A Battery Pack Damage Prediction Method Based on Location Value Cost-Aware Adaptive Sampling Multifidelity Gaussian Process

Abstract

This invention discloses a battery pack damage prediction method based on a location value cost-aware adaptive sampling multi-fidelity Gaussian process, belonging to the technical field of electric vehicle power battery pack collision safety assessment. The method includes: S1, constructing an integrated nested multi-fidelity Gaussian process model, containing single-layer and double-layer nested sub-models, and outputting the predicted mean and variance through inverse variance weighted fusion; S2, calculating the location value of candidate points based on the predicted variance; S3, fusing location value, sampling cost, and expected improvement to construct an LC-MF-EI acquisition function; S4, selecting the candidate point with the largest acquisition function and the fidelity level for finite element simulation, and updating the model; S5, iterating until the accuracy meets the requirements. This invention, using the above method, significantly reduces the demand for high-fidelity samples while ensuring prediction accuracy, improving sampling efficiency and model robustness, and providing a low-cost, high-precision solution for battery pack collision damage prediction.

Description

Technical Field

[0001] This invention relates to the field of collision safety assessment technology for electric vehicle power battery packs, and in particular to a battery pack damage prediction method based on a location value cost-aware adaptive sampling multi-fidelity Gaussian process. Background Technology

[0002] With the rapid development of the new energy vehicle industry, the power battery pack, as the core energy storage unit of electric vehicles, directly affects the overall vehicle safety performance through its collision safety. During the battery pack structure optimization design process, it is necessary to repeatedly predict the damage response (such as maximum intrusion, stress, and strain) under different collision conditions. While traditional finite element simulation methods offer high accuracy, they suffer from high computational costs, complex modeling processes, and difficulty in meeting the demands of rapid design iteration.

[0003] In recent years, the combination of machine learning surrogate models and finite element simulation has become a research hotspot. Among them, multi-fidelity data fusion technology, by integrating a small number of high-cost, high-fidelity samples with a large number of low-cost, low-fidelity samples, can reduce modeling costs while maintaining prediction accuracy. Gaussian process regression, with its inherent ability to quantify uncertainty, has been widely used in multi-fidelity surrogate modeling.

[0004] However, existing technologies still have the following shortcomings: (1) Most multi-fidelity fusion methods assume that there is a linear correlation between high-fidelity and low-fidelity data. For example, the co-kriging method based on the Kennedy-O'Hagan framework is difficult to accurately capture the complex nonlinear mapping between high-fidelity and low-fidelity data in actual engineering, which leads to limited model accuracy.

[0005] (2) Existing adaptive sampling methods are mainly designed for single-fidelity scenarios. When extended to multi-fidelity scenarios, it is necessary to decide on the sampling location and fidelity level at the same time. Existing acquisition functions often only consider a simple weighted sum of the expected improvement and the sampling cost, ignoring the positional value of different candidate points—that is, the degree to which sampling at that point contributes to the overall accuracy improvement of the model. This leads to the sampling resources being concentrated in local areas, with insufficient sampling in high uncertainty areas, thus reducing sampling efficiency.

[0006] (3) Single multifidelity models are sensitive to the distribution of training samples, lack robustness, and the estimation of prediction uncertainty is not accurate enough, making it difficult to guide efficient adaptive sampling.

[0007] Therefore, there is an urgent need for a battery pack collision damage prediction method that can adaptively sense location value and sampling cost, fuse nonlinear multi-fidelity data, and has high robustness, in order to reduce modeling costs and improve prediction accuracy and efficiency. Summary of the Invention

[0008] The purpose of this invention is to provide a battery pack damage prediction method based on a location value cost-aware adaptive sampling multi-fidelity Gaussian process, aiming to build a high-precision surrogate model with the lowest overall sampling cost and achieve rapid and accurate prediction of battery pack collision damage.

