A lithium ion battery temperature field rapid calculation method based on knowledge constraint optimization sample and POD-SSKAN agent model

Abstract

The application discloses a kind of based on knowledge constraint preferred sample and POD-SSKAN agent model lithium ion battery temperature field fast calculation method, belong to battery thermal simulation and digital twin field.The method is based on heat production rationality, boundary heat exchange consistency and safety temperature range and other knowledge constraints, combined with temperature sensitivity, POD modal uncertainty and boundary working condition importance to obtain preferred sample;Run high-fidelity simulation to obtain temperature field snapshot and carry out POD reduction;POD-SSKAN agent model is constructed to predict modal coefficient and reconstruct temperature field containing multi-scale causal convolution, selective state space and KAN output layer, and the source domain model is trained according to thermal constraints;Based on sparse measuring point inversion experimental domain modal coefficient and generate virtual sample to construct enhanced dataset;Freeze backbone network and update output layer and residual adapter to correct deviation;Full-field temperature is quickly reconstructed using calibrated model, and online correction is fused with real-time measuring point.

Description

Technical Field

[0001] This invention relates to the fields of lithium-ion battery thermal simulation, reduced-order modeling, surrogate computation, and digital twin technology, specifically to a method for rapid calculation of the temperature field of lithium-ion batteries based on knowledge-constrained optimal samples and the POD-SSKAN surrogate model. Background Technology

[0002] Lithium-ion batteries are widely used in new energy vehicles, energy storage power stations, and high-power power systems. The temperature field distribution during battery operation directly affects rate performance, cycle life, and thermal safety. Under complex operating conditions such as high-rate charging and discharging, ambient temperature changes, and fluctuating cooling conditions, localized areas of concentrated temperature rise can easily form inside and on the surface of the battery, thereby increasing the risk of thermal runaway. Therefore, establishing a rapid temperature field calculation method that combines high accuracy, speed, and engineering adaptability is of great significance for battery thermal management control, online safety early warning, and digital twin model updates.

[0003] High-fidelity electrochemical-thermal coupled simulation models can describe the internal heat generation, conduction, and boundary heat transfer processes of batteries. However, they typically require solving multiphysics coupled control equations on a mesh discretization basis, resulting in high computational complexity and slow online response times that are difficult to meet the demands of real-time applications. Reduced-order models can project high-dimensional temperature fields into low-dimensional modal spaces, significantly reducing the model's degrees of freedom. Surrogate models can learn the nonlinear mapping relationship between operating parameters and temperature response, improving online computational efficiency. However, conventional surrogate models still suffer from problems such as redundant training samples, insufficient coverage of key thermally sensitive operating conditions, lack of thermal consistency in prediction results, and insufficient calibration capabilities in small-sample experimental domains. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a fast calculation method for the temperature field of lithium-ion batteries based on knowledge-constrained optimized samples and POD-SSKAN surrogate models, so as to solve the problems of long online calculation time of high-fidelity simulation models, low sample construction efficiency, insufficient physical consistency of surrogate models, and difficulty in small sample calibration in the experimental domain.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows.

[0006] A fast method for calculating the temperature field of a lithium-ion battery based on knowledge-constrained sample optimization and the POD-SSKAN surrogate model includes the following steps: S1. Construct a parameter space for thermal simulation of lithium-ion batteries, and obtain knowledge-constrained optimal samples based on the rationality of heat generation, consistency of boundary heat transfer, safe temperature range, temperature sensitivity, POD mode uncertainty and importance of boundary conditions. S2. Based on the preferred samples, run a high-fidelity electrochemical-thermal coupling simulation model to obtain a snapshot of the temperature field, and obtain the POD principal mode and corresponding modal coefficients through POD order reduction; S3. Construct a POD-SSKAN surrogate model including a multi-scale causal convolutional layer, a selective state space layer, and a mode decomposition-based KAN output layer to predict the POD mode coefficients of each order and complete the temperature field reconstruction; train the POD-SSKAN surrogate model based on the thermal constraints of the reconstruction results to obtain the source domain surrogate model; S4. Based on the local modal priors and modal time continuity obtained from sparse measurement point temperatures and optimized sample retrieval, the experimental domain modal coefficients are inverted; virtual samples are generated near the experimental domain modal coefficients, and after being screened for measurement point consistency, thermal laws, and safe temperature range, an enhanced experimental domain dataset is constructed. S5. Freeze the backbone network parameters of the source domain proxy model and update some spline control parameters, experimental domain bias parameters and residual adapter parameters of the KAN output layer to correct the deviation between the simulation domain and the experimental domain. S6. Predict the modal coefficients under the test conditions and reconstruct the overall temperature using the calibrated POD-SSKAN surrogate model; if there are real-time sparse measurement point temperatures, use the residual adapter to fuse the real-time measurement point data for online correction.

[0007] Preferably, step S1 specifically includes: Selecting the charging and discharging current I Ambient temperature T ext Heat transfer coefficient h Define the operating condition vector as a parameter for thermal simulation. u for:

[0008] Let the operating parameter space Ω be:

[0009] in, I min and I max These are the set minimum and maximum current values, respectively. T min and T max These are the set minimum and maximum ambient temperatures, respectively. h min and h max These are the set minimum and maximum values ​​of the heat transfer coefficient, respectively. Generate a candidate sample pool within the operating parameter space Ω C :

[0010] in, N c The total number of candidate samples; u j For the first j One candidate sample; Imposing thermal knowledge constraints on candidate samples, including: First, a reasonable constraint on heat generation is imposed on the candidate samples to ensure that the total heat generation rate of the battery meets the preset allowable range:

[0011] in, For battery heat generation rate; U ocv This is the open-circuit voltage; U Terminal voltage; T The battery represents temperature. ε heat To allow for error tolerance; Secondly, a uniform constraint is applied to the convective heat transfer boundary on the battery surface:

[0012] in, λ is the thermal conductivity; n is the outward normal vector. For temperature gradient; Secondly, impose a safe temperature range constraint on the candidate operating conditions:

[0013] in, T min,safe and T max,safe These are the preset lower and upper safe temperature limits, respectively; Let be the temperature field distribution function, representing the temperature field distribution under operating conditions. u j Below, position x At the moment t Temperature value; Normalize the parameters of each operating condition for the candidate samples:

[0014] in, d The dimension of the operating condition parameters; u j,l For the first j In the candidate samples, the first l One operating condition parameter; u l,min and ul,max The first l Minimum and maximum values ​​of operating parameters; These are the normalized operating parameters; Select at least one initial sample from the candidate samples that meet the above thermal and safety constraints to form the selected sample set. S Calculate the working space coverage of the candidate sample relative to the selected sample set. :

[0015] in, and Candidate samples u j and selected samples u i The corresponding normalized process condition vector; Using a low-fidelity coarse-grid model obtained by spatial mesh coarsening of a high-fidelity electrochemical-thermal coupling simulation model, the temperature response of candidate samples is calculated, and the characteristic temperature rise of candidate samples is defined. for:

[0016] in, T L ( x , t ; u j Candidate samples obtained from low-fidelity coarse-grid model calculations. u j In position x ,time t Temperature; T ext,j Candidate samples u j The corresponding ambient temperature is also used as the initial temperature of the battery under this candidate operating condition; Temperature sensitivity is calculated based on the rate of change of characteristic temperature rise relative to various operating parameters:

[0017] Normalize the temperature sensitivity:

[0018] in, For the first l The disturbance step size of each operating parameter; e l For the first l Unit vectors in the direction of each working condition parameter; g T,min andg T,max These represent the minimum and maximum values ​​of temperature sensitivity in the candidate sample set, respectively. ε To prevent the use of pre-defined positive numbers with a denominator of zero; Based on the selected sample set S The corresponding low-fidelity coarse-grid temperature response snapshots are used to construct a temporary POD mode matrix, and the POD mode uncertainty of the candidate samples relative to the current POD mode space is calculated:

[0019] in, Candidate samples obtained from low-fidelity coarse mesh model u j The pulsating temperature snapshot matrix; To construct the frontier based on the currently selected sample set k Temporary POD mode matrix; It is the Frobenius norm; The importance of the boundary conditions is calculated based on how closely the normalized working condition parameters in the candidate samples approach the parameter space boundary.

[0020] Calculate the optimal score for candidate samples that meet the above constraints. S ( u j ):

[0021] in, α , β , γ and δ The weights for operating condition space coverage, temperature sensitivity, POD modal uncertainty, and boundary condition importance are respectively, and satisfy the following:

[0022] Select the candidate sample with the highest evaluation score from the unselected candidate samples:

[0023] And update the selected sample set:

[0024] After each new preferred sample is added, a temporary POD mode matrix is ​​reconstructed based on the updated selected sample set, and the operating condition space coverage and POD mode uncertainty of the remaining candidate samples are recalculated. The process of candidate sample scoring, selection, and POD mode space updating is repeated until the number of selected samples reaches a preset number. N We obtain the knowledge-constrained optimal sample set: .

