Method for designing and optimizing a body structure

Abstract

This application provides a design optimization method for vehicle body structures. Addressing the challenges of existing vehicle body crashworthiness analyses, such as the difficulty in efficiently quantifying the impact of input uncertainties, the difficulty in identifying key process material parameters leading to crashworthiness failure, and the heavy computational burden, a design optimization scheme based on a joint probabilistic surrogate model is proposed. This scheme constructs a Bayesian network based on the collision load transmission path. Using the conditional probability relationship between process material parameters, force transmission structure section forces, and crashworthiness response as a foundation, it inverts the posterior distribution of each process material parameter under crashworthiness failure conditions. The difference between the posterior and prior distributions is used to assess failure attribution, and the corresponding parameter design values ​​are adjusted accordingly. This enables precise tracing of the causes of crashworthiness failure, improves the ability to identify key parameters, reduces the cost of high-fidelity simulation calculations, and enhances design iteration efficiency and the targeted nature of vehicle body structure optimization.

Description

Technical Field

[0001] This application relates to the field of vehicle body structure design optimization technology, and in particular to a method for designing and optimizing vehicle body structures. Background Technology

[0002] In the design and optimization of automotive body structures, collision safety is a core indicator for measuring vehicle safety performance. Current automotive body crashworthiness design typically employs finite element collision simulation to evaluate the vehicle's response, combined with Monte Carlo analysis, response surface methodology, or surrogate models to conduct uncertainty studies.

[0003] However, the above methods are either based on fixed parameter assumptions, making it difficult to accurately characterize the transmission effects of manufacturing tolerances, material fluctuations, and assembly deviations on the collision response; or although they can describe the statistical distribution, they have high computational costs, making it difficult to support rapid iteration, and they mostly stay at the overall response level, making it difficult to further clarify the specific contribution of each input parameter to performance fluctuations.

[0004] Therefore, how to efficiently quantify the impact of input uncertainties in vehicle crashworthiness analysis and improve the ability to identify key impact parameters, thereby assisting in the design and optimization of vehicle body structures, has become an urgent technical problem to be solved. Summary of the Invention

[0005] This application provides a method for optimizing the design of a vehicle body structure to address the aforementioned technical problems. This solution addresses the difficulty in efficiently quantifying the impact of input uncertainties and accurately identifying key influencing parameters during the vehicle body crashworthiness design process. It establishes an analytical mechanism that characterizes the impact of parameter changes on performance failure, based on the correlation between process material parameters, structural force transmission processes, and crashworthiness response in the current vehicle body structure. Under crashworthiness failure scenarios, it traces the key factors leading to failure and optimizes the vehicle body structure design parameters accordingly.

[0006] In a first aspect, embodiments of this application provide a method for optimizing the design of a vehicle body structure, the method comprising:

[0007] Obtain the joint probabilistic proxy model of the current vehicle body structure; wherein, the joint probabilistic proxy model adopts a Bayesian network topology structure constructed based on the collision load transmission path, with process material parameters as root nodes, force transmission structure section force as intermediate nodes, and crashworthiness response as leaf nodes, and the joint probabilistic proxy model is used to characterize the conditional probability distribution between adjacent layer nodes;

[0008] Based on the joint probabilistic surrogate model, the posterior distribution information of the process material parameters is determined under the condition that a crashworthiness failure event occurs;

[0009] Based on the degree of difference between the posterior and prior distribution information of the process material parameters, the attribution result leading to the failure of impact resistance is determined;

[0010] Based on the attribution results, adjust the design values ​​of the process material parameters.

[0011] In one possible implementation, obtaining the joint probabilistic proxy model of the current vehicle body structure includes:

[0012] Obtain multiple sets of sample data regarding process material parameters; wherein each set of sample data includes the process material parameters, the corresponding force transmission structure section force and impact resistance response of the process material parameters;

[0013] Based on the collision load transmission path, a Bayesian network topology is constructed with the process material parameters as the root node, the force transmission structure section force as the intermediate node, and the impact resistance response as the leaf node.

[0014] Based on the sample data, the conditional probability distribution between adjacent layer nodes in the Bayesian network topology is learned, and the joint probability proxy model is established.

[0015] In one possible implementation, acquiring multiple sets of sample data regarding process material parameters includes:

[0016] The Latin hypercube sampling method is used to sample within the design space of the process material parameters to obtain multiple sets of sample points.

[0017] Explicit dynamic finite element simulation was used to perform collision simulation on each of the sample points, and the force and impact resistance response of the force transmission structure section corresponding to each sample point were extracted from the simulation results.

[0018] In one possible implementation, the step of learning the conditional probability distribution between adjacent layer nodes in the Bayesian network topology based on the sample data and establishing the joint probabilistic proxy model includes:

[0019] Obtain the prior distribution information of each of the process material parameters;

[0020] The sample data is preprocessed to standardize it, resulting in standardized sample data; wherein, the standardized sample data are all dimensionless values.

[0021] Based on the prior distribution information and the standardized sample data, the first conditional probability distribution of the force transmission structure section force with respect to the process material parameters and the second conditional probability distribution of the impact resistance response with respect to the force transmission structure section force are respectively fitted.

[0022] Based on the Bayesian network chain decomposition rule, the prior distribution information, the first conditional probability distribution, and the second conditional probability distribution are multiplied together to assemble the joint probabilistic proxy model.

[0023] In one possible implementation, fitting a first conditional probability distribution of the force transmission structure section force with respect to the process material parameters, and a second conditional probability distribution of the impact resistance response with respect to the force transmission structure section force, based on the prior distribution information and the standardized sample data, includes:

[0024] Construct a first joint vector of the process material parameters and the force of the cross section of the force transmission structure, fit the joint probability density distribution of the first joint vector using a hybrid probability density model, and derive the first conditional probability distribution based on the fitted joint probability density distribution and the prior distribution information according to Bayes' theorem.

[0025] A second joint vector of the force transmission structure section force and the impact resistance performance response is constructed. The joint probability density distribution of the second joint vector is fitted using a hybrid probability density model. Marginalization is performed based on the fitted joint probability density distribution. The second conditional probability distribution is derived based on Bayes' theorem.

[0026] In one possible implementation, the mixed probability density model is a Gaussian mixture model, and fitting the joint probability density distribution of the first joint vector using the mixed probability density model includes:

[0027] Set multiple candidate component numbers, and train a Gaussian mixture model with the number of candidate component numbers;

[0028] Calculate the Bayesian information criterion value for each trained Gaussian mixture model, and select the number of candidate components that minimizes the Bayesian information criterion value as the optimal number of components.

[0029] The Gaussian mixture model is trained with the optimal number of components, and the trained Gaussian mixture model is used as the joint probability density distribution of the fitted first joint vector.

[0030] In one possible implementation, training the Gaussian mixture model with the optimal number of components includes:

[0031] A clustering algorithm is used to cluster the sample data of the first joint vector, and the clustering results are used to initialize the parameters of each component of the Gaussian mixture model.

[0032] The expected step and the maximization step are executed alternately for iterative training until the preset convergence condition is met, and then the trained Gaussian mixture model is obtained.

[0033] In one possible implementation, the step of deriving the first conditional probability distribution based on the fitted joint probability density distribution and the prior distribution information, according to Bayes' theorem, includes:

[0034] Using the joint probability density distribution of the first joint vector as the numerator and the prior distribution information of the process material parameters as the denominator, the ratio of the two is calculated to obtain the first conditional probability distribution of the force of the force transmission structure section with respect to the process material parameters.

[0035] In one possible implementation, the marginalization process based on the fitted joint probability density distribution, and the derivation of the second conditional probability distribution according to Bayes' theorem, includes:

[0036] Integrating the joint probability density distribution of the second joint vector over the dimension of the crashworthiness response yields the edge probability density distribution of the force at the cross-section of the force transmission structure.

[0037] Using the joint probability density distribution of the second joint vector as the numerator and the marginal probability density distribution of the force at the cross-section of the force transmission structure as the denominator, the ratio of the two is calculated to obtain the second conditional probability distribution of the impact resistance response with respect to the force at the cross-section of the force transmission structure.

[0038] In one possible implementation, the method further includes a model verification step, which includes at least one of the following verification methods:

[0039] The first method is to use leave-one-out cross-validation, where a set of sample data is removed each time, and the joint probabilistic surrogate model is retrained with the remaining sample data; the trained joint probabilistic surrogate model is used to predict the force and impact resistance response of the force transmission structure section corresponding to the removed samples; the root mean square error between the predicted value and the actual simulation value is calculated to evaluate the prediction accuracy of the joint probabilistic surrogate model.

[0040] The second approach involves performing multiple samplings based on the joint probabilistic surrogate model to generate sampled samples of the force and impact resistance response of the force-transmitting structure section; then, the sampled samples are compared with the actual simulation samples used for training to verify the ability of the joint probabilistic surrogate model to reproduce the true collision response distribution.

[0041] In one possible implementation, determining the posterior distribution information of the process material parameters based on the joint probabilistic surrogate model under the condition that a crashworthiness failure event occurs includes:

[0042] Multiple candidate samples are extracted from the prior distribution information of the process material parameters;

[0043] Based on the joint probabilistic proxy model, the failure weight of each group of candidate samples under the crashworthiness failure event is determined respectively;

[0044] The candidate samples are resampled according to the failure weights to obtain a posterior sample set that follows the posterior distribution.

[0045] In one possible implementation, determining the attribution result for the crashworthiness failure based on the degree of difference between the posterior and prior distribution information of the process material parameters includes:

[0046] The KL divergence between the posterior distribution information and the prior distribution information of the process material parameters is calculated respectively to obtain the sensitivity index of each process material parameter;

[0047] Process material parameters with sensitivity indices greater than or equal to a first preset threshold are identified as key sensitive parameters, while process material parameters with sensitivity indices less than or equal to a second preset threshold are identified as non-sensitive parameters.

[0048] In one possible implementation, calculating the KL divergence between the posterior distribution information and the prior distribution information of the process material parameters includes:

[0049] The kernel density is estimated on the posterior sample set of the posterior distribution information to obtain the posterior probability density function;

[0050] For each sample point in the posterior sample set, calculate the logarithm of the ratio of the posterior probability density function value to the probability density value of the prior distribution information;

[0051] The logarithm is averaged over the posterior sample set to obtain a numerical estimate of the KL divergence.

[0052] In one possible implementation, adjusting the design values ​​of the process material parameters based on the attribution results includes:

[0053] Narrowing the manufacturing tolerance range of the critical sensitive parameters, and / or shifting the nominal design value of the critical sensitive parameters in a direction that is conducive to improving crashworthiness;

[0054] Expand the manufacturing tolerance range of the aforementioned non-sensitive parameters.

[0055] In one possible implementation, before determining the attribution result leading to the crashworthiness failure based on the degree of difference between the posterior and prior distribution information of the process material parameters, the method further includes:

[0056] Forward sampling is performed based on the joint probabilistic proxy model to obtain the probability density function or cumulative distribution function of the crashworthiness response;

[0057] Based on a preset failure threshold, calculate the failure probability that the impact resistance response exceeds the failure threshold;

[0058] If the failure probability is greater than a preset risk threshold, then the step of determining the attribution result that leads to the failure of the impact resistance performance is performed based on the difference between the posterior distribution information and the prior distribution information of the process material parameters.

[0059] In one possible implementation, the process material parameters include at least one of the following: front longitudinal beam sheet metal thickness, energy-absorbing box wall thickness, material yield strength, material tensile strength, material elongation, weld joint failure strain, and structural adhesive failure strain.

[0060] The force transmission structure section force includes: the front longitudinal beam section force and / or the subframe longitudinal beam section force;

[0061] The crashworthiness response includes: peak intrusion into the passenger compartment and / or B-pillar acceleration.

[0062] Secondly, embodiments of this application provide a vehicle body structure design optimization device, the device comprising:

[0063] The first processing unit is used to obtain the joint probabilistic proxy model of the current vehicle body structure; wherein, the joint probabilistic proxy model adopts a Bayesian network topology structure constructed based on the collision load transmission path, with process material parameters as root nodes, force transmission structure section force as intermediate nodes, and crashworthiness response as leaf nodes, and the joint probabilistic proxy model is used to characterize the conditional probability distribution between adjacent layer nodes.

[0064] The second processing unit is used to determine the posterior distribution information of the process material parameters under the condition that a crashworthiness failure event occurs, based on the joint probabilistic surrogate model.

[0065] The third processing unit is used to determine the attribution result that leads to the failure of the impact resistance performance based on the degree of difference between the posterior distribution information and the prior distribution information of the process material parameters.

[0066] The fourth processing unit is used to adjust the design values ​​of the process material parameters based on the attribution results.

