Tpt-based front subframe structure maop method, apparatus, medium, and program product

Abstract

The application discloses a MaOP method, equipment, medium and program product of a front subframe structure based on TPT, comprising: (1) based on the front subframe longitudinal beam and load analysis, a MaOP design model capable of optimizing weight, mode, strength and stiffness simultaneously is constructed; (2) based on the diversity criterion and Latin hypercube, an elite population is generated, each target value of the elite population is obtained, a data set is established, and a radial basis function model is constructed; (3) a TPT-driven coevolution operation is designed to generate a candidate frame set; (4) based on the advantage and disadvantage target set, an individual potential evaluation criterion is constructed to select an optimal candidate frame; (5) each target value of the optimal candidate frame is obtained, the data set and the radial basis function model are updated, step (3) is returned until all optimization targets meet the requirements, and optimal parameter values are output. The application adopts a TPT-driven coevolution mechanism and combines radial basis function model prediction, and can effectively balance the multi-performance index optimization process for the front subframe.

Description

Technical Field

[0001] This invention relates to the fields of artificial intelligence and swarm intelligence, and more specifically, to a method, apparatus, medium, and program product based on TPT (Target Potential Tracking) for front subframe structures using MaOP (Many-Objective Optimization). Background Technology

[0002] As a key load-bearing and connecting component in the automotive chassis system, the front subframe has a significant impact on the vehicle's safety, comfort, handling, and NVH (Noise, Vibration, and Harshness) performance. With the automotive industry moving towards lightweight, high-performance, and low-energy consumption, higher demands are placed on the structural design of the front subframe. It must minimize weight while ensuring strength and stiffness, and simultaneously meet modal performance requirements to avoid resonance and improve the overall dynamic quality of the vehicle.

[0003] Traditional front subframe design methods often rely on empirical design, single-objective optimization, or sequential optimization strategies, focusing primarily on optimizing a single performance metric and struggling to achieve an effective balance among multiple conflicting objectives. Furthermore, traditional methods typically depend on finite element simulation for iterative verification, resulting in high computational costs, long cycles, and a tendency to get trapped in local optima in high-dimensional design spaces, hindering global optimization. While some methods incorporate optimization algorithms, they still lack sufficient exploration and utilization of the inherent potential relationships between multiple objectives, leading to low optimization efficiency and insufficient convergence.

[0004] In recent years, machine learning technology has demonstrated great potential in the field of engineering optimization, enabling the establishment of nonlinear mapping relationships between design variables and performance indicators through data-driven approaches. Compared with traditional methods, machine learning technology offers higher efficiency and accuracy, quickly finding optimal solutions in complex design spaces, significantly reducing computational costs, and improving the automation level of the optimization process, thereby significantly enhancing modeling and optimization efficiency. However, existing technologies cannot systematically integrate the TPT mechanism with co-evolutionary strategies, making it difficult to achieve MaOP (Main Optimization Operations) for the front subframe. Summary of the Invention

[0005] Given that front subframe structure simulation based on TPT is time-consuming and complex, and considering the design requirements for optimizing four objectives—weight, modality, strength, and stiffness—this invention proposes a TPT-based MaOP method, device, medium, and program product for front subframe structure simulation.

[0006] In a first aspect, the present invention provides a front subframe structure MaOP method based on TPT, the method comprising the following steps:

[0007] (1) Based on the geometric characteristics of the longitudinal beams of the front subframe, the thickness, length and width of each longitudinal beam of the front subframe are used as design parameters. Combined with static load analysis, a MaOP design model that can simultaneously optimize the four optimization objectives of weight, modality, strength and stiffness is constructed.

[0008] (2) Construct a design space by combining the range of design parameters, generate an elite population based on the diversity criterion and Latin hypercube, simulate and evaluate the elite population to obtain each target value, establish a dataset, and construct a radial basis function model;

[0009] (3) Based on the potential of each target in the elite population, select the set of individuals with potential advantages and the set of individuals with potential disadvantages from the dataset, and use co-evolutionary operation to generate a set of candidate frames;

[0010] (4) Based on the candidate frame set, the radial basis function model selects the advantageous and disadvantageous target sets, uses them to construct individual potential evaluation criteria, and screens the optimal candidate frame;

[0011] (5) Obtain the target values ​​of the optimal candidate frame, update the dataset and radial basis function model, return to step (3) until all targets are met, and output the optimal parameter values.