[0009] To achieve the above objectives, this invention provides a battery pack damage prediction method based on a location value cost-aware adaptive sampling multi-fidelity Gaussian process, comprising the following steps: S1. Constructing the initial prediction model: Obtain a multi-fidelity training dataset containing high-fidelity samples and low-fidelity samples; Based on the multi-fidelity training dataset, construct an ensemble nested multi-fidelity Gaussian process model; The ensemble nested multi-fidelity Gaussian process model includes at least one single-layer nested Gaussian process sub-model and at least one double-layer nested Gaussian process sub-model, and fuses the prediction results of each sub-model through an inverse variance weighting strategy, outputting the prediction mean and prediction variance of each candidate point, where the candidate point is the location to be predicted in the design space; S2. Calculate the location value: Based on the prediction variance output by the integrated nested multi-fidelity Gaussian process model, calculate the location value of each candidate point; the location value is used to quantify the contribution of sampling at the candidate point to the overall accuracy improvement of the model. S3. Construct a value-cost coupled acquisition function: Obtain the sampling cost at different preset fidelity levels; Calculate the expected improvement value for each candidate point based on the predicted mean and predicted variance output by the integrated nested multi-fidelity Gaussian process model; Construct a value-cost coupled acquisition function based on the location value, sampling cost, and expected improvement value. S4. Adaptive Sampling and Model Update: Select the candidate point that maximizes the value-cost coupling acquisition function value and its corresponding fidelity level as the next sampling point and sampling fidelity; perform finite element simulation at the corresponding fidelity level on the sampling point to obtain new battery pack damage data and add it to the multi-fidelity training dataset, and retrain the integrated nested multi-fidelity Gaussian process model. S5. Iterative convergence judgment: Repeat steps S2 to S4 until the prediction accuracy of the integrated nested multi-fidelity Gaussian process model meets the preset requirements, and output the final battery pack damage prediction model.

[0010] Preferably, the multi-fidelity training dataset in step S1 is obtained through the following method: S1.1 For the target battery pack, establish a high-fidelity finite element model with a mesh size of 2mm and a low-fidelity finite element model with a mesh size of 8mm to 10mm; S1.2 Determine the design variables and their value range for the battery pack collision condition, and generate the collision condition parameters using the Latin hypercube sampling method; S1.3. Perform collision simulations using both high-fidelity and low-fidelity finite element models to obtain battery pack intrusion data under various operating conditions. S1.4. Using collision condition parameters as input features and intrusion amount data as output labels, after data cleaning and standardization, a multi-fidelity training dataset is formed.

[0011] Preferably, the single-layer nested Gaussian process sub-model in step S1 is constructed through the following steps: S1.5. Using low-fidelity samples from the multi-fidelity training dataset, train a basic Gaussian process model and output arbitrary candidate points. Low-fidelity prediction mean and the standard deviation of prediction ; S1.6 Determine the scaling factor This is used to correct the systematic amplitude difference between low-fidelity predictions and high-fidelity responses; S1.7. Based on the residual between the true response of the high-fidelity sample and the scaled low-fidelity predicted value, train the biased Gaussian process model and output the biased predicted value. and the standard deviation of the deviation prediction ; S1.8 High-fidelity predicted mean of a single-layer nested Gaussian process sub-model and the standard deviation of prediction Calculate according to the following formulas respectively: ; .

[0012] Preferably, the double-nested Gaussian process sub-model in step S1 is constructed through the following steps: S1.9. Using the single-layer nested Gaussian process sub-model obtained in step S1.8 as the first-layer sub-model of the double-layer nested Gaussian process sub-model, the high-fidelity predicted value of the first-layer sub-model is obtained. and the standard deviation of prediction ,in, , ; S1.10. Use the predicted value of the first-layer sub-model as an input feature of the second-layer sub-model, and combine it with the candidate points. By splicing them together, a second layer of fusion features is formed; S1.11. Based on the second-layer fusion features and high-fidelity samples, repeat steps S1.5 to S1.8 to train the second-layer sub-model and obtain the second-layer scaling factor. Second-level deviation prediction value Second-level deviation prediction standard deviation and the standard deviation of the second-layer basic model prediction ; S1.12 The high-fidelity prediction mean and prediction standard deviation of the double-nested Gaussian process sub-model are calculated according to the following formulas: ; .

