Multi-precision multi-objective optimization design method and system for integrated die-cast floor

Abstract

The invention discloses a multi-precision and multi-objective optimization design method and system for an integrated die-cast floor, and aims to solve the problems that multi-objective demand design is difficult to carry out and the design period is long in a traditional method. The method comprises the following steps: establishing a multi-objective optimization mathematical model; initializing a multi-precision evaluation data archiving set; a multi-target optimization mathematical model is decomposed into single-target sub-problems, and multi-target optimality conflicts are avoided; fusing the evaluation data with different precisions and the related information of the sub-problems, and establishing a multi-precision multi-task agent model; implementing multi-precision agent assisted evolution search to obtain an optimal candidate population; carrying out two-stage candidate solution selection based on non-dominated sorting and expected density estimation, and screening a high-quality solution set with convergence and target diversity to update an archive set; and after the specified algebra is optimized on line, an optimal solution set is output. According to the method, multi-objective optimization design of the floor after integrated die casting can be rapidly carried out, the design efficiency is improved by 50.0% compared with a traditional method, and the solution set multi-objective comprehensive index is improved by 15%.

Description

Technical Field

[0001] This invention belongs to the field of automotive structural design, specifically relating to a multi-precision, multi-objective optimization design method and system for integrated die-cast rear floor. Background Technology

[0002] The overall planning for automotive development emphasizes that "lightweighting remains a top priority," a key focus for carbon emission reduction in the automotive industry. Research data shows that for every 100kg reduction in weight of a gasoline-powered vehicle, fuel consumption decreases by 0.37L / 100km, and CO2 emissions decrease by 0.9kg; for every 100kg reduction in weight of a new energy vehicle, electricity consumption is reduced by 0.46kWh / 100km, and driving range increases by 5.5%. Therefore, safety and lightweighting remain core issues facing the modern automotive industry, and related structural optimization design has always been at the forefront and a hot topic in the automotive sector.

[0003] The rear floor, as one of the core load-bearing and protective components of a vehicle's body structure, plays a crucial role in overall vehicle safety. Its primary function is to form the bottom frame of the passenger compartment, ensuring sufficient structural integrity and energy transfer path during frontal and rear-end collisions. Furthermore, as the mounting base for critical components such as the body, suspension, fuel tank, and battery pack, the rear floor accounts for a significant portion of the vehicle's weight. Therefore, a well-designed, lightweight rear floor is essential for achieving a balance between overall vehicle weight and high safety.

[0004] Traditional rear floor manufacturing processes typically involve welding together multiple stamped steel or aluminum plates. This results in a large number of parts, complex manufacturing processes, and dense welds, presenting challenges such as limited welding precision, inconsistent local stiffness, and increased overall vehicle weight. To address these challenges, the industry has developed integrated die-cast rear floors. These floors are manufactured as a single unit using large die-casting equipment, significantly reducing the number of parts and welds, and substantially improving structural integrity and connection stiffness. This not only improves the continuity and stability of energy transfer during collisions but also shortens production cycles and reduces manufacturing costs. Furthermore, the die-casting process allows for greater freedom in topology optimization and lightweight design of the rear floor, contributing to further improvements in overall vehicle safety and weight reduction. Therefore, integrated die-casting offers the most comprehensive advantages in both weight reduction and safety, possessing the potential to simultaneously enhance both automotive body safety and weight reduction, leading the future development direction of automotive bodies.

[0005] However, due to the large-scale, monolithic structure of the integrated die-cast rear floor, its geometry is more complex, with a significant increase in local stiffeners, transition fillets, and multi-layered wall thickness variations. While this structural feature significantly improves the overall strength and energy transfer continuity of the rear floor, it also necessitates higher mesh fineness and more complex material modeling strategies in finite element simulation analysis to accurately capture local stress concentrations and deformation modes. This high-precision simulation analysis substantially increases the mesh element size and solution time of the finite element model. Furthermore, the often conflicting optimality requirements of safety and lightweight design lead to problems such as disordered optimization searches and slow convergence. Traditional methods struggle to simultaneously meet multiple design objectives (i.e., maximizing safety while minimizing weight) when designing integrated die-cast rear floors for safety and lightweight purposes, and suffer from low optimization search efficiency and long design cycles. Summary of the Invention

[0006] To address the shortcomings of existing methods, this invention provides a multi-precision, multi-objective optimization design method and system for integrated die-cast flooring. This addresses the challenges of traditional methods in conducting multi-objective design and the resulting long design cycles, thereby improving the quality and efficiency of multi-objective optimization design for integrated die-cast flooring and reducing the required time and economic costs.

