Automobile rear subframe rigidity and NVH (Noise Vibration and Harshness) two-target design method, equipment and medium

Abstract

The invention discloses an automobile rear subframe rigidity and NVH two-target design method, device and medium, and the method comprises the steps: (1) determining an automobile rear subframe optimization variable, and building an automobile rear subframe rigidity and NVH two-target mathematical optimization model; (2) generating a population based on Latin hypercube sampling, and obtaining stiffness values and NVH values of population individuals through simulation analysis; (3) in the first stage, generating a candidate solution through dimension reconstruction, and screening offspring individuals by adopting non-dominated sorting and angle penalty distance; (4) in the second stage, three groups are obtained based on mutual information and differential grouping and used for collaborative optimization to generate candidate solutions, and a multi-criterion method based on machine learning is adopted to screen offspring individuals; and (5) performing simulation evaluation on the offspring individuals, updating the database, updating the population in combination with an angle cosine screening function, and turning to the step (3) until the optimized structure meets the requirement. According to the method, efficient design is realized through an optimization strategy of dimension reconstruction and grouping collaboration.

Description

Technical Field

[0001] The present invention relates to the fields of general artificial intelligence technology and swarm intelligence, and more specifically, to a dual-objective design method, device, and medium for the stiffness and NVH of an automobile rear subframe. Background Art

[0002] As the core load-bearing component of the chassis system, the rear subframe directly impacts the vehicle's handling stability, ride comfort, and safety. Its stiffness determines its ability to resist deformation under dynamic loads, while NVH (Noise, Vibration, and Harshness) affects the transmission of noise and vibration inside the vehicle. Together, these two components constitute a key indicator of user-perceived quality. Maintaining or even optimizing stiffness and NVH performance while reducing material usage has become a technical bottleneck in chassis engineering design.

[0003] In current engineering practice, heuristic algorithms such as genetic algorithms and particle swarm optimization show strong adaptability in single-objective optimization, but there are significant bottlenecks when dealing with the dual-objective optimization of stiffness and NVH: First, the adjustment of stiffness parameters will cause modal frequency shifts and vibration node reorganization, and the nonlinear coupling relationship between the two is difficult to accurately model using traditional response surface methods; second, each design iteration requires the use of multidisciplinary models such as finite element static analysis, frequency response function calculation, and acoustic boundary element simulation. A single evaluation takes up to several hours, and the high computational load seriously restricts the full exploration of the design space, causing traditional methods to often fall into local optimal solutions and making it difficult to obtain a high-precision Pareto front within a limited engineering cycle.

[0004] Current machine learning technology has broken through the bottleneck of traditional optimization and reduced computing costs by constructing intelligent machine learning methods such as Gaussian process regression and deep neural networks. However, it still has systemic defects: the search space grows exponentially with the increase in the number of decision variables. Traditional evolutionary strategies and mutation operations may face a "two steps forward, one step back" situation, so the evolutionary trajectory may show different oscillations and the optimization efficiency is low; on the other hand, the traditional single-objective-oriented optimization architecture is difficult to meet the parallel optimization requirements of multi-dimensional performance indicators such as the stiffness modal matching of the rear subframe of the vehicle and the NVH frequency response control, making it difficult to achieve the global optimal solution search under engineering constraints. Summary of the Invention

[0005] In response to the above-mentioned defects and the improvement needs required by the existing technology, the present invention proposes a two-objective design method, equipment, and medium for automobile rear subframe stiffness and NVH, and realizes efficient design by constructing a two-stage optimization framework.

[0006] To achieve the above objectives, according to one aspect of the present invention, a dual-objective design method for automobile rear subframe stiffness and NVH is provided, the method comprising the following steps: Step (1): Taking the geometric parameters of the front and rear crossbeams, left and right longitudinal beams, and swing arm connecting plates of the rear subframe as optimization variables, a high-dimensional design space is determined simultaneously. Taking the stiffness and NVH of the rear subframe as optimization targets, a two-objective mathematical optimization model of stiffness and NVH is established based on the SFE-Concept. Step (2): In a high-dimensional design space, determine the population size based on the number of dimensions N ; Generated using Latin hypercube sampling method N The population is constructed by individual vectors, the stiffness value is extracted through static simulation, the first-order modal frequency is calculated using the Lanczos method of Nastran software to quantify the NVH value, and a database is constructed; Step (3): In the first stage before the simulation times are more than half, a dimension reconstruction strategy driven by screening preference is adopted to achieve dimension reduction of optimization variables by adjusting weights, a Kriging machine learning model is constructed and candidate solutions are generated based on the model, and offspring individuals are screened using non-dominated sorting and angle penalty distance; Step (4): In the second stage when the number of simulations exceeds half, the influence of the optimization variables on the target is analyzed based on the mutual information, and the nonlinear interaction characteristics between the optimization variables are analyzed by combining the differential grouping method. The high-dimensional design space is divided into high-sensitivity optimization variable groups, low-impact inert optimization variable groups, and strong-coupling optimization variable groups to achieve dimensionality reduction of the optimization variables. A local radial basis function machine learning model is constructed for each group. The optimization variables in each group are optimized through the group co-evolution strategy to generate candidate solutions, and the offspring individuals are screened using a multi-criteria method based on machine learning. Step (5): Simulate and evaluate the offspring individuals, update the database, calculate the directional difference between the offspring individuals and the database individuals based on the angle cosine screening function, and update the population based on the difference value. If the optimized structure does not meet the requirements, go to step (3); otherwise, output all the optimized structures obtained.