[0013] Preferably, the inverse variance weighting strategy in step S1 includes: S1.13, For any candidate point The integrated nested multi-fidelity Gaussian process model includes Sub-model, the first Sub-models in The predicted value at that location is The prediction standard deviation is ;No. Weights of each sub-model Calculate according to the following formula: ; in, For summation index; S1.14, Predicted mean of integrated nested multi-fidelity Gaussian process model Calculate according to the following formula: ; S1.15. The prediction variance of an integrated nested multi-fidelity Gaussian process model is determined by the model's internal variance. Variance between models The sum is constituted and calculated according to the following formula: .

[0014] Preferably, the location value in step S2 is calculated according to the following formula: ; in, Indicates candidate points, To integrate nested multifidelity Gaussian process models at candidate points The predicted variance at that location This represents the maximum predicted variance among all current candidate points.

[0015] Preferably, the value-cost coupling acquisition function in step S3 is calculated according to the following formula: ; in, Indicates candidate points, For fidelity level; For candidate points Fidelity is used The difference in expected improvement between sampling and using a different level of fidelity sampling. This is a coupling term between location value and sampling cost. , To ensure fidelity The corresponding preset sampling cost, The coupling parameter is greater than 1.

[0016] Preferably, when the fidelity level is high fidelity, the acquisition function is calculated according to the following formula: ; When the fidelity level is low, the acquisition function is calculated according to the following formula: ; in, To predict candidate points based on the current model The expected improvement when using high-fidelity sampling is given. This represents the expected improvement in high fidelity prediction under the assumption that the low fidelity prediction is known. for The mathematical expectation; To reduce the cost of high-fidelity sampling, To reduce the cost of low-fidelity sampling.

[0017] Preferably, in step S3, among the sampling costs of different fidelity levels preset, the sampling cost of high fidelity is higher than that of low fidelity.

[0018] Preferably, the prediction accuracy in step S5 meets the preset requirements, including: the prediction error of the integrated nested multi-fidelity Gaussian process model is less than a preset threshold or the decrease in prediction error in consecutive iterations is less than a preset threshold.

[0019] Therefore, the battery pack damage prediction method using the above-mentioned location value cost-aware adaptive sampling multi-fidelity Gaussian process has the following beneficial effects: (1) Reduced modeling cost: By defining the location value to quantify the contribution of candidate points to model accuracy, and constructing an LC-MF-EI acquisition function that integrates location value, sampling cost and expected improvement, the sampling location and fidelity level are automatically decided, which can significantly reduce the demand for expensive high-fidelity samples while ensuring prediction accuracy, and reduce the overall modeling cost. (2) Improved prediction accuracy and stability: An integrated nested multi-fidelity Gaussian process model is adopted, which combines single-layer nested and double-layer nested Gaussian process sub-models. The prediction results of each sub-model are fused through the inverse variance weighting strategy, which effectively captures the complex nonlinear mapping relationship between high and low fidelity data. At the same time, the uncertainty within and between models is quantified, which improves prediction accuracy and robustness. (3) Improved engineering practicality and efficiency: The location value, sampling cost and global expectation improvement are integrated into the adaptive sampling decision, enabling the model to quickly focus on the high uncertainty region and accelerate convergence. Numerical examples and engineering examples of battery pack side pillar collisions show that this method is superior to the existing mainstream methods in terms of determination coefficient, error index and sample efficiency, providing an efficient and reliable engineering solution for battery pack collision damage prediction.

[0020] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the overall structure of the battery pack damage prediction method integrating a nested multifidelity Gaussian process model based on the location value cost-aware adaptive sampling multifidelity Gaussian process of the present invention. Figure 2 This is a schematic diagram of the structure of the single-layer nested Gaussian process sub-model (single HNGP) of the present invention; Figure 3 This is a schematic diagram of the structure of the double-nested Gaussian process sub-model (double HNGP) of the present invention; Figure 4 This is a flowchart of the adaptive sampling process based on the LC-MF-EI acquisition function of this invention; Figure 5 The training process curves (coefficient of determination, RMSE, sample size, and acquisition function) of the model in the one-dimensional example of this invention are shown. Figure 6 This is a comparison chart of the prediction results of each model in a one-dimensional example of the present invention; Figure 7 This is a flowchart of a battery pack damage prediction method based on a location value cost-aware adaptive sampling multi-fidelity Gaussian process according to the present invention. Figure 8 This is a graph showing the training process of the model in the battery pack engineering case of this invention. Figure 9 This is a comparison chart of the prediction results of various models in the battery pack engineering case of the present invention. Detailed Implementation