[0007] The present invention is achieved using the following technical solutions:

[0008] A multi-precision, multi-objective optimization design method for integrated die-cast flooring.

[0009] Includes the following steps:

[0010] S1. Establish a multi-objective optimization mathematical model:

[0011] S2. Construct and initialize a multi-precision evaluation data archive based on the multi-objective optimization mathematical model; the multi-precision evaluation data archive includes a high-precision archive A and a low-precision archive A. L ;

[0012] S3. Decompose the multi-objective optimization mathematical model into a series of single-objective sub-problems;

[0013] S4, merge high-precision archive set A and low-precision archive set A L Based on the finite element simulation evaluation data and the relevant information between adjacent sub-problems, a multi-precision multi-task proxy model is established;

[0014] S5. Implement multi-precision agent-assisted evolutionary search to obtain the optimal candidate population;

[0015] S6. Conduct a two-stage candidate solution selection based on non-dominated ranking and expected density estimation to screen high-quality solution sets that combine convergence and objective diversity, and update the high-precision archive set A and the low-precision archive set A. L ;

[0016] S7. Repeat steps S4 to S6 until the stopping condition is met. Finally, output the solution set of the optimized design scheme based on the non-dominated solution of the high-precision archive set A.

[0017] Further improvements are made, and the optimized mathematical model expression in step S1 is as follows:

[0018] min FI D (x),-SEA(x)

[0019] stx=(x1,x2,x3,x4)∈[0.5c,2c]

[0020] FI D (x) represents the intrusion displacement of the passenger compartment, SEA(x) represents the specific energy absorbed during the collision process, c = [6,6,6,6] represents the original thickness vector of the structural component; x represents the design vector, c represents the original thickness vector of the structural component, x1 - x4 represents the thickness of the rear floor platform, longitudinal beam, wheel arch, and transverse support beam, respectively; min represents minimization.

[0021] Further improvements, step S2 includes the following steps:

[0022] S2.1 Construct high-precision archive set A and low-precision archive set A L A is used to store the design individuals and their corresponding fitness values ​​obtained through high-precision simulation evaluation during the optimization search process. L Used to store design individuals and their corresponding fitness values ​​during low-precision simulation evaluations in the optimization search process; archive sets A and A L Initially, all sets are empty;

[0023] S2.2 Initialize the high-precision archive set A: Based on the multi-objective optimization mathematical model in step S1, use the Latin hypercube sampling method to sample the design space and generate K solutions {x1,...,x}. K The K solutions are composed of dimensional design parameters; then, high-precision simulation performance evaluation is performed using structural finite element analysis software, and the calculated performance index values ​​are used as the fitness values ​​of the K solutions; finally, the K solutions and their corresponding fitness values ​​are stored in an archive set A = {(x i ,y i |i=1,...,K};

[0024] S2.3, For low-precision archive set A LInitialization: Based on the multi-objective optimization mathematical model in step S1, the design space is sampled using the Latin hypercube sampling method to generate K. L One solution K L Each solution is composed of dimensional design parameters; then, low-precision simulation performance evaluation is performed using structural finite element analysis software, and the calculated performance index values ​​are used as this K. L The fitness value of each solution; the low-precision simulation performance evaluation is achieved by deleting detailed features that do not affect collision performance in the high-precision simulation performance evaluation and implementing mesh coarsening; then, these K L Each solution and its corresponding fitness value are stored in a low-precision archive set A. L ={(x i ,y i |i=1,...,K L}

[0025] Further improvements include details that do not affect crash performance, such as small ribs, reinforcing ribs, and transition fillets.