[0025] Preferably, step S2 specifically includes: The preferred samples obtained in step S1 are input into the high-fidelity electrochemical-thermal coupling simulation model to obtain the full-field temperature vector at different time sampling points for each preferred operating condition. The full-field temperature vectors are then arranged in columns to construct a temperature field snapshot matrix. X ; Calculate the nodal mean vector of the temperature field snapshot matrix. The mean was removed from each temperature field snapshot to obtain the pulsating snapshot matrix. :

[0026] in, For the first j A snapshot vector of the temperature field; This is the nodal mean vector of a snapshot of the entire temperature field. n This represents the total number of temperature field snapshots. Construct a correlation matrix based on the pulse snapshot matrix. R And perform eigenvalue decomposition on the correlation matrix:

[0027] in, The eigenvector matrix, v i For the correlation matrix R Corresponding to the i Eigenvectors with eigenvalues; For the eigenvalue matrix, λ i For the eigenvector v i The corresponding eigenvalues; RV = VΛ Represents the correlation matrix R The eigenvalue decomposition relationship is given, and the eigenvalues ​​are arranged in descending order. Construct the POD mode matrix based on the eigenvectors and corresponding eigenvalues, and then... k The cutoff order is determined by the cumulative energy percentage of the first-order POD mode, whereby the cumulative energy percentage is:

[0028] The minimum order at which the cumulative energy percentage reaches the preset energy threshold is selected as the cutoff order. k , cut off k The POD principal mode matrix Φ is composed of the first-order POD modes.k ; Projecting the pulsation snapshot matrix onto the POD principal modal space yields the modal coefficient matrix:

[0029] in, A k This is the modal coefficient matrix corresponding to each temperature field snapshot; Any temperature field snapshot is reconstructed based on the nodal mean vector, the POD principal mode matrix, and the corresponding modal coefficient vector:

[0030] in, a j For the first j The modal coefficient vector corresponding to each temperature field snapshot; For the first j The POD corresponding to each temperature field snapshot reconstructs the full-field temperature vector.

[0031] Preferably, step S3 specifically includes: For the q Each time sampling point will be used to input the operating condition variables and time variables into the model. z q :

[0032] in, I q For the first q The charging and discharging current corresponding to each time sampling point; T ext,q For the first q The ambient temperature corresponding to each time sampling point; h conv,q For the first q The heat transfer coefficient corresponding to each time sampling point; t q For the current moment; Δ t q For time step; The model input is standardized and mapped to a high-dimensional feature space:

[0033] in, W e and b e These are the weight matrix and bias term of the input embedding layer, respectively; Multi-scale causal convolution features are constructed based on causal convolution branches with different receptive fields. g q :

[0034] in, R c For the set of convolutional receptive fields; τ This is the kernel offset; e q-τ:q For historical embedding feature sequences; Conv τ This represents the causal convolution operation within the corresponding receptive field; W τ and b τ These are the kernel weights and convolutional bias terms corresponding to the receptive field; The multi-scale causal convolutional features are input into a selective state space layer, and then generated by the parameter generation network Γ. θ Adaptively generate state-space parameters based on the current input conditions:

[0035] in, This is the discretized state transition matrix; The input control matrix is ​​discretized; To output the mapping matrix; For direct connection matrix; Update implied thermal state ξ q and output thermal dynamic characteristics. f q : in, ξ q and ξ q-1 These are the implied thermal states at the current moment and the previous moment, respectively; f q The state space parameters are adaptively generated based on the multi-scale causal convolutional features corresponding to the current input conditions and are updated as the input conditions change, so as to characterize the long-term thermal inertia differences under different current, ambient temperature and heat transfer conditions. A mode decomposition-based KAN output layer is set at the output end, and corresponding spline mapping branches are set for different orders of POD modes; for the th... i The predicted values ​​of the order POD mode coefficients are as follows:

[0036] in, B p For the first p indivualB spline basis functions; c i,l,p For the first i Trainable spline control coefficients corresponding to the order POD mode; b i For the first i Bias terms corresponding to the first-order POD mode; d f For thermal dynamics features; R b for B Number of spline basis functions; f l,q Thermal dynamic feature vector f q The l One element; By combining the predicted POD mode coefficients of different orders from the outputs of different mapping branches, the POD mode coefficient vector at the current time step is obtained:

[0037] The overall mapping relationship of the POD-SSKAN proxy model is as follows:

[0038] in, All the parameters to be trained for the POD-SSKAN surrogate model; The predicted temperature field is reconstructed based on the POD modal coefficients and POD principal mode matrix obtained by the POD-SSKAN surrogate model. The heat conduction residual, boundary heat transfer residual and measurement point consistency residual are calculated on the reconstructed temperature field to inversely constrain the POD modal coefficient prediction model through thermal constraints at the temperature field level. Define the modal coefficient prediction loss L a :

[0039] in, N b For training batch size; These are the modal coefficients obtained from POD projection; The modal coefficients predicted by the surrogate model; The predicted temperature field is obtained based on the POD reconstruction relationship:

[0040] The predicted node temperature vector Predicted temperature field function formed by spatial interpolation Substitute the heat conduction control equations into the heat conduction residuals and construct them. r heat,q:

[0041] in, ρ The equivalent density of the battery material; c p This refers to the equivalent isobaric specific heat capacity of the battery material. For predicting the time partial derivative of the temperature field; λ Thermal conductivity; For the first q Battery heat generation rate corresponding to each time sampling point; Corresponding thermal conduction constraint loss L heat for:

[0042] Construct boundary heat transfer residuals on the convective heat transfer boundary of the battery surface. r bc,q for:

[0043] in, Boundary heat flux density; For convective heat transfer heat flux density; Corresponding boundary heat transfer constraint loss L bc for:

[0044] Introducing modal time increment consistency loss L smooth :

[0045] in, To predict the time increment of the modal coefficients; This represents the time increment of the true modal coefficients; Normalization factor; If sparse temperature data exists, let H Select a matrix for the measurement points. y q For the first q The temperature vector corresponding to each time sampling point is then the measurement point consistency loss. L sen for:

[0046] Constructing a joint loss function constrained by thermal knowledge L :

[0047] in, ω 1 represents the thermal conduction constraint weight; ω 2 represents the boundary heat transfer constraint weight; ω 3 represents the modal time increment consistency constraint weight; ω 4 represents the consistency weight of the measurement points; The source domain training dataset is composed of the input variables and POD mode coefficients corresponding to the selected simulation samples. D s :

[0048] During training, the loss is first predicted using modal coefficients. L a The POD-SSKAN surrogate model is pre-trained to learn the basic mapping relationship between the input operating conditions and the POD modal coefficients; then, heat conduction constraint loss based on the reconstructed temperature field is gradually introduced. L heat Boundary heat transfer constraint loss L bc And modal time increment consistency loss L smooth This allows thermal constraints to act inversely on the POD modal coefficient prediction model through temperature field reconstruction; and a measurement point consistency loss is added when measurement point data is available. L sen Improve the model's ability to calibrate for experimental data; After training, the source domain POD-SSKAN surrogate model is obtained:

[0049] in, These are the parameters of the POD-SSKAN surrogate model trained in the source domain.

[0050] Preferably, step S4 specifically includes: A modal coefficient dataset for the experimental domain is constructed using sparse measurement point temperature information, and the measurement point observation subspace matrix Φ is used. H for:

[0051] For the q At each experimental sampling time, the average temperature at the measuring points is assumed to be... Then the temperature fluctuation vector at the measuring point for:

[0052] The observation equation for sparse measuring points is:

[0053] in, ε q For measuring noise; To improve the stability of modal coefficient inversion when the number of measurement points is insufficient, a knowledge-constrained prior inversion model is introduced:

[0054] in, These are the initial inversion mode coefficients; W s This is the confidence weight matrix for the measurement points; W p This is the prior accuracy matrix; μ q The mean of local modes is obtained from the preferred sample library; λ p For prior regularization weights; λ d Time-smoothing regularization weights; These are the inversion mode coefficients from the previous time step; These are candidate modal coefficients; To increase the number of samples in the experimental domain, virtual candidate mode samples are generated near the initial inversion mode coefficients:

[0055] in, L q It is the local covariance decomposition matrix; ξ l It is a standard normal random vector; I k for k An identity matrix of order 1; Reconstruct the virtual modal coefficients into a virtual temperature field:

[0056] Virtual samples must simultaneously meet the constraints of measurement point consistency, thermal conduction residual, and safe temperature range:

[0057] in, δ s This is the tolerance threshold for measurement point error; δ h This represents the tolerance threshold for thermal conductivity residuals. The experimental domain augmentation dataset is composed of real experimental inversion samples and virtual samples that satisfy the constraints. : .