[0007] Furthermore, the specific steps of step (1) are as follows: The first step is to build a geometric model in CATIA based on the rear subframe assembly and geometric requirements. Then, HyperMesh is used to clean up the geometric model in CATIA, including geometric repair and feature simplification. The second step is to determine the design tolerances for the height, thickness, and position of the rear subframe's front and rear cross members, left and right longitudinal members, and swing arm connecting plates, taking into account material strength, manufacturing process, and assembly space constraints. In the third step, based on the assumption of structural symmetry, the left and right longitudinal beams were simplified into a single-variable topology. This means that the parameters of one of the longitudinal beams were selected for optimization. Ultimately, the geometric parameters of the front and rear crossbeams and longitudinal beams, including shape, width, height, thickness position, curvature, thickness, and material, and the height, thickness, and position of the swing arm connecting plate parameters, were selected as optimization variables. In the fourth step, an implicit parameterized mathematical model was constructed based on the SFE-Concept platform, with the rear subframe stiffness and NVH as the optimization targets. The corresponding mathematical expression is as follows: , In the above formula, X represents the optimization variable of the rear subframe structure of the automobile. The number of optimization variables is 25. The front crossbeam is composed of the first front crossbeam in the front half and the second front crossbeam in the rear half. The rear crossbeam is composed of the first rear crossbeam in the front half and the second rear crossbeam in the rear half. Indicates the shape of the front crossbeam, Indicates the width of the first front crossbeam, Indicates the width of the second front crossbeam, Indicates the height of the upper end of the front crossbeam. Indicates the height of the lower end of the front crossbeam. Indicates the thickness of the first front cross member, Indicates the thickness of the second front cross member, Indicates the distance the rear crossbeam moves. Indicates the shape of the rear cross member, Indicates the width of the first rear cross member, Indicates the width of the second rear cross member, Indicates the height of the upper end of the rear crossbeam. Indicates the height of the lower end of the rear crossbeam. Indicates the thickness of the first rear cross member, Indicates the thickness of the second rear cross member, represents the curvature of the longitudinal beam, Indicates the length of the longitudinal beam, Indicates the width of the longitudinal beam, Indicates the longitudinal beam height, Indicates the thickness of the longitudinal beam, Indicates the height of the swing arm connecting plate, Indicates the thickness of the swing arm connecting plate, Indicates the position of the swing arm connecting plate. Indicates the height of the swing arm connecting plate, Indicates the thickness of the swing arm connecting plate, Indicates the stiffness value of the rear subframe of the car, The first order natural frequency of the NVH value of the rear subframe of the vehicle is expressed as follows: It represents the high-dimensional design space composed of the optimization variables of the rear subframe structure of the automobile. Find represents the definition of the optimization variables, Objective represents the optimization goal, Min represents the minimization of the optimization goal, and St represents the optimization variables being within the design allowable domain.

[0008] Furthermore, the specific steps of step (2) are as follows: The first step is to determine the value range of all optimization variables according to the assembly requirements and size requirements within the design allowable domain and construct a high-dimensional design space, where each dimension represents an optimization variable, and the population size is determined according to the number of dimensions and computing resources. N ; In the second step, the Latin hypercube sampling method is used to generate the N Individual vectors constitute a population; In the third step, relying on the HyperMesh and Nastran software platforms, the stiffness and NVH characteristics of the population are simulated and analyzed, the performance response data of each individual vector in the population is fully recorded, and a database is constructed. The Pareto front is obtained by using non-dominated sorting on all individual vectors in the database.

[0009] Furthermore, the specific steps of step (3) are as follows: In the first step, the elite reference temporary library is initialized by putting individual vectors in the database into the elite reference temporary library; In the second step, the target space is constructed based on the stiffness and NVH values ​​of the individual vectors in the elite reference temporary library. The K-means algorithm is used in the target space to perform clustering operations on the individual vectors in the elite reference temporary library, where the number of clusters is preset to Rn , calculate the Euclidean distance between the individual vector in each cluster and the current Pareto front, select the individual vector with the smallest Euclidean distance as the elite reference vector, and put it into the elite reference temporary library, then perform vector normalization on the elite reference vector in the elite reference temporary library to obtain the elite unit reference vector. The vector normalization operation is determined by the following two formulas: , , In the above formula, k Indicates the k optimization variables, n represents the number of optimization variables, upper represents the upper bound of the optimization variable in the high-dimensional design space, lower represents the lower bound of the optimization variable in the high-dimensional design space, RefPop express Rn The elite reference temporary library composed of elite reference vectors, w maxrepresents the weight calculated based on the upper and lower bounds of the optimization variables in the high-dimensional design space, x i Indicates the first i individual vectors, Points i Indicates the obtained i Elite unit reference vectors; The third step is based on weight w max Generate with N The weight matrix of the weight vectors W , the number of optimization variables for each weight vector is Rn , and construct the dimension reconstruction expression. The weight matrix generation and dimension reconstruction expression are determined by the following two formulas respectively: , , In the above formula, N represents the number of weight vectors in the weight matrix, Indicates the i The first of the weight vectors j The size of the optimization variable, Point j Indicates the j elite unit reference vectors, lower j Indicates the j The optimization variable lower bound of an elite unit reference vector in a high-dimensional design space, CPop i,j Indicates that the first i The optimization variable acts on the j The temporary population individuals obtained by the elite unit reference vector, rand Indicates generating a N OK Rn Random matrix of columns; The fourth step is to use the dimension reconstruction strategy to apply the weight vector to multiple elite unit reference vectors to generate new temporary population individuals, that is, a weight vector will act on Rn elite unit reference vectors, resulting in Rn temporary population individuals and calculate the hypervolume value HV of the temporary population individuals. This process transforms the high-dimensional multi-objective optimization problem into a single-objective optimization problem with the weight vector as the optimization variable and HV as the optimization target. The fifth step is to build a Kriging machine learning model for the temporary population individuals and perform N Perform sub-dimensional perturbation and mutation operations, and predict and select the weight vector corresponding to the maximum HV value based on the Kriging machine learning model; The sixth step is to apply the obtained weight vector to the Rn Elite unit reference vector, get Rn candidate solutions and screen them out from the candidate solutions based on efficient non-dominated sorting and crowding distance EN as offspring individuals; Step 7: By changing the currently used Rn Elite reference vectors are removed from the elite reference temporary library to update the elite reference temporary library.

