A temperature field reconstruction method based on compression sensing and physical information neural network fusion

Abstract

The application discloses a temperature field reconstruction method based on compression sensing and physical information neural network fusion. The temperature field reconstruction method comprises the following steps: constructing a temperature field reconstruction architecture comprising a sparse observation modeling module, a neural network parameterization module, a physical constraint embedding module, a joint optimization solving module and an engineering application expansion module; establishing a unified representation model of a sparse observation operator; constructing a neural network parameterized temperature field and a heat conduction physical constraint embedding model; constructing a joint optimization loss function of sparse observation consistency and physical mechanism consistency; adopting a two-stage training solving algorithm; performing engineering application expansion with a multi-physical field coupling expansion, parameter identification, online self-updating and hotspot index output as cores, and realizing closed-loop conversion of temperature field monitoring results to engineering control behaviors. The application realizes coordination and unification among temperature field reconstruction precision, physical consistency, real-time performance and engineering deployability.

Description

Technical Field

[0001] This invention belongs to the field of temperature field sensing and thermal management technology for energy and power equipment, and in particular, it is a temperature field reconstruction method based on the fusion of compressed sensing and physical information neural network, which is applicable to online monitoring and thermal management control of temperature field in energy storage battery systems, power electronic equipment and power transmission and transformation main equipment. Background Technology

[0002] Temperature field is a key physical quantity in the assessment of the operating status and safety control of energy and power equipment. In scenarios such as thermal safety of energy storage batteries, thermal reliability of power electronic devices, and aging assessment of transformer insulation, real-time and accurate perception of the internal temperature distribution of equipment is the foundation for thermal management decisions and fault early warning. However, with the continuous increase in equipment power density, the increase in internal structural complexity, and the drastic fluctuations in actual operating conditions, the applicability of traditional temperature field acquisition methods in engineering has been significantly limited.

[0003] Currently, there are two main types of methods for obtaining temperature fields in engineering practice. The first type involves directly measuring key points on the surface or inside of equipment using high-density temperature sensor arrays. However, this method is constrained by multiple factors such as sensor cost, electrical insulation safety, installation space, and communication bandwidth and power consumption, making it difficult to deploy a sufficient number of sensors to cover the entire temperature field. The second type involves offline calculation of the temperature field distribution based on numerical simulation methods such as the finite element method or computational fluid dynamics. However, this method is highly sensitive to boundary conditions and material properties, and the computational cost is high, making it difficult to meet the real-time requirements of online monitoring or edge deployment. This creates a structural contradiction in the thermal management of energy and power equipment: the temperature field itself is a high-dimensional distribution, but the observational information that can be obtained in engineering is extremely low-dimensional, sparse, and noisy.

[0004] To alleviate the aforementioned contradictions, two typical advanced methods have emerged in recent years. Compressed Sensing (CS) utilizes the sparsity or compressibility of the temperature field in an appropriate transform domain to achieve approximate reconstruction of the field through underdetermined linear observations, providing theoretical support for sensor placement optimization and communication compression. The Physics-Informed Neural Networks (PINN) method maintains the physical consistency of the reconstruction results under sparse data conditions by embedding the heat conduction control equations and their boundary / initial conditions into the training loss of the neural network.

[0005] However, using compressed sensing or physical information neural networks alone still has significant shortcomings. Pure compressed sensing methods rely on explicit sparse prior assumptions, limiting their robustness to measurement noise, model mismatch, and extremely sparse observations. Pure physical information neural network methods, under multi-scale problems, rigid problems, or complex boundary conditions, are highly sensitive to loss weights, collocation strategies, and optimizer selection during training, easily leading to ill-conditioned gradients and convergence instability. More importantly, the two have not yet formed a unified modeling framework, making it difficult to fully leverage their complementary advantages in "observation consistency" and "mechanistic constraints."

[0006] In summary, existing technologies still suffer from problems such as high sensor requirements, insufficient noise robustness, poor training stability, and the lack of unified modeling for sparse observations and mechanistic constraints. Therefore, it is necessary to propose a temperature field reconstruction method based on the fusion of compressed sensing and physical information neural networks to achieve high-precision, physically consistent, and real-time feasible temperature field reconstruction under limited measurement conditions, while also considering operational economy, engineering deployability, and portability to various types of equipment. Summary of the Invention

[0007] To address the challenges of high-precision temperature field sensing in existing energy and power equipment under limited sensor counts, insufficient robustness of pure compressed sensing methods to noise and model mismatch, poor training stability of pure physical information neural network methods, and the lack of a unified modeling framework between compressed sensing and physical information neural networks, this invention provides a temperature field reconstruction method based on the fusion of compressed sensing and physical information neural networks. This method constructs a unified observation operator model, a neural network-parameterized temperature field representation, and a multi-constraint joint optimization objective function. It unifies sparse observation consistency and heat conduction mechanism constraints into an end-to-end optimizable scalar objective, enabling the temperature field reconstruction process to utilize mechanistic knowledge for constraints while relying on only a small number of sparse observations. This reduces dependence on the number of sensors while achieving a coordinated balance between temperature field reconstruction accuracy, physical consistency, real-time performance, and engineering deployability.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: a temperature field reconstruction method based on the fusion of compressed sensing and physical information neural network, comprising the following steps: S1. Construct a temperature field reconstruction architecture that includes a sparse observation modeling module, a neural network parameterization module, a physical constraint embedding module, a joint optimization solution module, and an engineering application extension module; The sparse observation modeling module abstracts the two sensing modes of point temperature measurement and compression measurement in engineering into a unified linear observation operator; the neural network parameterization module is used to represent the continuous temperature field as a function using a deep neural network; the physical constraint embedding module applies the heat conduction control equation and its boundary / initial conditions as mechanistic soft constraints to the output of the deep neural network; the joint optimization solution module unifies sparse observation consistency, physical residuals, and boundary and initial constraints into a single weighted loss objective, and completes parameter training through backpropagation; the engineering application extension module further realizes multi-physics coupling extension, identification of thermal property parameters and convective heat transfer coefficients, lightweight correction during online operation, and output of key thermal indicators for thermal management control and fault early warning based on the continuous temperature field expression obtained by the training; S2. Establish a unified representation model for sparse observation operators; S3. Construct a neural network-parameterized temperature field and heat conduction physical constraint embedding model; S4. Construct a joint optimization loss function for sparse observation consistency and physical mechanism consistency; S5. A two-stage training and solution algorithm based on adaptive weight adjustment and adaptive point sampling is adopted; S6. Expand engineering applications with multi-physics coupling extension, parameter identification, online self-updating, and hotspot index output as the core, and realize the closed-loop transformation of temperature field monitoring results into engineering control behavior.

