acceleration, emergency stop, etc.). Small-sample measured data can be obtained by installing a small number of temperature sensors (such as thermocouples, RTDs, or infrared thermometers) on the target equipment, positioned in key heat-sensitive areas (e.g., bearing housings, motor windings, spindle front end, etc.); simultaneously, acquiring the corresponding operating condition physical parameters (e.g., speed, current, load, coolant flow rate, etc.) from the equipment control system or data acquisition system. Because it only needs to cover a few typical operating condition segments (e.g., a single start-up and shutdown process or a short-term load change test), the data acquisition cycle is short and the cost is low, hence the term "small sample."

[0052] Using the aforementioned small sample of measured data, combined with the established shared dominant modes, local temperature observations are inverted into approximate modal coefficients (e.g., through least squares fitting), thereby constructing a fine-tuned dataset specific to the target device. This dataset is then used to fine-tune the parameters of the initial time-series prediction model to adapt it to the actual thermal dynamic characteristics of the target scenario.

[0053] The target scenarios for actual application include, but are not limited to: deployment on specific device instances that are the same as or different from the source of the training data, and / or operation under new operating conditions that were not fully covered during the training process. That is, the target scenarios for actual application can involve different individual devices, unseen operating conditions, or a combination of both.

[0054] S4 performs feedback correction on the initial modal coefficients based on the correction mechanism to obtain the corrected modal coefficients.

[0055] Furthermore, the initial modal coefficients at future moments can be predicted based on the model, and the historical measured modal coefficients from the same period in the simulation can be used as a reference to correct them through deviation feedback.

[0056] Furthermore, step S4 includes: S401 acquires temperature data measured by sensors arranged on the target device; S402 performs feedback correction on the initial modal coefficients based on the temperature data to obtain the corrected modal coefficients.

[0057] Specifically, temperature sensors can be placed in key structural parts of the target equipment (such as high-stress areas, support connections, and heat-sensitive areas). The number of temperature sensors can be three, four, or five, etc. The temperature sensors can be connected to the data acquisition system via wired or wireless means.

[0058] Furthermore, the physical mounting position of the sensor on the target device is fixed, and its mapping position in the spatial sampling point set representing the multi-moment temperature field data is determined in the following way: A discrete search space is constructed using the index of the spatial sampling points. A local search strategy is used to optimize the mapping position of the sensor in the search space so that the evaluation index between the measurement data and the temperature value of the multi-time temperature field data at the mapping position is minimized.

[0059] First, all spatial sampling points used to represent the multi-time temperature field are sequentially numbered (e.g., from 1 to M), with each number uniquely corresponding to a specific spatial location. The set of these numbers constitutes a discrete index search space. The spatial sampling points represent the degrees of freedom in the simulation model. Then, the mapping position of each sensor is initialized: the number corresponding to the sampling point spatially closest to its physical installation location is selected as the initial mapping index.

[0060] Next, a local search strategy is employed for optimization: Centering on the spatial location corresponding to the current mapping index, a set of neighboring sampling points is determined within its physical neighborhood (e.g., a distance threshold is set, encompassing all sampling points within that threshold range), and the indices corresponding to these points are obtained. The sensor is then temporarily mapped sequentially to the locations represented by these neighboring indices. For each mapping, an evaluation index is calculated between the sensor's measured temperature sequence and the temperature field data at the same time and location. Evaluation indexes can include statistical measures reflecting the magnitude of the deviation, such as root mean square error and mean absolute error. If a location in the neighboring indices results in a smaller evaluation index, the index corresponding to that location is updated to the new current mapping point, and the next round of local search is initiated centered on this location.

[0061] Repeat the above process until no further reduction in the evaluation index can be found within the current neighborhood. The index at this point is determined as the optimal mapping position for the sensor in the temperature field sampling point set. This effectively aligns the fixedly mounted sensor with the discrete temperature field model, significantly improving the matching accuracy between temperature data and modal correction, thereby enhancing the reliability and accuracy of modal coefficient feedback correction.

[0062] Furthermore, step S402 includes: S4021 calculates the residual between the temperature data and the predicted temperature at the mapped location reconstructed from the initial mode coefficients and the K dominant modes.