[0010] Furthermore, the specific steps of step (4) are as follows: In the first step, the influence of each optimization variable in the population on the target is calculated by using mutual information, and finally the top 50% optimization variables ranked from high to low in mutual information entropy are determined as high-sensitivity optimization variable groups. sd 1. After sorting the mutual information entropy values, 50% of the optimization variables are determined as low-impact lazy optimization variable groups. sd 2; Step 2: Select high sensitivity optimization variable grouping sd 1, the first two optimization variables are calculated using the difference grouping method, and the variables that are inseparable from the two optimization variables in the entire optimization variable are calculated according to Score The top 50% of the optimization variables in the comprehensive value selection ranking constitute the strong coupling optimization variable grouping sd 3, so we can get three groups with different optimization variables. The mutual information and differential grouping are determined by the following two formulas: , , , In the above formula, and Represent random variables X k and Y The probability density function of represents the joint probability density function of two random variables, n represents the number of optimization variables, a represents a given threshold, Indicates the optimization variable you want to explore x 1 and x The correlation between 6, represents the predicted value based on the radial basis function machine learning model, It represents the difference between the individual's prediction after the first optimization variable is increased by the threshold and the original prediction. It represents the difference between the individual's prediction after the sixth optimization variable is increased by the threshold and the original prediction.Score Represents the inseparable comprehensive value between optimization variables. Represents the calculation of random variables X k and Y The mutual information value between The third step is to extract high-sensitivity optimization variable groups from the population sd The optimization variables and their stiffness and NVH values ​​in 1 constitute a new low-dimensional population; the low-dimensional optimization variables corresponding to the low-dimensional population constitute a new subspace and are optimized in this space. The simplex method is used to generate VNN reference vectors and construct intervals based on the vertical distances between these reference vectors and the low-dimensional population GCV , the construction formula is as follows: , In the above formula, Indicates the vertical distance between the reference vector and the low-dimensional population. express VNN The first of the reference vectors i reference vectors, Represents a database, Indicates the first j Population individual vectors and normalize them, Indicates the population with i The vertical distance of the reference vectors is N The subspace constructed by the population individual vectors; At the same time, a local radial basis function machine learning model is constructed using subintervals, and the maximum number of approximate evaluations of the machine learning model is set. Within this maximum number, an adaptive differential evolution operation is used to generate candidate individuals. The specific formula is as follows: , In the above formula, Indicates from GVC The population individual vector with the minimum Euclidean distance relative to the origin in a subspace of GVC express VNN subspaces, express GVC The population individual vector with the minimum vertical distance from x to the Pareto front in a subspace of and represents two population individual vectors randomly selected from the subspace, F represents the scaling factor that controls the amplitude of individual variation, Tx a Represents the population individual vector with the minimum vertical distance Candidate individuals generated by adaptive differential evolution operations; In the fourth step, candidate individuals are evaluated using a local radial basis function machine learning model to obtain predicted values. A comprehensive evaluation index is constructed based on the Pareto frontier obtained from the non-dominated sorting and the predicted values. The candidate individuals in the current group are screened using this comprehensive evaluation index. During this process, a random replacement mechanism is used to replace the screened individuals in the population, so that subsequent group optimization can inherit the advantages of the previous optimization and achieve co-evolution between optimization variables. Step 5: Loop through steps 3 and 4 to optimize the lazy optimization variable grouping. sd 2 and strongly coupled optimization variable grouping sd 3. Through three progressive group optimization iterations, multiple candidate solutions are finally obtained; Step 6: To address the missing dimension problem of candidate solution optimization variables caused by the dimensionality reduction operation, the corresponding optimization variables of other individuals are randomly selected from the population to compensate for the missing dimension, thereby ensuring the integrity of the candidate solution optimization variables. In the seventh step, the radial basis function machine learning model is used to evaluate the candidate solutions, and the offspring individuals are screened using a multi-criteria method based on machine learning. The multi-criteria method includes the maximum-minimum target improvement method, the minimum-maximum target descent method, and the Euclidean distance method, which are determined by the following three formulas: , , , In the above formula, represents the number of optimization targets, n represents the number of optimization variables, k Indicates the k The optimization goal, N PF is the number of individuals in the population on the Pareto front, PF represents the Pareto frontier obtained from the database, NX represents the set of optimization variables for candidate solutions, NF Represents the result set obtained by predicting candidate solutions based on the radial basis function machine learning model, j express N PF Middle j Individuals of a population, PF j,k express PF Middle j The first k target value, NF i,k Indicates the candidate solution i The first offspring individual k target value, NX i,lIndicates the i The candidate solution l optimization variables, Indicates that the maximum and minimum target lifting method is used to improve the first candidate solution. i Offspring individuals x i The calculated filter function value, Indicates that the first candidate solution is obtained according to the minimum maximum target descent method. i Offspring individuals x i The calculated filter function value, Indicates the first candidate solution according to the Euclidean distance method. i Offspring individuals x i Calculated filter function value; In the eighth step, the maximum-minimum objective lifting method is used to calculate the screening function values ​​of all offspring individuals in the candidate solution, and the offspring individual with the maximum screening function value is screened out; the minimum-maximum objective descent method is used to calculate the screening function values ​​of all offspring individuals in the candidate solution, and the offspring individual with the minimum screening function value is screened out; the Euclidean distance method is used to calculate the screening function values ​​of all offspring individuals in the candidate solution, and the offspring individual with the minimum screening function value is screened out. Therefore, three offspring individuals are finally obtained according to multi-criteria screening.

[0011] Furthermore, the specific steps of step (5) are as follows: The first step is to perform static analysis on the three selected offspring individuals in HyperMesh and read the stiffness value of the vehicle's rear subframe. The Lanczos method in Nastran software is used to extract the first-order modal frequency of the vehicle's rear subframe to quantify the NVH value. The stiffness and modal frequency of each offspring individual are obtained. The simulation results are then associated with the optimization variables and updated in the database. The second step is to initialize the dynamic candidate pool, store the offspring individuals that have been simulated and evaluated in the current stage into the candidate pool, and put them into the elite reference temporary library to achieve the update purpose; The third step is to determine whether the number of offspring individuals in the candidate pool has reached N If the value is not reached, the cosine similarity matrix of the offspring individuals in the candidate pool and the individuals in the database after excluding the candidate pool is calculated to characterize the directional differences between individuals; the maximum and minimum screening criteria are used to extract the maximum value of the matrix row by row to form a vector, and the individual with the minimum value in the vector in the database is selected to be added to the candidate pool; Step 4: Repeat step 3 until the number of offspring individuals in the candidate pool reaches N , to update the population; The fifth step is to check whether the current optimized structure meets the requirements. If so, all the optimized structures are output. Otherwise, go to step (3) until the optimization conditions are met.

[0012] In summary, compared with the prior art, the dual-objective design method for automobile rear subframe stiffness and NVH provided by the present invention has the following improvements over the limitations of the prior art: 1. To address the problem of uneven population distribution in the target space, a uniformly distributed population is generated using the Latin hypercube sampling method. The stiffness and NVH values ​​of the individual populations are then obtained based on simulation analysis to ensure that the stiffness and NVH targets are evenly covered during the optimization process.

[0013] 2. A phased evolutionary strategy was constructed to address the potential for oscillations in evolutionary trajectories and optimize inefficiencies. Phase switching was triggered by setting a 50% simulation threshold. The first phase employed a dimensional reconstruction strategy, combining weight adjustment with machine learning to accelerate convergence. The second phase implemented variable grouping coevolution, enhancing solution diversity through mutual information combined with differential grouping. Offspring individuals were dynamically selected using three acquisition functions: maximum and minimum objective improvement.

[0014] 3. Establish a difference value based on the angle cosine screening function to screen offspring individuals to update the population, integrating the simulation data of the screened offspring individuals with the evolutionary process data to continuously improve and optimize the population quality.