[0026] Further improvements, step S3 includes the following steps:

[0027] S3.1 Generate ideal points based on the fitness values ​​in the high-precision archive set. Where the j-th ideal point f j (x i ) represents the objective function value of the solution in the high-precision archive set, and |A| represents the number of solutions in the high-precision archive set A;

[0028] S3.2, uniformly generate N in the target space P Weight vectors

[0029] S3.3. Based on the Chebyshev scalarization method, decompose the multi-objective optimization mathematical model in S1 into N P For the sake of height

[0030] The problem has the following expression for the s-th subproblem:

[0031]

[0032] stx∈Ω

[0033] Among them, w s Let M represent the s-th weight vector, and M represent the number of optimization objectives. w represents the j-th element of the ideal point. s,j f represents the j-th element of the s-th weight vector. j(x) represents the j-th objective function of the multi-objective optimization mathematical model, and Ω is the range of values ​​for the design parameters;

[0034] S3.3. Generate neighborhood subproblems of the s-th subproblem based on the Eulerian distance of the weight vectors, and store them in the neighborhood subproblem set. middle.

[0035] In a further improvement, step S4 includes the following steps:

[0036] S4.1 Based on the co-kriging hypothesis and the correlation between adjacent subproblems, the objective function of the s-th subproblem and its neighboring subproblems is defined as follows:

[0037]

[0038] in, This represents the objective function for low-precision simulation performance evaluation. With G s () is obtained using the Chebyshev scalarization method, where Γ represents the scaling parameter. Let Ψ() represent the residual vector; let Ψ() follow a multi-task Gaussian process; In the s-th subproblem, the |N-th subproblem is represented by... s The objective function values ​​for each neighborhood subproblem. In the s-th low-precision subproblem, the |N-th... s The objective function values ​​for each neighborhood subproblem. Denotes the |Nth|th subproblem of the s-th subproblem. s | Residual terms of neighborhood subproblems, where T denotes matrix transpose;

[0039] S4.2. Employ a multi-task Gaussian process for... Modeling the elements in the middle yields the corresponding prediction function. The expression for the middle element is as follows:

[0040]

[0041] in, They represent the prediction functions respectively. For x m The predicted mean and standard deviation; express The m-th element, s represents the s-th subproblem. Indicates a Gaussian distribution; x m The design parameters for the m-th output in the set;

[0042] S4.3. Using a multi-task Gaussian process, the elements in Ψ() are modeled to obtain the corresponding prediction function. The element in the middle, expressed as follows:

[0043]

[0044] in, They represent the prediction functions respectively. For x m The corresponding predicted mean and standard deviation;

[0045] S4.4, Using the Adam optimizer and Perform joint training, and the joint loss function for training. as follows:

[0046]

[0047] in, and The covariance matrix of a multi-task Gaussian process. and Hyperparameters to be determined, g L This is low-precision evaluation data, where Ψ represents residual data. express loss function, express The loss function is defined as follows: N represents the total number of samples; by minimizing the joint loss function... Obtain the hyperparameter Γ. The value of x is used to construct a multi-precision multi-task proxy model, which predicts the output of a new solution x. Represented as:

[0048]

[0049] in, The middle element is That is, the objective function g of the s-th optimization subproblem in step S1 s The predicted value of the objective function of the s-th optimization subproblem of (x) Let represent the objective function of the |Ns|-th domain subproblem of the s-th subproblem.

[0050] Further improvements include the following steps in step S5: Multi-precision agent-assisted evolutionary search:

[0051] S5.1 Initialize the population Where x i The best solution in A corresponding to the i-th subproblem;

[0052] S5.2, For each individual x in the population i The differential evolution operator is used to generate λ test vectors O. i={o1,...,o λ};o λ Let O represent the λ-th trial vector. i This represents the set of test vectors for the i-th subproblem;

[0053] O i Input a multi-precision multi-task agent model, and calculate based on the output of the multi-precision multi-task agent model. For O i Conduct an evaluation and select one of them The minimum corresponding O i As the optimal individual Will and x i Compare survival outcomes and select the better ones to update x in the population. i Then through g max After the next iteration, the optimal candidate population is output.