[0058] Preferably, step S5 specifically includes: The source domain POD-SSKAN surrogate model was used as the initial model for experimental domain calibration. To reduce the risk of overfitting under small sample conditions, the main parameters of the input embedding layer, multi-scale causal convolutional layer and selective state space layer are kept unchanged, and only some spline control coefficients, domain bias vectors and lightweight residual adapter parameters of the KAN output layer are updated. The predicted modal coefficients after experimental domain calibration are expressed as follows:

[0059] in, G ψ For lightweight residual adapters; Experimental domain calibration loss function L cal for:

[0060] in, ψ These are the parameters for the residual adapter; L sen For measurement point consistency loss; Δ C KAN This represents the change in the control coefficient of the KAN spline; κ 1 represents the thermal conduction constraint weighting coefficient; κ 2 represents the boundary heat transfer constraint weighting coefficient; κ 3 represents the regularization weighting coefficients for the residual adapter parameters; κ 4 represents the regularization weighting coefficient for the change in the KAN control coefficient.

[0061] Preferably, step S6 specifically includes: For the new operating condition to be predicted, obtain its real-time input variables. z new The POD modal coefficients are then fed into the experimental domain-calibrated POD-SSKAN surrogate model to obtain the predicted values ​​of the POD modal coefficients.

[0062] in, These are the model parameters after calibration in the experimental domain; Reconstructing the full-field temperature based on the POD principal mode matrix:

[0063] in, These are the predicted values ​​of the POD modal coefficients; If there are real-time sparse temperature measurement points during the online phase y newThen, online correction is performed using a residual adapter:

[0064] The final online temperature field is obtained: .

[0065] Due to the adoption of the above technical solutions, the technical progress achieved by this invention is as follows.

[0066] This invention has high computational efficiency: it represents the high-dimensional temperature field as a small number of modal coefficients through POD, and directly predicts the low-dimensional modal coefficients through the POD-SSKAN surrogate model. In the online stage, it avoids repeated iterative solutions of the high-fidelity full-order model, and the computational efficiency is still far superior to that of the traditional surrogate model.

[0067] This invention offers high sample construction efficiency: by driving sample optimization through multiple knowledge constraints such as heat generation rationality, boundary heat transfer consistency, safe temperature range, temperature sensitivity, POD modal uncertainty, and boundary condition importance, a limited number of simulation samples are concentrated in areas of thermal sensitivity, boundary extreme regions, and regions with significant modal changes. Compared to random or uniform sampling methods, the number of simulation samples required can be significantly reduced while achieving the same surrogate model accuracy.

[0068] This invention has strong dynamic characterization capabilities: multi-scale causal convolution can extract short-term temperature rise change features at different time scales, selective state space units can characterize long-term thermal inertia, and KAN spline output layers can describe the nonlinear mapping relationship of modal coefficients. The organic combination of these three features enables the model to have the ability to model thermal dynamic behavior at multiple time scales.

[0069] This invention exhibits good thermal consistency: during the training process, heat conduction residual, boundary heat transfer residual, modal time increment consistency residual, and measurement point consistency residual are introduced to ensure that the predicted temperature field meets the basic thermal constraints and has high physical reliability.

[0070] This invention has strong experimental domain adaptability: by utilizing sparse measurement point inversion, knowledge-constrained virtual sample generation, and efficient parameter calibration, it can correct the deviation of temperature field prediction results under the condition of a small amount of experimental measurement point data, effectively solving the model mismatch problem between the simulation domain and the experimental domain. Attached Figure Description

[0071] Figure 1 This is a flowchart of the present invention; Figure 2 The preferred sample working condition spatial distribution diagram for the knowledge constraints of this invention; Figure 3 This is a time-series comparison of the predicted values ​​of the first-order POD modal coefficients and the reference modal coefficients of the POD-SSKAN surrogate model of the present invention. Figure 4This is a time-series comparison of the predicted values ​​of the second-order POD modal coefficients and the reference modal coefficients of the POD-SSKAN surrogate model of the present invention. Figure 5 This is a time-series comparison of the predicted values ​​of the third-order POD modal coefficients and the reference modal coefficients of the POD-SSKAN surrogate model of the present invention. Figure 6 This is a time-series comparison of the predicted values ​​of the fourth-order POD modal coefficients and the reference modal coefficients of the POD-SSKAN surrogate model of the present invention. Figure 7 This is a time-series comparison of the predicted values ​​of the fifth-order POD modal coefficients and the reference modal coefficients of the POD-SSKAN surrogate model of the present invention. Figure 8 This is a comparison chart of the modal coefficient inversion results under different operating conditions of the present invention, wherein, Figure 8 In the middle (a) and (c), respectively, the POD-SSKAN prediction results, unconstrained least squares inversion results and knowledge-constrained prior inversion results of the first-order POD mode coefficients under two representative working conditions are compared. Figure 8 Figures (b) and (d) show a comparison of the three results for the fourth-order POD modal coefficients under the corresponding working conditions. Figure 9 This is a comparison chart of temperature prediction results before and after calibration of the experimental domain of the POD-SSKAN surrogate model of the present invention. Figure 9 (a) is a time-series comparison of the experimentally measured temperature during the charging phase, the POD-SSKAN predicted temperature before calibration, and the POD-SSKAN predicted temperature after experimental domain calibration. Figure 9 (b) is a time-series comparison of the three temperature results during the discharge phase; Figure 10 This is a comparison chart of the online prediction error of POD-SSKAN and the prediction error after online correction by the residual adapter under operating condition 1, wherein... Figure 10 (a) is a time-series comparison of MAPE and RMSE during the charging phase under operating condition 1. Figure 10 (b) is a time series comparison of MAPE and RMSE during the discharge stage under operating condition 1; Figure 11 This is a comparison chart of the online prediction error of POD-SSKAN and the prediction error after online correction by the residual adapter under operating condition 2, wherein, Figure 11 (a) shows the timing comparison of MAPE and RMSE during the charging phase under operating condition 2. Figure 11 (b) is a time-series comparison of MAPE and RMSE during the discharge phase under operating condition 2; Figure 12 This is a comparison chart of the online prediction error of POD-SSKAN and the prediction error after online correction by the residual adapter under operating condition 3, wherein, Figure 12 (a) is a time-series comparison of MAPE and RMSE during the charging phase under operating condition 3. Figure 12 (b) is a time series comparison of MAPE and RMSE during the discharge stage under operating condition 3; Figure 13 This is a comparison chart of the online prediction error of POD-SSKAN and the prediction error after online correction by the residual adapter under operating condition 4, wherein, Figure 13 (a) shows the timing comparison of MAPE and RMSE during the charging phase under operating condition 4. Figure 13 (b) is a time series comparison of MAPE and RMSE during the discharge stage under operating condition 4; Figure 14 This is a comparison chart of the online prediction error of POD-SSKAN and the prediction error after online correction by the residual adapter under operating condition 5, wherein... Figure 14 (a) shows the timing comparison of MAPE and RMSE during the charging phase under operating condition 5. Figure 14 (b) is a time series comparison of MAPE and RMSE during the discharge stage under operating condition 5; Figure 15 This is a comparison chart of the online prediction error of POD-SSKAN and the prediction error after online correction by the residual adapter under operating condition 6, wherein... Figure 15 (a) shows the timing comparison of MAPE and RMSE during the charging phase under operating condition 6. Figure 15 (b) is a comparison of the MAPE and RMSE timings during the discharge phase under operating condition 6. Detailed Implementation

[0072] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0073] A fast method for calculating the temperature field of lithium-ion batteries based on knowledge-constrained sample optimization and the POD-SSKAN surrogate model, combined with Figure 1 As shown, it includes the following steps: S1. Construct a parameter space for thermal simulation of lithium-ion batteries, and obtain knowledge-constrained optimal samples based on the rationality of heat generation, consistency of boundary heat transfer, safe temperature range, temperature sensitivity, POD mode uncertainty and importance of boundary conditions.