[0012] Optionally, step (1) specifically includes the following steps:

[0013] The first step is to use the thickness, length, and width of the first longitudinal beam, the thickness, length, and width of the second longitudinal beam as design parameters, based on the geometric characteristics of the front subframe longitudinal beam.

[0014] The second step is to construct a 3D model in 3D modeling software and parametricize it, based on the stress conditions of the front subframe structure and the selected materials, to obtain a parametric model.

[0015] The third step is to import the parametric model, the stress conditions of the front subframe and the key boundary conditions into the finite element analysis pre- and post-processing software for finite element analysis to obtain the finite element analysis model.

[0016] The fourth step involves using the solver of structural optimization and multiphysics simulation software to perform static load analysis on the finite element analysis model, obtaining the modal, strength, and stiffness simulation model of the front subframe, and constructing a weight extraction interface based on the solver.

[0017] The fifth step involves constructing a MaOP design model for the front subframe based on its weight, modal, strength, and stiffness simulation models. The model uses these four optimization objectives as the specific expressions are as follows:

[0018] ,

[0019] ,

[0020] ,

[0021] In the above formula, Find represents finding the optimal solution for the design parameters. This indicates the design parameters of the front subframe. This indicates the thickness of the first longitudinal beam. Indicates the length of the first longitudinal beam. This indicates the width of the first longitudinal beam. This indicates the thickness of the second longitudinal beam. Indicates the length of the second longitudinal beam. This represents the width of the second longitudinal beam, and Min represents minimizing the total weight and first-order natural frequency of the front subframe. This indicates the total weight of the front subframe. Indicates design parameters The front subframe was divided into N The total mass function of the front subframe obtained by summing the components. This indicates the density of the front subframe. Indicates design parameters The corresponding volume of the front subframe, This indicates the front subframe's design parameters. The corresponding first natural frequency, This indicates the front subframe's design parameters. The corresponding first-order natural frequency function is given by Max, which represents maximizing the strength and stiffness of the front subframe. This indicates the front subframe's design parameters. The corresponding intensity at that time This indicates the front subframe's design parameters. The corresponding intensity function at time, This indicates the front subframe's design parameters. The corresponding stiffness, This indicates the front subframe's design parameters. The stiffness function corresponding to the time.

[0022] Optionally, step (2) specifically includes the following steps:

[0023] The first step is to determine the range of values ​​for design parameters based on material strength and design requirements, and then construct the design space based on the range of values.

[0024] The second step involves using Latin hypercube to generate multiple candidate populations within the design space.

[0025] The third step is to calculate the score of each candidate population according to the diversity criterion, and select the candidate population with the highest score as the elite population.

[0026] The fourth step involves using the simplex method to generate uniformly distributed reference vectors in the target space consisting of four optimization objectives: weight, first-order natural frequency, strength, and stiffness. The total mass function, first-order natural frequency function, strength function, and stiffness function of the front subframe are used to simulate and evaluate the elite population. The total mass, first-order natural frequency, strength, and stiffness of the front subframe are then used as real sample data to establish a dataset.

[0027] The fifth step involves using the individual vectors of all populations in the dataset to establish radial basis function models for the total mass function, first-order natural frequency function, strength function, and stiffness function of the front subframe.

[0028] Optionally, the specific steps for calculating the score are as follows:

[0029] The dispersion of each candidate population relative to the mass center is calculated using the following formula:

[0030] ,

[0031] ,

[0032] In the above formula, It is the dispersion of the candidate population and the center of mass. The function representing the dispersion of the candidate population and the center of mass. This represents the number of individual vectors in the candidate population. Indicates the number of design parameters. Indicates the first The first individual vector Each design parameter value, Indicates the quality center of the candidate population;

[0033] The dispersion of each candidate population from the mass center is used as the score for each candidate population.

[0034] Optionally, step (3) specifically includes the following steps:

[0035] The first step is to sort all individual vectors in ascending order according to the target values ​​of the elite population, and select the targets corresponding to the top 50% of individual vectors as advantageous targets and the targets corresponding to the bottom 50% as disadvantageous targets.