[0009] Compared with the prior art, the present invention has the following beneficial effects: (1) This invention unifies the sparse observation consistency of compressed sensing and the mechanism constraints of physical information neural networks into a weighted joint loss, so that the reconstruction process can simultaneously utilize observation information and mechanism knowledge for constraints when the number of sensors is limited. Compared with pure compressed sensing or pure physical information neural network methods, the accuracy of temperature field reconstruction, especially the accuracy of hot spot temperature prediction, is significantly improved.

[0010] (2) In this invention, the heat conduction control equation and boundary / initial conditions are embedded into the training process as soft constraints, and the physical residual term is used as a structured implicit prior, so that the reconstruction result can still satisfy the basic mechanism of heat conduction and boundary / initial conditions under sparse observation conditions, avoid non-physical phenomena, and improve the physical consistency of the reconstruction result.

[0011] (3) This invention alleviates the gradient ill-conditioning and convergence instability problems that are prone to occur in pure physical information neural networks under multi-scale, rigid or complex boundary conditions by using staged adaptive adjustment of loss weights, residual-based adaptive encryption of physical points, and two-stage optimization strategies of Adam and L-BFGS. It also improves the stability of the training process and the robustness to measurement noise, model mismatch and extremely sparse observations.

[0012] (4) The present invention represents the continuous temperature field as a neural network parameterized function. A single forward inference only requires milliseconds to complete the temperature query at any spatiotemporal point, which meets the real-time requirements of scenarios such as online thermal management control, early warning of thermal runaway and state assessment, and supports deployment on edge computing devices through model compression or quantization.

[0013] (5) The present invention extracts indicators with clear physical meaning from the reconstructed temperature field, such as temperature field distribution, hot spot temperature, heating rate, temperature difference gradient and thermal resistance / heat capacity identification results. These indicators can be directly connected to BMS / EMS, protection devices or insulation aging assessment systems, providing interpretable basis for thermal management control, life management and fault early warning.

[0014] (6) The method framework established by this invention is independent of the equipment type, and is achieved through the heat conduction control equation operator. By changing the specific coupling term form, it can be applied to temperature field monitoring and thermal management of various energy and power equipment such as energy storage battery systems, IGBT / SiC power electronic equipment, and oil-immersed transformers, and has good portability and engineering versatility. Attached Figure Description

[0015] Figure 1 is a flowchart of a temperature field reconstruction method based on the fusion of compressed sensing and physical information neural network according to the present invention; Figure 2 is a schematic diagram illustrating the application of the temperature field reconstruction method of the present invention in battery pack thermal management; Figure 3 is a schematic diagram of the application of the temperature field reconstruction method of the present invention in temperature monitoring of power electronics and transformer main equipment. Detailed Implementation

[0016] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings. It should be understood that the following embodiments are only for illustrating the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention. Equivalent substitutions or adjustments made by those skilled in the art to the network structure, form of the control equations, training hyperparameters, or specific application objects without departing from the concept of the present invention should all fall within the scope of protection of the present invention.

[0017] Example 1: Temperature Field Reconstruction Method This embodiment describes a temperature field reconstruction method based on the fusion of compressed sensing and physical information neural networks (CS-PINN temperature field for short). Figure 1 As shown, the steps for online monitoring and thermal management control of temperature field in energy and power equipment are as follows: S1. Construct a temperature field reconstruction architecture that includes a sparse observation modeling module, a neural network parameterization module, a physical constraint embedding module, a joint optimization solution module, and an engineering application extension module; The sparse observation modeling module abstracts the two sensing modes of point temperature measurement and compression measurement in engineering into a unified linear observation operator; the neural network parameterization module is used to represent the continuous temperature field as a function using a deep neural network; the physical constraint embedding module applies the heat conduction control equation and its boundary / initial conditions as mechanistic soft constraints to the output of the deep neural network; the joint optimization solution module unifies sparse observation consistency, physical residuals, and boundary and initial constraints into a single weighted loss objective, and completes parameter training through backpropagation; the engineering application extension module further realizes multi-physics coupling extension, identification of thermal property parameters and convective heat transfer coefficients, lightweight correction during online operation, and output of key thermal indicators for thermal management control and fault early warning based on the continuous temperature field expression obtained by the training; S2. Establish a unified representation model for sparse observation operators; S3. Construct a neural network-parameterized temperature field and heat conduction physical constraint embedding model; S4. Construct a joint optimization loss function for sparse observation consistency and physical mechanism consistency; S5. A two-stage training and solution algorithm based on adaptive weight adjustment and adaptive point sampling is adopted; S6. Expand engineering applications with multi-physics coupling extension, parameter identification, online self-updating, and hotspot index output as the core, and realize the closed-loop transformation of temperature field monitoring results into engineering control behavior.