[0074] This step specifically includes: Selecting the charging and discharging current I Ambient temperature T ext Heat transfer coefficient h Define the operating condition vector as a parameter for thermal simulation. u for:

[0075] Let the operating parameter space Ω be:

[0076] in, I min and I max These are the set minimum and maximum current values, respectively. T min and T max These are the set minimum and maximum ambient temperatures, respectively. h min and h max These are the set minimum and maximum values ​​of the heat transfer coefficient, respectively. Generate a candidate sample pool within the operating parameter space Ω C :

[0077] in, N c The total number of candidate samples; u j For the first j One candidate sample; Imposing thermal knowledge constraints on candidate samples, including: First, a reasonable constraint on heat generation is imposed on the candidate samples to ensure that the total heat generation rate of the battery meets the preset allowable range:

[0078] in, For battery heat generation rate; U ocv This is the open-circuit voltage; U Terminal voltage; T The battery represents temperature. ε heat To allow for error tolerance; Secondly, a uniform constraint is applied to the convective heat transfer boundary on the battery surface:

[0079] in, λ is the thermal conductivity; n is the outward normal vector. For temperature gradient; Secondly, impose a safe temperature range constraint on the candidate operating conditions:

[0080] in, T min,safe and T max,safeThese are the preset lower and upper safe temperature limits, respectively; Let be the temperature field distribution function, representing the temperature field distribution under operating conditions. u j Below, position x At the moment t Temperature value; To eliminate the dimensional differences between parameters under different operating conditions, the parameters of each operating condition in the candidate samples are normalized:

[0081] in, d The dimension of the operating condition parameters; u j,l For the first j In the candidate samples, the first l One operating condition parameter; u l,min and u l,max The first l Minimum and maximum values ​​of operating parameters; These are the normalized operating parameters; Select at least one initial sample from the candidate samples that meet the above thermal and safety constraints to form the selected sample set. S Calculate the working space coverage of the candidate sample relative to the selected sample set. :

[0082] in, and Candidate samples u j and selected samples u i The corresponding normalized process condition vector; The larger the value, the greater the difference between the candidate sample and the selected sample, and the stronger the ability to supplement and cover the working condition parameter space. Using a low-fidelity coarse-grid model obtained by spatial mesh coarsening of a high-fidelity electrochemical-thermal coupling simulation model, the temperature response of candidate samples is calculated, and the characteristic temperature rise of candidate samples is defined. for:

[0083] in, T L ( x , t ; u j Candidate samples obtained from low-fidelity coarse-grid model calculations. u j In positionx ,time t Temperature; T ext,j Candidate samples u j The corresponding ambient temperature is also used as the initial temperature of the battery under this candidate operating condition.

[0084] Temperature sensitivity is calculated based on the rate of change of characteristic temperature rise relative to various operating parameters:

[0085] Normalize the temperature sensitivity:

[0086] in, For the first l The disturbance step size of each operating parameter; e l For the first l Unit vectors in the direction of each working condition parameter; g T,min and g T,max These represent the minimum and maximum values ​​of temperature sensitivity in the candidate sample set, respectively. ε To prevent the use of pre-defined positive numbers with a denominator of zero; G T ( u j The larger the value, the more sensitive the temperature response near the candidate sample is to changes in operating parameters.

[0087] Based on the selected sample set S The corresponding low-fidelity coarse-grid temperature response snapshots are used to construct a temporary POD mode matrix, and the POD mode uncertainty of the candidate samples relative to the current POD mode space is calculated:

[0088] in, Candidate samples obtained from low-fidelity coarse mesh model u j The pulsating temperature snapshot matrix; To construct the frontier based on the currently selected sample set k Temporary POD mode matrix; It is the Frobenius norm; U POD ( u j The larger the value, the more difficult it is for the temperature field features contained in the candidate sample to be represented by the current POD mode space, and the greater the amount of supplementary information it provides to the POD mode space.

[0089] The importance of the boundary conditions is calculated based on how closely the normalized working condition parameters in the candidate samples approach the parameter space boundary.

[0090] in, P b ( u j The larger the value, the closer at least one operating condition parameter in the candidate sample is to the upper or lower boundary of its value range.

[0091] Calculate the optimal score for candidate samples that meet the above constraints. S ( u j ):

[0092] in, α , β , γ and δ The weights for operating condition space coverage, temperature sensitivity, POD modal uncertainty, and boundary condition importance are respectively, and satisfy the following:

[0093] Select the candidate sample with the highest evaluation score from the unselected candidate samples:

[0094] And update the selected sample set:

[0095] After each new preferred sample is added, a temporary POD mode matrix is ​​reconstructed based on the updated selected sample set, and the operating condition space coverage and POD mode uncertainty of the remaining candidate samples are recalculated. The process of candidate sample scoring, selection, and POD mode space updating is repeated until the number of selected samples reaches a preset number. N We obtain the knowledge-constrained optimal sample set: .

[0096] S2. Based on the preferred sample, run a high-fidelity electrochemical-thermal coupling simulation model to obtain a snapshot of the temperature field, and obtain the POD principal mode and corresponding modal coefficients by POD order reduction.

[0097] This step specifically includes: The preferred samples obtained in step S1 are input into the high-fidelity electrochemical-thermal coupling simulation model to obtain the full-field temperature vector at different time sampling points for each preferred operating condition. The full-field temperature vectors are then arranged in columns to construct a temperature field snapshot matrix. X ; Calculate the nodal mean vector of the temperature field snapshot matrix. The mean was removed from each temperature field snapshot to obtain the pulsating snapshot matrix. :

[0098] in, For the first j A snapshot vector of the temperature field; This is the nodal mean vector of a snapshot of the entire temperature field. n This represents the total number of temperature field snapshots. Construct a correlation matrix based on the pulse snapshot matrix. R And perform eigenvalue decomposition on the correlation matrix:

[0099]

[0100] in, The eigenvector matrix, v i For the correlation matrix R Corresponding to the i Eigenvectors with eigenvalues; For the eigenvalue matrix, λ i For the eigenvector v i The corresponding eigenvalues; RV = VΛ Represents the correlation matrix R The eigenvalue decomposition relationship is given, and the eigenvalues ​​are arranged in descending order.

[0101] Construct the POD mode matrix based on the eigenvectors and corresponding eigenvalues, and then... k The cutoff order is determined by the cumulative energy percentage of the first-order POD mode, whereby the cumulative energy percentage is:

[0102] The minimum order at which the cumulative energy percentage reaches the preset energy threshold is selected as the cutoff order. k , cut off k The POD principal mode matrix Φ is composed of the first-order POD modes. k ; Projecting the pulsation snapshot matrix onto the POD principal modal space yields the modal coefficient matrix:

[0103] in, A kThis is the modal coefficient matrix corresponding to each temperature field snapshot; Any temperature field snapshot is reconstructed based on the nodal mean vector, the POD principal mode matrix, and the corresponding modal coefficient vector:

[0104] in, a j For the first j The modal coefficient vector corresponding to each temperature field snapshot; For the first j The POD corresponding to each temperature field snapshot reconstructs the full-field temperature vector.

[0105] S3. Construct a POD-SSKAN surrogate model including a multi-scale causal convolutional layer, a selective state space layer, and a mode decomposition-based KAN output layer to predict the POD mode coefficients of each order and complete the temperature field reconstruction; train the POD-SSKAN surrogate model based on the thermal constraints of the reconstruction results to obtain the source domain surrogate model.

[0106] For the q Each time sampling point will be used to input the operating condition variables and time variables into the model. z q :

[0107] in, I q For the first q The charging and discharging current corresponding to each time sampling point; T ext,q For the first q The ambient temperature corresponding to each time sampling point; h conv,q For the first q The heat transfer coefficient corresponding to each time sampling point; t q For the current moment; Δ t q For time step; The model input is standardized and mapped to a high-dimensional feature space:

[0108] in, W e and b e These are the weight matrix and bias term of the input embedding layer, respectively; Multi-scale causal convolution features are constructed based on causal convolution branches with different receptive fields. g q :

[0109] in, R c For the set of convolutional receptive fields; τ This is the kernel offset; e q-τ:q For historical embedding feature sequences; Conv τ This represents the causal convolution operation within the corresponding receptive field; W τ and b τ These are the convolution kernel weights and convolution bias terms under the corresponding receptive fields, respectively; the causal convolution branches of different receptive fields are used to extract the short-term temperature rise characteristics caused by rapid changes in current and the medium-time scale temperature rise characteristics during continuous battery operation, respectively. The multi-scale causal convolutional features are input into a selective state space layer, and then generated by the parameter generation network Γ. θ Adaptively generate state-space parameters based on the current input conditions:

[0110] in, This is the discretized state transition matrix; The input control matrix is ​​discretized; To output the mapping matrix; For direct connection matrix; Update implied thermal state ξ q and output thermal dynamic characteristics. f q :

[0111] in, ξ q and ξ q-1 These are the implied thermal states at the current moment and the previous moment, respectively; f q The state space parameters are adaptively generated based on the multi-scale causal convolutional features corresponding to the current input conditions and are updated as the input conditions change, so as to characterize the long-term thermal inertia differences under different current, ambient temperature and heat transfer conditions. A modal decomposition-based KAN output layer is set at the output end, and corresponding spline mapping branches are set for different orders of POD modes; for the th... i The predicted values ​​of the order POD mode coefficients are as follows:

[0112] in,B p For the first p indivual B spline basis functions; c i,l,p For the first i Trainable spline control coefficients corresponding to the order POD mode; b i For the first i Bias terms corresponding to the first-order POD mode; d f For thermal dynamics features; R b for B Number of spline basis functions; f l,q Thermal dynamic feature vector f q The l One element; By combining the predicted POD mode coefficients of different orders from the outputs of different mapping branches, the POD mode coefficient vector at the current time step is obtained:

[0113] The overall mapping relationship of the POD-SSKAN proxy model is as follows:

[0114] in, All the parameters to be trained for the POD-SSKAN surrogate model; The predicted temperature field is reconstructed based on the POD modal coefficients and POD principal mode matrix obtained by the POD-SSKAN surrogate model. The heat conduction residual, boundary heat transfer residual and measurement point consistency residual are calculated on the reconstructed temperature field to inversely constrain the POD modal coefficient prediction model through thermal constraints at the temperature field level. Define the modal coefficient prediction loss L a :

[0115] in, N b For training batch size; These are the modal coefficients obtained from POD projection; The modal coefficients predicted by the surrogate model; The predicted temperature field is obtained based on the POD reconstruction relationship:

[0116] The predicted node temperature vector Predicted temperature field function formed by spatial interpolation Substitute the heat conduction control equations into the heat conduction residuals and construct them. r heat,q :

[0117] in, ρ The equivalent density of the battery material; c p This refers to the equivalent isobaric specific heat capacity of the battery material. For predicting the time partial derivative of the temperature field; λ Thermal conductivity; For the first q Battery heat generation rate corresponding to each time sampling point; Corresponding thermal conduction constraint loss L heat for:

[0118] Construct boundary heat transfer residuals on the convective heat transfer boundary of the battery surface. r bc,q for:

[0119] in, Boundary heat flux density; For convective heat transfer heat flux density; Corresponding boundary heat transfer constraint loss L bc for:

[0120] To suppress non-physical oscillations in the predicted mode coefficient time series, a mode time increment consistency loss is introduced. L smooth :

[0121] in, To predict the time increment of the modal coefficients; This represents the time increment of the true modal coefficients; Normalization factor; If sparse temperature data exists, let H Select a matrix for the measurement points. y q For the first q The temperature vector corresponding to each time sampling point is then the measurement point consistency loss. L sen for:

[0122] Constructing a joint loss function constrained by thermal knowledgeL :

[0123] in, ω 1 represents the thermal conduction constraint weight; ω 2 represents the boundary heat transfer constraint weight; ω 3 represents the modal time increment consistency constraint weight; ω 4 represents the consistency weight of the measurement points; The source domain training dataset is composed of the input variables and POD mode coefficients corresponding to the selected simulation samples. D s :

[0124] During training, the loss is first predicted using modal coefficients. L a The POD-SSKAN surrogate model is pre-trained to learn the basic mapping relationship between the input operating conditions and the POD modal coefficients; then, heat conduction constraint loss based on the reconstructed temperature field is gradually introduced. L heat Boundary heat transfer constraint loss L bc And modal time increment consistency loss L smooth This allows thermal constraints to act inversely on the POD modal coefficient prediction model through temperature field reconstruction; and a measurement point consistency loss is added when measurement point data is available. L sen Improve the model's ability to calibrate for experimental data; After training, the source domain POD-SSKAN surrogate model is obtained:

[0125] in, These are the parameters of the POD-SSKAN surrogate model trained in the source domain.

[0126] S4. Based on the local modal priors and modal time continuity obtained from sparse measurement point temperatures and optimized sample retrieval, the experimental domain modal coefficients are inverted; virtual samples are generated near the experimental domain modal coefficients, and after being screened for measurement point consistency, thermal laws, and safe temperature range, an enhanced experimental domain dataset is constructed.

[0127] Initial modal coefficients are obtained by introducing a knowledge-constrained prior inversion model that integrates measurement point consistency, prior knowledge, and time smoothness, and virtual samples that meet thermal and safety constraints are generated to construct an experimental domain augmentation dataset.

[0128] This step specifically includes: During experiments, temperature sensors are typically placed in only a few locations, such as the battery tabs, the center of the surface, or the sides. A modal coefficient dataset for the experimental domain is constructed using the sparse measurement point temperature information, and the measurement point observation subspace matrix Φ is used. H for:

[0129] For the q At each experimental sampling time, the average temperature at the measuring points is assumed to be... Then the temperature fluctuation vector at the measuring point for:

[0130] The observation equation for sparse measuring points is:

[0131] in, ε q For measuring noise.

[0132] To improve the stability of modal coefficient inversion when the number of measurement points is insufficient, a knowledge-constrained prior inversion model is introduced:

[0133] in, These are the initial inversion mode coefficients; W s This is the confidence weight matrix for the measurement points; W p This is the prior accuracy matrix; μ q The mean of local modes is obtained from the preferred sample library; λ p For prior regularization weights; λ d Time-smoothing regularization weights; These are the inversion mode coefficients from the previous time step; These are candidate modal coefficients.

[0134] To increase the number of samples in the experimental domain, virtual candidate mode samples are generated near the initial inversion mode coefficients:

[0135] in, L q It is the local covariance decomposition matrix; ξ l It is a standard normal random vector; I k for k An identity matrix of order 1.

[0136] Reconstruct the virtual modal coefficients into a virtual temperature field:

[0137] Virtual samples must simultaneously meet the constraints of measurement point consistency, thermal conduction residual, and safe temperature range:

[0138] in, δ s This is the tolerance threshold for measurement point error; δ h This represents the tolerance threshold for thermal conduction residuals.

[0139] The experimental domain augmentation dataset is composed of real experimental inversion samples and virtual samples that satisfy the constraints. : .

[0140] S5. Freeze the backbone network parameters of the source domain proxy model and update some spline control parameters, experimental domain bias parameters and residual adapter parameters of the KAN output layer to correct the deviation between the simulation domain and the experimental domain.

[0141] This step specifically includes: The source domain POD-SSKAN surrogate model was used as the initial model for experimental domain calibration. To reduce the risk of overfitting under small sample conditions, the main parameters of the input embedding layer, multi-scale causal convolutional layer, and selective state space layer are kept unchanged, and only the spline control coefficients, domain bias vector, and lightweight residual adapter parameters of the KAN output layer are updated.

[0142] The predicted modal coefficients after experimental domain calibration are expressed as follows:

[0143] in, G ψ As a lightweight residual adapter, the inputs include operating condition variables and sparse measurement point residuals, and the output is the experimental domain deviation correction amount, which is used to output the POD modal coefficient correction amount based on the operating condition variables and sparse measurement point temperature residuals.

[0144] Experimental domain calibration loss function L cal for:

[0145] in, ψ These are the parameters for the residual adapter; Lsen For measurement point consistency loss; Δ C KAN This represents the change in the control coefficient of the KAN spline; κ 1 represents the thermal conduction constraint weighting coefficient; κ 2 represents the boundary heat transfer constraint weighting coefficient; κ 3 represents the regularization weighting coefficients for the residual adapter parameters; κ 4 represents the regularization weighting coefficient for the change in the KAN control coefficient.

[0146] S6. Predict the modal coefficients under the test conditions and reconstruct the overall temperature using the calibrated POD-SSKAN surrogate model; if there are real-time sparse measurement point temperatures, use the residual adapter to fuse the real-time measurement point data for online correction.

[0147] This step specifically includes: For the new operating condition to be predicted, obtain its real-time input variables. z new The POD modal coefficients are then fed into the experimental domain-calibrated POD-SSKAN surrogate model to obtain the predicted values ​​of the POD modal coefficients.

[0148] in, These are the model parameters after calibration in the experimental domain.

[0149] Reconstructing the full-field temperature based on the POD principal mode matrix:

[0150] in, These are the predicted values ​​for the POD modal coefficients.

[0151] If there are real-time sparse temperature measurement points during the online phase y new Then, online correction is performed using a residual adapter:

[0152] The final online temperature field is obtained:

[0153] In the online phase, there is no need to resolve the high-fidelity full-order simulation model. Only low-dimensional modal coefficient prediction and POD linear reconstruction are required to quickly obtain the full-field temperature distribution of the lithium-ion battery.

[0154] The computational efficiency and accuracy of the method proposed in this invention are as follows: (1) Computational efficiency analysis: In terms of computational efficiency, this paper compares FOM (full-order model), DNN (deep neural network), POD-DNN (intrinsic orthogonal decomposition-deep neural network), POD-LSTM (intrinsic orthogonal decomposition-long short-term memory network), POD-SSKAN (intrinsic orthogonal decomposition-selective state space KAN network), and POD-SSKAN with online correction of residual adapter. The time consumption of each method for calculating the target working condition at each stage is shown in Table 1.

[0155] Table 1 compares the time taken to solve the temperature field of a lithium battery under a set of operating conditions using different methods.