[0036] The second step is to select the individual vectors that rank in the bottom 50% of the advantageous targets from the dataset to form the potential advantageous individuals set, and to select the individual vectors that rank in the top 50% of the disadvantageous targets from the dataset to form the potential disadvantageous individuals set.

[0037] The third step involves performing a TPT-driven co-evolution operation on each individual vector in the elite population to generate temporary candidate offspring individual vectors. The formula for the co-evolution operation is as follows:

[0038] ,

[0039] In the above formula, Indicates the first Temporary candidate offspring individual vectors Indicates the first Individual vectors of an elite population Indicates the first variable factor. This represents the vector of the first individual randomly selected from the set of potentially disadvantaged individuals. This represents the vector of the first individual randomly selected from the set of potentially dominant individuals. Indicates the second variable factor. This represents the vector of the second individual randomly selected from the set of potentially disadvantaged individuals. This represents the vector of the second individual randomly selected from the set of potentially advantageous individuals;

[0040] The fourth step is to use the radial basis function model to predict the weight, first natural frequency, strength, and stiffness of all temporary candidate offspring individual vectors, and obtain the target values ​​of all temporary candidate offspring individual vectors.

[0041] The fifth step is to construct a Chebyshev aggregation function based on the ideal reference vector and the nadir reference vector, calculate the fitness values ​​of all temporary candidate offspring vectors, and perform non-dominated sorting based on the target values ​​and fitness values ​​of the temporary candidate offspring vectors to obtain the non-dominated ranking level of all temporary candidate offspring vectors.

[0042] The Chebyshev aggregation functions, constructed based on the ideal reference vector and the nadir reference vector respectively, are as follows:

[0043] ,

[0044] ,

[0045] In the above formula, It is a Chebyshev aggregation function constructed based on an ideal reference vector. It is a Chebyshev aggregation function constructed based on the nadir reference vector. It is a reference vector. It is a temporary candidate offspring individual vector. Indicates the reference vector at the th The weight of each goal The temporary candidate offspring individual vector is in the th... The target value on each target, This indicates that the ideal reference vector in the dataset is at the th . Minimum value on each objective This indicates that the nadir reference vector in the dataset is at the [missing information] th [missing information]. The maximum value on each target;

[0046] The sixth step involves combining the obtained non-dominated ranking levels with the calculated fitness value as the screening criterion to select temporary candidate offspring vectors to form a temporary candidate population.

[0047] Step 7: Combining uniformly distributed random numbers, select a temporary candidate offspring individual vector from the temporary candidate population as a reference point, and use the DPM evolution strategy to generate candidate offspring individual vectors to form a candidate chassis set.

[0048] Optionally, step (4) specifically includes the following steps:

[0049] The first step is to use a radial basis function model to predict the weight, modal, strength and stiffness of the candidate frame set. According to the target values ​​of the candidate frame set, for each optimization target, all candidate individual vectors are sorted in ascending order. The targets corresponding to the top 50% of the candidate individual vectors are selected to form the advantageous target set, and the targets corresponding to the bottom 50% are selected to form the disadvantageous target set.

[0050] The second step is to construct individual potential evaluation criteria based on the set of strengths and weaknesses, and then select the optimal candidate chassis through the constructed individual potential evaluation criteria.

[0051] The rules followed in constructing individual potential assessment criteria based on strengths and weaknesses target sets are as follows:

[0052] If both solutions are feasible, the one with the better objective function value wins.

[0053] If one is a feasible solution and the other is not, the feasible solution automatically wins;

[0054] If both solutions are infeasible, the solution with the less severe constraint violation should be chosen.

[0055] When two infeasible solutions have the same number of constraint violations, the solution with the smaller number of constraint violations is selected as the better solution.