[0018] Specifically, in step S2, during the operation of the energy and power equipment, the real continuous temperature field It is defined in the solution domain With time interval A continuous scalar field on, , Its spatially discretized discrete temperature field vector is expressed as: , Represents the set of real numbers. N This represents the number of degrees of freedom after the temperature field is spatially discretized; constrained by sensor cost, installation space, and electrical insulation, it represents the number of observation dimensions that can be obtained in engineering. much smaller Construct a unified representation model for sparse observation operators using a unified linear observation operator: ,in, For the observation vector, For a unified linear observation operator, Zero-mean measurement noise; Choose a sparse representation base or a redundant dictionary The discrete temperature field vector is represented as ,in, For the sparse coefficient vector under the sparse representation basis or redundant dictionary; or for As a sparse representation of discrete temperature field vectors in the transform domain, the compressible prior of discrete temperature field is incorporated into the sparse observation reconstruction process.

[0019] Linear observation operator The selected point matrix is ​​one or more of the following: random projection matrix, sparse binary matrix, and compressed coding matrix; zero-mean measurement noise. The statistical properties are incorporated into the reconstruction modeling process to improve the robustness of the reconstruction to noise.

[0020] When Φ is the point selection matrix, the sparse observation operator unified representation model degenerates into a point temperature measurement model. ,in S Each row is used to select the temperature degree of freedom corresponding to a sensor deployment location. In engineering practice, which involves deploying NTC, thermocouple, or fiber optic temperature sensors at key locations of equipment, S represents the point selection matrix, which is a specific form of Φ. When Φ is a random projection matrix, a sparse binary matrix, or a compressed coding matrix, the sparse observation operator uniformly represents the compressed reconstruction scenario based on sparse priors.

[0021] Specifically, in step S3, the deep neural network adopts a multilayer perceptron structure, with 4 to 8 hidden layers and 32 to 128 neurons in each layer, and the activation function is selected. Alternatively, higher-order differentiable functions such as Swish can be used to ensure that the neural network output has higher-order differentiability with respect to the input coordinates, making it easier to calculate the physical residuals through automatic differentiation.

[0022] Introducing deep neural networks to predict or reconstruct (i.e., parametrically represent) real continuous temperature fields yields the reconstructed temperature field. Where x∈Ω and t∈[0,T] are the input spatiotemporal coordinates. These are the weights for a trainable network; simultaneously, a heat conduction control equation operator is introduced. Boundary condition operators With initial condition operator Embedded reconstruction process as a mechanism constraint , , , , These represent material density, specific heat capacity at constant pressure, spatial differential operator, thermal conductivity, and internal heat generation per unit volume, respectively; when boundary condition parameters in engineering (such as equivalent convective heat transfer coefficient h, internal heat source intensity) are used... When it is difficult to measure directly, it is used as a physical parameter to be identified. With network weights These variables are incorporated into the optimization variables to achieve a coordinated inversion of the temperature field, parameters, and heat source.

[0023] Specifically, in step S4, four types of training point sets are constructed according to a preset sampling strategy: measurement point sets. , physical configuration point set Boundary point set With the initial point set ; Among them, the measurement point set Composed of actual sensor measurement points, compressed observation points, or spatiotemporal sampling points corresponding to experimental / simulation observable data, it is used to constrain the consistency between the reconstructed temperature field and the observed data; physical collocation set. The set of boundary points consists of spatiotemporal sampling points selected within the solution region Ω and the time interval [0,T], used to calculate the physical residual after substituting the neural network output into the heat conduction control equation; From the solution domain boundary Ω and its corresponding sampling points over the time interval constitute the initial point set, used to apply boundary condition constraints; It consists of sampling points within the solution region Ω at the initial time t=0, and is used to apply the initial temperature field constraint.

[0024] Construct data consistency losses on the aforementioned point set respectively. Physical residual loss Boundary loss loss from initial value Simultaneously construct compressed sensing sparse prior loss This is used to constrain the sparsity of coefficients in the reconstructed temperature field under a preset sparse representation basis or redundant dictionary, and to synthesize the total loss in the form of a weighted sum: ,in, , , , , These are the loss weights corresponding to the five loss items.

[0025] The data consistency loss is expressed as mean square error in the case of point temperature measurement: ,in, Represents the measurement point set D m The measured temperature value at the mid-spatial position (x,t) is taken under the compression measurement condition. , Right now This indicates the reconstruction of the temperature field. The reconstructed temperature field vector is output and assembled at discrete spatial nodes; during training, due to the discrete temperature field vector... Unknown, using reconstructed temperature field vector replace Participating in sparsity constraints, i.e., letting and take or ,in, To reconstruct the temperature field vector The corresponding sparse coefficient vector; the physical residual loss The residuals output by the automatic differential calculation neural network on the heat conduction PDE are injected with mechanistic knowledge in a soft constraint manner; the boundary loss and initial value loss are respectively in and Apply on and The squared error constraint.

[0026] The data consistency loss In engineering scenarios with high noise or many outliers, the mean squared error form is replaced by... One or more of the following loss methods—Huber loss or Charbonnier loss—are used to reduce the impact of outlier observations on the training process and improve the model’s robustness to heavy-tailed noise and complex noise environments.