[0054] A further improvement is made to the two-stage candidate solution selection in step S6 based on non-dominated ordination and expected density estimation, which includes the following steps:

[0055] S6.1 Based on the high-precision archive set A, establish a local Gaussian process model for each original objective function of the multi-objective optimization mathematical model in S1;

[0056] S6.2. Using the predicted values ​​from the local Gaussian process model, the optimal candidate population is selected through non-dominated sorting. The solutions with a non-dominant level of 1 are selected and stored in the solution set. China; against After performing low-precision simulation evaluation, The corresponding low-precision fitness value FEs = FEs + η is stored in the low-precision archive set A. L In, and set

[0057] FEs represents the equivalent high-precision evaluation number;

[0058] S6.2, from the solution set In the solution set, the solution with the minimum expected density in the high-precision archive set A is selected sequentially and stored in the solution set. In the middle, until The number of solutions reaches η; the expected density Density(x) is calculated as follows:

[0059]

[0060] in, This represents the predicted value of the local Gaussian process model for the j-th target. Indicates about The expectation of the distribution is calculated using the Monte Carlo estimation method; x′ represents the solution in the high-precision archive set A; for After conducting high-precision simulation evaluation The corresponding high-precision fitness values ​​are stored in the high-precision archive set A, and FEs = FEs + η is set.

[0061] A large-scale multi-material hybrid vehicle structure optimization design system includes a computer device; the computer device is configured and programmable to perform the steps of the above-described method.

[0062] Compared with the prior art, the advantages of this invention are as follows:

[0063] 1. In S1, an optimization mathematical model is established based on the characteristics of multi-objective optimization design of integrated die-cast floor, making the mathematical description of multi-objective optimization design of integrated die-cast floor more concise and clear.

[0064] 2. In S3, the multi-objective optimization mathematical model established for the multi-objective optimization design of the integrated die-cast floor is decomposed into a series of optimization sub-problems based on Chebyshev scalar decomposition. This helps avoid optimality conflicts between different objectives and clarifies the overall search direction. Furthermore, adjacent sub-problems exhibit similarity, and collaborative optimization can significantly improve search efficiency.

[0065] 3. The multi-precision, multi-task surrogate model in S4, on the one hand, can obtain landscape information of the original objective function through low-cost, low-precision simulation evaluation, reducing the number of high-precision simulation evaluations required for modeling; on the other hand, it can fully utilize the similarity between adjacent sub-problems to further enhance the model's predictive performance. Therefore, the multi-precision, multi-task surrogate model can provide accurate predictions of the sub-problem objective function.

[0066] 4. In S5, the multi-precision assisted differential evolution search adopts a multi-precision multi-task proxy model to assist decomposition-based collaborative differential evolution, which can quickly obtain the potential optimal solution set, thereby ensuring the rapid convergence of the overall optimization process.

[0067] 5. S6 employs a two-stage approach based on non-dominated sorting and expected density estimation. First, a local Gaussian process model is used to filter non-dominated solutions from the potential solution set. Then, based on the expected density estimation strategy, solutions with diversity are further selected. These solutions, which possess both convergence and diversity, will be used as high-quality candidate solutions for high-precision function evaluation to improve the quality of the non-dominated solution set in the archive, ensuring that the algorithm can efficiently and effectively perform multi-objective optimization design of the integrated die-cast floor. Attached Figure Description

[0068] Figure 1 This is a flowchart of the method of the present invention;

[0069] Figure 2 A schematic diagram for designing an integrated die-cast rear floor for automobiles;

[0070] Figure 3 This diagram illustrates the optimized effect of the present invention. Detailed Implementation

[0071] Now Figure 2 The method proposed in this invention will be illustrated using the optimized design of the shown vehicle side panel structure as an example. In this example, it mainly consists of a rear floor platform, longitudinal beams running through the left and right sides, wheel arches on the left and right sides, and transverse support beams. The design variables are the maximum thicknesses of these main structures, denoted as x1, x2, x3, and x4, respectively. Based on the requirements of ensuring passenger space integrity and lightweighting in the integrated die-cast rear floor design, the design objective is to maximize specific energy absorption and minimize collision intrusion displacement. The optimization design process is as follows... Figure 1 As shown, the implementation steps are as follows:

[0072] Step 1, according to Figure 2 A mathematical model for a multi-objective optimization design problem is established for the integrated die-cast rear floor of the automobile shown.