[0056] The objective function and constraints are as follows, within the rules to be followed:

[0057] ,

[0058] ,

[0059] In the above formula, It is about maximizing the objective function of the individual potential assessment criteria. It is the objective function of the individual potential assessment criteria. This represents the candidate individual vector of the candidate frame set. This represents the set of candidate vehicle frames. Denotes the neighbor solution set of the candidate vehicle frame set. Represents the set of advantageous objectives. It is the first The neighbor solutions are constructed using a Chebyshev aggregation function based on an ideal reference vector. It is the Chebyshev aggregation function constructed from the candidate individual vectors based on the ideal reference vector. Indicates the first solution in the neighbor set A neighbor explained. Indicates the reference vector at the th The weight of each goal This indicates that the ideal reference vector in the dataset is at the th . Minimum value on each objective Indicates constraints. This represents the set of disadvantaged targets. It is the first The neighbor solutions are constructed using Chebyshev aggregation functions based on the nadir reference vector. It is a Chebyshev aggregation function constructed from candidate individual vectors based on the nadir reference vector. Indicates the reference vector at the th The weight of each goal This indicates that the nadir reference vector in the dataset is at the [missing information] th [missing information]. The maximum value on each target.

[0060] Optionally, step (5) specifically includes the following steps:

[0061] The first step is to use a simulation model of the front subframe weight, first-order natural frequency, strength and stiffness to simulate and evaluate the optimal candidate frame, and obtain the target values ​​corresponding to the optimal candidate frame, namely the front subframe weight, first-order natural frequency, strength and stiffness.

[0062] The second step is to store the optimal candidate frame and its corresponding target values ​​into the dataset, and update the radial basis function model based on all individual vectors in the dataset.

[0063] The third step is to verify whether the four objectives of weight, first natural frequency, strength and stiffness corresponding to the current optimal candidate frame meet the requirements respectively; if they do, output the optimal parameter values; otherwise, return to step (3) to continue iterative optimization until all objectives meet the requirements and output the optimal parameter values.

[0064] Secondly, the present invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the aforementioned TPT-based front subframe structure MaOP method.

[0065] Thirdly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the aforementioned TPT-based front subframe structure MaOP method.

[0066] Fourthly, the present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the aforementioned TPT-based front subframe structure MaOP method.

[0067] In summary, the MaOP method, device, medium, and program product for a front subframe structure based on TPT provided by this invention have the following improvements over the limitations of the prior art:

[0068] 1. To address the limitations of existing technologies that cannot systematically integrate the TPT mechanism with the co-evolution strategy, making it difficult to achieve MaOP (Maintenance of Optimization) for the front subframe, this invention designs a TPT-driven co-evolution operation based on the potential of the optimization objectives during the optimization process. In the early stages of optimization, this co-evolution operation focuses on stimulating the potential of the solution's disadvantageous objectives while maintaining the advantages of the solution's advantageous objectives. In the later stages of optimization, it focuses on maintaining the diversity of solutions, thereby effectively balancing the exploration and development process.

[0069] 2. To address the limitations of traditional methods, such as low optimization efficiency and insufficient convergence, this invention constructs an individual potential evaluation criterion for screening and combines it with a radial basis function model for prediction. This allows for targeted selection of individuals for simulation evaluation of the front subframe weight, modal characteristics, strength, and stiffness, thereby improving the efficiency and accuracy of optimization.

[0070] In summary, this invention can optimize multi-objective problems involving complex simulations, adapting to optimization stagnation caused by complex simulations and achieving higher accuracy and efficiency. Simultaneous optimization of multiple objectives to achieve overall optimum can be applied not only to the optimization design of the four objectives of front subframe structure (weight, modal, strength, and stiffness), but also to provide a usable algorithmic structure for the MaOP design of other complex structures. Attached Figure Description

[0071] Figure 1 A simplified flowchart of a front subframe structure MaOP method based on TPT provided by the present invention. Detailed Implementation

[0072] To more clearly illustrate the objectives, technical solutions, and advantages of this invention, a detailed description will be provided below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention. Furthermore, the technical features in the following embodiments can be combined with each other as long as they do not conflict with each other.

[0073] Please see Figure 1 This invention provides a multi-objective design optimization method (MaOP) for front subframe structures based on TPT, which is applicable to the multi-objective design optimization problem of optimizing the weight, modal, strength, and stiffness of front subframe structures. Specifically, the method includes steps (1) to (5).

[0074] (1) Based on the geometric characteristics of the longitudinal beams of the front subframe, the thickness, length and width of each longitudinal beam of the front subframe are used as design parameters. Combined with static load analysis, a MaOP design model is constructed that can simultaneously optimize the four optimization objectives of weight, modality, strength and stiffness.