[0067] Thirdly, embodiments of this application provide an electronic device, including: a memory and a processor;

[0068] The memory stores computer-executed instructions;

[0069] The processor executes computer execution instructions stored in the memory, causing the processor to perform the first aspect and / or various possible implementations of the first aspect as described above.

[0070] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the first aspect and / or various possible implementations of the first aspect.

[0071] Fifthly, embodiments of this application provide a computer program product, including a computer program that, when executed by a processor, implements the first aspect and / or various possible implementations of the first aspect.

[0072] The vehicle body structure design optimization method provided in this application obtains a joint probabilistic surrogate model characterizing the conditional probability distribution relationship between process material parameters, force transmission structure section forces, and crashworthiness response. Based on crashworthiness failure events, it determines the posterior distribution information of process material parameters, enabling reverse quantification of the influence of each process material parameter on the failure from the performance failure results. Furthermore, based on the difference between the posterior and prior distribution information of process material parameters, it determines the attribution results leading to crashworthiness failure and adjusts the design values ​​of process material parameters according to the attribution results. This achieves efficient identification and targeted optimization of key influencing parameters, improving the analytical efficiency and optimization accuracy of vehicle body structure crashworthiness design. Attached Figure Description

[0073] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0074] Figure 1 A flowchart illustrating a method for designing and optimizing a vehicle body structure, as provided in an embodiment of this application;

[0075] Figure 2 A flowchart illustrating another method for designing and optimizing a vehicle body structure provided in this application embodiment;

[0076] Figure 3 A topological diagram of a Bayesian network topology provided in this application embodiment;

[0077] Figure 4 A schematic diagram of a vehicle body structure design optimization device provided in this application embodiment;

[0078] Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application.

[0079] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0080] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0081] Automotive body crashworthiness design falls under the field of vehicle safety development and structural optimization, and typically involves crash performance assessments conducted during the vehicle development phase using computer-aided engineering platforms. In this scenario, an analysis process is generally established around the vehicle body structure, manufacturing and material parameters, and crash response, examining the impact of local structural changes on the overall vehicle crashworthiness through crash load transfer relationships.

[0082] Traditional methods rely on finite element simulation (such as explicit dynamic analysis) to assess vehicle crashworthiness. However, the "deterministic" simulations they employ assume that all input parameters (such as front longitudinal beam sheet metal thickness, material strength, and weld performance) are fixed values, failing to reflect uncertainties in actual manufacturing processes such as batch-to-batch material variations, stamping process tolerances, and assembly errors. For example, the yield strength of steel may fluctuate by ±20MPa depending on the batch, and sheet metal thickness tolerances can reach ±0.05mm. These uncertainties are transmitted to the collision response (such as passenger compartment intrusion and B-pillar acceleration) through complex nonlinear coupling effects, causing the crashworthiness of actual mass-produced vehicles to deviate from design expectations.

[0083] In engineering practice, while Monte Carlo simulation can simulate the impact of parameter fluctuations, it requires tens of thousands of high-fidelity collision simulations, resulting in extremely high computational costs that are difficult to meet the needs of design iteration. While surrogate models based on neural networks improve computational efficiency, their "black box" nature lacks physical interpretability, and they are prone to overfitting with small samples, failing to quantify the causal dependencies between parameters. Furthermore, existing methods often focus on the statistical characteristics of the overall response (such as mean and variance), failing to identify which specific process parameter or material property contributes most to crashworthiness fluctuations, leading to a lack of targeted design improvements. Therefore, there is an urgent need for a method that can efficiently quantify the impact of uncertainty and provide physically interpretable attribution analysis to guide manufacturing tolerance optimization and design parameter adjustments, thereby reducing manufacturing costs while ensuring safety.

[0084] To address the aforementioned issues, this application provides a method for optimizing the design of a vehicle body structure. By acquiring a joint probabilistic surrogate model and characterizing the conditional probability relationship between process material parameters, force transmission structure section forces, and crashworthiness response based on a Bayesian network topology constructed according to the collision load transmission path, the method determines the posterior distribution information of process material parameters when a crashworthiness failure event occurs. Then, based on the difference between the posterior and prior distribution information, the method determines the attribution result leading to crashworthiness failure and adjusts the design values ​​of process material parameters accordingly, thereby balancing failure tracing capability and design optimization efficiency.

[0085] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0086] It should be noted that the execution subject of the vehicle body structure design optimization method provided in this application embodiment can be a vehicle body structure design optimization device, which can be deployed in electronic devices such as computers, mobile phones, tablets, computers, and servers. This application embodiment does not impose any restrictions.

[0087] Figure 1 This is a flowchart illustrating a method for designing and optimizing a vehicle body structure, as provided in an embodiment of this application. Figure 1 As shown, the vehicle body structure design optimization method provided in this embodiment may include:

[0088] S101. Obtain the joint probabilistic proxy model of the current vehicle body structure.

[0089] The joint probabilistic surrogate model employs a Bayesian network topology constructed based on the collision load transmission path. This topology uses process material parameters as root nodes, force at the cross-section of the load-transmitting structure as intermediate nodes, and impact resistance response as leaf nodes. The joint probabilistic surrogate model characterizes the conditional probability distribution between adjacent layer nodes. This model is typically stored in electronic devices in the form of analytical expressions.

[0090] For example, in the embodiments of this application, the joint probabilistic proxy model adopts a Bayesian network topology structure constructed based on the collision load transmission path, specifically including three levels: with process material parameters as the root node, with the force of the force transmission structure section as the intermediate node, and with the impact resistance performance response as the leaf node.

[0091] Among these, process material parameters refer to the manufacturing process parameters and material performance parameters that affect the collision performance of the vehicle body structure. Optionally, taking the front body structure of an automobile as an example, process material parameters may include, but are not limited to: front longitudinal beam sheet metal thickness, energy-absorbing box wall thickness, material yield strength, material tensile strength, material elongation, weld failure strain, and structural adhesive failure strain. These parameters are affected by factors such as stamping processes and batch differences in materials during actual mass production, and are objectively subject to unavoidable fluctuations. For example, sheet metal thickness typically has a tolerance of ±0.05mm, and steel yield strength has a dispersion of ±20MPa. Fluctuations in process material parameters are the fundamental cause of the uncertainty in the crashworthiness performance of the vehicle body.

[0092] The cross-sectional force of the load-transmitting structure refers to the maximum cross-sectional force borne by the load-transmitting structure of the vehicle body during a collision. Optionally, taking a frontal collision as an example, the cross-sectional force of the load-transmitting structure may include, but is not limited to, the cross-sectional force of the front longitudinal beam and the cross-sectional force of the subframe longitudinal beam. When a collision occurs, the impact load is first borne by the front structure, such as the energy-absorbing box and the front longitudinal beam, and the load is transferred step by step to the surrounding structure of the passenger compartment along the load transmission path. The cross-sectional force is a physical intermediate quantity connecting the process material parameters and the vehicle's collision response. Fluctuations in the process material parameters directly affect the magnitude and distribution of the cross-sectional force, and changes in the cross-sectional force further determine the crashworthiness performance of the entire vehicle. Incorporating the cross-sectional force as an intermediate node into a Bayesian network makes the probabilistic model have clear mechanical interpretability. That is, once the attribution result indicates that the cross-sectional force of a certain load transmission path is abnormal, engineers can directly locate the corresponding vehicle body structural component, avoiding the limitation of a purely data-driven model that "knows what but not why".

[0093] Crashworthiness response refers to the output indicators used to evaluate the collision safety performance of a vehicle body structure. Optionally, crashworthiness response may include, but is not limited to, peak intrusion into the passenger compartment and B-pillar acceleration. Peak intrusion into the passenger compartment directly reflects the degree of compression of the occupant survival space, while B-pillar acceleration is highly correlated with the risk of occupant injury; both are core evaluation indicators in automotive collision safety regulations and corporate design specifications. In the definition of failure events, a peak intrusion into the passenger compartment exceeding a first preset threshold and / or a B-pillar acceleration exceeding a second preset threshold is typically considered a crashworthiness failure. The first and second preset thresholds are determined by the frontal collision crashworthiness design specifications.

[0094] It is worth noting that constructing the model based on the collision load transmission path means that the directed connections between nodes in the Bayesian network are not arbitrarily set, but rather established step by step according to the actual physical transmission direction of the collision load in the vehicle body structure: from process material parameters to the force of the load-transmitting structural section and then to the crashworthiness response. This construction method ensures that the causal flow in the probabilistic model is consistent with the mechanical mechanism, making the subsequent backward inference results physically interpretable.

[0095] In one possible implementation, the joint probabilistic surrogate model can be pre-established as follows: First, multiple sets of sample data on process material parameters are acquired, each set including process material parameters, corresponding force transmission structure section forces, and corresponding crashworthiness responses; second, the aforementioned three-layer Bayesian network topology is constructed based on the collision load transmission path; finally, the conditional probability distribution between adjacent layer nodes is learned based on the sample data, and the joint probabilistic surrogate model is assembled. Once this model is established, it can be repeatedly used in subsequent optimization iterations, provided that the nominal design values ​​of the vehicle body structure do not substantially change beyond the original design space, without needing to re-execute high-fidelity collision simulations and model training each time tolerance allocation is adjusted or the design is optimized. If the nominal design values ​​are significantly adjusted, causing the original design space to be unable to cover the parameter range of the new design scheme, the sample extraction, simulation, and modeling steps can be re-executed based on the new design space.

[0096] In this embodiment, a joint probabilistic surrogate model is used to characterize the conditional probability distribution between adjacent layer nodes. Specifically, it represents the first conditional probability distribution from process material parameters to the force of the load-transmitting structural section, and the second conditional probability distribution from the force of the load-transmitting structural section to the crashworthiness response. This model is stored in an electronic device in the form of analytical mathematical expressions. Given any set of process material parameter values, it can calculate the corresponding probability distributions of the load-transmitting structural section force and the crashworthiness response within milliseconds, thus completely replacing the role of high-fidelity collision simulation in uncertainty propagation and attribution analysis.

[0097] This application embeds the collision load transfer relationship into a joint probabilistic surrogate model, transforming the relationship between process material parameters and crashworthiness response from a black-box mapping to a traceable conditional probability chain formed through the intermediate physical quantity of the force-transferring structural section force. This approach, while maintaining the computational efficiency of the surrogate model, decomposes the impact of local parameter fluctuations on the overall vehicle crashworthiness into specific force transmission paths, providing a computationally achievable basis for subsequent failure attribution. Furthermore, by acquiring the pre-established joint probabilistic surrogate model, this step provides an efficient and physically interpretable computational engine for subsequent crashworthiness failure probability assessment and reverse attribution analysis, eliminating the need to rerun high-fidelity collision simulations in every analysis or optimization iteration, thus significantly reducing computational costs.

[0098] S102. Based on the joint probabilistic surrogate model, determine the posterior distribution information of process material parameters under the condition that a crashworthiness failure event occurs.

[0099] For example, posterior distribution information is used to characterize the updated probability distribution of each process material parameter relative to the original prior distribution when the condition of known crashworthiness failure is met. Prior distribution information describes the original statistical characteristics of each process material parameter before the failure condition is applied. It can be determined based on manufacturing tolerances, material batch fluctuations, connection quality fluctuations, and assembly deviation statistics, and serves as a benchmark for subsequent posterior comparisons. Optionally, the prior distribution can be a normal distribution, a truncated normal distribution, a log-normal distribution, a uniform distribution, or an empirical distribution. The crashworthiness response participates in the failure event definition as a leaf node. A failure event can be defined as one or more crashworthiness responses exceeding a threshold, falling below a threshold, or falling into a predetermined failure range.

[0100] From a Bayesian statistical perspective, under normal mass production conditions, process material parameters follow a priori distribution (i.e., the distribution of parameters according to their inherent tolerance fluctuations when there is no failure information). However, under conditions of failure events, the posterior distribution of each parameter may deviate to varying degrees from the prior distribution. The degree of this deviation reflects the strength of the correlation between the parameter and the failure event—the greater the deviation, the more likely the fluctuation of the parameter is to cause failure, and vice versa.

[0101] In one possible embodiment, a direct Bayesian inversion approach can be used. First, using the crashworthiness failure event as observational evidence, the conditional distribution of the root node process material parameters under this evidence is calculated. For cases where the topology is clear and the conditional distribution can be analytically expressed, updates can be performed according to Bayes' theorem. The joint probability can be expressed as the product of the conditional probabilities of each layer. The posterior distribution of the process material parameters is proportional to the likelihood of the failure event and the prior distribution, where the likelihood of the failure event is obtained from the chain integral of the conditional probability of the force transmission structure section of the intermediate nodes and the crashworthiness response of the leaf nodes. For cases where analytical solutions are difficult, numerical approximation can also be used to obtain the posterior distribution information; this embodiment does not impose limitations on this approach.