[0015] 4. The present invention can effectively optimize large-scale optimization variable multi-objective problems involving complex simulations, addressing the problem that traditional single-objective-oriented optimization architectures are unable to meet the parallel optimization requirements of multi-dimensional performance indicators such as automotive rear subframe stiffness modal matching and NVH frequency response control. It achieves Pareto front approximation of stiffness and NVH performance, improves the optimization efficiency of complex simulations, and is beneficial to the optimization application of various complex structures, thus having practical application. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a simplified flow chart of a two-objective design method for automobile rear subframe stiffness and NVH provided by the present invention. DETAILED DESCRIPTION

[0017] In order to more clearly illustrate the purpose, technical solutions and advantages of the present invention, it will be described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to illustrate the present invention and are not intended to limit it. In addition, as long as the technical features in the following embodiments do not conflict with each other, they can be combined with each other.

[0018] See also Figure 1 The present invention provides a dual-objective design method for automobile rear subframe stiffness and NVH, which is applicable to automobile rear subframe design optimization problems. Specifically, the method includes steps (1) to (5).

[0019] Step (1): The geometric parameters of the front and rear crossbeams, left and right longitudinal beams, and swing arm connecting plates of the rear subframe of the vehicle are used as optimization variables to simultaneously determine the high-dimensional design space. The stiffness and NVH of the rear subframe of the vehicle are used as optimization targets. A two-objective mathematical optimization model of stiffness and NVH is established based on the SFE-Concept.

[0020] The specific steps of step (1) are as follows: The first step is to build a geometric model in CATIA based on the rear subframe assembly and geometric requirements. Then, HyperMesh is used to clean up the geometric model in CATIA, including geometric repair and feature simplification. The second step is to determine the design tolerances for the height, thickness, and position of the rear subframe's front and rear cross members, left and right longitudinal members, and swing arm connecting plates, taking into account material strength, manufacturing process, and assembly space constraints. In the third step, based on the assumption of structural symmetry, the left and right longitudinal beams were simplified into a single-variable topology. This means that the parameters of one of the longitudinal beams were selected for optimization. Ultimately, the geometric parameters of the front and rear crossbeams and longitudinal beams, including shape, width, height, thickness position, curvature, thickness, and material, and the height, thickness, and position of the swing arm connecting plate parameters, were selected as optimization variables. In the fourth step, an implicit parameterized mathematical model was constructed based on the SFE-Concept platform, with the rear subframe stiffness and NVH as the optimization targets. The corresponding mathematical expression is as follows: , In the above formula, X represents the optimization variable of the rear subframe structure of the automobile. The number of optimization variables is 25. The front crossbeam is composed of the first front crossbeam in the front half and the second front crossbeam in the rear half. The rear crossbeam is composed of the first rear crossbeam in the front half and the second rear crossbeam in the rear half. Indicates the shape of the front crossbeam, Indicates the width of the first front crossbeam, Indicates the width of the second front crossbeam, Indicates the height of the upper end of the front crossbeam. Indicates the height of the lower end of the front crossbeam. Indicates the thickness of the first front cross member, Indicates the thickness of the second front cross member, Indicates the distance the rear crossbeam moves. Indicates the shape of the rear cross member, Indicates the width of the first rear cross member, Indicates the width of the second rear cross member, Indicates the height of the upper end of the rear crossbeam. Indicates the height of the lower end of the rear crossbeam. Indicates the thickness of the first rear cross member, Indicates the thickness of the second rear cross member, represents the curvature of the longitudinal beam, Indicates the length of the longitudinal beam, Indicates the width of the longitudinal beam, Indicates the longitudinal beam height, Indicates the thickness of the longitudinal beam, Indicates the height of the swing arm connecting plate, Indicates the thickness of the swing arm connecting plate, Indicates the position of the swing arm connecting plate. Indicates the height of the swing arm connecting plate, Indicates the thickness of the swing arm connecting plate, Indicates the stiffness value of the rear subframe of the car, The first order natural frequency of the NVH value of the rear subframe of the vehicle is expressed as follows: It represents the high-dimensional design space composed of the optimization variables of the rear subframe structure of the automobile. Find represents the definition of the optimization variables, Objective represents the optimization goal, Min represents the minimization of the optimization goal, and St represents the optimization variables being within the design allowable domain.

[0021] Step (2): In a high-dimensional design space, determine the population size based on the number of dimensions N ; Generated using Latin hypercube sampling method N The population is composed of individual vectors, the stiffness value is extracted through static simulation, and the first-order modal frequency is calculated by the Lanczos method of Nastran software to quantify the NVH value and build a database.

[0022] The specific steps of step (2) are as follows: The first step is to determine the value range of all optimization variables according to the assembly requirements and size requirements within the design allowable domain and construct a high-dimensional design space, where each dimension represents an optimization variable, and the population size is determined according to the number of dimensions and computing resources. N ; In the second step, the Latin hypercube sampling method is used to generate the N Individual vectors constitute a population; In the third step, relying on the HyperMesh and Nastran software platforms, the stiffness and NVH characteristics of the population are simulated and analyzed, the performance response data of each individual vector in the population is fully recorded, and a database is constructed. The Pareto front is obtained by using non-dominated sorting on all individual vectors in the database.

[0023] Step (3): In the first stage when the number of simulations is less than half, a dimension reconstruction strategy driven by screening preference is adopted to achieve dimension reduction of optimization variables by adjusting weights, a Kriging machine learning model is constructed and candidate solutions are generated based on the model, and offspring individuals are screened using non-dominated sorting and angle penalty distance.