[0063] Specifically, firstly, using the current initial modal coefficients and the extracted K dominant modes related to temperature field strength, the predicted temperature field of the device at each time and each spatial sampling point is reconstructed through modal superposition. Then, the predicted temperature at the corresponding time is extracted at the optimal mapping position of each sensor. Next, this predicted temperature is compared with the actual temperature measured by the sensor at the same time and location on a time-by-time basis, and the difference is calculated to obtain a residual sequence. This residual reflects the prediction deviation of the current modal model for the actual thermal state, including nonlinear effects not fully characterized by the initial modes, environmental disturbances, or material performance degradation.

[0064] S4022 uses a gradient enhancement tree model to model the residual, and corrects the initial modal coefficients based on the output of the gradient enhancement tree model to obtain the corrected modal coefficients.

[0065] Specifically, using the residual sequence as the training target and current operating conditions (such as time, ambient temperature, equipment load, runtime, and initial modal coefficients) as input variables, a gradient boosting tree model (such as XGBoost or LightGBM) is trained. After model training, the systematic temperature deviation of the modal model at the mapping location can be predicted based on real-time input features. Then, through a pre-defined sensitivity relationship or mapping rule between the temperature deviation and modal coefficients, this predicted deviation is converted into a correction amount for the initial modal coefficients. For example, if the predicted deviation is positive, it indicates that the model temperature is underestimated, and the coefficient values ​​of the relevant modes are increased accordingly. Finally, the correction amount is superimposed on the initial modal coefficients to obtain the corrected modal coefficients.

[0066] Gradient-enhanced tree models can be incrementally trained or updated online periodically using newly acquired data during equipment operation to adapt to long-term performance drift. The corrected modal coefficients can be used for tasks such as structural health monitoring, vibration control, or digital twin state synchronization, significantly improving the real-time accuracy of dynamic models and achieving high-precision, adaptive feedback correction.

[0067] Furthermore, during the target device initialization phase, steps S401 and S402 are executed; and / or, During the operation of the target device, steps S401 and S402 are repeated.

[0068] Specifically, during the target equipment initialization phase (such as installation and commissioning), steps S401 and S402 can be executed once to perform the initial correction of the modal coefficients using initial temperature measurement data, thereby establishing an accurate initial dynamic model; or, During the operation of the target equipment, S401 and S402 can be repeatedly executed periodically or in an event-driven manner based on preset time intervals (e.g., every hour), operating condition change events (e.g., sudden load changes, start-up and shutdown), or temperature drift threshold trigger conditions, to continuously update the modal coefficients, achieve dynamic adaptive correction, and ensure that the model tracks the actual state of the equipment over a long period of time; or, Steps S401 and S402 can be executed during the target device initialization phase and during the target device operation.

[0069] S5 uses the corrected modal coefficients and the K dominant modes to reconstruct the temperature field of the target device.

[0070] Specifically, the corrected modal coefficients obtained in step S4 are multiplied by the extracted K dominant modes, and the results are superimposed at each spatial sampling point to reconstruct the complete thermal field distribution of the target device at the current moment. This process is computationally efficient, and because the modal coefficients have been corrected for actual temperatures, the reconstruction accuracy is significantly improved. The reconstruction results can generate temperature cloud maps or dynamic thermal maps to visualize the temperature distribution on or inside the device, and support subsequent thermal management, anomaly warnings, or digital twin monitoring.

[0071] The temperature field reconstruction method based on digital twins provided in the first aspect of this application extracts K dominant modes by performing spatial dimensionality reduction processing on high-dimensional, multi-time temperature field data. This compresses the original space, such as tens of thousands of degrees of freedom, into a low-dimensional modal space (such as 5 dimensions). This fundamental compression constructs a compact spatial basis for the digital twin model, enabling all subsequent modeling, prediction, and correction processes to be carried out in the low-dimensional coefficient space. This significantly reduces computational complexity and memory usage, meeting the millisecond-level response requirements of real-time inference of digital twins in industrial scenarios.