[0102] This step establishes a quantitative probabilistic relationship between vehicle crashworthiness failure and upstream process material parameters by performing back inference under failure conditions on a joint probabilistic surrogate model. Since the model includes the intermediate node of the force-transmitting structural section force, the posterior update essentially comprehensively considers the impact of parameter changes on the load transfer path and the impact of load transfer on the final response. Therefore, the posterior distribution information can reflect the failure source more accurately than analysis based solely on input-output correlation.

[0103] S103. Based on the degree of difference between the posterior and prior distribution information of the process material parameters, determine the attribution result that led to the failure of the impact resistance performance.

[0104] For example, in this embodiment, the degree of difference refers to the extent to which the posterior distribution changes relative to the prior distribution. The attribution results are used to identify key sensitive parameters and non-key sensitive parameters, and to give the relative contribution of each parameter to the failure of crashworthiness performance. If the posterior distribution of a certain parameter deviates significantly from the prior distribution, it indicates that the probability structure of the parameter appearing in the failure sample is significantly different from that of the overall sample, and the parameter can be identified as an important attribution object leading to the failure.

[0105] In practice, the executing entity can read the prior distribution information of each process material parameter and the posterior distribution information obtained in step S102, and compare each parameter in the same dimension. For continuous parameters, the prior and posterior samples can be unified under the same discrete grid or the same kernel density estimation framework to form comparable probability density functions; for discrete parameters, a probability mass function is directly formed. In one possible embodiment, the degree of difference can be calculated using relative entropy (Kullback-Leibler, KL) divergence. If the prior distribution of the i-th process material parameter is denoted as Pi and the posterior distribution as Qi, then its degree of difference Di can be calculated as the KL divergence of Qi relative to Pi, that is, integrating or summing the product of Qi on each discrete or continuous interval with the logarithm of its ratio to Pi. This quantity reflects the degree to which the parameter distribution deviates from the original distribution when a failure event occurs. The greater the degree of difference, the greater the information increment of the parameter under failure conditions, and the more sensitive it is to failure attribution. For intervals where the prior probability is too small and the values ​​are unstable, a smoothing term can be added to the density estimation, or truncation and normalization can be used to ensure that the divergence calculation is feasible.

[0106] In another possible embodiment, a composite dissimilarity index can be formed by simultaneously combining posterior mean shift, variance shrinkage rate, and quantile interval shift, but the attribution ranking still uses KL divergence or equivalent information content index as the core. After completing the dissimilarity calculation of each parameter, the executing entity sorts all process material parameters from largest to smallest dissimilarity and determines key sensitive parameters. If further output of attribution results related to structural location is required, the key parameters can be mapped back to the corresponding parts, connection areas, or process stations.

[0107] When a process material parameter in a joint probabilistic surrogate model affects multiple force nodes in the load-transferring structural sections, and these multiple force nodes collectively contribute to the same crashworthiness response, the difference ranking can reflect the comprehensive contribution of that parameter to the failure event through the entire load transfer chain, rather than being limited to a single response curve. If necessary, the implementing entity can also output corresponding attribution results based on different failure events. For example, it can output one set of parameter rankings for passenger compartment intrusion failures and another set for peak deceleration failures, comparing the intersection of the two sets as common sensitive parameters in multi-objective collision safety design.

[0108] This application transforms the attribution of crashworthiness failure from a qualitative to a quantitative judgment by converting the deviation between the posterior and prior distributions into a rankable dissimilarity index. Since the dissimilarity is calculated under failure conditions, the identified key parameters directly correspond to the failure sample set, rather than merely reflecting the global variance contribution. Therefore, it can focus more on the actual dominant factors leading to substandard crashworthiness.

[0109] S104. Adjust the design values ​​of process material parameters based on the attribution results.

[0110] For example, the design values ​​of process material parameters are used to represent the target values ​​and allowable deviation ranges of process material parameters in the vehicle body structure design. The adjustment objects include both the nominal values ​​of the parameters and the manufacturing tolerance ranges. The attribution results are used to distinguish between critical and insensitive parameters, and to implement differentiated design adjustments to the parameters accordingly.

[0111] In practical implementation, the executing entity can first read the attribution results output in step S103 and divide the process material parameters into a set of critical sensitive parameters and a set of non-sensitive parameters. For critical sensitive parameters, if their posterior distribution shows a unilateral shift towards the failure direction relative to the prior distribution, the adjustment method can include moving the nominal design value of the parameter towards the safe side and simultaneously adjusting the allowable deviation range. For example, when the thickness of a certain front longitudinal beam plate is significantly biased towards a thinner range in the posterior failure distribution, the nominal design value of the plate thickness can be increased by a preset increment, and the thickness tolerance zone can be adjusted; when a certain connection strength parameter is concentrated at a low level in the posterior failure distribution, the target value of the connection strength can be increased, and the relevant process control range can be adjusted accordingly. The increment magnitude of critical sensitive parameters can be jointly determined based on the offset between the mean of the posterior distribution and the mean of the prior distribution, the failure probability gradient, or the difference ranking result. For example, parameters with larger differences can be assigned larger design correction weights.

[0112] For non-sensitive parameters, since their posterior and prior distributions differ little, the implementing entity can appropriately adjust their allowable deviation range while meeting the structural performance boundary conditions, or maintain the original nominal design value and only adjust the manufacturing control level, thereby concentrating design and manufacturing resources on key sensitive parameters. After adjusting the design values, update the parameter definition file, material card, or connection attribute database of the current vehicle body structure, and re-invoke the joint probabilistic surrogate model for rapid verification. If necessary, perform a new round of evaluation on the updated design values ​​to confirm whether the crashworthiness failure probability has decreased and whether the attribution parameter ranking has converged. If the verification results still do not meet the target requirements, the design values ​​can be iteratively updated according to the attribution results until the preset crashworthiness performance indicators are met.

[0113] It should be understood that adjusting the design values ​​of process material parameters includes adjusting the nominal design values ​​(i.e., target values ​​or center values) of the process material parameters, adjusting the manufacturing tolerance ranges (i.e., the upper and lower limits of allowable fluctuations) of the process material parameters, and also adjusting a combination of the two. Adjustments to the nominal design values ​​typically involve changes to product design drawings, while adjustments to the manufacturing tolerance ranges involve modifications to manufacturing process specifications; both constitute actual engineering changes to the vehicle body structure design parameters. These adjustments will ultimately be reflected in the updated product design drawings and manufacturing process documents, directly guiding production practice.

[0114] This application directly corrects the design values ​​of process and material parameters based on failure attribution results, so that optimization no longer relies on large-scale blind trial and error, but instead focuses on targeted adjustments around the dominant failure parameters. This maintains the efficiency of design iteration and establishes a clear mapping relationship between tolerance allocation, material selection and connection control and collision failure risk, thereby achieving design optimization of the vehicle body structure.

[0115] Optionally, in one possible implementation, before step S103, the vehicle body structure design optimization method provided in this application embodiment may further include a forward propagation step. Specifically, forward sampling is performed based on a joint probability surrogate model to obtain the probability density function or cumulative distribution function of the crashworthiness response; according to a preset failure threshold, the failure probability of the crashworthiness response exceeding the failure threshold is calculated; if the failure probability is less than or equal to the preset risk threshold, it is determined that the current vehicle body structure design meets the crashworthiness requirements, and no subsequent attribution analysis and design adjustment steps are required; if the failure probability is greater than the preset risk threshold, step S103 and subsequent step S104 are triggered. In this way, this application embodiment forms a complete technical chain of "first forward assessment of risk level, then reverse diagnosis of failure root cause" in actual engineering applications, which avoids unnecessary attribution calculations when the risk meets the standard, and ensures that the problem can be accurately located when the risk exceeds the standard, thus realizing the rational allocation of computing resources.

[0116] The vehicle body structure design optimization method provided in this application transforms high-fidelity collision simulation into an analytical probability model that can be computed in seconds by pre-establishing a three-layer Bayesian network proxy model based on the collision load transmission path. This completely eliminates the need for subsequent uncertainty propagation and attribution analysis from simulation iteration, fundamentally solving the problem of high computational cost of traditional Monte Carlo methods. Furthermore, by utilizing importance sampling, the posterior distribution under failure conditions can be accurately obtained even with extremely low failure probabilities. Quantitative attribution at the input variable level is achieved by calculating the difference between the posterior and prior distributions of various process and material parameters, such as the KL divergence. This allows for precise identification of which parameter fluctuation contributes most to crashworthiness failure, overcoming the shortcomings of existing technologies that compress all uncertainties into overall statistical characteristics without tracing back to specific parameter sources. Moreover, based on the attribution results, tolerances are tightened for key sensitive parameters and relaxed for non-sensitive parameters, forming a differentiated tolerance optimization strategy that maximizes cost reduction while ensuring the vehicle body structure meets collision safety performance standards. In the entire technical chain of "forward modeling → reverse attribution → difference optimization", under the condition that the nominal design value of the vehicle body structure has not undergone substantial changes beyond the original design space, modeling only needs to be performed once. Subsequent optimization iterations for tolerance allocation adjustments do not require rerunning the collision simulation, which greatly reduces the computational cost. It has high computational efficiency, strong physical interpretability, and convenient engineering implementation, providing an efficient, accurate, and low-cost solution for the robust design of vehicle body structures.

[0117] Figure 2 This is a flowchart illustrating another method for designing and optimizing a vehicle body structure, as provided in an embodiment of this application. Figure 2 As shown, the vehicle body structure design optimization method provided in this embodiment may include:

[0118] S201. Obtain multiple sets of sample data on process material parameters.

[0119] Each set of sample data includes process material parameters, the corresponding force transmission structure section force and impact resistance response of the process material parameters.

[0120] For example, in this embodiment, the sample data is the basic data used to train the joint probabilistic surrogate model. Each set of sample data includes the specific values ​​of the process material parameters, as well as the force transmission structure section force and crashworthiness response corresponding to that set of process material parameters. In a specific implementation, the executing entity can perform discrete or random sampling of the process material parameters based on the design variable range of the vehicle body structure, write each set of sampled values ​​into the corresponding sample record, and then input the set of process material parameters into the collision simulation model to obtain the corresponding force transmission structure section force and crashworthiness response.

[0121] Optionally, in one possible embodiment, obtaining multiple sets of sample data regarding process material parameters may include:

[0122] S21. Using the Latin hypercube sampling method, sampling is carried out within the design space of process material parameters to obtain multiple sets of sample points.

[0123] S22. Explicit dynamic finite element simulation is used to perform collision simulation on each group of sample points, and the force and impact resistance response of the force transmission structure section corresponding to each sample point are extracted from the simulation results.

[0124] For example, Latin hypercube sampling is a stratified sampling technique that can achieve uniform coverage of the entire design space with a smaller number of samples in a multidimensional parameter space, ensuring the representativeness of the samples. The design space refers to the range of values ​​allowed for each process material parameter during the engineering design phase. It is typically larger than the manufacturing tolerance range in the mass production phase, aiming to cover a wider range of parameter combinations to fully train the surrogate model's fitting ability in the nonlinear region. For example, if the design value (nominal value) of a sheet metal thickness is 2.0 mm, the design space can be set to 1.6 mm to 2.4 mm (i.e., nominal value ± 20%), while the manufacturing tolerance range in the mass production phase is only ± 0.05 mm. This application's embodiment uses the Latin hypercube sampling method to sample within the design space of each process material parameter, obtaining multiple sets of representative sample points.

[0125] Subsequently, collision simulations were performed on each set of sample points using any feasible explicit dynamic finite element simulation (preferably simulation software employing efficient contact algorithms and time integration formats to facilitate obtaining transient collision responses). During the simulation of each set of sample points, the process material parameters of the sample points were written into the corresponding component attribute files or material cards, ensuring that the finite element model was updated synchronously with parameter changes. Initial velocity boundary conditions and collision constraints were then applied in the explicit solver, recording the axial force, shear force, bending moment, or combined force transmission structure section forces during the collision, as well as the crashworthiness responses such as passenger compartment intrusion, peak acceleration, and energy absorption. Each set of sample points and its corresponding section forces and responses constitute a complete set of sample data.