[0073] min FI D (x),-SEA(x)

[0074] stx=(x1,x2,x3,x4)∈[0.5c,2c]

[0075] Among them, FI D (x) represents the intrusion displacement of the passenger compartment, SEA(x) represents the displacement during the collision process (this sentence is incomplete), c = [6,6,6,6] represents the original thickness vector of the structural component. x represents the design vector, c represents the original thickness vector of the structural component, x1 - x4 represents the thickness of the rear floor platform, longitudinal beam, wheel arch, and transverse support beam, respectively.

[0076] Step 2: Initialize the archive set for the described optimization problem:

[0077] High-precision archive set A and low-precision archive set A L Initially, all sets are empty; the design space is sampled using the Latin hypercube sampling method to generate 10 solutions {x1,...,x}. 10}, high-precision simulation performance evaluation was performed using structural finite element analysis software. The calculated performance index values ​​were used as the fitness values ​​of these 10 solutions. These 10 solutions and their corresponding fitness values ​​were stored in an archive set A = {(x i ,y i)|i=1,...,10}; Next, the Latin hypercube sampling method is used to sample the design space, generating 50 solutions {x1,...,x 50 The structural finite element analysis software was used for low-precision simulation performance evaluation. The calculated performance index values ​​were used as the fitness values ​​of these 50 solutions. These 50 solutions and their corresponding fitness values ​​were stored in a low-precision archive set A. L ={(x i ,y i )|i=1,...,50}. It is worth noting that low-precision simulation simplifies the finite element collision model by removing some details that do not affect collision performance (such as small ribs, stiffeners, and transition fillets) from the high-precision simulation. Its simulation time is only 1 / 5 of the high-precision simulation time. Initial evaluation count FEs=20.

[0078] Step 3: Decompose the multi-objective optimization mathematical model into a series of single-objective sub-problems:

[0079] First, ideal points are generated based on the fitness values ​​in the high-precision archive. in Next, 10 weight vectors W = {w} are uniformly generated in the target space. 1 ,...,w 10 Finally, based on the Chebyshev scalarization method, the multi-objective optimization mathematical model in step 1 is decomposed into 10 sub-problems, where the expression of the s-th sub-problem is as follows:

[0080]

[0081] stx∈Ω

[0082] s∈{1,...,10}

[0083] Finally, based on the Eulerian distance of the weight vectors, a neighborhood subproblem of the s-th subproblem is generated and stored. middle.

[0084] Step 4: Integrate finite element simulation evaluation data of different precisions and relevant information between adjacent sub-problems to establish a multi-precision, multi-task proxy model:

[0085] 1. Based on the co-kriging hypothesis and the correlation between adjacent subproblems, the s-th subproblem is compared with its neighborhood.

[0086] The objective function of the subproblem is defined as:

[0087]

[0088] in, This represents the objective function for low-precision simulation performance evaluation. With G s (·) is obtained using the decomposition method in step S1, where Γ represents the scaling parameter. Let represent the residual term. Considering the correlation between the terms in Ψ(x), we can assume that Ψ(·) follows a multi-task Gaussian process.

[0089] 2. A multi-task Gaussian process is used to... Modeling the elements in the middle yields the corresponding prediction function. The expression for the middle element is as follows:

[0090]

[0091] in, These represent the predicted mean and standard deviation, respectively.

[0092] 3. A multi-task Gaussian process is used to model the elements in Ψ(·) to obtain the corresponding prediction function. The element in the middle, expressed as follows:

[0093]

[0094] in, These represent the corresponding predicted mean and standard deviation, respectively.