[0156] As shown in Table 1, FOM requires repeated solving of high-dimensional electrochemical-thermal coupling control equations in the online phase, with a single set of operating conditions taking up to 283 seconds, which is insufficient to meet the real-time temperature field update requirements. Although DNN reduces the online computation time to 1.68 seconds, its training time is relatively long, and the DNN in this embodiment does not incorporate the POD spatial basis, so it can only obtain a limited temperature response and cannot directly complete the rapid reconstruction of the full-field temperature distribution of the lithium-ion battery. POD-DNN and POD-LSTM have the ability to reconstruct the full-field temperature by introducing POD order reduction, but their model training and online computation time are still relatively high. POD-SSKAN also requires the construction of a high-fidelity dataset, POD decomposition, and surrogate model training in the offline phase, which has a certain offline computation cost, but its model training time is lower than that of DNN, POD-DNN, and POD-LSTM, and its online computation time is only 0.013 seconds. After incorporating the residual adapter, the offline dataset construction time and model training time increase due to the need for experimental domain data construction, parameter calibration, online measurement point residual calculation, and modal coefficient correction. The online computation time increases slightly to 0.017 s, but is still significantly lower than other comparative methods. Therefore, this invention concentrates the computational load in the offline stage, maintaining the ability to rapidly reconstruct and correct the full-field temperature while meeting the computational efficiency requirements for high-frequency updates of the lithium-ion battery temperature field.

[0157] (2) Calculation accuracy analysis: To evaluate the experimental domain calibration effect of the POD-SSKAN surrogate model and the effectiveness of the online correction method for the residual adapter, this embodiment selects typical charge and discharge conditions for temperature prediction curve comparison and sets up 6 sets of test conditions to conduct error verification.

[0158] The comparison results of experimentally measured temperature, POD-SSKAN predicted temperature before calibration, and POD-SSKAN predicted temperature after experimental domain calibration are as follows: Figure 9 As shown.

[0159] Depend on Figure 9It can be seen that there was a significant systematic deviation between the POD-SSKAN predicted temperature and the experimentally measured temperature before calibration. After calibration using experimental domain data, the model's predicted curve is much closer to the experimentally measured curve, enabling it to more accurately track the temperature change trends during the charging and discharging phases. Figure 9 The overall prediction bias of the charging stage shown in (a) is significantly reduced; Figure 9 The temperature changes in the early and middle stages of the discharge phase and the rapid temperature rise trend at the end, as shown in (b), were also well corrected, indicating that experimental domain calibration can effectively reduce the temperature response deviation between the simulation domain and the experimental domain.

[0160] Table 2 shows the error statistics between the online prediction results of POD-SSKAN and the prediction results after online correction by the residual adapter: Table 2 Comparison of error indices after POD-SSKAN online prediction and residual adapter online correction under six test conditions.

[0161] Table 2 shows that after online correction using the residual adapter, both MAPE and RMSE decreased overall under all six test conditions. The average MAPE of the POD-SSKAN online prediction decreased from 3.40% to 2.10%, and the average RMSE decreased from 0.832 ℃ to 0.545 ℃, with an average error reduction rate of approximately 35.28% across the six conditions. Condition 3 showed the highest error reduction rate at 47.06%; the error reduction rates for the other conditions ranged from 26.50% to 37.62%. The results indicate that the residual adapter can utilize the residual between the real-time sparse measurement point temperature and the corresponding predicted temperature to correct the POD modal coefficients online, thereby reducing the deviation between the online prediction results and the actual temperature response and improving the accuracy of temperature field reconstruction under different operating conditions. This result is consistent with the overall trend in related rapid temperature field prediction studies of reducing model prediction errors through experimental domain calibration.

[0162] Comparison of time-varying errors (MAPE and RMSE) of POD-SSKAN and residual adapter after online correction under different test conditions. Figures 10 to 15 As shown.

[0163] Depend on Figure 10It can be seen that, under operating condition 1, after online correction by the residual adapter, the MAPE and RMSE were lower than the POD-SSKAN online prediction results for most of the charging phase. The maximum MAPE decreased from 4.80% to 3.12%, and the maximum RMSE decreased from 0.51 ℃ to 0.36 ℃. During the discharging phase, the error reduction was more significant in the early and middle stages, but the errors of both methods rebounded during the rapid temperature change phase at the end, with the maximum MAPE and maximum RMSE only decreasing slightly. This indicates that there is still room for further optimization during the phase with a large temperature change rate.

[0164] Depend on Figure 11 It can be seen that under operating condition 2, the MAPE and RMSE after correction by the residual adapter during the charging phase are generally lower than the online prediction results. The maximum MAPE decreases from 10.69% to 8.10%, and the maximum RMSE decreases from 1.86 ℃ to 1.41 ℃. The error is significantly suppressed in the early stage of the discharging phase, but during the rapid temperature rise at the end of the discharge, the corrected error shows a local rebound, and the maximum error at certain moments is not reduced. This indicates that the residual adapter can improve the prediction results for most operating phases, but the constraint on the modal coefficient correction amount still needs to be further strengthened during periods of sudden changes in operating conditions or drastic temperature changes.

[0165] Depend on Figure 12 It can be seen that under operating condition 3, the residual adapter's online correction achieved a significant error suppression effect. During the charging phase, the maximum MAPE decreased from 4.21% to 2.24%, and the maximum RMSE decreased from 1.04 ℃ to 0.64 ℃; during the discharging phase, the maximum MAPE decreased from 5.92% to 1.34%, and the maximum RMSE decreased from 1.48 ℃ to 0.39 ℃. The corrected error curve was more stable throughout the entire operation, indicating that the residual adapter could effectively correct the systematic prediction bias under this operating condition.

[0166] Depend on Figure 13 It can be seen that, under operating condition 4, the errors in both the charging and discharging stages are significantly reduced after online correction. During the charging stage, the maximum MAPE decreases from 4.46% to 2.47%, and the maximum RMSE decreases from 1.16 ℃ to 0.71 ℃; during the discharging stage, the maximum MAPE decreases from 7.44% to 2.72%, and the maximum RMSE decreases from 2.15 ℃ to 0.86 ℃. Particularly at the end of the discharge, the uncorrected prediction error increases rapidly, while the error corrected by the residual adapter remains at a relatively low level, indicating that this method can suppress error accumulation during periods of rapid temperature change.

[0167] Depend on Figure 14It can be seen that, under operating condition 5, the error curve of the residual adapter after online correction is generally lower than the online prediction error of POD-SSKAN. During the charging phase, the maximum MAPE decreased from 3.10% to 1.69%, and the maximum RMSE decreased from 1.24 ℃ to 0.73 ℃; during the discharging phase, the maximum MAPE decreased from 4.01% to 0.94%, and the maximum RMSE decreased from 1.63 ℃ to 0.45 ℃. The corrected MAPE and RMSE remained stable for most of the time, indicating that the residual adapter has a good ability to correct prediction deviations under medium-to-high ambient temperature conditions.

[0168] Depend on Figure 15 It can be seen that under operating condition 6, the maximum MAPE during the charging phase decreased from 2.16% to 1.67%, and the maximum RMSE decreased from 1.00 ℃ to 0.80 ℃; during the discharging phase, the maximum MAPE decreased from 6.16% to 1.42%, and the maximum RMSE decreased from 2.61 ℃ to 0.65 ℃. Especially at the end of the discharge, the uncorrected online prediction error increased significantly, while the error corrected by the residual adapter did not increase synchronously, indicating that the real-time measurement point residual can effectively correct the shift of the POD modal coefficients during operation and improve the stability of the online temperature field reconstruction.

[0169] Combined Table 2 and Figures 10 to 15 It can be seen that the residual adapter online correction method can reduce MAPE and RMSE in most test conditions and operation stages, and the improvement is more significant at the discharge end, the rapid temperature change stage, and the condition with obvious system deviation. Although there is still error rebound at some local moments in individual conditions, the average evaluation results of the six groups of conditions show that the prediction error after online correction is reduced by about 35.28% overall, indicating that the residual adapter can effectively improve the accuracy of online temperature prediction and full-field temperature reconstruction of the POD-SSKAN surrogate model under complex conditions.

[0170] like Figure 2 As shown, the knowledge-constrained optimal samples are distributed in a three-dimensional operating condition parameter space consisting of charging and discharging current, ambient temperature, and heat transfer coefficient. This can cover different parameter ranges and boundary conditions, providing representative operating condition samples for subsequent high-fidelity electrochemical-thermal coupling simulation, POD mode extraction, and POD-SSKAN surrogate model training.

[0171] Depend on Figures 3 to 7 It can be seen that the first order ( α 1) and the second order ( α 2) The predicted results of the POD modal coefficients generally agree well with the reference modal coefficients, and the POD-SSKAN surrogate model can accurately capture their main changing trends during the charge and discharge process. In contrast, the third to fifth order ( α 3. α 4.α 5) The POD mode coefficients are characterized by small amplitude and high fluctuation frequency. Their time evolution does not show a stable and clear change pattern, so there is a certain deviation between the prediction results and the reference results. However, the energy proportion of the third to fifth POD modes is relatively low, and their contribution to the overall temperature reconstruction results is relatively limited. Therefore, their prediction deviation has little impact on the accuracy of the final reconstructed temperature field.