[0024] The specific steps of step (3) are as follows: In the first step, the elite reference temporary library is initialized by putting individual vectors in the database into the elite reference temporary library; In the second step, the target space is constructed based on the stiffness and NVH values ​​of the individual vectors in the elite reference temporary library. The K-means algorithm is used in the target space to perform clustering operations on the individual vectors in the elite reference temporary library, where the number of clusters is preset to Rn , calculate the Euclidean distance between the individual vector in each cluster and the current Pareto front, select the individual vector with the smallest Euclidean distance as the elite reference vector, and put it into the elite reference temporary library, then perform vector normalization on the elite reference vector in the elite reference temporary library to obtain the elite unit reference vector. The vector normalization operation is determined by the following two formulas: , , In the above formula, k Indicates the k optimization variables, n represents the number of optimization variables, upper represents the upper bound of the optimization variable in the high-dimensional design space, lower represents the lower bound of the optimization variable in the high-dimensional design space, RefPop express Rn The elite reference temporary library composed of elite reference vectors, w max represents the weight calculated based on the upper and lower bounds of the optimization variables in the high-dimensional design space, x i Indicates the first i individual vectors, Points i Indicates the obtained i Elite unit reference vectors; The third step is based on weight w max Generate with N The weight matrix of the weight vectors W , the number of optimization variables for each weight vector is Rn , and construct the dimension reconstruction expression. The weight matrix generation and dimension reconstruction expression are determined by the following two formulas respectively: , , In the above formula, N represents the number of weight vectors in the weight matrix, Indicates the i The first of the weight vectors j The size of the optimization variable, Pointj Indicates the j elite unit reference vectors, lower j Indicates the j The optimization variable lower bound of an elite unit reference vector in a high-dimensional design space, CPop i,j Indicates that the first i The optimization variable acts on the j The temporary population individuals obtained by the elite unit reference vector, rand Indicates generating a N OK Rn Random matrix of columns; The fourth step is to use the dimension reconstruction strategy to apply the weight vector to multiple elite unit reference vectors to generate new temporary population individuals, that is, a weight vector will act on Rn elite unit reference vectors, resulting in Rn temporary population individuals and calculate the hypervolume value HV of the temporary population individuals. This process transforms the high-dimensional multi-objective optimization problem into a single-objective optimization problem with the weight vector as the optimization variable and HV as the optimization target. The fifth step is to build a Kriging machine learning model for the temporary population individuals and perform N Perform sub-dimensional perturbation and mutation operations, and predict and select the weight vector corresponding to the maximum HV value based on the Kriging machine learning model; The sixth step is to apply the obtained weight vector to the Rn Elite unit reference vector, get Rn candidate solutions and screen them out from the candidate solutions based on efficient non-dominated sorting and crowding distance EN as offspring individuals; Step 7: By changing the currently used Rn Elite reference vectors are removed from the elite reference temporary library to update the elite reference temporary library.

[0025] Step (4): In the second stage when the number of simulations exceeds half, the influence of the optimization variables on the target is analyzed based on the mutual information, and the nonlinear interaction characteristics between the optimization variables are analyzed by combining the differential grouping method. The high-dimensional design space is divided into high-sensitivity optimization variable groups, low-impact inert optimization variable groups and strong-coupling optimization variable groups to achieve dimensionality reduction of the optimization variables. A local radial basis function machine learning model is constructed for each group. The optimization variables in each group are optimized through the group co-evolution strategy to generate candidate solutions, and the offspring individuals are screened using a multi-criteria method based on machine learning.

[0026] The specific steps of step (4) are as follows: In the first step, the influence of each optimization variable in the population on the target is calculated by using mutual information, and finally the top 50% optimization variables ranked from high to low in mutual information entropy are determined as high-sensitivity optimization variable groups. sd 1. After sorting the mutual information entropy values, 50% of the optimization variables are determined as low-impact lazy optimization variable groups. sd 2; Step 2: Select high sensitivity optimization variable grouping sd 1, the first two optimization variables are calculated using the difference grouping method, and the variables that are inseparable from the two optimization variables in the entire optimization variable are calculated according to Score The top 50% of the optimization variables in the comprehensive value selection ranking constitute the strong coupling optimization variable grouping sd 3, so we can get three groups with different optimization variables. The mutual information and differential grouping are determined by the following two formulas: , , , In the above formula, and Represent random variables X k and Y The probability density function of represents the joint probability density function of two random variables, n represents the number of optimization variables, a represents a given threshold, Indicates the optimization variable you want to explore x 1 and x The correlation between 6, represents the predicted value based on the radial basis function machine learning model, It represents the difference between the individual's prediction after the first optimization variable is increased by the threshold and the original prediction. It represents the difference between the individual's prediction after the sixth optimization variable is increased by the threshold and the original prediction. Score Represents the inseparable comprehensive value between optimization variables. Represents the calculation of random variables X k and Y The mutual information value between The third step is to extract high-sensitivity optimization variable groups from the population sd The optimization variables and their stiffness and NVH values ​​in 1 constitute a new low-dimensional population; the low-dimensional optimization variables corresponding to the low-dimensional population constitute a new subspace and are optimized in this space. The simplex method is used to generate VNN reference vectors and construct intervals based on the vertical distances between these reference vectors and the low-dimensional populationGCV , the construction formula is as follows: , In the above formula, Indicates the vertical distance between the reference vector and the low-dimensional population. express VNN The first of the reference vectors i reference vectors, Represents a database, Indicates the first j Population individual vectors and normalize them, Indicates the population with i The vertical distance of the reference vectors is N The subspace constructed by the population individual vectors; At the same time, a local radial basis function machine learning model is constructed using subintervals, and the maximum number of approximate evaluations of the machine learning model is set. Within this maximum number, an adaptive differential evolution operation is used to generate candidate individuals. The specific formula is as follows: , In the above formula, Indicates from GVC The population individual vector with the minimum Euclidean distance relative to the origin in a subspace of GVC express VNN subspaces, express GVC The population individual vector with the minimum vertical distance from x to the Pareto front in a subspace of and represents two population individual vectors randomly selected from the subspace, F represents the scaling factor that controls the amplitude of individual variation, Tx a Represents the population individual vector with the minimum vertical distance Candidate individuals generated by adaptive differential evolution operations; In the fourth step, candidate individuals are evaluated using a local radial basis function machine learning model to obtain predicted values. A comprehensive evaluation index is constructed based on the Pareto frontier obtained from the non-dominated sorting and the predicted values. The candidate individuals in the current group are screened using this comprehensive evaluation index. During this process, a random replacement mechanism is used to replace the screened individuals in the population, so that subsequent group optimization can inherit the advantages of the previous optimization and achieve co-evolution between optimization variables. Step 5: Loop through steps 3 and 4 to optimize the lazy optimization variable grouping. sd 2 and strongly coupled optimization variable grouping sd 3. Through three progressive group optimization iterations, multiple candidate solutions are finally obtained; Step 6: To address the missing dimension problem of candidate solution optimization variables caused by the dimensionality reduction operation, the corresponding optimization variables of other individuals are randomly selected from the population to compensate for the missing dimension, thereby ensuring the integrity of the candidate solution optimization variables. In the seventh step, the radial basis function machine learning model is used to evaluate the candidate solutions, and the offspring individuals are screened using a multi-criteria method based on machine learning. The multi-criteria method includes the maximum-minimum target improvement method, the minimum-maximum target descent method, and the Euclidean distance method, which are determined by the following three formulas: , , , In the above formula, represents the number of optimization targets, n represents the number of optimization variables, k Indicates the k The optimization goal, N PF is the number of individuals in the population on the Pareto front, PF represents the Pareto frontier obtained from the database, NX represents the set of optimization variables for candidate solutions, NF Represents the result set obtained by predicting candidate solutions based on the radial basis function machine learning model, j express N PF Middle j Individuals of a population, PF j,k express PF Middle j The first k target value, NF i,k Indicates the candidate solution i The first offspring individual k target value, NX i,l Indicates the i The candidate solution l optimization variables, Indicates that the maximum and minimum target lifting method is used to improve the first candidate solution. i Offspring individuals x i The calculated filter function value, Indicates that the first candidate solution is obtained according to the minimum maximum target descent method. i Offspring individuals x i The calculated filter function value, Indicates the first candidate solution according to the Euclidean distance method. i Offspring individuals x iCalculated filter function value; In the eighth step, the maximum-minimum objective lifting method is used to calculate the screening function values ​​of all offspring individuals in the candidate solution, and the offspring individual with the maximum screening function value is screened out; the minimum-maximum objective descent method is used to calculate the screening function values ​​of all offspring individuals in the candidate solution, and the offspring individual with the minimum screening function value is screened out; the Euclidean distance method is used to calculate the screening function values ​​of all offspring individuals in the candidate solution, and the offspring individual with the minimum screening function value is screened out. Therefore, three offspring individuals are finally obtained according to multi-criteria screening.