[0095] 4. Use the Adam optimizer to optimize the system. and Joint training is performed, and the loss function for training is as follows:

[0096]

[0097] in, and The covariance matrix of a multi-task Gaussian process. and Hyperparameters to be determined, g L For low-precision evaluation data, Ψ represents the residual data. This is achieved by minimizing the joint loss function. Γ can be obtained. By considering hyperparameters, a multi-precision, multi-task proxy model is ultimately constructed. The prediction output for a new solution x can be expressed as:

[0098]

[0099] in, The middle element is That is, the objective function g of the s-th optimization subproblem in step S1 s The predicted value of (x).

[0100] Step 5: Implement multi-precision proxy-assisted evolutionary search to obtain the optimal candidate population:

[0101] 1. Initialize the population Where x i This is the best solution in A corresponding to the i-th subproblem.

[0102] 2. For each individual x in the population i Fifty test vectors O are generated using the differential evolution operator. i ={o1,...,o 50 Next, based on the output of the multi-precision multi-task agent model... For O i An evaluation is conducted to pre-select the best individual. 3. and x i Compare survival outcomes and select the better ones to update x in the population. i .

[0103] 4. The above steps are performed by g max After the next iteration, the optimal candidate population is output.

[0104] Step 6: Conduct a two-stage candidate solution selection based on non-dominated ranking and expected density estimation to screen high-quality solution sets that combine convergence and objective diversity, and update the archive set:

[0105] 1. Based on the high-precision archive set A, establish a local Gaussian process model for each original objective function in S1.

[0106] 2. Using the predicted values ​​from the local Gaussian process model, the optimal candidate population is selected through non-dominated sorting. The solutions with a non-dominant level of 1 are selected and stored in the solution set. In the middle. To After performing low-precision simulation evaluation, The corresponding low-precision fitness values ​​are stored in low-precision archive set A. L In, and update

[0107] 3. From the solution set In the solution set, the solution with the minimum expected density in the archive set A is selected sequentially and stored in the solution set. In the middle, until The number of solutions reaches 4. The expected density is calculated as follows:

[0108]

[0109] in, This represents the predicted value of the local Gaussian process model for the j-th target. Indicates about The expected value of the distribution is calculated using the Monte Carlo estimation method. After conducting high-precision simulation evaluation The corresponding high-precision fitness values ​​are stored in the high-precision archive set A, and FEs = FEs + 4 is updated.

[0110] Step 7: Repeat steps 3 to 6 until the number of evaluations (FEs) reaches 50, and output the high-precision archived non-dominated solutions as the solution set for the optimization design scheme.

[0111] The convergence process of multi-objective optimization design of integrated die-cast floor is as follows: Figure 3 As shown, the hypervolume index is used to evaluate the comprehensive performance of multi-objective requirements. Compared with traditional design methods (single-precision differential multi-objective optimization), the method of this invention obtains the same optimization results in about 25 finite element evaluations as the traditional method in 50 finite element evaluations, representing a 50.0% improvement in efficiency. Furthermore, the final optimization effect is improved by approximately 15% compared to the traditional method. Since the time and economic cost of automotive structural design are often directly proportional to the number of evaluations, the method of this invention can improve the efficiency of optimization solutions, thereby shortening the optimization design time and saving design costs.

[0112] The examples described above are only used to illustrate the technical solutions of the present invention, but the present invention is not limited to the above embodiments. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A multi-precision, multi-objective optimization design method for integrated die-cast flooring, characterized in that, Includes the following steps: S1. Establish a multi-objective optimization mathematical model: S2. Construct and initialize a multi-precision evaluation data archive based on the multi-objective optimization mathematical model; the multi-precision evaluation data archive includes a high-precision archive A and a low-precision archive A. L ; S3. Decompose the multi-objective optimization mathematical model into a series of single-objective sub-problems; S4, merge high-precision archive set A and low-precision archive set A L Based on the finite element simulation evaluation data and the relevant information between adjacent sub-problems, a multi-precision multi-task proxy model is established; S5. Implement multi-precision agent-assisted evolutionary search to obtain the optimal candidate population; S6. Conduct a two-stage candidate solution selection based on non-dominated ranking and expected density estimation to screen high-quality solution sets that combine convergence and objective diversity, and update the high-precision archive set A and the low-precision archive set A. L ; S7. Repeat steps S4 to S6 until the stopping condition is met. Finally, output the solution set of the optimized design scheme based on the non-dominated solution of the high-precision archive set A.