[0027] Specifically, in step S5, the neural network weight parameters are initialized. Physical parameters to be identified After setting the loss weights and training hyperparameters, the network is trained according to the following procedure: In the first stage, the Adam first-order optimizer is used with a learning rate of... The parameters are rapidly decreased to quickly guide the network from random initialization to the vicinity of the loss basin; in the second stage, the L-BFGS quasi-Newton optimizer is switched to utilize approximate Hessian information for refined local search, further improving convergence accuracy; in each parameter update, [the following steps are taken]... , , , Forward assessment Through automatic differentiation Calculate the PDE residuals, then calculate the total loss in step S4, and finally obtain the gradient through backpropagation. Parameter update complete.

[0028] The loss weights throughout the training process The point set is dynamically adjusted according to the training phase. During training, the sampling density is adaptively increased based on the residual size, with regions of larger residuals designated as key sampling areas for the next stage, thus concentrating training resources on high-gradient regions. In the early stages of training, the physical residual loss is given a larger weight to ensure the network learns the temperature field structure that satisfies the mechanistic constraints from the outset, avoiding premature overfitting of sparse observations. In the middle stages of training, the weight of the data consistency loss is gradually increased to make the reconstruction results converge towards the measured points. In the later stages of training, the weights are adjusted again to achieve a balance between physical consistency and observational fit.

[0029] The physical coordinate set The sampling method is constructed using one or more of the following: uniform random sampling, Latin hypercube sampling, and adaptive encrypted sampling based on residual size. Specifically, the adaptive encrypted sampling involves evaluating the residual distribution on the collocation points every few training epochs, and designating regions with larger residuals as the focus sampling regions for the next stage. The training convergence criterion is based on the total loss. The magnitude of the decrease, the gradient norm The training is considered to have converged when all three factors—the prediction error on the validation point set, the error on the validation point set, and the prediction error on the validation point set—are all less than a preset threshold.

[0030] Specifically, in step S6, the optimal parameters obtained from training in S5 are... With the optimal reconstructed temperature field Extract temperature field distribution and hotspot temperatures from the reconstructed temperature field. Temperature gradient The system also identifies key thermal management indicators, such as thermal resistance / thermal capacity, as the output of the quantities to be identified. These indicators are then integrated with BMS / EMS, protection devices, or insulation aging assessment systems to achieve a closed-loop transformation of temperature field monitoring results into engineering control behaviors. When the engineering objects involved exhibit thermal-fluid coupling or electro-thermal coupling characteristics, the thermal conduction control equation operator can be used... Corresponding coupling terms are added to extend the applicability of this invention to scenarios such as transformer oil flow-temperature field coupling and battery electro-thermal coupling. When the operating conditions drift or the physical parameters change during equipment operation, the engineering paradigm of "offline pre-training + online lightweight correction" is adopted. The network parameters are lightly fine-tuned with a few steps using newly collected sparse observation data, so that the CS-PINN temperature field reconstruction model after online lightweight correction can adapt to the current operating conditions and equipment status.

[0031] The online self-update mechanism specifically includes a three-level update process: an offline pre-training stage, an online lightweight calibration stage, and an event-triggered retraining stage. In the offline pre-training stage, offline pre-training parameters are obtained by training using historical operating data, factory temperature rise test data, or low-fidelity finite element simulation data according to the algorithm described in S5. During the online lightweight calibration phase, with Alternatively, using the online parameters from the previous time window as initial values, a small amount of Adam fine-tuning can be performed using newly acquired sparse observation data to obtain the online correction parameters for the current time window. When the device undergoes a significant state change, a full retraining of the model is triggered.

[0032] The temperature field reconstruction method supports real-time deployment on edge computing devices through model compression or quantization, with single temperature field inference latency controlled in the millisecond range to meet the real-time requirements of online thermal management control.

[0033] At a general level, this invention employs a two-stage optimization strategy of Adam and L-BFGS for training, with the learning rate in the Adam stage set to... The number of iterations typically ranges from several thousand to several hundred in the L-BFGS stage; initial values ​​for loss weights. Typically set to ,in To compress the initial weights of the sparse prior loss, the weights can be set according to the magnitudes of the sparse prior loss and other loss terms, and dynamically adjusted according to the adaptive strategy described in S5. The above hyperparameters are general guiding values ​​for different specific application scenarios of this invention. In subsequent embodiments 2 to 4, they can be specifically adjusted according to the physical scale of the object under test, the form of the governing equations, and the available observation conditions.

[0034] The overall operation flow of the method described in this embodiment is as follows: In the offline stage, the governing equation operator is determined based on the physical characteristics of the object under test. Boundary condition operators With initial condition operator The observation operator is determined based on the sensor layout. The optimal network parameters are obtained through offline training using the algorithms described in S4-S5. During the online phase, the continuously acquired sparse observation signal y(t) is used as the basis for data consistency correction, and the optimal reconstructed temperature field is obtained through a single forward inference of a neural network based on the current query spatiotemporal coordinates (x,t). Key indicators such as hotspot temperature, heating rate, and temperature gradient are extracted for thermal management decisions. During long-term operation, the network parameters are lightly corrected or retrained by events according to the three-level update mechanism described in S6 to adapt to operating condition drift and equipment status changes.