[0027] Step (5): Simulate and evaluate the offspring individuals, update the database, calculate the directional difference between the offspring individuals and the database individuals based on the angle cosine screening function, and update the population based on the difference value. If the optimized structure does not meet the requirements, go to step (3); otherwise, output all the optimized structures obtained.

[0028] The specific steps of step (5) are as follows: The first step is to perform static analysis on the three selected offspring individuals in HyperMesh and read the stiffness value of the vehicle's rear subframe. The Lanczos method in Nastran software is used to extract the first-order modal frequency of the vehicle's rear subframe to quantify the NVH value. The stiffness and modal frequency of each offspring individual are obtained. The simulation results are then associated with the optimization variables and updated in the database. The second step is to initialize the dynamic candidate pool, store the offspring individuals that have been simulated and evaluated in the current stage into the candidate pool, and put them into the elite reference temporary library to achieve the update purpose; The third step is to determine whether the number of offspring individuals in the candidate pool has reached N If the value is not reached, the cosine similarity matrix of the offspring individuals in the candidate pool and the individuals in the database after excluding the candidate pool is calculated to characterize the directional differences between individuals; the maximum and minimum screening criteria are used to extract the maximum value of the matrix row by row to form a vector, and the individual with the minimum value in the vector in the database is selected to be added to the candidate pool; Step 4: Repeat step 3 until the number of offspring individuals in the candidate pool reaches N , to update the population; The fifth step is to check whether the current optimized structure meets the requirements. If so, all the optimized structures are output. Otherwise, go to step (3) until the optimization conditions are met.

[0029] This embodiment uses the benchmark test function LSMOP1 to illustrate the optimization performance of the dual-objective design method for the rear subframe stiffness and NVH provided by this embodiment. The expression of the dual-objective benchmark test function LSMOP1 is as follows: , In this embodiment, and is the objective function, n represents the number of optimization variables, k Indicates the first variable in the entire optimization k optimization variables, x i represents the individual x's i The above-mentioned benchmark test function is processed through steps (1) to (5) of the automobile rear subframe stiffness and NVH design method based on machine learning provided by the present invention to obtain experimental results.

[0030] To further illustrate the effectiveness of this embodiment, a dual-objective design method for rear subframe stiffness and NVH in this embodiment was compared with another excellent RBF machine learning-assisted adaptive decision variable grouping evolutionary algorithm (AVG-SAEA). The maximum number of simulation evaluations for this embodiment was set to 300, and the number of optimization variables was set to 100. The experimental results are shown in Table 1. The comparison was based on the average IGD value of 20 independent runs. With the same maximum number of simulation evaluations, the method of this embodiment significantly outperformed the RBF machine learning-assisted adaptive decision variable grouping evolutionary algorithm (AVG-SAEA), demonstrating its ability to effectively address the optimization design of rear subframe stiffness and NVH.

[0031] Table 1 Comparison of optimization results of different algorithms

[0032] The present invention provides a dual-objective design method for automobile rear subframe stiffness and NVH. The method achieves efficient design by constructing a dimensional reconstruction strategy driven by screening preferences and combining mutual information and differential grouping methods to construct a subspace for collaborative optimization within a two-stage optimization framework, providing a systematic solution for the dual-objective design of automobile rear subframe stiffness and NVH.

[0033] It will be easily understood by those skilled in the art that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A dual-objective design method for automobile rear subframe stiffness and NVH, characterized in that: The method comprises: Step (1): Taking the geometric parameters of the front and rear crossbeams, left and right longitudinal beams, and swing arm connecting plates of the rear subframe as optimization variables, a high-dimensional design space is determined simultaneously. Taking the stiffness and NVH of the rear subframe as optimization targets, a two-objective mathematical optimization model of stiffness and NVH is established based on the SFE-Concept. Step (2): In a high-dimensional design space, determine the population size based on the number of dimensions N ; Generated using Latin hypercube sampling method N The population is constructed by individual vectors, the stiffness value is extracted through static simulation, the first-order modal frequency is calculated using the Lanczos method of Nastran software to quantify the NVH value, and a database is constructed; Step (3): In the first stage before the simulation times are more than half, a dimension reconstruction strategy driven by screening preference is adopted to achieve dimension reduction of optimization variables by adjusting weights, a Kriging machine learning model is constructed and candidate solutions are generated based on the model, and offspring individuals are screened using non-dominated sorting and angle penalty distance; Step (4): In the second stage when the number of simulations exceeds half, the influence of the optimization variables on the target is analyzed based on the mutual information, and the nonlinear interaction characteristics between the optimization variables are analyzed by combining the differential grouping method. The high-dimensional design space is divided into high-sensitivity optimization variable groups, low-impact inert optimization variable groups, and strong-coupling optimization variable groups to achieve dimensionality reduction of the optimization variables. A local radial basis function machine learning model is constructed for each group. The optimization variables in each group are optimized through the group co-evolution strategy to generate candidate solutions, and the offspring individuals are screened using a multi-criteria method based on machine learning. Step (5): Simulate and evaluate the offspring individuals, update the database, calculate the directional difference between the offspring individuals and the database individuals based on the angle cosine screening function, and update the population based on the difference value. If the optimized structure does not meet the requirements, go to step (3); otherwise, output all the optimized structures obtained.