[0172] Depend on Figure 8 It can be seen that the unconstrained least squares inversion results exhibit significant amplitude distortion, high-frequency oscillations, and local abrupt changes, especially for the fourth order with smaller amplitudes. α 4) The POD modal coefficients show a significant order-of-magnitude deviation from the POD-SSKAN prediction results. In contrast, the knowledge-constrained prior inversion, by fusing local modal priors obtained from optimized sample retrieval, measurement point confidence, and modal time continuity constraints, makes the inverted modal coefficients closer to the POD-SSKAN model prediction results in both variation trend and numerical magnitude. The experimental domain modal coefficients obtained in this way can be limited to a reasonable modal space range, avoiding excessive modal coefficient correction amounts when used for model calibration or online correction, thus reducing excessive perturbation to the initial POD-SSKAN prediction results. Simultaneously, online correction mainly affects the POD modal coefficients and residual adapter output, without directly changing the POD-SSKAN backbone network parameters, which helps maintain the learned operating condition-modal mapping relationship and temperature field spatial characteristics of the source domain model.

Claims

1. A fast calculation method for the temperature field of a lithium-ion battery based on knowledge-constrained sample optimization and the POD-SSKAN surrogate model, characterized in that: Includes the following steps: S1. Construct a parameter space for thermal simulation of lithium-ion batteries, and obtain knowledge-constrained optimal samples based on the rationality of heat generation, consistency of boundary heat transfer, safe temperature range, temperature sensitivity, POD mode uncertainty and importance of boundary conditions. S2. Based on the preferred samples, run a high-fidelity electrochemical-thermal coupling simulation model to obtain a snapshot of the temperature field, and obtain the POD principal mode and corresponding modal coefficients through POD order reduction; S3. Construct a POD-SSKAN surrogate model including a multi-scale causal convolutional layer, a selective state space layer, and a mode decomposition-based KAN output layer to predict the POD mode coefficients of each order and complete the temperature field reconstruction; train the POD-SSKAN surrogate model based on the thermal constraints of the reconstruction results to obtain the source domain surrogate model; S4. Based on the local modal priors and modal time continuity obtained from sparse measurement point temperatures and optimized sample retrieval, the experimental domain modal coefficients are inverted; virtual samples are generated near the experimental domain modal coefficients, and after being screened for measurement point consistency, thermal laws, and safe temperature range, an enhanced experimental domain dataset is constructed. S5. Freeze the backbone network parameters of the source domain proxy model and update some spline control parameters, experimental domain bias parameters and residual adapter parameters of the KAN output layer to correct the deviation between the simulation domain and the experimental domain. S6. Predict the modal coefficients under the test conditions and reconstruct the overall temperature using the calibrated POD-SSKAN surrogate model; if there are real-time sparse measurement point temperatures, use the residual adapter to fuse the real-time measurement point data for online correction.

2. The method for rapid calculation of lithium-ion battery temperature field based on knowledge-constrained optimal samples and POD-SSKAN surrogate model according to claim 1, characterized in that: Step S1 specifically includes: Selecting the charging and discharging current I Ambient temperature T ext Heat transfer coefficient h Define the operating condition vector as a parameter for thermal simulation. u for: Let the operating parameter space Ω be: in, I min and I max These are the set minimum and maximum current values, respectively. T min and T max These are the set minimum and maximum ambient temperatures, respectively. h min and h max These are the set minimum and maximum values ​​of the heat transfer coefficient, respectively. Generate a candidate sample pool within the operating parameter space Ω C : in, N c The total number of candidate samples; u j For the first j One candidate sample; Imposing thermal knowledge constraints on candidate samples, including: First, a reasonable constraint on heat generation is imposed on the candidate samples to ensure that the total heat generation rate of the battery meets the preset allowable range: in, For battery heat generation rate; U ocv This is the open-circuit voltage; U Terminal voltage; T The battery represents temperature. ε heat To allow for error tolerance; Secondly, a uniform constraint is applied to the convective heat transfer boundary on the battery surface: in, λ is the thermal conductivity; n is the outward normal vector. For temperature gradient; Secondly, impose a safe temperature range constraint on the candidate operating conditions: in, T min,safe and T max,safe These are the preset lower and upper safe temperature limits, respectively; Let be the temperature field distribution function, representing the temperature field distribution under operating conditions. u j Below, position x At the moment t Temperature value; Normalize the parameters of each operating condition for the candidate samples: in, d The dimension of the operating condition parameters; u j,l For the first j In the candidate samples, the first l One operating condition parameter; u l,min and u l,max The first l Minimum and maximum values ​​of operating parameters; These are the normalized operating parameters; Select at least one initial sample from the candidate samples that meet the above thermal and safety constraints to form the selected sample set. S Calculate the working space coverage of the candidate sample relative to the selected sample set. : in, and Candidate samples u j and selected samples u i The corresponding normalized process condition vector; Using a low-fidelity coarse-grid model obtained by spatial mesh coarsening of a high-fidelity electrochemical-thermal coupling simulation model, the temperature response of candidate samples is calculated, and the characteristic temperature rise of candidate samples is defined. for: in, T L ( x , t ; u j Candidate samples obtained from low-fidelity coarse-grid model calculations. u j In position x ,time t Temperature; T ext,j Candidate samples u j The corresponding ambient temperature is also used as the initial temperature of the battery under this candidate operating condition; Temperature sensitivity is calculated based on the rate of change of characteristic temperature rise relative to various operating parameters: Normalize the temperature sensitivity: in, For the first l The disturbance step size of each operating parameter; e l For the first l Unit vectors in the direction of each working condition parameter; g T,min and g T,max These represent the minimum and maximum values ​​of temperature sensitivity in the candidate sample set, respectively. ε To prevent the use of pre-defined positive numbers with a denominator of zero; Based on the selected sample set S The corresponding low-fidelity coarse-grid temperature response snapshots are used to construct a temporary POD mode matrix, and the POD mode uncertainty of the candidate samples relative to the current POD mode space is calculated: in, Candidate samples obtained from low-fidelity coarse mesh model u j The pulsating temperature snapshot matrix; To construct the frontier based on the currently selected sample set k Temporary POD mode matrix; It is the Frobenius norm; The importance of the boundary conditions is calculated based on how closely the normalized working condition parameters in the candidate samples approach the parameter space boundary. Calculate the optimal score for candidate samples that meet the above constraints. S ( u j ): in, α , β , γ and δ The weights for operating condition space coverage, temperature sensitivity, POD modal uncertainty, and boundary condition importance are respectively, and satisfy the following: Select the candidate sample with the highest evaluation score from the unselected candidate samples: And update the selected sample set: After each new preferred sample is added, a temporary POD mode matrix is ​​reconstructed based on the updated selected sample set, and the operating condition space coverage and POD mode uncertainty of the remaining candidate samples are recalculated. The process of candidate sample scoring, selection, and POD mode space updating is repeated until the number of selected samples reaches a preset number. N We obtain the knowledge-constrained optimal sample set: 。 3. The method for rapid calculation of lithium-ion battery temperature field based on knowledge-constrained optimal samples and POD-SSKAN surrogate model according to claim 2, characterized in that: Step S2 specifically includes: The preferred samples obtained in step S1 are input into the high-fidelity electrochemical-thermal coupling simulation model to obtain the full-field temperature vector at different time sampling points for each preferred operating condition. The full-field temperature vectors are then arranged in columns to construct a temperature field snapshot matrix. X ; Calculate the nodal mean vector of the temperature field snapshot matrix. The mean was removed from each temperature field snapshot to obtain the pulsating snapshot matrix. : in, For the first j A snapshot vector of the temperature field; This is the nodal mean vector of a snapshot of the entire temperature field. n This represents the total number of temperature field snapshots. Construct a correlation matrix based on the pulse snapshot matrix. R And perform eigenvalue decomposition on the correlation matrix: in, The eigenvector matrix, v i For the correlation matrix R Corresponding to the i Eigenvectors with eigenvalues; For the eigenvalue matrix, λ i For the eigenvector v i The corresponding eigenvalues; RV = VΛ Represents the correlation matrix R The eigenvalue decomposition relationship is given, and the eigenvalues ​​are arranged in descending order. Construct the POD mode matrix based on the eigenvectors and corresponding eigenvalues, and then... k The cutoff order is determined by the cumulative energy percentage of the first-order POD mode, whereby the cumulative energy percentage is: The minimum order at which the cumulative energy percentage reaches the preset energy threshold is selected as the cutoff order. k , cut off k The POD principal mode matrix Φ is composed of the first-order POD modes. k ; Projecting the pulsation snapshot matrix onto the POD principal modal space yields the modal coefficient matrix: in, A k This is the modal coefficient matrix corresponding to each temperature field snapshot; Any temperature field snapshot is reconstructed based on the nodal mean vector, the POD principal mode matrix, and the corresponding mode coefficient vector: in, a j For the first j The modal coefficient vector corresponding to each temperature field snapshot; For the first j The POD corresponding to each temperature field snapshot reconstructs the full-field temperature vector.