2. The multi-precision, multi-objective optimization design method for integrated die-cast flooring according to claim 1, characterized in that, The optimized mathematical model expression in step S1 is: min FI D (x),-SEA(x) stx=(x1,x2,x3,x4)∈[0.5c,2c] FI D (x) represents the intrusion displacement of the passenger compartment, SEA(x) represents the specific energy absorbed during the collision process, c = [6,6,6,6] represents the original thickness vector of the structural component; x represents the design vector, c represents the original thickness vector of the structural component, x1 - x4 represents the thickness of the rear floor platform, longitudinal beam, wheel arch, and transverse support beam, respectively; min represents minimization.

3. The multi-precision, multi-objective optimization design method for integrated die-cast flooring according to claim 1, characterized in that, Step S2 includes the following steps: S2.1 Construct high-precision archive set A and low-precision archive set A L A is used to store the design individuals and their corresponding fitness values ​​obtained through high-precision simulation evaluation during the optimization search process. L Used to store design individuals and their corresponding fitness values ​​during low-precision simulation evaluations in the optimization search process; archive sets A and A L Initially, all sets are empty; S2.2 Initialize the high-precision archive set A: Based on the multi-objective optimization mathematical model in step S1, use the Latin hypercube sampling method to sample the design space and generate K solutions {x1,...,x}. K The K solutions are composed of dimensional design parameters; then, high-precision simulation performance evaluation is performed using structural finite element analysis software, and the calculated performance index values ​​are used as the fitness values ​​of the K solutions; finally, the K solutions and their corresponding fitness values ​​are stored in an archive set A = {(x i ,y i |i=1,...,K}; S2.3, For low-precision archive set A L Initialization: Based on the multi-objective optimization mathematical model in step S1, the design space is sampled using the Latin hypercube sampling method to generate K. L One solution K L Each solution is composed of dimensional design parameters; then, low-precision simulation performance evaluation is performed using structural finite element analysis software, and the calculated performance index values ​​are used as this K. L The fitness value of each solution; the low-precision simulation performance evaluation is achieved by deleting detailed features that do not affect collision performance in the high-precision simulation performance evaluation and implementing mesh coarsening; then, these K L Each solution and its corresponding fitness value are stored in a low-precision archive set A. L ={(x i ,y i |i=1,...,K L } 4. The multi-precision, multi-objective optimization design method for integrated die-cast flooring according to claim 3, characterized in that, The details that do not affect crash performance include small ribs, stiffeners, and transition fillets.

5. The multi-precision, multi-objective optimization design method for integrated die-cast flooring according to claim 1, characterized in that, Step S3 includes the following steps: S3.1 Generate ideal points based on the fitness values ​​in the high-precision archive set. Where the j-th ideal point f j (x i ) represents the objective function value of the solution in the high-precision archive set, and |A| represents the number of solutions in the high-precision archive set A; S3.2, uniformly generate N in the target space P Weight vectors S3.

3. Based on the Chebyshev scalarization method, decompose the multi-objective optimization mathematical model in S1 into N P Let there be ... stx∈Ω Among them, w s Let M represent the s-th weight vector, and M represent the number of optimization objectives. w represents the j-th element of the ideal point. s,j f represents the j-th element of the s-th weight vector. j (x) represents the j-th objective function of the multi-objective optimization mathematical model, and Ω is the range of values ​​for the design parameters; S3.

3. Generate neighborhood subproblems of the s-th subproblem based on the Eulerian distance of the weight vectors, and store them in the neighborhood subproblem set. middle.