[0022] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0023] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0024] Example 1 This embodiment provides a battery pack damage prediction method based on a location-value and cost-aware adaptive sampling multi-fidelity Gaussian process, for rapid prediction of collision damage to electric vehicle power battery packs. The method described in this embodiment is the EHNGP-LCA (EnsembleNested Gaussian process with Location-value and Cost-aware Adaptive sampling surrogate model) proposed in this invention. The overall model structure is as follows: Figure 1 .

[0025] The method and process are as follows Figure 7 As shown, it includes the following steps: S1. Constructing the initial prediction model S1.1 Obtaining the multi-fidelity training dataset For the target battery pack, high-fidelity finite element models and low-fidelity finite element models were established respectively. In this embodiment, the high-fidelity model uses a fine mesh with a mesh size of 2mm, and the low-fidelity model uses a coarse mesh with a mesh size of 8mm to 10mm. Taking the side-impact collision of a certain type of electric vehicle battery pack as an example, the design variables include four key parameters: collision velocity, collision angle, and impact diameter. The Latin hypercube sampling method was used to generate 86 high-fidelity simulation schemes and 240 low-fidelity simulation schemes. Simulations were performed using LS-DYNA software, and the maximum intrusion amount of the battery pack under each condition was obtained as the response output. Using the design variables as input features and the intrusion amount as the output label, data was cleaned (removing outliers with energy non-conservation and excessive hourglass energy) and standardized (normalized to a mean of 0 and a standard deviation of 1) to form a multi-fidelity training dataset (low-fidelity training dataset and high-fidelity training dataset).

[0026] S1.2 Construct a single-layer nested Gaussian process sub-model (single HNGP) The structure of a single HNGP model is as follows: Figure 2 As shown, it is constructed through the following sub-steps: S1.2.1 Train a basic Gaussian process model using a low-fidelity training dataset and output arbitrary candidate points. Low-fidelity prediction With the predicted standard deviation Using the Matern kernel function: ; in, This is the kernel function constant term, used to control the overall magnitude of the function; For Matern core, The length scale is used to determine the smoothness of the function; degrees of freedom parameter This ensures that the model can capture non-stationary features while balancing the smoothness of the function. This represents the noise variance of the low-fidelity model. The Kronecker function characterizes model noise. If the value is 1, then the value is 0; otherwise, the value is 0.

[0027] By scaling factor This is used to correct for systematic amplitude differences between low-fidelity predictions and high-fidelity responses. The location of the high-fidelity sample is... Input the above basic Gaussian process model to obtain the low-fidelity predicted values ​​at high-fidelity sample points. ; Record the first The true response value of a high-fidelity sample is Solving using regularized least squares: ; Wherein, regularization coefficient This is used to prevent overfitting. Taking the derivative of the above equation and setting it to zero, we can derive... Closed-form solution: ; in, This is the identity matrix. To ensure model stability, [the matrix is...]. The constraint is within the interval [0.1, 5.0].

[0028] S1.2.3 Based on the residual between the true response of the high-fidelity sample and the scaled low-fidelity predicted value, a biased Gaussian process model is trained, and the biased predicted value is output. and the standard deviation of the deviation prediction .

[0029] S1.2.4 High-fidelity predicted mean of a single-layer nested Gaussian process sub-model and the standard deviation of prediction Calculate according to the following formulas respectively: ; ; S1.3 Construct a double-layer nested Gaussian process sub-model (double HNGP) The structure of the dual HNGP model is as follows Figure 3 As shown, it is constructed through the following sub-steps: S1.3.1 Using the single-layer nested Gaussian process sub-model obtained in step S1.2 as the first-layer sub-model, the high-fidelity predicted value of the first-layer sub-model is obtained. and the standard deviation of prediction ,in, , ; S1.3.2 The predicted values ​​of the first-layer sub-model As an input feature of the second-layer sub-model, along with candidate points splicing together to form a second layer of fusion features .