4. The method for rapid calculation of lithium-ion battery temperature field based on knowledge-constrained optimal samples and POD-SSKAN surrogate model according to claim 3, characterized in that: Step S3 specifically includes: For the q Each time sampling point will be used to input the operating condition variables and time variables into the model. z q : in, I q For the first q The charging and discharging current corresponding to each time sampling point; T ext,q For the first q The ambient temperature corresponding to each time sampling point; h conv,q For the first q The heat transfer coefficient corresponding to each time sampling point; t q For the current moment; Δ t q For time step; The model input is standardized and mapped to a high-dimensional feature space: in, W e and b e These are the weight matrix and bias term of the input embedding layer, respectively; Multi-scale causal convolution features are constructed based on causal convolution branches with different receptive fields. g q : in, R c For the set of convolutional receptive fields; τ This is the kernel offset; e q-τ:q For historical embedding feature sequences; Conv τ This represents the causal convolution operation within the corresponding receptive field; W τ and b τ These are the kernel weights and convolutional bias terms corresponding to the receptive field; The multi-scale causal convolutional features are input into a selective state space layer, and then generated by the parameter generation network Γ. θ Adaptively generate state-space parameters based on the current input conditions: in, This is the discretized state transition matrix; The input control matrix is ​​discretized; To output the mapping matrix; For direct connection matrix; Update implied thermal state ξ q and output thermal dynamic characteristics. f q : in, ξ q and ξ q-1 These are the implied thermal states at the current moment and the previous moment, respectively; f q The state space parameters are adaptively generated based on the multi-scale causal convolutional features corresponding to the current input conditions and are updated as the input conditions change, so as to characterize the long-term thermal inertia differences under different current, ambient temperature and heat transfer conditions. A modal decomposition-based KAN output layer is set at the output end, and corresponding spline mapping branches are set for different orders of POD modes; for the th... i The predicted values ​​of the order POD mode coefficients are as follows: in, B p For the first p indivual B spline basis functions; c i,l,p For the first i Trainable spline control coefficients corresponding to the order POD mode; b i For the first i Bias terms corresponding to the first-order POD mode; d f For thermal dynamics features; R b for B Number of spline basis functions; f l,q Thermal dynamic feature vector f q The l One element; By combining the predicted POD mode coefficients of different orders from the outputs of different mapping branches, the POD mode coefficient vector at the current time step is obtained: The overall mapping relationship of the POD-SSKAN proxy model is as follows: in, All the parameters to be trained for the POD-SSKAN surrogate model; The predicted temperature field is reconstructed based on the POD modal coefficients and POD principal mode matrix obtained by the POD-SSKAN surrogate model. The heat conduction residual, boundary heat transfer residual and measurement point consistency residual are calculated on the reconstructed temperature field to inversely constrain the POD modal coefficient prediction model through thermal constraints at the temperature field level. Define the modal coefficient prediction loss L a : in, N b For training batch size; These are the modal coefficients obtained from POD projection; The modal coefficients predicted by the surrogate model; The predicted temperature field is obtained based on the POD reconstruction relationship: The predicted node temperature vector Predicted temperature field function formed by spatial interpolation Substitute the heat conduction control equations into the heat conduction residuals and construct them. r heat,q : in, ρ The equivalent density of the battery material; c p This refers to the equivalent isobaric specific heat capacity of the battery material. For predicting the time partial derivative of the temperature field; λ Thermal conductivity; For the first q Battery heat generation rate corresponding to each time sampling point; Corresponding thermal conduction constraint loss L heat for: Construct boundary heat transfer residuals on the convective heat transfer boundary of the battery surface. r bc,q for: in, Boundary heat flux density; For convective heat transfer heat flux density; Corresponding boundary heat transfer constraint loss L bc for: Introducing modal time increment consistency loss L smooth : in, To predict the time increment of the modal coefficients; This represents the time increment of the true modal coefficients; Normalization factor; If sparse temperature data exists, let H Select a matrix for the measurement points. y q For the first q The temperature vector corresponding to each time sampling point is then the measurement point consistency loss. L sen for: Constructing a joint loss function constrained by thermal knowledge L : in, ω 1 represents the thermal conduction constraint weight; ω 2 represents the boundary heat transfer constraint weight; ω 3 represents the modal time increment consistency constraint weight; ω 4 represents the consistency weight of the measurement points; The source domain training dataset is composed of the input variables and POD mode coefficients corresponding to the selected simulation samples. D s : During training, the loss is first predicted using modal coefficients. L a The POD-SSKAN surrogate model is pre-trained to learn the basic mapping relationship between the input operating conditions and the POD modal coefficients; then, heat conduction constraint loss based on the reconstructed temperature field is gradually introduced. L heat Boundary heat transfer constraint loss L bc And modal time increment consistency loss L smooth This allows thermal constraints to act inversely on the POD modal coefficient prediction model through temperature field reconstruction; and a measurement point consistency loss is added when measurement point data is available. L sen Improve the model's ability to calibrate for experimental data; After training, the source domain POD-SSKAN surrogate model is obtained: in, These are the parameters of the POD-SSKAN surrogate model trained in the source domain.

5. The method for rapid calculation of lithium-ion battery temperature field based on knowledge-constrained optimal samples and POD-SSKAN surrogate model according to claim 4, characterized in that: Step S4 specifically includes: A modal coefficient dataset for the experimental domain is constructed using sparse measurement point temperature information, and the measurement point observation subspace matrix Φ is used. H for: For the q At each experimental sampling time, the average temperature at the measuring points is assumed to be... Then the temperature fluctuation vector at the measuring point for: The observation equation for sparse measuring points is: in, ε q For measuring noise; To improve the stability of modal coefficient inversion when the number of measurement points is insufficient, a knowledge-constrained prior inversion model is introduced: in, These are the initial inversion mode coefficients; W s This is the confidence weight matrix for the measurement points; W p This is the prior accuracy matrix; μ q The mean of local modes is obtained from the preferred sample library; λ p For prior regularization weights; λ d For time-smoothing regularization weights; These are the inversion mode coefficients from the previous time step; These are candidate modal coefficients; To increase the number of samples in the experimental domain, virtual candidate mode samples are generated near the initial inversion mode coefficients: in, L q It is the local covariance decomposition matrix; ξ l It is a standard normal random vector; I k for k An identity matrix of order 1; Reconstruct the virtual modal coefficients into a virtual temperature field: Virtual samples must simultaneously meet the constraints of measurement point consistency, thermal conduction residual, and safe temperature range: in, δ s This is the tolerance threshold for measurement point errors; δ h This represents the tolerance threshold for thermal conductivity residuals. The experimental domain augmentation dataset is composed of real experimental inversion samples and virtual samples that satisfy the constraints. : 。 6. The method for rapid calculation of lithium-ion battery temperature field based on knowledge-constrained optimal samples and POD-SSKAN surrogate model according to claim 5, characterized in that: Step S5 specifically includes: The source domain POD-SSKAN surrogate model was used as the initial model for experimental domain calibration. To reduce the risk of overfitting under small sample conditions, the main parameters of the input embedding layer, multi-scale causal convolutional layer and selective state space layer are kept unchanged, and only some spline control coefficients, domain bias vectors and lightweight residual adapter parameters of the KAN output layer are updated. The predicted modal coefficients after experimental domain calibration are expressed as follows: in, G ψ For lightweight residual adapters; Experimental domain calibration loss function L cal for: in, ψ These are the parameters for the residual adapter; L sen For measurement point consistency loss; Δ C KAN This represents the change in the control coefficient of the KAN spline; κ 1 represents the thermal conduction constraint weighting coefficient; κ 2 represents the boundary heat transfer constraint weighting coefficient; κ 3 represents the regularization weighting coefficients for the residual adapter parameters; κ 4 represents the regularization weighting coefficient for the change in the KAN control coefficient.

7. The method for rapid calculation of lithium-ion battery temperature field based on knowledge-constrained optimal samples and POD-SSKAN surrogate model according to claim 6, characterized in that: Step S6 specifically includes: For the new operating condition to be predicted, obtain its real-time input variables. z new The POD modal coefficients are then fed into the experimental domain-calibrated POD-SSKAN surrogate model to obtain the predicted values ​​of the POD modal coefficients. in, These are the model parameters after calibration in the experimental domain; Reconstructing the full-field temperature based on the POD principal mode matrix: in, These are the predicted values ​​of the POD modal coefficients; If there are real-time sparse temperature measurement points during the online phase y new Then, online correction is performed using a residual adapter: The final online temperature field is obtained: 。

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