[0035] Example 2: Energy Storage System and Battery Thermal Management This embodiment applies the temperature field reconstruction method described in Embodiment 1 to temperature field sensing and thermal management of an energy storage battery system, as shown in Figure 2. During long-term operation, energy storage batteries are affected by factors such as charge / discharge rate, ambient temperature, and aging, resulting in a complex three-dimensional temperature distribution within the battery cell. Relying solely on a small number of surface temperature sensors makes it difficult to directly obtain the true temperature field inside the cell, and even more difficult to identify local hotspots and potential thermal runaway risks in a timely manner. This embodiment focuses on two typical sub-scenarios: three-dimensional temperature field reconstruction of the battery pack and early warning of battery thermal runaway.

[0036] (1) Reconstruction of the three-dimensional temperature field of the battery pack For individual battery cells, modules, or entire battery packs, a sparse observation operator is first constructed according to the method described in S2. In engineering practice, the observation operator can be taken as a point selection matrix, that is, a small number of NTC temperature sensors, thermocouples or fiber optic measurement points are arranged on the battery surface or key locations of the module, and each measurement point corresponds to an observation vector. One component; it can also be taken as a sparse binary sampling operator in wireless sensor networks, that is, randomizing and compressing multi-node sampling according to communication bandwidth and power consumption constraints. Regardless of the form used, the output dimension of the observation operator is Much smaller than the discrete grid dimension of the internal temperature field of the battery Thus constitute Extremely sparse observation conditions.

[0037] Subsequently, a neural network parameterization and physical constraint embedding model of the battery temperature field was constructed according to the method described in S3. The governing equation was taken as a three-dimensional unsteady-state heat conduction equation. Among them, body heat source According to the current and equivalent internal resistance Calculated as The boundary conditions are taken as the third type of boundary conditions for convective heat transfer. ,in For ambient temperature, This is the equivalent convective heat transfer coefficient. The equivalent convective heat transfer coefficient of the battery under different operating conditions... Distribution of internal heat sources It is usually difficult to measure accurately, so in this embodiment it is used as a parameter to be identified. With network weights Together, they are optimized to achieve coordinated inversion of "state-parameter-heat source".

[0038] In terms of training data organization, this embodiment adopts a multi-fidelity training data strategy of "low-fidelity + a small amount of high-fidelity". The low-fidelity data comes from temperature evolution results obtained based on simplified lumped parameter models or low-resolution finite element simulations, and is used to enable the network to quickly learn the basic structure and spatiotemporal trends of the temperature field with a large number of training samples. The high-fidelity data comes from multi-point temperature measurement experiments on battery test benches or high-resolution three-dimensional numerical simulations, and is used to refine the parameters during the network convergence phase. This multi-fidelity data organization strategy can alleviate the problem of high cost of battery experimental data acquisition and fine simulation calculations, enabling the method of this invention to still achieve high reconstruction accuracy under the condition of limited engineering data.

[0039] In the online inference phase, with sparse surface temperature As observational correction data, current current, ambient temperature, cooling status, and other operating conditions are used as the basis for determining heat source terms or boundary conditions. Given the query spatiotemporal coordinates (x,t), the reconstructed temperature field inside the battery can be obtained through a single forward inference by a neural network. And extract the hot spot temperature from it. Maximum temperature difference within the module This includes key indicators such as hotspot location coordinates. These indicators can be directly connected to the thermal management controller of the BMS / EMS to adjust cooling fan speed, coolant pump flow rate, valve opening, or battery available power limits, thereby achieving online dynamic optimization of the cooling strategy.

[0040] (2) Early warning of battery thermal runaway Based on the reconstruction of the battery pack temperature field, the early warning and location of battery thermal runaway are further achieved by combining indicators such as heating rate and hot spot propagation path.

[0041] First, define the hotspot temperature. And through the Regarding time Automatic differentiation to obtain heating rate Simultaneously calculate the temperature gradient. and its maximum modulus It is used to reflect the distribution of areas of concentrated thermal stress inside the battery.

[0042] Subsequently, multi-level warning thresholds are set based on battery type. For lithium-ion batteries, the hot spot temperature threshold is typically set to 60~80℃, the heating rate threshold is typically set to 2℃ / min, and the temperature gradient threshold is typically set to 5℃ / cm. During online operation, when... A level one warning is triggered when the set threshold is exceeded, indicating that the battery has entered the thermal risk zone; when A level-two warning is triggered when the set threshold is exceeded, indicating that the battery hotspot temperature is rising rapidly and there are signs of impending thermal runaway; when When the set threshold is exceeded, a level three warning is triggered, indicating the presence of a significant area of ​​thermal stress concentration inside the battery. After the warning signal is triggered, the system automatically adjusts the cooling strategy or limits the charging and discharging power; when multiple warnings are triggered simultaneously or the hot spot temperature continues to exceed the critical threshold, the faulty battery module is disconnected to prevent the spread of thermal runaway.

[0043] With the continuous temperature field representation and millisecond-level online inference capabilities provided by this invention, the above-mentioned early warning process can be completed within a relatively long time window before the battery actually experiences thermal runaway, thereby providing an effective safety protection measure for the battery system.

[0044] Example 3: Temperature Monitoring of Power Electronic Equipment This embodiment applies the temperature field reconstruction method described in Embodiment 1 to the temperature monitoring of power electronic equipment, such as... Figure 3 As shown, power modules in power electronic equipment undergo frequent power and temperature cycles during long-term operation. Junction temperature fluctuations are a major factor leading to bond wire fatigue, solder layer aging, and module failure. Simultaneously, critical components in the converter, such as IGBT modules, capacitors, and reactors, are thermally coupled to each other during operation, making it difficult to comprehensively reflect the internal temperature distribution of the equipment using only single-point temperature measurement. This embodiment focuses on two typical sub-scenarios: online estimation of IGBT module junction temperature and thermal management of converter equipment.