[0075] Step (1) specifically includes the following steps:

[0076] The first step is to use the thickness, length, and width of the first longitudinal beam, the thickness, length, and width of the second longitudinal beam as design parameters, based on the geometric characteristics of the front subframe longitudinal beams.

[0077] The second step involves constructing a 3D model in 3D modeling software and parametricizing it, based on the stress conditions of the front subframe structure and the selected materials, to obtain a parametric model.

[0078] The third step is to import the parametric model, the stress conditions of the front subframe, and the key boundary conditions into the finite element analysis pre- and post-processing software for finite element analysis to obtain the finite element analysis model.

[0079] The fourth step involves using the solver of structural optimization and multiphysics simulation software to perform static load analysis on the finite element analysis model, obtaining the modal, strength, and stiffness simulation model of the front subframe, and constructing a weight extraction interface based on the solver.

[0080] The fifth step involves constructing a MaOP design model for the front subframe based on its weight, modal, strength, and stiffness simulation models. The model uses these four optimization objectives as the specific expressions are as follows:

[0081] ,

[0082] ,

[0083] ,

[0084] In the above formula, Find represents finding the optimal solution for the design parameters. This indicates the design parameters of the front subframe. This indicates the thickness of the first longitudinal beam. Indicates the length of the first longitudinal beam. This indicates the width of the first longitudinal beam. This indicates the thickness of the second longitudinal beam. Indicates the length of the second longitudinal beam. This represents the width of the second longitudinal beam, and Min represents minimizing the total weight and first-order natural frequency of the front subframe. This indicates the total weight of the front subframe. Indicates design parameters The front subframe was divided into N The total mass function of the front subframe obtained by summing the components. This indicates the density of the front subframe. Indicates design parameters The corresponding volume of the front subframe, This indicates the front subframe's design parameters. The corresponding first natural frequency, This indicates the front subframe's design parameters. The corresponding first-order natural frequency function is given by Max, which represents maximizing the strength and stiffness of the front subframe. This indicates the front subframe's design parameters. The corresponding intensity at that time This indicates the front subframe's design parameters. The corresponding intensity function at time, This indicates the front subframe's design parameters. The corresponding stiffness, This indicates the front subframe's design parameters. The stiffness function corresponding to the time.

[0085] (2) Construct a design space by combining the range of design parameters, generate an elite population based on the diversity criterion and the Latin hypercube, simulate and evaluate the elite population to obtain each target value, establish a dataset, and construct a radial basis function model.

[0086] Step (2) specifically includes the following steps:

[0087] The first step is to determine the range of design parameters based on material strength and design requirements, and then construct the design space based on the range of values.

[0088] The second step involves using Latin hypercubes to generate multiple candidate populations within the design space.

[0089] The third step is to calculate the score of each candidate population according to the diversity criterion, and select the candidate population with the highest score as the elite population.

[0090] The specific steps for calculating the score are as follows:

[0091] The dispersion of each candidate population relative to the mass center is calculated using the following formula:

[0092] ,

[0093] ,

[0094] In the above formula, It is the dispersion of the candidate population and the center of mass. The function representing the dispersion of the candidate population and the center of mass. This represents the number of individual vectors in the candidate population. Indicates the number of design parameters. Indicates the first The first individual vector Each design parameter value, This indicates the quality center of the candidate population.

[0095] The dispersion of each candidate population from the mass center is used as the score for each candidate population.

[0096] The fourth step involves using the simplex method to generate uniformly distributed reference vectors in the target space comprised of four optimization objectives: weight, first-order natural frequency, strength, and stiffness. The elite population is then simulated and evaluated using the total mass function, first-order natural frequency function, strength function, and stiffness function of the front subframe. The obtained total mass, first-order natural frequency, strength, and stiffness of the front subframe are used as real sample data to establish a dataset.

[0097] The fifth step involves using the individual vectors of all populations in the dataset to establish radial basis function models for the total mass function, first-order natural frequency function, strength function, and stiffness function of the front subframe.

[0098] (3) Based on the potential of each target in the elite population, select the set of individuals with high potential and the set of individuals with low potential from the dataset, and use co-evolution to generate a set of candidate frames. That is, the set of individuals with high potential and the set of individuals with low potential are selected based on the elite population to use the corresponding individual vectors for the co-evolution operation in step (3), thereby generating a set of candidate frames.