[0072] By accurately projecting the original temperature field onto the dominant mode space, a time series of mode coefficients corresponding one-to-one with each mode is generated. This effectively characterizes the complex full-field thermal evolution process as a low-dimensional time-series signal. This representation inherits the high fidelity of physical simulation, preserving the main physical characteristics of the temperature field while achieving extreme compression, providing reliable input for high-precision dynamic prediction. Using the target equipment's operating condition physical parameters, aligned with the mode coefficient time, as auxiliary input to the time-series prediction model enables the digital twin model to proactively sense changes in operating conditions and adaptively adjust its prediction behavior, significantly enhancing the model's adaptability and generalization ability under changing operating conditions.

[0073] The initial modal coefficients are corrected by feedback based on the correction mechanism. This closed-loop correction link effectively compensates for system errors caused by sensor bias, unmodeled thermal effects, or local nonlinearity, ensuring that the reconstructed temperature field can still maintain a high degree of consistency with the physical entity under actual deployment conditions where sensors are sparse and measurement noise exists.

[0074] By linearly superimposing the corrected low-dimensional modal coefficients with the dominant modes characterizing the spatial distribution, the real-time temperature field of the entire surface of the target device is reconstructed with high fidelity. This digital twin method can not only accurately reproduce the temperature at the locations of deployed sensors, but also reliably infer the thermal state of unmeasured areas, achieving a leap from point monitoring to field sensing, and breaking through the limitation of traditional methods that can only predict local measurement points.

[0075] This method employs a technical chain that includes spatial dimensionality reduction to construct a twin substrate, operating condition fusion to drive dynamic evolution, feedback correction to ensure consistency between virtual and real data, and modal superposition to achieve full-field reconstruction. It achieves synergistic optimization in four dimensions: computational efficiency, operating condition adaptability, anti-interference robustness, and full-domain perception capability. This results in high-precision, low-latency, and robust temperature field reconstruction, providing reliable and feasible core technical support for constructing a high-fidelity digital twin of the temperature rise field.

[0076] A second aspect of this application provides a temperature field reconstruction system based on digital twins, used in the temperature field reconstruction method based on digital twins described in the first aspect, comprising: The spatial dimensionality reduction module is used to acquire multi-moment temperature field data of the target device and perform spatial dimensionality reduction processing to obtain K dominant modes; The modal coefficient calculation module is used to calculate the modal coefficients of the temperature field at each time step under each of the dominant modes based on the multi-time temperature field data and the K dominant modes, forming a modal coefficient time series that corresponds one-to-one with each of the dominant modes; The time series prediction module is used to train a time series prediction model based on the modal coefficient time series and the operating condition physical parameters of the target device that are time-aligned with it, and to use the time series prediction model to predict the initial modal coefficients at future times. The feedback correction module is used to perform feedback correction on the initial modal coefficients based on the correction mechanism to obtain the corrected modal coefficients; The temperature field reconstruction module is used to reconstruct the temperature field of the target device using the corrected modal coefficients and the K dominant modes.

[0077] The temperature field reconstruction system based on digital twins in the second aspect of this application has similar technical effects to the temperature field reconstruction method based on digital twins provided in the first aspect of this application.

[0078] A third aspect of this application provides an application method for a temperature field reconstruction system based on digital twins as described in the second aspect, comprising: The temperature value of the reconstructed temperature field of the target device is compared with a preset temperature threshold. Based on the comparison results, it was determined whether there were any localized high-temperature areas. When the local high-temperature region exists, a cooling control command corresponding to the location of the local high-temperature region is generated. The cooling system is adjusted based on the cooling control command to cool the local high-temperature area.

[0079] Specifically, the surface of the target equipment can be divided into multiple cooling zones, and each cooling zone can be configured with an independent execution unit (such as a water pump, proportional control valve, oil-gas mixer, etc.).

[0080] Taking the target equipment as an electric spindle as an example, its cooling system may include: a cooling water jacket surrounding the stator and rotor, achieving axial or circumferential zoned cooling through segmented flow channels; and / or, The oil-air lubrication system at the front and rear bearings continuously supplies lubricating oil while using compressed air to carry oil mist to lubricate and assist in heat dissipation in the bearing area.

[0081] Based on the reconstructed temperature field, the control system can identify localized high-temperature areas (such as overheating of a section of stator winding or abnormal temperature rise in the front bearing) and generate corresponding cooling control commands. For example, if the high-temperature area is located in the axial section at the front end of the stator, the coolant flow rate of the cooling water jacket branch in that section will be increased (by adjusting the opening of the proportional valve or the speed of the variable frequency pump); if the high-temperature area appears at the front bearing location, the air supply pressure or oil mist concentration of the corresponding oil-air lubrication system will be increased to enhance its cooling effect.