[0030] S1.3.3 Based on the second-layer fused features and high-fidelity samples, repeat steps S1.2.1 to S1.2.4 to train the second-layer sub-model and obtain the second-layer scaling factor. Second-level deviation prediction value Second-level deviation prediction standard deviation and the standard deviation of the second-layer basic model prediction ; S1.3.4 High-fidelity predictions of a double-nested Gaussian process sub-model and the standard deviation of prediction Calculate according to the following formulas respectively: ; ; S1.4 Constructing an integrated nested multi-fidelity Gaussian process model To overcome the overfitting risk of a single model, an ensemble learning strategy is adopted. (Construction) A differentiated configuration of single HNGP and dual HNGP sub-models (in this embodiment, we take...) =5, including 3 single HNGPs and 2 double HNGPs. The sub-models are differentiated by different kernel function initial parameters, length scale optimization range, and number of optimization restarts. The prediction results of each sub-model are fused using an inverse variance weighting strategy. S1.4.1 For any candidate point Let the first Sub-models in The predicted value at that location is The prediction standard deviation is The weights of this sub-model Calculate according to the following formula: ; in, For summation index; S1.4.2 Predicted Mean of Integrated Nested Multifidelity Gaussian Process Model Calculate according to the following formula: ; S1.4.3 Prediction Variance of Integrated Nested Multi-Fidelity Gaussian Process Model From the model's internal variance Variance between models The sum is constituted and calculated according to the following formula: .

[0031] This completes the construction of the initial integrated nested multi-fidelity Gaussian process model, and outputs each candidate point. Predicted mean and prediction variance .

[0032] S2, Calculate Location Value Location value is defined as the contribution of sampling at a candidate point to the overall improvement in model accuracy, quantified by normalized prediction variance. It is calculated using the following formula: ; in, The location value is the maximum predicted variance among all current candidate points. The larger the value, the higher the location value, meaning the greater the uncertainty of the model in that area, and the more worthwhile it is to sample.

[0033] S3. Construct a value-cost coupled acquisition function. S3.1 Obtain the sampling cost for different preset fidelity levels. In this embodiment, the single sampling cost for high fidelity is... =5, Low-fidelity single-sampling cost =1. High-fidelity sampling costs more than low-fidelity sampling.

[0034] S3.2 Based on the predicted mean of the current ensemble model and prediction variance Calculate the expected improvement value for each candidate point according to the standard expected improvement formula. The expected improvement value is used to quantify the potential improvement that can be obtained by sampling at candidate points compared to the current best value.

[0035] S3.3 Constructing a value-cost coupled acquisition function. First, define the coupling term between location value and sampling cost: ; in, For the cost of original fidelity, The coupling parameter is greater than 1 (in this embodiment, it is taken as...). =2), used to enhance the cost sensitivity of high-value areas, its core meaning is to achieve cost differentiation of high-value areas through non-linear amplification.

[0036] The general form of the value-cost coupled acquisition function is: ; in, For candidate points Fidelity is used The difference in expected improvement between sampling and sampling with a different fidelity.

[0037] S3.4 When the fidelity level is high fidelity ( When =1), the acquisition function is as follows: ; When the fidelity level is low fidelity (k=0), the acquisition function is calculated according to the following formula: ; in, To predict candidate points based on the current model The expected improvement when using high-fidelity sampling is given. This represents the expected improvement in high fidelity prediction under the assumption that the low fidelity prediction is known. for The mathematical expectation.

[0038] S4, Adaptive Sampling and Model Update, such as Figure 4 The diagram shows the adaptive sampling flowchart based on the LC-MF-EI acquisition function.

[0039] S4.1 Traverse all candidate points, calculate the acquisition function values ​​under high fidelity and low fidelity conditions respectively, and select the one that makes the acquisition function more suitable for the target location. The largest point and their corresponding fidelity levels As the next sampling scheme.

[0040] S4.2 Perform finite element simulation at the appropriate fidelity level: If =1, perform high-fidelity simulation (mesh size 2mm); if =0, perform low-fidelity simulation (mesh size 8-10mm). Obtain the battery pack intrusion amount at this point. .