[0126] In practical implementation, the collision scenario can be set as one or more of frontal, offset, or side collisions. The location of the force transmission structure section is determined based on the structural layout of the target vehicle platform. This location can correspond to key load-transfer points such as the front and middle sections of the longitudinal beams, sill beams, A-pillars, or crossbeams. Taking a frontal rigid wall collision scenario of the vehicle's front body structure as an example, process material parameters can include the thickness of the front longitudinal beam sheet metal, the wall thickness of the energy-absorbing box, the material yield strength, the material tensile strength, the material elongation, weld failure strain, and structural adhesive failure strain. The force transmission structure section force can include the front longitudinal beam section force and / or the subframe longitudinal beam section force. The crashworthiness response can include the peak intrusion of the passenger compartment and / or the B-pillar acceleration. The values ​​of these parameters vary within their respective design spaces during the sampling process, and simulation can obtain the section force and response values ​​under different parameter combinations.

[0127] By employing the aforementioned sample data acquisition method, the main variation range of process material parameters can be covered with a relatively small number of samples. Furthermore, the force of the load-transmitting structural section and the impact resistance response corresponding to each set of parameters are output together, providing a data foundation for subsequently constructing the conditional probability relationship between process material parameters, load-transmitting structural section force, and impact resistance response. This approach preserves local load transfer information during the collision process while simultaneously forming an input-output sample set suitable for Bayesian network learning, thereby supporting subsequent analysis of impact resistance failure attribution and parameter design value adjustment.

[0128] S202. Based on the collision load transmission path, construct a Bayesian network topology with process material parameters as the root node, force transmission structure section force as the intermediate node, and impact resistance performance response as the leaf node.

[0129] For example, a Bayesian network is a probabilistic graphical model that uses a directed acyclic graph to represent the probabilistic dependencies between variables. Nodes represent random variables, and directed edges represent conditional dependencies between variables. The collision load transfer path refers to the physical path by which the impact load is transferred from the front of the vehicle body to the surrounding structure of the passenger compartment during a car collision. Specifically, fluctuations in manufacturing process material parameters first affect the cross-sectional force of the force-transmitting structure, and the change in the cross-sectional force then determines the crashworthiness response of the entire vehicle. Based on this physical mechanism, the three-layer Bayesian network topology constructed in this embodiment is: manufacturing process material parameters (root node) → cross-sectional force of the force-transmitting structure (intermediate nodes) → crashworthiness response (leaf nodes).

[0130] This network structure design ensures that the causal flow in the probabilistic model perfectly aligns with the actual physical force transmission direction. When performing subsequent reverse attribution (i.e., tracing the cause from the failure event), the reasoning path can backtrack along the direction of "crash resistance response → force transmission structure section force → process material parameters," thereby accurately pinpointing which process parameter of which force transmission path caused the failure. This physical interpretability is a key feature that distinguishes this embodiment from purely data-driven models.

[0131] The specific method for constructing the Bayesian network topology is as follows: Each process material parameter involved in step S201 is used as a root node, the force transmission structure section force as an intermediate node, and the crashworthiness response as a leaf node; directed connections are established between adjacent layer nodes according to the causal relationship A→F→B. For example, the root nodes such as "front longitudinal beam sheet metal thickness" and "material yield strength" point to the intermediate node "front longitudinal beam section force," and then the intermediate node points to the leaf node "peak intrusion into the passenger compartment." Once this topology is determined, it remains unchanged throughout the subsequent modeling and inference process.

[0132] For example, Figure 3 This is a topological diagram illustrating a Bayesian network topology provided in an embodiment of this application. Figure 3 As shown, this Bayesian network topology uses process material parameters as the root node, force transmission structural section forces as intermediate nodes, and crashworthiness response as leaf nodes. Its directed edges point from the root node to the intermediate node and from the intermediate node to the leaf node, representing the physical transmission direction of the collision load along the process material parameters → force transmission structural section forces → crashworthiness response. The process material parameters include, but are not limited to: front longitudinal beam sheet metal thickness A1, energy-absorbing box wall thickness A2, longitudinal beam material yield strength A3, longitudinal beam material tensile strength A4, longitudinal beam material elongation A5, weld failure strain A6, structural adhesive failure strain A7, etc. Force transmission structural section forces include, but are not limited to: front longitudinal beam section force F1, subframe longitudinal beam section force F2, etc. Crashworthiness response includes, but is not limited to: peak intrusion into the passenger compartment B1, B-pillar acceleration B2, etc.

[0133] This application constructs a physically interpretable probabilistic graphical model framework by explicitly embedding the collision load transfer path into the topology of a Bayesian network, providing a structural foundation for subsequent conditional probability distribution learning and reverse attribution analysis.

[0134] S203. Based on sample data, learn the conditional probability distribution between adjacent layer nodes in the Bayesian network topology and establish a joint probability proxy model.

[0135] For example, in this embodiment of the application, after constructing the Bayesian network topology and obtaining sample data, it is necessary to learn the conditional probability distribution between adjacent layer nodes from the data in order to complete the parameterization of the joint probabilistic surrogate model.

[0136] For example, based on this topology, the conditional probability distributions between adjacent layer nodes can be learned by parameter learning. The first conditional probability distribution of the force transmission structure section force with respect to the process material parameters, and the second conditional probability distribution of the impact resistance response with respect to the force transmission structure section force, can both be obtained using maximum likelihood estimation or parameter estimation with regularization terms. This allows the construction of a probabilistic surrogate model that expresses the joint relationship between input parameters, load transfer, and collision response. If a Gaussian distribution is used to model the node variables, the model computational efficiency is high. In practical applications, other probability distributions can also be chosen, and this application does not limit this choice.

[0137] The joint probabilistic proxy model constructed in this application connects process material parameters, force transmission structure section forces, and crashworthiness response through load transfer paths, enabling input fluctuations to propagate layer by layer along the topology, and outputting joint probability relationships from the learned conditional probability distribution. Therefore, in subsequent crashworthiness analysis, this model can be directly used to infer the force state and response distribution of the force transmission structure section under different combinations of process material parameters, eliminating the need to repeatedly perform costly full-scale simulation calculations.

[0138] By adopting the above method, a calculable joint probability expression is formed between the process material parameters of the vehicle body structure, the cross-sectional force of the force transmission structure, and the crashworthiness response. This can simultaneously retain the load transfer mechanism and statistical uncertainty information, enabling the model to have a stronger ability to characterize crashworthiness behavior under mass production fluctuation conditions, and providing a consistent data basis for subsequent failure attribution and parameter adjustment.

[0139] Optionally, in one possible embodiment, based on sample data, learning the conditional probability distribution between adjacent layer nodes in the Bayesian network topology and establishing a joint probabilistic surrogate model may include:

[0140] S31. Obtain the prior distribution information of each process material parameter;

[0141] S32. Perform standardization preprocessing on the sample data to obtain standardized sample data; wherein, the standardized sample data are all dimensionless values.

[0142] S33. Based on prior distribution information and standardized sample data, fit the first conditional probability distribution of the force of the force transmission structure section with respect to the process material parameters, and the second conditional probability distribution of the impact resistance response with respect to the force of the force transmission structure section.

[0143] S34. Based on the Bayesian network chain decomposition rule, the prior distribution information, the first conditional probability distribution, and the second conditional probability distribution are multiplied together to assemble a joint probabilistic surrogate model.

[0144] For example, prior distribution information refers to the inherent fluctuation patterns of various process material parameters in mass production without any collision simulation or failure information. The prior distribution can be set based on at least one of the following: production line process capability, material testing data, or assembly tolerance standards. For instance, the prior distribution of the sheet metal thickness of a certain front longitudinal beam can be set as a normal distribution with a mean of 2.0 mm and a standard deviation of 0.05 mm, and the prior distribution of the yield strength of a certain material can be set as a normal distribution with a mean of 420 MPa and a standard deviation of 20 MPa. Since each process parameter originates from independent manufacturing processes (e.g., sheet thickness is determined by the stamping process, material yield strength by the heat treatment process, and weld joint failure strain by the welding process; different manufacturing processes have different physical sources and different causes of fluctuation), the prior distributions of each parameter are independent. Therefore, their joint prior distribution is the product of the prior distributions of each parameter. The prior distribution is an analytical explicit expression, allowing for direct density calculation and random sampling.

[0145] Then, the sample data undergoes standardization preprocessing. Due to significant differences in magnitude and dimensions between process material parameters (such as thickness and strength), force transmission structure cross-sectional forces (such as cross-sectional force values), and impact resistance responses (such as intrusion depth and acceleration), the data is affected. For example, the thickness is approximately 2 mm, the cross-sectional force can reach tens of kN, and the intrusion depth can reach hundreds of mm. Directly using the raw data for model training would lead to severe numerical ill-conditioning of the covariance matrix, affecting the stability and convergence of the model training. The purpose of standardization preprocessing is to eliminate the differences in magnitude and dimensions between variables, placing all variables on a uniform numerical scale. One possible implementation is the Z-score standardization method, which transforms the sample data of each variable into dimensionless values ​​with a mean of 0 and a standard deviation of 1.

[0146] Next, the process material parameters are used as the root node input, the force of the force transmission structure section is used as the intermediate node input, and the impact resistance response is used as the leaf node input. The conditional dependencies between adjacent layer nodes in the Bayesian network topology are used as constraints to perform parameter estimation or non-parametric fitting on the first conditional probability distribution and the second conditional probability distribution, respectively.

[0147] When forming the joint probabilistic surrogate model, the distributions of each layer are combined according to the Bayesian network chain decomposition relationship, so that the prior distribution of process material parameters, the conditional probability distribution of the force transmission structure section force with respect to the process material parameters, and the conditional probability distribution of the crashworthiness response with respect to the force transmission structure section force together constitute the joint probabilistic expression. For example, according to the Bayesian network chain decomposition rule, the prior distribution information, the first conditional probability distribution, and the second conditional probability distribution are multiplied to assemble the complete joint probabilistic surrogate model. This model completely describes the entire link probabilistic propagation relationship from process material parameters to force transmission structure section force and then to crashworthiness response in analytical mathematical expression form. Once this model is established, all subsequent uncertainty propagation, failure probability calculation, and reverse attribution analysis are based on this model, without the need to run any high-fidelity collision simulations.

[0148] This application transforms high-fidelity collision simulation into an analytical probability model that can be efficiently computed and repeatedly used by learning the conditional probability distribution from sample data and assembling a joint probability surrogate model, providing a computational engine for subsequent forward propagation and backward attribution analysis.

[0149] In this way, the joint probabilistic surrogate model, while maintaining the hierarchical relationship of load transfer, realizes the probabilistic transfer expression from process material parameters to structural response and then to impact resistance performance response. This allows the model to learn inter-layer dependencies using sample data while retaining the constraint effect of prior information on small sample modeling, thus obtaining a probabilistic surrogate model with a clear structure, derivability, and suitability for subsequent inference analysis.

[0150] It should be noted that the prior distribution information and sample data in this application are obtained based on manufacturing process statistics and design space sampling, respectively. The two are independent of each other and have different sources. The prior distribution information is used to characterize the parameter fluctuation range under mass production conditions, and the sample data is used to train the conditional probability distribution model.

[0151] Optionally, in one possible embodiment, fitting a first conditional probability distribution of the force on the cross-section of the force transmission structure with respect to the process material parameters, and a second conditional probability distribution of the impact resistance response with respect to the force on the cross-section of the force transmission structure, based on prior distribution information and standardized sample data, may include:

[0152] S41. Construct the first joint vector of process material parameters and force of force transmission structure section, use a hybrid probability density model to fit the joint probability density distribution of the first joint vector, and derive the first conditional probability distribution based on the fitted joint probability density distribution and prior distribution information according to Bayes' theorem.

[0153] S42. Construct a second joint vector of force transmission structure section force and impact resistance performance response, use a hybrid probability density model to fit the joint probability density distribution of the second joint vector, and perform marginalization processing based on the fitted joint probability density distribution, and derive the second conditional probability distribution based on Bayes' theorem.

[0154] For example, in a specific implementation, after standardizing the collected sample data to convert the parameters of each dimension into dimensionless values ​​and eliminating the influence of dimensional differences on the fitting results, the process material parameter samples and the force samples of the force transmission structure section can be combined into a first joint vector (for example, combining 7 process parameters and 2 section forces into a 9-dimensional vector), and then input into the mixed probability density model to obtain the first joint probability density distribution. Then, combined with the prior distribution information, the force distribution of the force transmission structure section under the constraints of the process material parameter conditions is derived based on the relationship between the joint probability and the marginal probability.

[0155] Optionally, in one possible embodiment, based on the fitted joint probability density distribution and prior distribution information, deriving the first conditional probability distribution according to Bayes' theorem may include: using the joint probability density distribution of the first joint vector as the numerator and the prior distribution information of the process material parameters as the denominator, calculating the ratio between the two to obtain the first conditional probability distribution of the force on the cross section of the force transmission structure with respect to the process material parameters.