2. The method according to claim 1, wherein The specific steps of step (1) are as follows: The first step is to build a geometric model in CATIA based on the rear subframe assembly and geometric requirements. Then, HyperMesh is used to clean up the geometric model in CATIA, including geometric repair and feature simplification. The second step is to determine the design tolerances for the height, thickness, and position of the rear subframe's front and rear cross members, left and right longitudinal members, and swing arm connecting plates, taking into account material strength, manufacturing process, and assembly space constraints. In the third step, based on the assumption of structural symmetry, the left and right longitudinal beams were simplified into a single-variable topology. This means that the parameters of one of the longitudinal beams were selected for optimization. Ultimately, the geometric parameters of the front and rear crossbeams and longitudinal beams, including shape, width, height, thickness position, curvature, thickness, and material, and the height, thickness, and position of the swing arm connecting plate parameters, were selected as optimization variables. In the fourth step, an implicit parameterized mathematical model was constructed based on the SFE-Concept platform, with the rear subframe stiffness and NVH as the optimization targets. The corresponding mathematical expression is as follows: ， In the above formula, X represents the optimization variable of the rear subframe structure of the automobile. The number of optimization variables is 25. The front crossbeam is composed of the first front crossbeam in the front half and the second front crossbeam in the rear half. The rear crossbeam is composed of the first rear crossbeam in the front half and the second rear crossbeam in the rear half. Indicates the shape of the front crossbeam, Indicates the width of the first front crossbeam, Indicates the width of the second front crossbeam, Indicates the height of the upper end of the front crossbeam. Indicates the height of the lower end of the front crossbeam. Indicates the thickness of the first front cross member, Indicates the thickness of the second front cross member, Indicates the distance the rear crossbeam moves. Indicates the shape of the rear cross member, Indicates the width of the first rear cross member, Indicates the width of the second rear cross member, Indicates the height of the upper end of the rear crossbeam. Indicates the height of the lower end of the rear crossbeam. Indicates the thickness of the first rear cross member, Indicates the thickness of the second rear cross member, represents the curvature of the longitudinal beam, Indicates the length of the longitudinal beam, Indicates the width of the longitudinal beam, Indicates the longitudinal beam height, Indicates the thickness of the longitudinal beam, Indicates the height of the swing arm connecting plate, Indicates the thickness of the swing arm connecting plate, Indicates the position of the swing arm connecting plate. Indicates the height of the swing arm connecting plate, Indicates the thickness of the swing arm connecting plate, Indicates the stiffness value of the rear subframe of the car, The first order natural frequency of the NVH value of the rear subframe of the vehicle is expressed as follows: It represents the high-dimensional design space composed of the optimization variables of the rear subframe structure of the automobile. Find represents the definition of the optimization variables, Objective represents the optimization goal, Min represents the minimization of the optimization goal, and St represents the optimization variables being within the design allowable domain.

3. The method according to claim 1, wherein The specific steps of step (2) are as follows: The first step is to determine the value range of all optimization variables according to the assembly requirements and size requirements within the design allowable domain and construct a high-dimensional design space, where each dimension represents an optimization variable, and the population size is determined according to the number of dimensions and computing resources. N ; In the second step, the Latin hypercube sampling method is used to generate the N Individual vectors constitute a population; In the third step, relying on the HyperMesh and Nastran software platforms, the stiffness and NVH characteristics of the population are simulated and analyzed, the performance response data of each individual vector in the population is fully recorded, and a database is constructed. The Pareto front is obtained by using non-dominated sorting on all individual vectors in the database.

4. The method according to claim 1, wherein The specific steps of step (3) are as follows: In the first step, the elite reference temporary library is initialized by putting individual vectors in the database into the elite reference temporary library; In the second step, the target space is constructed based on the stiffness and NVH values ​​of the individual vectors in the elite reference temporary library. The K-means algorithm is used in the target space to perform clustering operations on the individual vectors in the elite reference temporary library, where the number of clusters is preset to Rn , calculate the Euclidean distance between the individual vector in each cluster and the current Pareto front, select the individual vector with the smallest Euclidean distance as the elite reference vector, and put it into the elite reference temporary library, then perform vector normalization on the elite reference vector in the elite reference temporary library to obtain the elite unit reference vector. The vector normalization operation is determined by the following two formulas: ， ， In the above formula, k Indicates the k optimization variables, n represents the number of optimization variables, upper represents the upper bound of the optimization variable in the high-dimensional design space, lower represents the lower bound of the optimization variable in the high-dimensional design space, RefPop express Rn The elite reference temporary library composed of elite reference vectors, w max represents the weight calculated based on the upper and lower bounds of the optimization variables in the high-dimensional design space, x i Indicates the first i individual vectors, Points i Indicates the obtained i Elite unit reference vectors; The third step is based on weight w max Generate with N The weight matrix of the weight vectors W , the number of optimization variables for each weight vector is Rn , and construct the dimension reconstruction expression. The weight matrix generation and dimension reconstruction expression are determined by the following two formulas respectively: ， ， In the above formula, N represents the number of weight vectors in the weight matrix, Indicates the i The first of the weight vectors j The size of the optimization variable, Point j Indicates the j elite unit reference vectors, lower j Indicates the j The optimization variable lower bound of an elite unit reference vector in a high-dimensional design space, CPop i,j Indicates that the first i The optimization variable acts on the j The temporary population individuals obtained by the elite unit reference vector, rand Indicates generating a N OK Rn Random matrix of columns; The fourth step is to use the dimension reconstruction strategy to apply the weight vector to multiple elite unit reference vectors to generate new temporary population individuals, that is, a weight vector will act on Rn elite unit reference vectors, resulting in Rn temporary population individuals and calculate the hypervolume value HV of the temporary population individuals. This process transforms the high-dimensional multi-objective optimization problem into a single-objective optimization problem with the weight vector as the optimization variable and HV as the optimization target. The fifth step is to build a Kriging machine learning model for the temporary population individuals and perform N Perform sub-dimensional perturbation and mutation operations, and predict and select the weight vector corresponding to the maximum HV value based on the Kriging machine learning model; The sixth step is to apply the obtained weight vector to the Rn Elite unit reference vector, get Rn candidate solutions and screen them out from the candidate solutions based on efficient non-dominated sorting and crowding distance EN as offspring individuals; Step 7: By changing the currently used Rn Elite reference vectors are removed from the elite reference temporary library to update the elite reference temporary library.