[0082] By activating only the cooling zone corresponding to the high-temperature area, redundant cooling of the entire system is avoided, significantly reducing energy consumption while ensuring thermal safety.

[0083] Furthermore, the spatial division of the multiple cooling zones is based on the temperature distribution characteristics of at least one of the K dominant modes, so that each cooling zone covers the high temperature gradient region or high energy region under the corresponding dominant mode.

[0084] The application of the temperature field reconstruction system based on digital twins in the third aspect of this application has similar technical effects to the temperature field reconstruction method based on digital twins provided in the first aspect of this application.

[0085] Example 1

[0086] Multi-time temperature field data with 114,805 degrees of freedom was obtained using simulation software, and a set of dominant modes was constructed using the POD method. Energy retention rate verification during the model construction phase confirmed that only the first five POD dominant modes are needed to retain over 99% of the training data's energy, with the first dominant mode contributing 99.62% of the energy. The second to fifth dominant modes primarily capture local thermal variations and minor details. Figure 1 As shown, the energy distribution spectra of the five dominant modes clearly indicate that the energy is highly concentrated in the first few modes.

[0087] The original high-dimensional temperature field was thus compressed to 5-dimensional POD modal coefficients, a reduction in dimensionality of approximately 23,000 times. This low-dimensional representation significantly reduces the complexity and memory footprint of subsequent online computations, while effectively suppressing the impact of measurement noise on the reconstruction results, providing a high-fidelity and lightweight foundation for real-time inference. Figure 2 , Figure 3 As shown, the system achieves an ultra-high compression ratio while maintaining near-perfect temperature field reconstruction fidelity.

[0088] Using modal coefficients as the target variable, a GRU time series prediction model is constructed, and physical constraints are introduced during the training process. This time series prediction model is then used to predict the initial modal coefficients at future times.

[0089] A discrete search space is constructed using the index of spatial sampling points. A local search strategy is employed to optimize the mapping position of each sensor within the search space, minimizing the evaluation index between the sensor's measurement data and the temperature values ​​at the mapping positions from multiple time points. For example... Figure 4 The image shows a comparison of the actual (i.e., actual temperature data measured by physical sensors), predicted (i.e., temperature values ​​at the corresponding mapped locations in the temperature field reconstructed from the modal coefficients output by the time-series prediction model), and simulated (i.e., temperature values ​​at the corresponding mapped locations in the theoretical temperature field calculated by simulation software) values ​​at the sensor mapping locations of four key heat-sensitive areas of the electric spindle in the constructed digital twin system. Each sub-image shows a comparison of three temperature values ​​at the following four locations: Front end face: The sensor at this location is used to monitor the impact of the main heat sources at the front end of the device; Cooling top 1: The sensor at this location is used to monitor the effectiveness of the cooling system and its impact on local temperature. Front bearing inner ring: The sensor at this location is used to monitor the temperature changes of the front bearing, reflecting mechanical load and frictional heat effects; Rear bearing inner ring: The sensor at this location is used to monitor the temperature changes of the rear bearing and provide feedback on the thermal status of the equipment's rear end.

[0090] Using the determined mapping location, the residual between the temperature data measured by the temperature sensor and the predicted temperature at the mapping location reconstructed from the initial modal coefficients and five dominant modes is calculated. A gradient enhancement tree model is used to model the residual, learning the systematic errors caused by unmodeled dynamics, sensor bias, or local nonlinearity. The initial modal coefficients are then corrected based on the model output to obtain the corrected modal coefficients.

[0091] The corrected modal coefficients are weighted and superimposed with the five dominant modes to reconstruct the real-time temperature field of the entire surface of the target device. For example... Figure 5 As shown, under typical operating conditions of 12000 RPM (revolutions per minute), the prediction error is controlled within 1°C.