[0041] S4.3 will use new samples Add the model to the training dataset with the corresponding fidelity, and repeat steps S1.2 to S1.4 to update the integrated nested multifidelity Gaussian process model.

[0042] S5. Iterative Convergence Judgment Repeat steps S2 to S4 until the model accuracy meets the preset requirements. In this embodiment, the termination condition is: on the independent validation set, the determination coefficient R of the integrated nested multi-fidelity Gaussian process model is [value missing]. 2 >0.95, or R >0.95 in three consecutive iterations 2 The increase is less than 0.01. When the condition is met, the iteration stops, and the final battery pack damage prediction model is output.

[0043] To verify the effectiveness of the method in this embodiment, a quantitative evaluation was first performed using artificially constructed test functions (numerical examples) with multiple known mathematical expressions to simulate the nonlinear and non-stationary function characteristics commonly encountered in practical engineering. Subsequently, the engineering applicability of this method was further verified using a real-world electric vehicle battery pack side-pillar collision engineering problem as the application object.

[0044] (1) One-dimensional numerical example The following artificially constructed test function is used: High-fidelity function: Low-fidelity function: Initial samples: 13 low-fidelity samples and 5 high-fidelity samples. After 10 adaptive sampling iterations, the model training process is as follows: Figure 5 As shown. Figure 5 (Top left) shows the coefficient of determination rapidly increasing from the initial 0.55 to above 0.97; (Top right) shows the RMSE decreasing from 3.0 to below 0.7; (Bottom left) shows the low-fidelity samples increasing from 13 to 21, while the high-fidelity samples only increased from 5 to 7; (Bottom right) shows the high-fidelity acquisition function decaying after reaching its peak in the second iteration. The final model prediction results are as follows. Figure 6 As shown in (c), it closely matches the true function. The comparison results with other models are shown in Table 1.

[0045] Table 1 Comparison of errors of various models in one-dimensional examples

[0046] (2) Four-dimensional and six-dimensional numerical examples The advantages of this method become more apparent as the input dimension increases. Table 2 presents the comparison results for four-dimensional and six-dimensional examples. In the four-dimensional example, the R... 2 It achieves an accuracy of 0.9635, and maintains 0.8655 in the six-dimensional example, both of which are better than the comparison model, and require the fewest high-precision samples.

[0047] Table 2 Comparison of errors for each model in the four-dimensional / six-dimensional examples.

[0048] (3) Engineering examples of side column collision of battery pack Taking a certain type of electric vehicle battery pack as the object, the design variables are four parameters: collision speed, collision angle, and pillar diameter. The high-fidelity model has a mesh size of 2mm, and the low-fidelity model has a mesh size of 8mm. Initial samples: 20 low-fidelity samples and 12 high-fidelity samples. After 10 adaptive sampling iterations, the model training process is as follows: Figure 8 As shown in the figure. It can be seen from the figure that in the 6th iteration, R... 2 The RMSE jumped from approximately 0.81 to over 0.95, while the high-fidelity sample size decreased simultaneously, with only one additional high-fidelity sample (from 12 to 13). The final model prediction results are as follows: Figure 9 As shown in Table 3, a comparison with other models is provided.

[0049] Table 3. Comparative experimental results of the model under the side pillar collision condition of the battery pack.

[0050] Experimental results show that this method significantly reduces the number of high-fidelity samples required while ensuring prediction accuracy, effectively controlling modeling costs.