[0156] For example, in this application, by substituting the joint probability density distribution into the joint term in Bayes' theorem and normalizing it with the prior distribution of the corresponding process material parameters, the probability distribution function of the force on the cross section of the load-bearing structure under the condition of the process material parameters can be obtained. The output of this conditional distribution function can be directly used for subsequent posterior inference and attribution analysis.

[0157] In practical applications, if a Gaussian mixture model is chosen as the mixed probability density model, it can use multiple Gaussian components to characterize the force dispersion under different working conditions, enabling the fitted joint probability density distribution to simultaneously reflect linear correlation and local clustering characteristics. In this application, the prior distribution corresponding to the denominator can be in the form of a continuous probability density function or an approximate discretized expression; this application does not impose any limitation on this. Through the above processing, the sample statistical relationship can be transformed into a conditional probability expression without increasing the number of simulations, providing a unified probabilistic basis for calculating the correlation between process material parameters and the force of the force-transmitting structural section.

[0158] Furthermore, the force samples of the load-transmitting structural sections and the crashworthiness response samples are constructed into a second joint vector (e.g., combining two section forces and two responses into a 4-dimensional vector). A similar mixed probability density model is used to fit the joint probability density distribution. Then, this joint distribution is integrated over the crashworthiness response dimension to obtain the marginal probability density of the load-transmitting structural section forces. Finally, the second conditional probability distribution of the crashworthiness response with respect to the load-transmitting structural section forces is obtained using Bayes' theorem. The crashworthiness response may include the passenger compartment intrusion, peak acceleration, or structural instability response. In practical applications, other equivalent characterization quantities can also be selected for this response index, which is not limited in this application.

[0159] Optionally, in one possible embodiment, the marginalization processing based on the fitted joint probability density distribution and the derivation of the second conditional probability distribution according to Bayes' theorem may include: integrating the joint probability density distribution of the second joint vector over the dimension of the crashworthiness response to obtain the marginal probability density distribution of the force transmission structure section force; using the joint probability density distribution of the second joint vector as the numerator and the marginal probability density distribution of the force transmission structure section force as the denominator, calculating the ratio between the two to obtain the second conditional probability distribution of the crashworthiness response with respect to the force transmission structure section force.

[0160] For example, the joint probability density function obtained by fitting the force of the load-transmitting structure section and the crashworthiness response can be denoted as f(x, y), where x represents the force of the load-transmitting structure section and y represents the crashworthiness response. Then, continuous integration is performed along the dimension containing y, and the integral result is used as the marginal probability density distribution of the force of the load-transmitting structure section. When the crashworthiness response is a multidimensional variable, integration is performed one by one along the corresponding integration interval of each dimension until a probability density expression is obtained only regarding the force of the load-transmitting structure section. Then, the fitted joint probability density distribution f(x, y) is used as the numerator, and the marginal probability density distribution f(x) is used as the denominator. Substituting these into Bayes' theorem, the second conditional probability distribution of the crashworthiness response with respect to the force of the load-transmitting structure section can be calculated. This second conditional probability distribution can be directly written into the joint probability surrogate model to characterize the influence of changes in the load of the load-transmitting structure on the collision response distribution.

[0161] The above processing explicitly expresses the statistical correlation between the force of the load-transferring structural section and the impact resistance response, and transforms the joint distribution into a conditional distribution, thus providing a probabilistic basis for deriving posterior information on process material parameters under impact failure events. Since the conditional probability distribution is determined by both the joint density and the marginal density, it can reflect the distribution shift of the impact resistance response under different load-transferring structural section force levels, thereby improving the consistency and interpretability of load transfer relationship modeling.

[0162] Understandably, in the embodiments of this application, the first conditional probability distribution is used to characterize the statistical transmission relationship of the force on the cross-section of the load-transfer structure after changes in process material parameters, and the second conditional probability distribution is used to characterize the transmission relationship of the force on the cross-section of the load-transfer structure to the impact resistance response. Together, they constitute the probabilistic relationship between adjacent nodes in the Bayesian network. By first fitting the joint distribution and then deriving the conditional distribution based on prior information and marginalization results, the model can both retain the correlation characteristics in the samples and reflect the causal dependence on the load transfer path.

[0163] After adopting the above method, the conditional probability distribution no longer relies on a single deterministic mapping, but can reflect the uncertainty propagation of manufacturing fluctuations and collision response, making the statistical relationship between the force of the force transmission structure section and the crashworthiness performance closer to the actual working conditions; at the same time, the joint distribution and marginalization derivation process can provide a calculable probabilistic basis for subsequent failure attribution and parameter adjustment, thereby improving the parameter identification accuracy and modeling consistency in vehicle body crashworthiness design.

[0164] Optionally, in one possible embodiment, the mixture probability density model is a Gaussian mixture model, and fitting the joint probability density distribution of the first joint vector using the mixture probability density model includes:

[0165] S51. Set multiple candidate component numbers and train the Gaussian mixture model using the candidate component numbers.

[0166] S52. Calculate the Bayesian information criterion value for each trained Gaussian mixture model, and select the number of candidate components that minimizes the Bayesian information criterion value as the optimal number of components.

[0167] S53. Train the Gaussian mixture model with the optimal number of components, and use the trained Gaussian mixture model as the joint probability density distribution of the first joint vector after fitting.

[0168] For example, the aforementioned mixture probability density model can employ a Gaussian Mixture Model (GMM). A Gaussian Mixture Model approximates any continuous probability distribution by a weighted sum of multiple Gaussian components, accurately representing the nonlinear relationships and coupling between variables. When training a Gaussian Mixture Model, the optimal number of components can be automatically selected using the Bayesian Information Criterion (BIC) to balance model fitting accuracy and overfitting risk. Specifically, multiple candidate component numbers (e.g., K=1, 2, 3, 4, etc.) can be set, and corresponding Gaussian Mixture Models can be trained and their BIC values ​​calculated. The candidate component number with the smallest BIC value is taken as the optimal component number, and the Gaussian Mixture Model is then retrained using this optimal component number to obtain the first joint vector joint probability density distribution used for subsequent probability derivation.

[0169] This model determines the component size by comparing candidate components, enabling the joint probability density distribution to both cover the multimodal features in the samples and avoid redundant fitting caused by too many components. The resulting joint probability density distribution can provide a stable statistical basis for subsequent derivation of the first conditional probability distribution based on Bayes' theorem, and improve the accuracy of modeling the correlation between process material parameters and the forces in the cross-section of the force transmission structure.

[0170] Optionally, in one possible embodiment, training the Gaussian mixture model with the optimal number of components may include:

[0171] S61. Cluster the sample data of the first joint vector using a clustering algorithm, and initialize the parameters of each component of the Gaussian mixture model with the clustering results.

[0172] S62. Iterate through the expected step and the maximization step alternately until the preset convergence condition is met, and then stop to obtain the trained Gaussian mixture model.

[0173] For example, during model training, a clustering algorithm (such as the K-Means algorithm) can be used to cluster the sample data. The clustering results are used to initialize the parameters of each component of the Gaussian mixture model. Then, the expectation step (E-step) and the maximization step (M-step) are executed alternately for iterative training until a preset convergence condition is met (e.g., the log-likelihood change is less than 10⁻). 6 Stop when ).

[0174] Specifically, after initialization, for each training iteration, an expectation step (E-step) is first executed to calculate the responsibility of each sample belonging to each Gaussian component based on the current component parameters. Then, a maximization step (M-step) is executed to re-estimate the mean, covariance, and weights of each component based on the responsibility, so that the model parameters approximate the sample distribution of the first joint vector round by round. The preset convergence condition can be set as the log-likelihood increment between two adjacent iterations being less than a threshold, or the change in each component parameter being less than a threshold, etc., which is not limited in this embodiment. When the preset convergence condition is met, the iteration stops and the trained Gaussian mixture model is output. This trained Gaussian mixture model serves as the joint probability density distribution of the first joint vector, which is used to derive the corresponding conditional probability distribution based on Bayes' theorem in subsequent iterations.

[0175] By using clustering results for initialization and combining expectation step and maximization step for iterative training, the model parameters can enter the stable convergence interval more quickly, and the fit to the sample distribution is closer to the local structure of the joint data. This provides a stable density representation for modeling the probabilistic relationship between process material parameters and force transmission structure section forces, thereby supporting the subsequent construction of joint probabilistic surrogate models and attribution analysis.

[0176] Furthermore, model accuracy verification is also a necessary step to ensure that the joint probabilistic surrogate model can reliably replace high-fidelity collision simulations. If the model accuracy is insufficient, the posterior inferences and attribution analysis results based on the model may deviate from the actual physical laws, leading to incorrect optimization directions. Therefore, after the model training is completed, the model's prediction accuracy and distribution reproducibility can be systematically verified.

[0177] Optionally, in one possible embodiment, after assembling the joint probabilistic surrogate model by multiplying the prior distribution information, the first conditional probability distribution, and the second conditional probability distribution according to the Bayesian network chain decomposition rule, the method provided in this application embodiment may further include a model verification step, which may include at least one of the first method and the second method. The first method is as follows:

[0178] S71. Leave-one-out cross-validation is used. Each time, a set of sample data is removed, and the joint probabilistic proxy model is retrained with the remaining sample data.

[0179] S72. Use the trained joint probabilistic surrogate model to predict the force and impact resistance response of the force transmission structure section corresponding to the removed samples.

[0180] S73. Calculate the root mean square error between the predicted value and the actual simulation value to evaluate the prediction accuracy of the joint probabilistic surrogate model.

[0181] For example, in a specific implementation, sample data can be sequentially removed according to single-group sample numbers. After each removal, the joint probabilistic surrogate model is retrained with the remaining samples. The trained model is then used to output the predicted values ​​of the force transmission structure section force and the crashworthiness response corresponding to the removed sample. The joint probabilistic surrogate model can be composed of previously learned process material parameters, the conditional probability relationship between the force transmission structure section force and the crashworthiness response, etc. Therefore, during retraining, only the probability distribution parameters are updated while keeping the Bayesian network topology unchanged. After the prediction is completed, the predicted value of each sample is compared with the corresponding finite element simulation results to obtain the error sequences of the force transmission structure section force and the crashworthiness response, respectively. The root mean square error is calculated for both types of error sequences, serving as the accuracy evaluation result of the model on the current sample set.

[0182] By employing leave-one-out cross-validation, the joint probabilistic surrogate model can fully expose the differences in response to different sample combinations under limited sample size conditions. It also quantifies the model's ability to fit the load transfer link and collision response mapping relationship as an error index, thus providing a reliable model foundation for subsequent information inference and attribution analysis based on posterior distribution. Therefore, model accuracy verification can be completed without adding a large number of additional simulation samples, and the established joint probabilistic surrogate model is verifiable and traceable.

[0183] The second method is as follows:

[0184] S81. Based on the joint probabilistic proxy model, multiple samplings are performed to generate sampled samples of the force and impact resistance response of the force transmission structure section.

[0185] S82. Perform a distribution consistency test between the sampled samples and the actual simulation samples used for training to verify the ability of the joint probabilistic surrogate model to reproduce the true collision response distribution.

[0186] For example, in specific implementation, the process material parameters can be jointly sampled using the established joint probabilistic surrogate model. Then, based on the conditional probability relationship between adjacent nodes in the Bayesian network topology, the corresponding force transmission structure section force and impact resistance response samples can be derived successively. The number of samplings can be set to a preset number that is the same as or greater than the training sample size to ensure that the sample set can cover the main probabilistic quality region. During the sampling process, the inputs of each sampling can maintain independent randomness, while the outputs are generated according to the conditional probabilities given by the model to form correlated response pairs. Subsequently, the generated samples are compared with the actual simulation samples obtained from the explicit dynamic finite element simulation during the training phase to check the distribution consistency. The comparison methods such as KS test, QQ plot, or empirical cumulative distribution function can be used to perform consistency analysis on the force transmission structure section force and impact resistance response, and the joint distribution of the two can be further jointly checked. If the difference between the sampled sample and the actual simulation sample is within a preset threshold range, it is determined that the joint probability surrogate model can reproduce the distribution of the real collision response; if the difference exceeds the threshold, it indicates that the model is insufficient in characterizing local correlation or tail probability, and it needs to return to the model parameter learning stage for correction.

[0187] This approach involves repeatedly sampling the joint probabilistic surrogate model, expanding the model output from a single prediction to a distributed set of responses. Combined with statistical tests of actual simulation samples, this verifies whether the model maintains the probabilistic structure under load transfer relationships. Therefore, without increasing the number of high-fidelity collision simulations, it confirms the model's ability to fit the real collision response distribution and provides a reliable probabilistic basis for subsequent failure attribution and design value adjustments.