[0045] (1) Online estimation of junction temperature of IGBT module Junction temperature of IGBT / SiC power modules For online monitoring requirements, the physical constraint framework used in this embodiment is a state-space model based on a Foster or Cauer equivalent thermal network. The equivalent thermal network consists of several thermal resistances. With heat capacity Composition, describing the heat conduction between the layers within the module and its thermal coupling relationship with the cold plate / heat sink, can be uniformly represented by state-space equations:

[0046] in, This represents the temperature vector of each node in the thermal network. This is the power loss vector; This is the temperature vector on the cooling side; The diagonal matrix represents the node heat capacity. The node thermal resistance coupling matrix; , These are the input matrices for power loss and cooling boundary, respectively. When a significant three-dimensional temperature gradient exists within the module, the lumped heat network described above can be further replaced with a three-dimensional heat conduction PDE to more precisely characterize the temperature distribution within the module.

[0047] In the CS-PINN implementation, the residuals of the thermal network state equations are treated as physical terms as described in S3. The neural network output is forced to satisfy energy conservation and thermal inertia constraints; an observation operator is constructed using a finite number of measurable signals such as NTC, shell temperature, and cold plate temperature, as described in S2. And construct data items according to the method described in S4. The equivalent thermal resistance is calculated according to the method described in S6. Heat capacity Key physical properties such as convective heat transfer coefficient and loss coefficient are used as parameters to be identified. With network weights Joint optimization. After training, the neural network can simultaneously output the junction temperature. and its fluctuation amplitude, thermal resistance drift And cooling capacity evaluation metrics. These metrics can be used for IGBT / SiC module lifespan management and thermal failure early warning, among which thermal resistance drift... The cumulative trend of change can be used as an indirect characterization of module solder layer aging and bond line fatigue.

[0048] (2) Thermal management of converter equipment The above method can be further extended to the monitoring of the overall temperature field of grid-connected converters, flexible DC converter valves, and other equipment. In such converter equipment, key components such as IGBT modules, capacitors, and reactors are distributed in different locations and have significant thermal coupling with each other. Furthermore, the internal airflow organization of the entire unit is complex, making it difficult to reflect the overall thermal state of the unit by relying solely on the temperature measurement of a single key component.

[0049] In the engineering implementation, this sub-scenario includes the following data flow: collecting a small number of temperature measurement points at the sensor level for key components such as IGBT modules, capacitors, and reactors. , forming a sparse observation vector At the electrical parameter level, operating parameters such as converter output current, voltage, switching frequency, and modulation ratio are collected as losses. The calculation inputs include: collecting cooling boundary parameters such as fan speed, water pump flow rate, and coolant inlet temperature at the cooling state level, which are used as the cooling boundary. The input is then used. Based on the above data stream, the three-dimensional temperature field of the entire converter is reconstructed according to the CS-PINN method described in this invention, and the hot spot temperature of each key component is predicted.

[0050] Based on the above prediction results, the thermal management controller dynamically adjusts the cooling fan speed or water pump flow rate according to the proximity of the hot spot temperature of each component to the set threshold. When the hot spot temperature of a component approaches its safety threshold, it can actively reduce the modulation depth of the converter or limit its output power, thereby achieving coordinated allocation of cooling resources and power limits among different components inside the converter equipment, and improving the thermal management effect and operational reliability of the entire equipment.

[0051] Example 4: Transformer Hotspot Temperature Prediction This embodiment applies the CS-PINN temperature field reconstruction method to temperature monitoring of the main equipment of an oil-immersed transformer, as shown in Figure 3. As a key main piece of equipment in a power system, the winding hot spot temperature of a transformer is a core indicator for assessing insulation aging and lifespan loss. Furthermore, during long-term operation, transformers experience various complex factors such as oil deterioration, cooling device performance degradation, and uneven load distribution. Relying solely on traditional empirical thermal models is insufficient to guarantee the accuracy of hot spot temperature prediction. This embodiment elaborates on two typical sub-scenarios: transformer winding hot spot temperature prediction and transformer digital twin construction.

[0052] (1) Prediction of hot spot temperature of transformer winding To address the need for predicting transformer winding hot spot temperature (HST), this embodiment employs a physical constraint framework that combines a one-dimensional or two-dimensional thermal diffusion PDE with a thermo-liquid network model, striking a balance between physical interpretability and computational cost. The one-dimensional thermal diffusion PDE describes the temperature evolution of the winding along its axial direction, while the thermo-liquid network model describes the heat exchange relationships between the winding, oil flow channels, and external cooling devices. Together, they constitute a winding-oil flow coupled unsteady-state thermal diffusion equation system, serving as the governing equation operator for the CS-PINN in this sub-scenario. .

[0053] In the CS-PINN implementation, the top oil temperature is collected by the transformer online monitoring system according to the method described in S2. The temperature observation vector yT(t) is formed by other deployable temperature measurement points, and the corresponding temperature observation operator Φ is constructed such that yT(t) = Φu(t) + v(t); at the same time, the ambient temperature is... Load current The non-temperature quantities, such as the operating status of the cooling device, constitute the operating condition input vector z(t), which is used to determine the heat source terms, boundary conditions, or physical parameters to be identified. Following the method described in S3, a neural network is used to parameterize the winding-oil flow coupled temperature field. This parameterized representation, combined with the operating condition input vector z(t), constrains or identifies the heat source terms, boundary heat transfer conditions, and oil flow-related parameters. Key physical properties such as winding thermal resistance, oil flow velocity, and equivalent thermal conductivity of the cooling device are used as parameters to be identified. With network weights Joint optimization; offline pre-training parameters are obtained by offline training according to the algorithm described in S5. And use it as the initial parameter for the online lightweight correction stage; adapt to transformer operating condition drift and equipment status changes according to the "offline pre-training + online lightweight correction" engineering paradigm described in S6.