[0051] Therefore, this invention employs the aforementioned battery pack damage prediction method based on a location value cost-aware adaptive sampling multi-fidelity Gaussian process. By defining the contribution of location value quantification sampling points to model accuracy improvement, an LC-MF-EI acquisition function is constructed to fuse location value, sampling cost, and expected improvement, automatically determining the sampling location and fidelity level. Numerical examples and engineering examples of battery pack side pillar collisions demonstrate that this method achieves high accuracy in predicting the coefficient of determination R0. 2 While achieving a high-fidelity coefficient of determination (R0.9593), the required high-fidelity sample size is significantly less than mainstream methods such as E2NN and IR co-kriging. The model can approximate high-fidelity simulation accuracy with lower computational cost, significantly improving modeling efficiency and engineering applicability. By defining the location value to quantify the contribution of sampling points to model accuracy improvement, an LC-MF-EI acquisition function is constructed to fuse location value, sampling cost, and expected improvement, automatically deciding on sampling location and fidelity level. Numerical examples and engineering examples of battery pack side pillar collisions validate that this method achieves a high R0.9593. 2While achieving a high fidelity of 0.9593, the required high-fidelity sample size is far less than that of mainstream methods such as E2NN and IR co-kriging; the model can approximate high-fidelity simulation accuracy with lower computational cost, significantly improving modeling efficiency and engineering applicability.

[0052] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for predicting battery pack damage using a location-value-cost-aware adaptive sampling multi-fidelity Gaussian process, characterized in that, Includes the following steps: S1. Constructing the initial prediction model: Obtain a multi-fidelity training dataset containing high-fidelity samples and low-fidelity samples; Based on the multi-fidelity training dataset, construct an ensemble nested multi-fidelity Gaussian process model; The ensemble nested multi-fidelity Gaussian process model includes at least one single-layer nested Gaussian process sub-model and at least one double-layer nested Gaussian process sub-model, and fuses the prediction results of each sub-model through an inverse variance weighting strategy, outputting the prediction mean and prediction variance of each candidate point, where the candidate point is the location to be predicted in the design space; S2. Calculate the location value: Based on the prediction variance output by the integrated nested multi-fidelity Gaussian process model, calculate the location value of each candidate point; the location value is used to quantify the contribution of sampling at the candidate point to the overall accuracy improvement of the model. S3. Construct a value-cost coupled acquisition function: Obtain the sampling cost at different preset fidelity levels; Calculate the expected improvement value for each candidate point based on the predicted mean and predicted variance output by the integrated nested multi-fidelity Gaussian process model; Construct a value-cost coupled acquisition function based on the location value, sampling cost, and expected improvement value. S4. Adaptive Sampling and Model Update: Select the candidate point that maximizes the value-cost coupling acquisition function value and its corresponding fidelity level as the next sampling point and sampling fidelity; perform finite element simulation at the corresponding fidelity level on the sampling point to obtain new battery pack damage data and add it to the multi-fidelity training dataset, and retrain the integrated nested multi-fidelity Gaussian process model. S5. Iterative convergence judgment: Repeat steps S2 to S4 until the prediction accuracy of the integrated nested multi-fidelity Gaussian process model meets the preset requirements, and output the final battery pack damage prediction model.

2. The battery pack damage prediction method based on a location value cost-aware adaptive sampling multi-fidelity Gaussian process according to claim 1, characterized in that, The multi-fidelity training dataset in step S1 is obtained in the following way: S1.1 For the target battery pack, establish a high-fidelity finite element model with a mesh size of 2mm and a low-fidelity finite element model with a mesh size of 8mm to 10mm; S1.2 Determine the design variables and their value range for the battery pack collision condition, and generate the collision condition parameters using the Latin hypercube sampling method; S1.

3. Perform collision simulations using both high-fidelity and low-fidelity finite element models to obtain battery pack intrusion data under various operating conditions. S1.

4. Using collision condition parameters as input features and intrusion amount data as output labels, after data cleaning and standardization, a multi-fidelity training dataset is formed.

3. The battery pack damage prediction method based on a location value cost-aware adaptive sampling multi-fidelity Gaussian process according to claim 1, characterized in that, The single-layer nested Gaussian process sub-model in step S1 is constructed through the following steps: S1.

5. Using low-fidelity samples from the multi-fidelity training dataset, train a basic Gaussian process model and output arbitrary candidate points. Low-fidelity prediction mean and low-fidelity prediction standard deviation ; S1.6 Determine the scaling factor This is used to correct the systematic amplitude difference between low-fidelity predictions and high-fidelity responses; S1.