[0092] The above description is merely a specific embodiment 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 temperature field reconstruction method based on digital twins, characterized in that, include: S1 acquires multi-moment temperature field data of the target device and performs spatial dimensionality reduction processing to obtain K dominant modes; S2 calculates the modal coefficients of the temperature field at each time step under each dominant mode based on the multi-time temperature field data and the K dominant modes, forming a modal coefficient time series that corresponds one-to-one with each dominant mode; S3 trains a time-series prediction model based on the modal coefficient time series and the operating condition physical parameters of the target device that are time-aligned with it, and uses the time-series prediction model to predict the initial modal coefficients at future times. S4 performs feedback correction on the initial modal coefficients based on the correction mechanism to obtain the corrected modal coefficients; S5 uses the corrected modal coefficients and the K dominant modes to reconstruct the temperature field of the target device.

2. The temperature field reconstruction method based on digital twin according to claim 1, characterized in that, Step S4 includes: S401 acquires temperature data measured by sensors arranged on the target device; S402 performs feedback correction on the initial modal coefficients based on the temperature data to obtain the corrected modal coefficients.

3. The temperature field reconstruction method based on digital twins according to claim 2, characterized in that, The sensor's physical mounting position on the target device is fixed, and its mapping position in the spatial sampling point set used to represent the multi-moment temperature field data is determined in the following way: A discrete search space is constructed using the index of the spatial sampling points. A local search strategy is used to optimize the mapping position of the sensor in the search space so that the evaluation index between the measurement data and the temperature value of the multi-time temperature field data at the mapping position is minimized.

4. The temperature field reconstruction method based on digital twin according to claim 3, characterized in that, Step S402 includes: S4021 calculates the residual between the temperature data and the predicted temperature at the mapped location reconstructed from the initial mode coefficients and the K dominant modes; S4022 uses a gradient enhancement tree model to model the residual, and corrects the initial modal coefficients based on the output of the gradient enhancement tree model to obtain the corrected modal coefficients.

5. The temperature field reconstruction method based on digital twin according to claim 2, characterized in that, During the target device initialization phase, steps S401 and S402 are executed; and / or, During the operation of the target device, steps S401 and S402 are repeated.

6. The temperature field reconstruction method based on digital twin according to claim 1, characterized in that, The method for training the time series prediction model includes: A physical constraint term is introduced into the loss function of the training time-series prediction model. The physical constraint term is constructed based on the physical laws followed by the target device. The physical laws mentioned include at least one of the following: the heat conduction equation, the law of conservation of energy, or thermal boundary conditions.

7. The temperature field reconstruction method based on digital twin according to claim 1, characterized in that, The method for training the time series prediction model includes: An initial time series prediction model is trained based on the modal coefficient time series under multiple operating conditions and the time-aligned physical parameters of the operating conditions. In the target application scenario, the initial time series prediction model is fine-tuned using small sample measured data to obtain the time series prediction model.

8. The temperature field reconstruction method based on digital twin according to claim 1, characterized in that, The K dominant modes satisfy: The cumulative energy retention rate of the first K dominant modes is not less than 99%, where K is a positive integer not exceeding 5.

9. A temperature field reconstruction system based on digital twins, used in the temperature field reconstruction method based on digital twins as described in any one of claims 1-8, characterized in that, include: The spatial dimensionality reduction module is used to acquire multi-moment temperature field data of the target device and perform spatial dimensionality reduction processing to obtain K dominant modes; The modal coefficient calculation module is used to calculate the modal coefficients of the temperature field at each time step under each of the dominant modes based on the multi-time temperature field data and the K dominant modes, forming a modal coefficient time series that corresponds one-to-one with each of the dominant modes; The time series prediction module is used to train a time series prediction model based on the modal coefficient time series and the operating condition physical parameters of the target device that are time-aligned with it, and to use the time series prediction model to predict the initial modal coefficients at future times. The feedback correction module is used to perform feedback correction on the initial modal coefficients based on the correction mechanism to obtain the corrected modal coefficients; The temperature field reconstruction module is used to reconstruct the temperature field of the target device using the corrected modal coefficients and the K dominant modes.

10. An application method of the temperature field reconstruction system based on digital twins as described in claim 9, characterized in that, include: The temperature value of the reconstructed temperature field of the target device is compared with a preset temperature threshold. Based on the comparison results, it was determined whether there were any localized high-temperature areas. When the local high-temperature region exists, a cooling control command corresponding to the location of the local high-temperature region is generated. The cooling system is adjusted based on the cooling control command to cool the local high-temperature area.

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