[0188] By adopting the above method, the consistency of the distribution pattern can be further verified beyond the mean prediction of the collision response, so that the credibility of the joint probabilistic surrogate model can be quantitatively evaluated. At the same time, by jointly verifying the force of the force transmission structure section and the crashworthiness response, the deviation of the model in the characterization of correlation can be identified, thereby improving the consistency between the subsequent attribution analysis and design optimization results and the actual crashworthiness performance of the vehicle body.

[0189] S204. Draw multiple candidate samples from the prior distribution of process material parameters.

[0190] For example, in this application embodiment, in order to obtain the posterior distribution information of process material parameters under the condition of failure event occurrence, it is first necessary to extract a large number of candidate samples from the prior distribution as the basic sample pool for subsequent importance sampling.

[0191] Specifically, based on the prior distribution information of each process material parameter obtained in step S203 (e.g., the normal or log-normal distribution followed by each parameter and its corresponding mean and standard deviation parameters), multiple sets of candidate samples are independently drawn from the prior distribution of each parameter. Each set of candidate samples contains a complete set of values ​​for all process material parameters (e.g., 7 parameters). The number of candidate samples can be set according to actual needs, and the number of candidate samples should maintain a sufficient multiple relationship with the reciprocal of the failure probability, for example, it can be set to 10. 6 Grouped to ensure an extremely low probability of failure (e.g., 10). -3 Up to 10 -4 Even at the scale of (number of samples), there are still enough candidate samples to cover important areas near the failure domain.

[0192] Since the prior distribution is an analytical and explicit expression (such as the probability density function of the normal distribution having a clear mathematical formula), efficient random number generation and sampling operations can be performed directly using computers without relying on any simulation calculations. Therefore, the computational cost of this step is extremely low, and millions of samples can be drawn in milliseconds to seconds. By drawing a large number of candidate samples from the prior distribution, a sufficient sample base is provided for subsequently obtaining the posterior distribution under failure conditions through importance sampling.

[0193] S205. Based on the joint probabilistic surrogate model, determine the failure weight of each group of candidate samples under the crashworthiness failure event.

[0194] For example, in this embodiment of the application, for each group of candidate samples extracted in step S204, it is necessary to calculate its failure weight under the impact resistance failure event. The failure weight can be expressed as: under the condition of the force of the load-bearing structure section, the conditional probability density of the impact resistance response is integrated over the failure domain to obtain the failure weight of the candidate sample group. This failure weight reflects the tendency of the values ​​of the process material parameters of this group to cause impact resistance failure. The larger the weight, the more likely the values ​​of this group are to lead to failure in collision performance.

[0195] Specifically, for any set of candidate samples, the process material parameter values ​​in the sample are first substituted into the joint probabilistic surrogate model. The model then passes through a first conditional probability distribution to obtain the probability distribution of the force on the load-bearing structural section, and a second conditional probability distribution to obtain the probability distribution of the crashworthiness response. Then, based on preset failure event definitions (e.g., peak intrusion into the passenger compartment exceeding a first preset threshold, or B-pillar acceleration exceeding a second preset threshold), the probability that the crashworthiness response falls into the failure domain under a given load-bearing structural section force is calculated. This probability value is used as the failure weight for that set of candidate samples. The failure domain refers to the set of all possible values ​​for which the crashworthiness response does not meet design requirements.

[0196] It is worth noting that this step is calculated entirely based on the analytical expression of the joint probabilistic surrogate model, without requiring any high-fidelity collision simulations. Even with millions of candidate samples, this step can complete the calculation of all failure weights within seconds.

[0197] This step calculates the failure weight of each group of candidate samples based on a joint probabilistic surrogate model, and quantifies the correlation between "the process parameter value of the candidate sample" and "the tendency of the value to cause failure", providing a weight basis for the subsequent resampling step.

[0198] S206. Resample the candidate samples according to the failure weight to obtain a posterior sample set that follows a posterior distribution.

[0199] For example, in this embodiment of the application, after obtaining the failure weights of each group of candidate samples, the candidate samples are resampled with replacement according to the magnitude of the failure weights. Specifically, the candidate sample with the larger failure weight has a higher probability of being selected during the resampling process; the candidate sample with the smaller failure weight has a lower probability of being selected. The sample set obtained after resampling has a distribution that converges precisely to the posterior distribution of the process material parameters under the condition that the failure event occurs.

[0200] A key advantage of importance sampling is that even under conditions of extremely low failure probability (i.e., almost no failed samples in the original simulation samples), this method can still reliably obtain a sufficient number of high-weighted samples by drawing a large number of candidate samples from the prior distribution and calculating their theoretical failure weights, thereby constructing a reliable posterior distribution. This enables the embodiments of this application to achieve stable reverse attribution analysis even in high-reliability design scenarios.

[0201] Through importance sampling and resampling operations, the posterior sample set of each process material parameter under failure conditions was accurately obtained. This sample set is the data basis for subsequent calculation of KL divergence and attribution analysis.

[0202] S207. Perform forward sampling based on the joint probabilistic surrogate model to obtain the probability density function or cumulative distribution function of the crashworthiness performance response.

[0203] For example, in this application embodiment, in order to assess the failure risk level of the current vehicle body structure design under mass production conditions, it is necessary to perform forward sampling based on a joint probability surrogate model to obtain the probability distribution of the crashworthiness performance response.

[0204] Optionally, forward sampling can employ a Gibbs sampling strategy, updating the state of each node sequentially according to the network topology hierarchy to achieve the step-by-step transmission of probability fluctuations. Specifically, forward sampling proceeds step-by-step according to the hierarchical order of the Bayesian network topology: first, a large number of root node samples are extracted from the prior distribution of process material parameters; then, the root node samples are substituted into the first conditional probability distribution to extract the corresponding force samples of the force transmission structure cross-section; and finally, the cross-section force samples are substituted into the second conditional probability distribution to extract the corresponding crashworthiness response samples. After a large number of iterative samplings, a large-scale sample set of crashworthiness response can be obtained. Based on this sample set, methods such as kernel density estimation or histogram statistics can be used to obtain the probability density function or cumulative distribution function of the crashworthiness response (such as peak intrusion of the passenger compartment and B-pillar acceleration). This distribution reflects the statistical law of the vehicle's collision performance under the current design conditions (i.e., when the process material parameters fluctuate according to their mass production prior distribution). Through this distribution, engineers can intuitively understand the central trend, dispersion, and tail characteristics of the crashworthiness response.

[0205] It should be noted that forward sampling and importance sampling in steps S204 to S206 differ fundamentally in their technical purpose and sampling method: forward sampling proceeds step-by-step along the causal direction A→F→B to obtain the overall distribution characteristics of the response variable to assess the failure probability; while importance sampling first extracts candidate samples and then resamples them using failure weights to obtain the posterior distribution of parameters under failure conditions for attribution analysis. Both provide the data foundation for "forward vectorization" and "reverse attribution," respectively.

[0206] By using forward sampling based on a joint probabilistic surrogate model, the complete probability distribution of the crashworthiness response was obtained at extremely low computational cost, providing a statistical basis for subsequent calculation of failure probability.

[0207] S208. Calculate the failure probability when the impact resistance performance response exceeds the preset failure threshold based on the preset failure threshold.

[0208] For example, in this embodiment of the application, after obtaining the probability density function or cumulative distribution function of the crashworthiness response, the failure probability is calculated in conjunction with a preset failure threshold. The preset failure threshold is determined by the frontal collision crashworthiness design specifications, such as a first preset threshold for peak intrusion of the passenger compartment and / or a second preset threshold for under-B-pillar acceleration.

[0209] The failure probability can be calculated by using the failure threshold as the integration boundary and integrating the probability density function of the crashworthiness response over the failure domain (i.e., the region exceeding the threshold), or by directly reading the probability value exceeding the threshold using the cumulative distribution function. This failure probability quantitatively reflects the risk level of the current design failing to meet crash performance standards under fluctuations in mass production parameters. For example, if the calculated failure probability is 2 × 10⁻⁶... −3 This means that out of every million mass-produced vehicles, approximately 2,000 are at risk of failing to meet crash performance standards.

[0210] This step combines the probability distribution of crashworthiness response with a preset failure threshold, transforming "parameter fluctuations" into "failure risk," a quantifiable indicator that can be directly used for engineering decisions. This provides a basis for determining whether reverse attribution and design adjustments are necessary.

[0211] S209. Determine whether the failure probability is greater than the preset risk threshold.

[0212] If so, proceed to step S210.

[0213] For example, in this application embodiment, the preset risk threshold is an upper limit of acceptable failure probability pre-set by the engineer or design specifications, for example, 10. −4 Or 10 −3 The specific value can be determined based on the vehicle model positioning, regulatory requirements, and corporate quality objectives.

[0214] The failure probability calculated in step S208 is compared with a preset risk threshold. If the failure probability is less than the preset risk threshold (i.e., the judgment result is "No"), it indicates that the current vehicle body structure design has sufficient robustness under mass production parameter fluctuations, and the risk of crashworthiness failure is within an acceptable range. No further attribution analysis or design adjustments are required, and the optimization process can end. If the failure probability is greater than or equal to the preset risk threshold (i.e., the judgment result is "Yes"), it indicates that the failure risk of the current design exceeds the acceptable level. Further steps S210 to S213 are required for reverse attribution and design optimization to identify the key parameters leading to failure and make targeted adjustments.

[0215] This "assessment first, diagnosis later" process design enables the embodiments of this application to automatically determine whether in-depth analysis is needed based on the risk level in actual engineering applications, avoiding unnecessary attribution calculations when the risk meets the standard, and achieving reasonable allocation of computing resources. This step compares the calculated failure probability with a preset risk threshold to determine whether the conditions for triggering subsequent reverse attribution analysis are met, forming a complete technical chain of "forward assessment → condition triggering → reverse diagnosis".

[0216] S210. Calculate the KL divergence between the posterior and prior distribution information of the process material parameters to obtain the sensitivity index of each process material parameter.

[0217] For example, in this embodiment of the application, when the failure probability is greater than a preset risk threshold, reverse attribution analysis is initiated. In this process, a quantitative index needs to be calculated for each process material parameter to measure its contribution to impact resistance failure.

[0218] Specifically, for each process material parameter, the KL divergence between its prior distribution and the posterior distribution obtained in step S206 is calculated. KL divergence is an index in information theory that measures the degree of difference between two probability distributions. A larger value indicates a more significant shift in the posterior distribution relative to the prior distribution, meaning the parameter provides greater information gain in failure events and contributes more significantly to impact resistance failure. The calculated KL divergence value is used as a sensitivity index for the process material parameter. A larger sensitivity index indicates a greater contribution of the parameter's fluctuations to impact resistance failure, meaning the parameter is more "sensitive"; a smaller sensitivity index indicates a weaker correlation between the parameter and failure, meaning the parameter is less "sensitive."

[0219] This application does not limit how the KL divergence is calculated. Optionally, in one possible embodiment, calculating the KL divergence between the posterior and prior distribution information of the process material parameters may include:

[0220] S91. Perform kernel density estimation on the posterior sample set of posterior distribution information to obtain the posterior probability density function;

[0221] S92. For each sample point in the posterior sample set, calculate the logarithm of the ratio of the posterior probability density function value to the probability density value of the prior distribution information.

[0222] S93. Average the logarithm over the posterior sample set to obtain a numerical estimate of the KL divergence.

[0223] For example, in a specific implementation, candidate samples can first be resampled based on failure weights to form a posterior sample set. Then, a Gaussian kernel or other kernel function that meets the smooth estimation requirements is used to estimate the density of the posterior sample set. The kernel bandwidth can be determined based on the sample dispersion, sample dimension, and cross-validation results to obtain the posterior probability density function. Based on this, for each sample point in the posterior sample set, the ratio of the posterior probability density function to the prior probability density is calculated, and the natural logarithm is taken to obtain the logarithmic ratio. Subsequently, the arithmetic mean of the logarithmic ratios of all sample points is calculated to obtain a numerical estimate of the KL divergence. The prior probability density can be given by the parameter distribution before training the aforementioned joint probabilistic surrogate model, while the posterior probability density function is obtained from the statistics of the resampled samples.

[0224] This implementation transforms the empirical distribution on the posterior sample set into a continuous density form and compares the density difference between the posterior and prior at the same sample point, thus forming a stable divergence estimation result. Because it uses kernel density estimation instead of directly relying on parameterized distribution assumptions, it can adapt to the non-Gaussian, skewed, or multimodal distribution characteristics of process material parameters under failure conditions, thereby enabling the KL divergence to more accurately reflect the attribution strength of process material parameters in failure events. After adopting this numerical estimation method, the divergence value can be directly input into the subsequent threshold discrimination process to distinguish between key sensitive parameters and non-sensitive parameters, thus providing a basis for adjusting the design values ​​of the vehicle body structure process material parameters.