5. The method according to claim 1, wherein The specific steps of step (4) are as follows: In the first step, the influence of each optimization variable in the population on the target is calculated by using mutual information, and finally the top 50% optimization variables ranked from high to low in mutual information entropy are determined as high-sensitivity optimization variable groups. sd 1. After sorting the mutual information entropy values, 50% of the optimization variables are determined as low-impact lazy optimization variable groups. sd 2; Step 2: Select high sensitivity optimization variable grouping sd 1, the first two optimization variables are calculated using the difference grouping method, and the variables that are inseparable from the two optimization variables in the entire optimization variable are calculated according to Score The top 50% of the optimization variables in the comprehensive value selection ranking constitute the strong coupling optimization variable grouping sd 3, so we can get three groups with different optimization variables. The mutual information and differential grouping are determined by the following two formulas: ， ， ， In the above formula, and Represent random variables X k and Y The probability density function of represents the joint probability density function of two random variables, n represents the number of optimization variables, a represents a given threshold, Indicates the optimization variable you want to explore x 1 and x The correlation between 6, represents the predicted value based on the radial basis function machine learning model, It represents the difference between the individual's prediction after the first optimization variable is increased by the threshold and the original prediction. It represents the difference between the individual's prediction after the sixth optimization variable is increased by the threshold and the original prediction. Score Represents the inseparable comprehensive value between optimization variables. Represents the calculation of random variables X k and Y The mutual information value between The third step is to extract high-sensitivity optimization variable groups from the population sd The optimization variables and their stiffness and NVH values ​​in 1 constitute a new low-dimensional population; the low-dimensional optimization variables corresponding to the low-dimensional population constitute a new subspace and are optimized in this space. The simplex method is used to generate VNN reference vectors and construct intervals based on the vertical distances between these reference vectors and the low-dimensional population GCV , the construction formula is as follows: ， In the above formula, Indicates the vertical distance between the reference vector and the low-dimensional population. express VNN The first of the reference vectors i reference vectors, Represents a database, Indicates the first j Population individual vectors and normalize them, Indicates the population with i The vertical distance of the reference vectors is N The subspace constructed by the population individual vectors; At the same time, a local radial basis function machine learning model is constructed using subintervals, and the maximum number of approximate evaluations of the machine learning model is set. Within this maximum number, an adaptive differential evolution operation is used to generate candidate individuals. The specific formula is as follows: ， In the above formula, Indicates from GVC The population individual vector with the minimum Euclidean distance relative to the origin in a subspace of GVC express VNN subspaces, express GVC The population individual vector with the minimum vertical distance from x to the Pareto front in a subspace of and represents two population individual vectors randomly selected from the subspace, F represents the scaling factor that controls the amplitude of individual variation, Tx a Represents the population individual vector with the minimum vertical distance Candidate individuals generated by adaptive differential evolution operations; In the fourth step, candidate individuals are evaluated using a local radial basis function machine learning model to obtain predicted values. A comprehensive evaluation index is constructed based on the Pareto frontier obtained from the non-dominated sorting and the predicted values. The candidate individuals in the current group are screened using this comprehensive evaluation index. During this process, a random replacement mechanism is used to replace the screened individuals in the population, so that subsequent group optimization can inherit the advantages of the previous optimization and achieve co-evolution between optimization variables. Step 5: Loop through steps 3 and 4 to optimize the lazy optimization variable grouping. sd 2 and strongly coupled optimization variable grouping sd 3. Through three progressive group optimization iterations, multiple candidate solutions are finally obtained; Step 6: To address the missing dimension problem of candidate solution optimization variables caused by the dimensionality reduction operation, the corresponding optimization variables of other individuals are randomly selected from the population to compensate for the missing dimension, thereby ensuring the integrity of the candidate solution optimization variables. In the seventh step, the radial basis function machine learning model is used to evaluate the candidate solutions, and the offspring individuals are screened using a multi-criteria method based on machine learning. The multi-criteria method includes the maximum-minimum target improvement method, the minimum-maximum target descent method, and the Euclidean distance method, which are determined by the following three formulas: ， ， ， In the above formula, represents the number of optimization targets, n represents the number of optimization variables, k Indicates the k The optimization goal, N PF is the number of individuals in the population on the Pareto front, PF represents the Pareto frontier obtained from the database, NX represents the set of optimization variables for candidate solutions, NF Represents the result set obtained by predicting candidate solutions based on the radial basis function machine learning model, j express N PF Middle j Individuals of a population, PF j,k express PF Middle j The first k target value, NF i,k Indicates the candidate solution i The first offspring individual k target value, NX i,l Indicates the i The candidate solution l optimization variables, Indicates that the maximum and minimum target lifting method is used to improve the first candidate solution. i Offspring individuals x i The calculated filter function value, Indicates that the first candidate solution is obtained according to the minimum maximum target descent method. i Offspring individuals x i The calculated filter function value, Indicates the first candidate solution according to the Euclidean distance method. i Offspring individuals x i Calculated filter function value; Step 8: Use the maximum-minimum objective lifting method to calculate the screening function values ​​of all offspring individuals in the candidate solution, and select the offspring individual with the largest screening function value; The minimum maximum target descent method is used to calculate the screening function values ​​of all offspring individuals in the candidate solution, and the offspring individual with the minimum screening function value is screened out; The Euclidean distance method is used to calculate the screening function values ​​of all offspring individuals in the candidate solution, and the offspring individual with the minimum screening function value is screened out. Therefore, three offspring individuals are finally obtained according to the multi-criteria screening.

6. The method according to claim 1, wherein The step (5) specifically includes the following steps: The first step is to perform static analysis on the three selected offspring individuals in HyperMesh and read the stiffness value of the vehicle's rear subframe. The Lanczos method in Nastran software is used to extract the first-order modal frequency of the vehicle's rear subframe to quantify the NVH value. The stiffness and modal frequency of each offspring individual are obtained. The simulation results are then associated with the optimization variables and updated in the database. The second step is to initialize the dynamic candidate pool, store the offspring individuals that have been simulated and evaluated in the current stage into the candidate pool, and put them into the elite reference temporary library to achieve the update purpose; The third step is to determine whether the number of offspring individuals in the candidate pool has reached N If the value is not reached, the cosine similarity matrix of the offspring individuals in the candidate pool and the individuals in the database after excluding the candidate pool is calculated to characterize the directional differences between individuals; the maximum and minimum screening criteria are used to extract the maximum value of the matrix row by row to form a vector, and the individual with the minimum value in the vector in the database is selected to be added to the candidate pool; Step 4: Repeat step 3 until the number of offspring individuals in the candidate pool reaches N , to update the population; The fifth step is to check whether the current optimized structure meets the requirements. If so, all the optimized structures are output. Otherwise, go to step (3) until the optimization conditions are met.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 6 are implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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