6. The multi-precision, multi-objective optimization design method for integrated die-cast flooring according to claim 1, characterized in that, Step S4 includes the following steps: S4.1 Based on the co-kriging hypothesis and the correlation between adjacent subproblems, the objective function of the s-th subproblem and its neighboring subproblems is defined as follows: in, This represents the objective function for low-precision simulation performance evaluation. With G s () is obtained using the Chebyshev scalarization method, where Γ represents the scaling parameter. Let Ψ() represent the residual vector; let Ψ() follow a multi-task Gaussian process; In the s-th subproblem, the |N-th subproblem is represented by... s The objective function values ​​for each neighborhood subproblem. In the s-th low-precision subproblem, the |N-th... s The objective function values ​​for each neighborhood subproblem. Denotes the |Nth|th subproblem of the s-th subproblem. s | Residual terms of neighborhood subproblems, where T denotes matrix transpose; S4.

2. Employ a multi-task Gaussian process for... Modeling the elements in the middle yields the corresponding prediction function. The expression for the middle element is as follows: in, They represent the prediction functions respectively. For x m The predicted mean and standard deviation; express The m-th element, s represents the s-th subproblem. Indicates a Gaussian distribution; x m The design parameters for the m-th output in the set; S4.

3. Using a multi-task Gaussian process, the elements in Ψ() are modeled to obtain the corresponding prediction function. The element in the middle, expressed as follows: in, They represent the prediction functions respectively. For x m The corresponding predicted mean and standard deviation; S4.4, Using the Adam optimizer and Perform joint training, and the joint loss function for training. as follows: in, and The covariance matrix of a multi-task Gaussian process. and Hyperparameters to be determined, g L This is low-precision evaluation data, where Ψ represents residual data. express loss function, express The loss function is defined as follows: N represents the total number of samples; by minimizing the joint loss function... Obtain the hyperparameter Γ. The value of x is used to construct a multi-precision multi-task proxy model, which predicts the output of a new solution x. Represented as: in, The middle element is That is, the objective function g of the s-th optimization subproblem in step S1 s The predicted value of the objective function of the s-th optimization subproblem of (x) Let represent the objective function of the |Ns|-th domain subproblem of the s-th subproblem.

7. The large-scale multi-material hybrid vehicle structure optimization design method according to claim 1, characterized in that, Step S5, multi-precision agent-assisted evolutionary search, includes the following steps: S5.1 Initialize the population Where x i The best solution in A corresponding to the i-th subproblem; S5.2, For each individual x in the population i The differential evolution operator is used to generate λ test vectors O. i ={o1,…,o λ };o λ Let O represent the λ-th trial vector. i This represents the set of test vectors for the i-th subproblem; O i Input a multi-precision multi-task agent model, and calculate based on the output of the multi-precision multi-task agent model. For O i Conduct an evaluation and select one of them The minimum corresponding O i As the optimal individual Will and x i Compare survival outcomes and select the better ones to update x in the population. i Then through g max After the next iteration, the optimal candidate population is output.

8. The large-scale multi-material hybrid vehicle structure optimization design method according to claim 1, characterized in that, Step S6, the two-stage candidate solution selection based on non-dominated ordination and expected density estimation, includes the following steps: S6.1 Based on the high-precision archive set A, establish a local Gaussian process model for each original objective function of the multi-objective optimization mathematical model in S1; S6.

2. Using the predicted values ​​from the local Gaussian process model, the optimal candidate population is selected through non-dominated sorting. The solutions with a non-dominant level of 1 are selected and stored in the solution set. China; against After performing low-precision simulation evaluation, The corresponding low-precision fitness value FEs = FEs + η is stored in the low-precision archive set A. L In, and set FEs represents the equivalent high-precision evaluation number; S6.2, from the solution set In the solution set, the solution with the minimum expected density in the high-precision archive set A is selected sequentially and stored in the solution set. In the middle, until The number of solutions reaches η; the expected density Density(x) is calculated as follows: in, This represents the predicted value of the local Gaussian process model for the j-th target. Indicates about The expectation of the distribution is calculated using the Monte Carlo estimation method; x′ represents the solution in the high-precision archive set A; for After conducting high-precision simulation evaluation The corresponding high-precision fitness values ​​are stored in the high-precision archive set A, and FEs = FEs + η is set.

9. A large-scale multi-material hybrid vehicle structure optimization design system, characterized in that, Includes a computer device; said computer device is configured and programmable to perform the steps of the method according to any one of claims 1 to 8.

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