7. Based on the residual between the true response of the high-fidelity sample and the scaled low-fidelity predicted value, train the biased Gaussian process model and output the biased predicted value. and the predicted standard deviation of the deviation ; S1.8 High-fidelity predicted mean of a single-layer nested Gaussian process sub-model and high-fidelity prediction standard deviation Calculate according to the following formulas respectively: ； 。 4. The battery pack damage prediction method based on a location value cost-aware adaptive sampling multi-fidelity Gaussian process according to claim 3, characterized in that, The double-nested Gaussian process sub-model in step S1 is constructed through the following steps: S1.

9. Using the single-layer nested Gaussian process sub-model obtained in step S1.8 as the first-layer sub-model of the double-layer nested Gaussian process sub-model, the high-fidelity predicted value of the first-layer sub-model is obtained. and the high-fidelity prediction standard deviation of the first-layer sub-model ,in, , ; S1.

10. Use the predicted value of the first-layer sub-model as an input feature of the second-layer sub-model, and combine it with the candidate points. The components are spliced ​​together to form a second layer of fusion features; S1.

11. Based on the second-layer fusion features and high-fidelity samples, repeat steps S1.5 to S1.8 to train the second-layer sub-model and obtain the second-layer scaling factor. Second-level deviation prediction value Second-level deviation prediction standard deviation and the standard deviation of the second-layer basic model prediction ; S1.12 The high-fidelity prediction mean and prediction standard deviation of the double-nested Gaussian process sub-model are calculated according to the following formulas: ； 。 5. The battery pack damage prediction method based on a location value cost-aware adaptive sampling multi-fidelity Gaussian process according to claim 1, characterized in that, The inverse variance weighting strategy in step S1 includes: S1.13, For any candidate point The integrated nested multi-fidelity Gaussian process model includes The sub-model, the first Sub-models in The predicted value at that location is The prediction standard deviation is ;No. Weights of each sub-model Calculate according to the following formula: ； in, For summation index; S1.14, Predicted mean of integrated nested multi-fidelity Gaussian process model Calculate according to the following formula: ； S1.

15. The prediction variance of an integrated nested multi-fidelity Gaussian process model is determined by the model's internal variance. Variance between models The sum is constituted by the following formula: 。 6. The battery pack damage prediction method based on a location value cost-aware adaptive sampling multi-fidelity Gaussian process according to claim 1, characterized in that, The location value in step S2 is calculated according to the following formula: ； in, Indicates candidate points, To integrate nested multifidelity Gaussian process models at candidate points The predicted variance at that location This represents the maximum predicted variance among all current candidate points.

7. The battery pack damage prediction method based on a location value cost-aware adaptive sampling multi-fidelity Gaussian process according to claim 6, characterized in that, The value-cost coupling acquisition function in step S3 is calculated according to the following formula: ； in, Indicates candidate points, For fidelity level; For candidate points Fidelity is used The difference in expected improvement between sampling and using a different level of fidelity sampling. This is a coupling term between location value and sampling cost. , To ensure fidelity The corresponding preset sampling cost, The coupling parameter is greater than 1.

8. The battery pack damage prediction method based on a location value cost-aware adaptive sampling multi-fidelity Gaussian process according to claim 7, characterized in that, When the fidelity level is high fidelity, the acquisition function is calculated according to the following formula: ； When the fidelity level is low, the acquisition function is calculated according to the following formula: ； in, To predict candidate points based on the current model The expected improvement when using high-fidelity sampling is given. This represents the expected improvement in high fidelity prediction under the assumption that the low fidelity prediction is known. for The mathematical expectation; To reduce the cost of high-fidelity sampling, To reduce the cost of low-fidelity sampling.

9. The battery pack damage prediction method based on a location value cost-aware adaptive sampling multi-fidelity Gaussian process according to claim 1, characterized in that, In step S3, among the sampling costs of different fidelity levels preset, the sampling cost of high fidelity is higher than that of low fidelity.

10. The battery pack damage prediction method based on a location value cost-aware adaptive sampling multi-fidelity Gaussian process according to claim 1, characterized in that, In step S5, the prediction accuracy must meet the preset requirements, including: the prediction error of the integrated nested multi-fidelity Gaussian process model is less than a preset threshold, or the decrease in prediction error in consecutive iterations is less than a preset threshold.

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