[0054] After training is complete, the neural network can output the winding hot spot temperature. Temperature rise margin In addition, insulation life loss assessment indicators. These indicators can be used for transformer load dispatching, overload capacity assessment, and insulation aging management, among which temperature rise margin... The safe distance between the transformer and the insulation temperature limit is reflected. The insulation life loss assessment index can be given by combining the IEC 60076-7 and other standards to provide a quantitative insulation life loss rate.

[0055] (2) Construction of digital twin of transformer Based on the prediction of transformer winding hot spot temperature, a "digital twin" of the transformer temperature field is further constructed by combining the Reduced-Order Model (ROM) with CS-PINN.

[0056] The digital twin is structured in four layers at the system level. The physical layer consists of the transformer physical equipment and its existing small number of temperature sensors and load current transformers, serving as the physical entity and data source for the digital twin. The data layer is responsible for real-time acquisition of measurement data such as ambient temperature, top oil temperature, load current, and the operating status of the cooling device, and for performing data cleaning, alignment, and compression. The model layer is the core of the digital twin, with the ROM providing a low-dimensional skeleton structure of the transformer temperature field dynamics. Based on the low-dimensional state trajectory given by the ROM, CS-PINN uses physical residuals and sparse measurement points to correct and compensate for the ROM state, thereby ensuring the accuracy and physical consistency of the temperature field reconstruction while maintaining low computational overhead. The application layer provides transformer operators with status assessment, life management, thermal management control, and maintenance decision support based on the temperature field distribution, hot spot temperature, and temperature rise margin indicators output by the digital twin.

[0057] The digital twin is continuously maintained during long-term operation according to the three-level update mechanism described in S6: initially, the network parameters established during the offline pre-training phase are updated over a long period. As a foundation, the network parameters are lightly corrected using newly acquired sparse observation data every preset time window (e.g., every few hours or days) over a short period. When the transformer experiences significant changes in its condition (e.g., cooling system failure, oil deterioration, insulation performance degradation, etc.), a complete retraining of the model is triggered. Through this three-level update mechanism, the digital twin maintains high prediction accuracy and condition assessment capabilities throughout the entire life cycle of the transformer, providing strong support for the intelligent operation and maintenance of the transformer's main equipment.

Claims

1. A method for reconstructing a temperature field based on the fusion of compressed sensing and physical information neural networks, characterized in that, Includes the following steps: S1. Construct a temperature field reconstruction architecture that includes a sparse observation modeling module, a neural network parameterization module, a physical constraint embedding module, a joint optimization solution module, and an engineering application extension module; The sparse observation modeling module is used to abstract the two types of sensing modes, point temperature measurement and compressed measurement, in engineering into a unified linear observation operator. The neural network parameterization module is used to represent the continuous temperature field as a function using a deep neural network; the physical constraint embedding module is used to apply the heat conduction control equation and its boundary / initial conditions as mechanistic soft constraints to the output of the deep neural network; the joint optimization solution module is used to unify sparse observation consistency, physical residuals and boundary and initial constraints into a single weighted loss objective, and complete parameter training through backpropagation. The engineering application extension module is used to further realize multi-physics field coupling extension, identification of thermal property parameters and convective heat transfer coefficient, lightweight correction in the online operation stage, and output of key thermal indicators for thermal management control and fault early warning, based on the continuous temperature field expression obtained in the training. S2. Establish a unified representation model for sparse observation operators; S3. Construct a neural network-parameterized temperature field and heat conduction physical constraint embedding model; S4. Construct a joint optimization loss function for sparse observation consistency and physical mechanism consistency; S5. A two-stage training and solution algorithm based on adaptive weight adjustment and adaptive point sampling is adopted; S6. Expand engineering applications with multi-physics coupling extension, parameter identification, online self-updating, and hotspot index output as the core, and realize the closed-loop transformation of temperature field monitoring results into engineering control behavior.

2. The temperature field reconstruction method according to claim 1, characterized in that, In step S2, during the operation of the energy and power equipment, the actual continuous temperature field It is defined in the solution domain With time interval A continuous scalar field on, , Its spatially discretized discrete temperature field vector is expressed as: , Represents the set of real numbers. N This represents the number of degrees of freedom after the temperature field is spatially discretized; constrained by sensor cost, installation space, and electrical insulation, it represents the number of observation dimensions that can be obtained in engineering. much smaller Construct a unified representation model for sparse observation operators using a unified linear observation operator: ,in, For the observation vector, For a unified linear observation operator, Zero-mean measurement noise; Choose a sparse representation base or a redundant dictionary The discrete temperature field vector is represented as ,in, For the sparse coefficient vector under the sparse representation basis or redundant dictionary; or for As a sparse representation of discrete temperature field vectors in the transform domain, the compressible prior of discrete temperature field is incorporated into the sparse observation reconstruction process.