[0225] This step quantifies the contribution of each process material parameter to failure into a specific numerical value by calculating the KL divergence, achieving quantitative attribution at the input variable level and providing accurate numerical basis for subsequent parameter classification and differentiated adjustment.

[0226] S211. Process material parameters with sensitivity indices greater than or equal to a first preset threshold are identified as key sensitive parameters, and process material parameters with sensitivity indices less than or equal to a second preset threshold are identified as non-sensitive parameters.

[0227] For example, in this embodiment of the application, after obtaining the sensitivity index (i.e., KL divergence value) of each process material parameter, the parameters are classified according to a preset threshold. Specifically, process material parameters with a sensitivity index greater than or equal to a first preset threshold are identified as key sensitive parameters. The posterior distribution of these parameters is significantly shifted relative to the prior distribution, indicating that their fluctuations are the main contributing factor to crashworthiness failure, and they need to be focused on being controlled in subsequent optimizations. Process material parameters with a sensitivity index less than or equal to a second preset threshold are identified as non-sensitive parameters. The posterior distribution of these parameters is basically consistent with the prior distribution, indicating that their fluctuations are weakly or unrelated to failure events, and their control requirements can be relaxed in subsequent optimizations to reduce manufacturing costs.

[0228] For process material parameters whose sensitivity index falls between the first preset threshold and the second preset threshold, they can be flexibly handled according to actual engineering needs. They can be moderately controlled according to medium sensitivity, or classified into one of the two categories mentioned above. This application does not impose any restrictions on this. The first preset threshold and the second preset threshold can be set by engineers according to the safety requirements and cost targets of the actual project. They can be the same or different.

[0229] Based on the above classification, the embodiments of this application divide numerous process material parameters into two categories: "a few critical" and "most insensitive," providing a clear classification basis for differentiated tolerance optimization strategies.

[0230] This step discretizes the continuously distributed sensitivity index into parameter categories through threshold comparison, making the attribution results more intuitive and easier to understand, and allowing engineers to directly formulate targeted optimization plans based on the classification results.

[0231] S212. Narrow the manufacturing tolerance range of critical sensitive parameters, and / or shift the nominal design value of critical sensitive parameters in a direction that is conducive to improving crashworthiness.

[0232] For example, in this application embodiment, for process material parameters identified as critical sensitive parameters, since their fluctuations contribute the most to impact resistance failure, strict optimization measures should be taken to reduce their adverse effects. Specifically, at least one of the following two methods can be adopted:

[0233] (1) Narrowing the manufacturing tolerance range of critical sensitive parameters. The manufacturing tolerance range refers to the upper and lower limits within which the parameter is allowed to fluctuate during mass production. Narrowing the tolerance range means increasing the manufacturing precision requirements, thereby reducing the actual fluctuation range of the parameter and minimizing its adverse impact on impact resistance. For example, if the manufacturing tolerance of a sheet metal thickness was originally ±0.05mm (the nominal design value), and it is identified as a critical sensitive parameter through attribution analysis, the tolerance can be tightened to ±0.02mm. This method directly reduces the uncertainty of the parameter and is one of the most effective means of improving product robustness.

[0234] (2) Shift the nominal design values ​​of key sensitive parameters in a direction that is conducive to improving crashworthiness. The nominal design value refers to the target value marked on the design drawings. Shifting it in a direction that is conducive to improving crashworthiness means that if increasing the parameter is conducive to improving crashworthiness (for example, the higher the yield strength, the better the energy absorption effect), then the nominal value is adjusted to increase; conversely, if decreasing the parameter is conducive to improving crashworthiness, then the nominal value is adjusted to decrease. Shifting the nominal value increases the safety margin, making it less likely that the parameter value will fall into the failure domain even if there are certain manufacturing fluctuations.

[0235] The two methods described above can be used individually or in combination. For example, for a material whose yield strength is identified as a critical sensitive parameter, its nominal value can be increased from 420MPa to 440MPa, while its tolerance can be tightened from ±20MPa to ±10MPa, thus providing double protection to reduce the risk of failure.

[0236] This step precisely suppresses the adverse effects of major failure sources by tightening tolerances and / or shifting nominal values ​​for key sensitive parameters, achieving an effective reduction in failure risk at minimal cost (tightening only a few key parameters).

[0237] S213. Expand the manufacturing tolerance range of non-sensitive parameters.

[0238] For example, in the embodiments of this application, for process material parameters identified as non-sensitive parameters, since their fluctuations contribute little or almost nothing to the failure of impact resistance performance, their manufacturing tolerance range can be appropriately increased.

[0239] Expanding the manufacturing tolerance range means reducing the precision requirements for that parameter, which directly leads to lower manufacturing costs, reduces product sorting, rework, and scrap costs, and improves manufacturing yield and production efficiency. For example, if the manufacturing tolerance for the failure strain of a structural adhesive was originally the nominal design value of ±0.02mm, but is identified as a non-sensitive parameter through attribution analysis, the tolerance can be widened to ±0.05mm, thereby reducing the manufacturing cost of that process.

[0240] It is worth noting that the tolerance relaxation for non-sensitive parameters should be carried out on the premise that the overall failure probability does not exceed the preset risk threshold. In practical engineering applications, the tolerance of non-sensitive parameters can be gradually relaxed. After each relaxation, the failure probability should be quickly recalculated using a joint probability surrogate model. Once it is confirmed that the failure probability still meets the requirements, the tolerance can be further relaxed until the optimal balance between cost and performance is achieved.

[0241] This step, by relaxing the tolerances of non-sensitive parameters, minimizes manufacturing costs while ensuring that the vehicle body structure meets crashworthiness standards. Together with S212, it constitutes a differentiated optimization strategy of "tightening key sensitive parameters and relaxing non-sensitive parameters".

[0242] The vehicle body structure design optimization method provided in this application establishes a joint probabilistic surrogate model through steps S201 to S203, transforming high-fidelity crash simulation into an analytical probabilistic model that can be efficiently computed. Then, through steps S207 to S209, forward propagation is performed to calculate the failure probability, assessing the failure risk level of the current design and determining whether optimization is necessary. When the failure risk exceeds the limit, importance sampling is performed through steps S204 to S206 to obtain the posterior distribution under failure conditions. Then, through steps S210 to S211, KL divergence is calculated for quantitative attribution, accurately identifying key sensitive and insensitive parameters. Finally, through steps S212 to S213, tolerances for key sensitive parameters are tightened or nominal values ​​are shifted, while tolerances for insensitive parameters are relaxed, achieving differentiated design optimization. Throughout the entire process, provided that the optimization iterations do not exceed the original design space boundaries, the joint probabilistic surrogate model only needs to be established once. Subsequent forward propagation, failure probability calculation, and reverse attribution analysis do not require rerunning the high-fidelity crash simulation, resulting in high computational efficiency. When design iterations exceed the original design space, modeling can be re-executed within the updated design space to ensure the model's prediction accuracy in the new region. A three-layer Bayesian network topology ensures the physical interpretability of probabilistic inference; KL divergence attribution enables precise attribution at the input variable level; and a differentiated tolerance adjustment strategy minimizes manufacturing costs while ensuring safety.

[0243] Figure 4 A schematic diagram of a vehicle body structure design optimization device provided in this application embodiment is shown below. Figure 4 As shown, the vehicle body structure design optimization device 40 provided in this embodiment includes: a first processing unit 401, a second processing unit 402, a third processing unit 403, and a fourth processing unit 404.

[0244] The first processing unit 401 is used to obtain the joint probability proxy model of the current vehicle body structure. The joint probability proxy model adopts a Bayesian network topology structure constructed based on the collision load transmission path, with process material parameters as the root node, force transmission structure section force as the intermediate node, and crashworthiness response as the leaf node. The joint probability proxy model is used to characterize the conditional probability distribution between adjacent layer nodes.

[0245] The second processing unit 402 is used to determine the posterior distribution information of process material parameters under the condition that a crashworthiness failure event occurs, based on a joint probabilistic surrogate model.

[0246] The third processing unit 403 is used to determine the attribution result that leads to the failure of impact resistance performance based on the degree of difference between the posterior distribution information and the prior distribution information of the process material parameters.

[0247] The fourth processing unit 404 is used to adjust the design values ​​of process material parameters based on the attribution results.

[0248] In one possible implementation, the first processing unit 401 is specifically used for:

[0249] Obtain multiple sets of sample data on process material parameters; each set of sample data includes the process material parameters, the corresponding force transmission structure section force and impact resistance response of the process material parameters;

[0250] Based on the collision load transmission path, a Bayesian network topology is constructed with process material parameters as the root node, force transmission structure section force as the intermediate node, and impact resistance performance response as the leaf node.

[0251] Based on sample data, we learn the conditional probability distribution between adjacent layer nodes in the Bayesian network topology and establish a joint probability proxy model.

[0252] In one possible implementation, the first processing unit 401 is specifically used for:

[0253] The Latin hypercube sampling method is used to sample within the design space of process material parameters to obtain multiple sets of sample points.

[0254] Explicit dynamic finite element simulation was used to perform collision simulations on each group of sample points, and the force and impact resistance response of the force transmission structure section corresponding to each sample point were extracted from the simulation results.

[0255] In one possible implementation, the first processing unit 401 is specifically used for:

[0256] Obtain prior distribution information of various process material parameters;

[0257] The sample data is preprocessed to standardize it, resulting in standardized sample data; all standardized sample data are dimensionless values.

[0258] Based on prior distribution information and standardized sample data, the first conditional probability distribution of the force of the force transmission structure section with respect to the process material parameters and the second conditional probability distribution of the impact resistance response with respect to the force of the force transmission structure section are fitted respectively.

[0259] Based on the Bayesian network chain decomposition rule, the prior distribution information, the first conditional probability distribution, and the second conditional probability distribution are multiplied together to assemble a joint probabilistic surrogate model.

[0260] In one possible implementation, the first processing unit 401 is specifically used for:

[0261] A first joint vector of process material parameters and force of force transmission structure section is constructed. The joint probability density distribution of the first joint vector is fitted by a hybrid probability density model. Based on the fitted joint probability density distribution and prior distribution information, the first conditional probability distribution is derived according to Bayes' theorem.

[0262] A second joint vector of force transmission structure section force and impact resistance performance response is constructed. The joint probability density distribution of the second joint vector is fitted by a hybrid probability density model. Based on the fitted joint probability density distribution, marginalization is performed. The second conditional probability distribution is derived according to Bayes' theorem.

[0263] In one possible implementation, the mixture probability density model is a Gaussian mixture model, and the first processing unit 401 is specifically used for:

[0264] Set multiple candidate component numbers and train the Gaussian mixture model using the candidate component numbers;

[0265] Calculate the Bayesian information criterion value for each trained Gaussian mixture model, and select the number of candidate components that minimizes the Bayesian information criterion value as the optimal number of components.

[0266] The Gaussian mixture model is trained with the optimal number of components, and the trained Gaussian mixture model is used as the joint probability density distribution of the first joint vector after fitting.

[0267] In one possible implementation, the first processing unit 401 is specifically used for:

[0268] A clustering algorithm is used to cluster the sample data of the first joint vector, and the clustering results are used to initialize the parameters of each component of the Gaussian mixture model.

[0269] The expected step and the maximization step are executed alternately for iterative training until the preset convergence condition is met, and then the trained Gaussian mixture model is obtained.

[0270] In one possible implementation, the first processing unit 401 is specifically used for:

[0271] Using the joint probability density distribution of the first joint vector as the numerator and the prior distribution information of the process material parameters as the denominator, the ratio of the two is calculated to obtain the first conditional probability distribution of the force on the cross section of the force transmission structure with respect to the process material parameters.

[0272] In one possible implementation, the first processing unit 401 is specifically used for:

[0273] Integrating the joint probability density distribution of the second joint vector over the dimension of the crashworthiness response yields the edge probability density distribution of the force at the cross section of the force-transmitting structure.

[0274] Using the joint probability density distribution of the second joint vector as the numerator and the marginal probability density distribution of the force at the cross section of the force transmission structure as the denominator, the ratio of the two is calculated to obtain the second conditional probability distribution of the impact resistance performance response with respect to the force at the cross section of the force transmission structure.

[0275] In one possible implementation, the first processing unit 401 is further configured to perform a model verification step, which includes at least one of the following verification methods:

[0276] The first method:

[0277] Leave-one-out cross-validation is used, where a set of sample data is removed each time, and the joint probabilistic surrogate model is retrained with the remaining sample data.