3. The temperature field reconstruction method according to claim 2, characterized in that, In step S3, a deep neural network is introduced to predict or reconstruct the real continuous temperature field, resulting in a reconstructed temperature field. Where x∈Ω and t∈[0,T] are the input spatiotemporal coordinates. These are the weights for a trainable network; simultaneously, a heat conduction control equation operator is introduced. Boundary condition operators With initial condition operator Embedded reconstruction process as a mechanism constraint , , , , These represent material density, specific heat capacity at constant pressure, spatial differential operator, thermal conductivity, and heat generation per unit volume, respectively. When boundary condition parameters are difficult to measure directly in engineering, they are used as physical parameters to be identified. With network weights These variables are incorporated into the optimization variables to achieve a coordinated inversion of the temperature field, parameters, and heat source.

4. The temperature field reconstruction method according to claim 3, characterized in that, In step S4, four types of training point sets are constructed according to a preset sampling strategy: measurement point set. , physical configuration point set Boundary point set With the initial point set Construct data consistency loss on the aforementioned point set respectively. Physical residual loss Boundary loss loss from initial value Simultaneously construct compressed sensing sparse prior loss This is used to constrain the sparsity of coefficients in the reconstructed temperature field under a preset sparse representation basis or redundant dictionary, and to synthesize the total loss in the form of a weighted sum: ,in, , , , , These are the loss weights corresponding to the five loss items; The data consistency loss is expressed as mean square error in the case of point temperature measurement: ,in, Represents the measurement point set D m The measured temperature value at the mid-spatial position (x,t) is taken under the compression measurement condition. , Right now This indicates the reconstruction of the temperature field. The reconstructed temperature field vector is output and assembled at discrete spatial nodes; during training, due to the discrete temperature field vector... Unknown, using reconstructed temperature field vector replace Participating in sparsity constraints, i.e., letting and take or ,in, To reconstruct the temperature field vector The corresponding sparse coefficient vector; the physical residual loss The residuals output by the automatic differential calculation neural network on the heat conduction PDE are injected with mechanistic knowledge in a soft constraint manner; the boundary loss and initial value loss are respectively in and Apply on and The squared error constraint.

5. The temperature field reconstruction method according to claim 4, characterized in that, In step S5, the neural network weights are initialized. Physical parameters to be identified After setting the loss weights and training hyperparameters, the network is trained according to the following procedure: In the first stage, the Adam first-order optimizer is used with a learning rate of... The parameters are rapidly decreased, quickly guiding the network from random initialization to the vicinity of the loss basin; In the second stage, the system switches to the L-BFGS quasi-Newton optimizer, utilizing approximate Hessian information for refined local search, further improving convergence accuracy. During each parameter update, [the following steps are taken / implemented]: , , , Forward assessment Through automatic differentiation Calculate the PDE residuals, then calculate the total loss in step S4, and finally obtain the gradient through backpropagation. Parameter update complete.

6. The temperature field reconstruction method according to claim 5, characterized in that, In step S6, the optimal network parameters obtained from training in S5 are... With the optimal reconstructed temperature field Extract temperature field distribution and hotspot temperatures from the reconstructed temperature field. Temperature gradient In addition, the thermal resistance / thermal capacity identification results, which are the key thermal management indicators of the output to be identified, are connected to the BMS / EMS, protection devices or insulation aging assessment system to realize the closed-loop transformation of temperature field monitoring results into engineering control behavior.

7. The temperature field reconstruction method according to claim 2, characterized in that, In step S2, the linear observation operator It can be one or more of the following: point selection matrix, random projection matrix, sparse binary matrix, and compressed coding matrix; Zero-mean measurement noise The statistical characteristics are incorporated into the reconstruction modeling process; in step S3, the deep neural network adopts a multilayer perceptron structure, with 4 to 8 hidden layers and 32 to 128 neurons in each layer, and the activation function is selected. Or Swish; in step S4, the data consistency loss In engineering scenarios with high noise or many outliers, the mean squared error form is replaced by... One or more of the following: loss, Huber loss, or Charbonnier loss.

8. The temperature field reconstruction method according to claim 2, characterized in that, In step S5, the loss weight The training process is dynamically adjusted according to the training phase: In the early stage of training, the physical residual loss is given a large weight to ensure that the network learns the temperature field structure that satisfies the mechanism constraint from the beginning; in the middle stage of training, the weight of the data consistency loss is gradually increased to make the reconstruction results converge to the measured points; in the later stage of training, the weight is adjusted again to achieve a balance between physical consistency and observational agreement.

9. The temperature field reconstruction method according to claim 2, characterized in that, In step S5, the physical point set The sampling method is constructed by one or more of the following methods: uniform random sampling, Latin hypercube sampling, and adaptive encrypted sampling based on residual size. Specifically, the adaptive encrypted sampling is characterized by evaluating the residual distribution on the collocation points every few training cycles and taking the region with larger residual as the key sampling region in the next stage. Training convergence criterion based on total loss The magnitude of the decrease, the gradient norm The training is considered to have converged when all three factors—the prediction error on the validation point set, the error on the validation point set, and the prediction error on the validation point set—are all less than a preset threshold.

10. The temperature field reconstruction method according to claim 2, characterized in that, In step S6, the online self-update mechanism specifically includes a three-level update process: an offline pre-training stage, an online lightweight calibration stage, and an event-triggered retraining stage. In the offline pre-training stage, the optimal network parameters are obtained by training using historical operating data, factory temperature rise test data, or low-fidelity finite element simulation data according to the algorithm described in S5. During the online lightweight calibration phase, the optimal network parameters are fine-tuned with Adam steps using newly acquired sparse observation data every preset time window; when the device undergoes a significant state change, the model is fully retrained.

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