[0278] The trained joint probabilistic surrogate model is used to predict the force and impact resistance response of the force transmission structure section corresponding to the removed samples.

[0279] Calculate the root mean square error between the predicted values ​​and the actual simulated values ​​to evaluate the prediction accuracy of the joint probabilistic surrogate model;

[0280] The second method:

[0281] Multiple samplings are performed based on a joint probabilistic proxy model to generate sampled samples of the force and impact resistance response of the force-transmitting structure section.

[0282] The sampled samples were compared with the actual simulation samples used for training to verify the ability of the joint probabilistic surrogate model to reproduce the true collision response distribution.

[0283] In one possible implementation, the second processing unit 402 is specifically used for:

[0284] Multiple candidate samples are extracted from the prior distribution information of process material parameters;

[0285] Based on the joint probabilistic surrogate model, the failure weight of each group of candidate samples under the crashworthiness failure event is determined respectively.

[0286] Candidate samples are resampled based on failure weights to obtain a posterior sample set that follows a posterior distribution.

[0287] In one possible implementation, the third processing unit 403 is specifically used for:

[0288] The KL divergence between the posterior and prior distribution information of the process material parameters is calculated to obtain the sensitivity index of each process material parameter.

[0289] Process material parameters with sensitivity indices greater than or equal to a first preset threshold are identified as critical sensitive parameters, while process material parameters with sensitivity indices less than or equal to a second preset threshold are identified as non-sensitive parameters.

[0290] In one possible implementation, the third processing unit 403 is specifically used for:

[0291] The kernel density is estimated on the posterior sample set of the posterior distribution information to obtain the posterior probability density function;

[0292] For each sample point in the posterior sample set, calculate the logarithm of the ratio of the posterior probability density function value to the probability density value of the prior distribution information.

[0293] The logarithm is averaged over the posterior sample set to obtain a numerical estimate of the KL divergence.

[0294] In one possible implementation, the fourth processing unit 404 is specifically used for:

[0295] Narrow the manufacturing tolerance range of critical sensitive parameters, and / or shift the nominal design values ​​of critical sensitive parameters in a direction that is conducive to improving crashworthiness;

[0296] Expand the manufacturing tolerance range of non-sensitive parameters.

[0297] In one possible implementation, the third processing unit 403 is further configured to:

[0298] Forward sampling is performed based on a joint probabilistic surrogate model to obtain the probability density function or cumulative distribution function of the crashworthiness response;

[0299] Based on the preset failure threshold, calculate the failure probability when the impact resistance performance response exceeds the failure threshold;

[0300] If the failure probability is greater than the preset risk threshold, then the step of determining the attribution result that caused the crashworthiness failure is executed based on the difference between the posterior distribution information and the prior distribution information of the process material parameters.

[0301] In one possible implementation, the process material parameters include at least one of the following: front longitudinal beam sheet metal thickness, energy-absorbing box wall thickness, material yield strength, material tensile strength, material elongation, weld joint failure strain, and structural adhesive failure strain.

[0302] The forces transmitted through the structural sections include: the forces on the front longitudinal beams and / or the forces on the subframe longitudinal beams;

[0303] Crash resistance response includes: peak intrusion into the passenger compartment and / or B-pillar acceleration.

[0304] The apparatus provided in this embodiment can execute the method provided in the above method embodiment. Its implementation principle and technical effect are similar, and will not be described in detail here.

[0305] Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Figure 5 As shown, the electronic device 50 provided in this embodiment includes at least one processor 501 and a memory 502. Optionally, the device 50 further includes a communication component 503. The processor 501, memory 502, and communication component 503 are connected via a bus 504.

[0306] In a specific implementation, at least one processor 501 executes computer execution instructions stored in memory 502, causing at least one processor 501 to perform the above-described method.

[0307] The specific implementation process of processor 501 can be found in the above method embodiments, and its implementation principle and technical effect are similar. It will not be repeated here.

[0308] In the above embodiments, it should be understood that the processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor.

[0309] The memory may include random access memory (RAM) and may also include non-volatile memory (NVM), such as at least one disk storage device.

[0310] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, the buses shown in the accompanying drawings are not limited to a single bus or a single type of bus.

[0311] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0312] This application also provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the above-described method.

[0313] The aforementioned readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The readable storage medium can be any available medium accessible to a general-purpose or special-purpose computer.

[0314] An exemplary readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the readable storage medium. Of course, the readable storage medium can also be a component of the processor. The processor and the readable storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and the readable storage medium can exist as discrete components in the device.

[0315] The division of units is merely a logical functional division; in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or units, and may be electrical, mechanical, or other forms.

[0316] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0317] In addition, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0318] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0319] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0320] Finally, it should be noted that other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This invention is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein, and is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is limited only by the appended claims.

Claims

1. A method for designing and optimizing a vehicle body structure, characterized in that, The method comprises: obtaining a joint probability proxy model of a current vehicle body structure; wherein the joint probability proxy model adopts a Bayesian network topological structure constructed according to a crash load transmission path, with process material parameters as root nodes, with force transmission structure section forces as intermediate nodes, and with crashworthiness responses as leaf nodes, and the joint probability proxy model is used to represent the conditional probability distribution between adjacent layer nodes; based on the joint probability proxy model, determining the posterior distribution information of the process material parameters under the condition that a crashworthiness failure event occurs; determining the attribution result of causing the crashworthiness failure according to the difference between the posterior distribution information and the prior distribution information of the process material parameters; adjusting the design value of the process material parameters according to the attribution result.

2. The method of claim 1, wherein, The method comprises: obtaining a plurality of sets of sample data about process material parameters; wherein each set of sample data comprises the process material parameters, the corresponding force transmission structure section forces of the process material parameters, and the crashworthiness responses; constructing a Bayesian network topological structure according to the crash load transmission path, with the process material parameters as root nodes, with the force transmission structure section forces as intermediate nodes, and with the crashworthiness responses as leaf nodes; based on the sample data, learning the conditional probability distribution between adjacent layer nodes in the Bayesian network topological structure, and establishing the joint probability proxy model.

3. The method of claim 2, wherein, The method comprises: using the Latin hypercube sampling method to sample in the design space of the process material parameters, and obtaining a plurality of sets of sample points; using explicit dynamics finite element simulation to perform crash simulation on each set of sample points, and extracting the corresponding force transmission structure section forces and crashworthiness responses from the simulation results.

4. The method of claim 2, wherein, The method comprises: obtaining prior distribution information of each process material parameter; performing standardization preprocessing on the sample data to obtain standardized sample data; wherein the standardized sample data are all dimensionless values; based on the prior distribution information and the standardized sample data, fitting a first conditional probability distribution of the force transmission structure section forces with respect to the process material parameters, and a second conditional probability distribution of the crashworthiness responses with respect to the force transmission structure section forces; according to the Bayesian network chain decomposition rule, multiplying the prior distribution information, the first conditional probability distribution, and the second conditional probability distribution to assemble the joint probability proxy model.

5. The method of claim 4, wherein, The method comprises: based on the prior distribution information and the standardized sample data, fitting a first conditional probability distribution of the force transmission structure section forces with respect to the process material parameters, and a second conditional probability distribution of the crashworthiness responses with respect to the force transmission structure section forces. Construct a first joint vector of the process material parameters and the force of the cross section of the force transmission structure, fit the joint probability density distribution of the first joint vector using a hybrid probability density model, and derive the first conditional probability distribution based on the fitted joint probability density distribution and the prior distribution information according to Bayes' theorem. A second joint vector of the force transmission structure section force and the impact resistance performance response is constructed. The joint probability density distribution of the second joint vector is fitted using a hybrid probability density model. Marginalization is performed based on the fitted joint probability density distribution. The second conditional probability distribution is derived based on Bayes' theorem.

6. The method of claim 5, wherein, The mixed probability density model is a Gaussian mixture model, and the fitting of the joint probability density distribution of the first joint vector using the mixed probability density model includes: Set multiple candidate component numbers, and train a Gaussian mixture model with the number of candidate component numbers; Calculate the Bayesian information criterion value for each trained Gaussian mixture model, and select the number of candidate components that minimizes the Bayesian information criterion value as the optimal number of components. The Gaussian mixture model is trained with the optimal number of components, and the trained Gaussian mixture model is used as the joint probability density distribution of the fitted first joint vector.

7. The method of claim 6, wherein, Training the Gaussian mixture model with the optimal number of components includes: A clustering algorithm is used to cluster the sample data of the first joint vector, and the clustering results are used to initialize the parameters of each component of the Gaussian mixture model. The expected step and the maximization step are executed alternately for iterative training until the preset convergence condition is met, and then the trained Gaussian mixture model is obtained.

8. The method of claim 5, wherein, The derivation of the first conditional probability distribution based on the joint probability density distribution obtained from the fitting and the prior distribution information, according to Bayes' theorem, includes: Using the joint probability density distribution of the first joint vector as the numerator and the prior distribution information of the process material parameters as the denominator, the ratio of the two is calculated to obtain the first conditional probability distribution of the force of the force transmission structure section with respect to the process material parameters.

9. The method of claim 5, wherein, The marginalization process of the joint probability density distribution obtained from the fitting, and the derivation of the second conditional probability distribution based on Bayes' theorem, includes: Integrating the joint probability density distribution of the second joint vector over the dimension of the crashworthiness response yields the edge probability density distribution of the force at the cross-section of the force transmission structure. Using the joint probability density distribution of the second joint vector as the numerator and the marginal probability density distribution of the force at the cross-section of the force transmission structure as the denominator, the ratio of the two is calculated to obtain the second conditional probability distribution of the impact resistance response with respect to the force at the cross-section of the force transmission structure.

10. The method of claim 4, wherein, The method further includes a model validation step, which includes at least one of the following validation methods: The first method is to use leave-one-out cross-validation, where a set of sample data is removed each time, and the joint probabilistic surrogate model is retrained with the remaining sample data; the trained joint probabilistic surrogate model is used to predict the force and impact resistance response of the force transmission structure section corresponding to the removed samples; the root mean square error between the predicted value and the actual simulation value is calculated to evaluate the prediction accuracy of the joint probabilistic surrogate model. The second approach involves performing multiple samplings based on the joint probabilistic surrogate model to generate sampled samples of the force and impact resistance response of the force-transmitting structure section; then, the sampled samples are compared with the actual simulation samples used for training to verify the ability of the joint probabilistic surrogate model to reproduce the true collision response distribution.

11. The method of claim 1, wherein, The determination of the posterior distribution information of the process material parameters based on the joint probabilistic surrogate model under the condition of a crashworthiness failure event includes: Multiple candidate samples are extracted from the prior distribution information of the process material parameters; Based on the joint probabilistic proxy model, the failure weight of each group of candidate samples under the crashworthiness failure event is determined respectively; The candidate samples are resampled according to the failure weights to obtain a posterior sample set that follows the posterior distribution.

12. The method of claim 1, wherein, The determination of the attribution result for the failure of impact resistance performance based on the difference between the posterior distribution information and the prior distribution information of the process material parameters includes: The KL divergence between the posterior distribution information and the prior distribution information of the process material parameters is calculated respectively to obtain the sensitivity index of each process material parameter; Process material parameters with sensitivity indices greater than or equal to a first preset threshold are identified as key sensitive parameters, while process material parameters with sensitivity indices less than or equal to a second preset threshold are identified as non-sensitive parameters.

13. The method of claim 12, wherein, The calculation of the KL divergence between the posterior distribution information and the prior distribution information of the process material parameters includes: The kernel density is estimated on the posterior sample set of the posterior distribution information to obtain the posterior probability density function; For each sample point in the posterior sample set, calculate the logarithm of the ratio of the posterior probability density function value to the probability density value of the prior distribution information; The logarithm is averaged over the posterior sample set to obtain a numerical estimate of the KL divergence.

14. The method of claim 12, wherein, The step of adjusting the design values ​​of the process material parameters based on the attribution results includes: Narrowing the manufacturing tolerance range of the critical sensitive parameters, and / or shifting the nominal design value of the critical sensitive parameters in a direction that is conducive to improving crashworthiness; Expand the manufacturing tolerance range of the aforementioned non-sensitive parameters.

15. The method of any one of claims 1-14, wherein, Before determining the attribution result for the impact resistance failure based on the difference between the posterior and prior distribution information of the process material parameters, the method further includes: Forward sampling is performed based on the joint probabilistic proxy model to obtain the probability density function or cumulative distribution function of the crashworthiness response; Based on a preset failure threshold, calculate the failure probability that the impact resistance response exceeds the failure threshold; If the failure probability is greater than a preset risk threshold, then the step of determining the attribution result that leads to the failure of the impact resistance performance is performed based on the difference between the posterior distribution information and the prior distribution information of the process material parameters.

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