[0099] Step (3) specifically includes the following steps:

[0100] The first step is to sort all individual vectors in ascending order according to the target values ​​of the elite population, and select the targets corresponding to the top 50% of individual vectors as advantageous targets and the targets corresponding to the bottom 50% as disadvantageous targets.

[0101] The second step involves selecting the bottom 50% of individual vectors ranked in ascending order for advantageous targets from the dataset to form a potentially advantageous individual set, and selecting the top 50% of individual vectors ranked in ascending order for disadvantageous targets from the dataset to form a potentially disadvantageous individual set. In other words, the dataset selects individual vectors that perform poorly on advantageous targets to form a potentially advantageous individual set, and selects individual vectors that perform well on disadvantageous targets to form a potentially disadvantageous individual set.

[0102] The third step involves performing a TPT-driven co-evolution operation on each individual vector in the elite population to generate temporary candidate offspring individual vectors. The formula for the co-evolution operation is as follows:

[0103] ,

[0104] In the above formula, Indicates the first Temporary candidate offspring individual vectors Indicates the first Individual vectors of an elite population Indicates the first variable factor. This represents the vector of the first individual randomly selected from the set of potentially disadvantaged individuals. This represents the vector of the first individual randomly selected from the set of potentially dominant individuals. Indicates the second variable factor. This represents the vector of the second individual randomly selected from the set of potentially disadvantaged individuals. This represents the vector of the second individual randomly selected from the set of individuals with high potential.

[0105] The fourth step involves using a radial basis function model to predict the weight, first-order natural frequency, strength, and stiffness of all temporary candidate offspring individual vectors, thereby obtaining the target values ​​for each of the temporary candidate offspring individual vectors.

[0106] The fifth step involves constructing a Chebyshev aggregation function based on the ideal reference vector and the nadir reference vector, calculating the fitness values ​​of all temporary candidate offspring vectors, and performing non-dominated sorting based on the target values ​​and fitness values ​​of the temporary candidate offspring vectors to obtain the non-dominated ranking levels of all temporary candidate offspring vectors.

[0107] The Chebyshev aggregation functions, constructed based on the ideal reference vector and the nadir reference vector respectively, are as follows:

[0108] ,

[0109] ,

[0110] In the above formula, It is a Chebyshev aggregation function constructed based on an ideal reference vector. It is a Chebyshev aggregation function constructed based on the nadir reference vector. It is a reference vector. It is a temporary candidate offspring individual vector. Indicates the reference vector at the th The weight of each goal The temporary candidate offspring individual vector is in the th... The target value on each target, This indicates that the ideal reference vector in the dataset is at the th . Minimum value on each objective This indicates that the nadir reference vector in the dataset is at the [missing information] th [missing information]. The maximum value on each target.

[0111] The sixth step involves combining the obtained non-dominated ranking levels and, based on the ascending order principle, using the calculated fitness value as the screening criterion, selecting temporary candidate offspring individual vectors to form a temporary candidate population.

[0112] Step 7: Combining uniformly distributed random numbers, select a temporary candidate offspring individual vector from the temporary candidate population as a reference point, and use the DPM evolution strategy to generate candidate offspring individual vectors to form a candidate chassis set.

[0113] (4) Based on the candidate frame set, the radial basis function model selects the set of advantageous and disadvantageous targets, uses them to construct individual potential evaluation criteria, and screens the optimal candidate frame.

[0114] Step (4) specifically includes the following steps:

[0115] The first step is to use a radial basis function model to predict the weight, modal, strength and stiffness of the candidate frame set. According to the target values ​​of the candidate frame set, for each optimization target, all candidate individual vectors are sorted in ascending order. The targets corresponding to the top 50% of the candidate individual vectors are selected to form the advantageous target set, and the targets corresponding to the bottom 50% are selected to form the disadvantageous target set.

[0116] The second step is to construct individual potential evaluation criteria based on the set of advantages and disadvantages, and then select the optimal candidate chassis through the constructed individual potential evaluation criteria.

[0117] The rules followed in constructing individual potential assessment criteria based on strengths and weaknesses target sets are as follows:

[0118] If both solutions are feasible, the one with the better objective function value wins.

[0119] If one is a feasible solution and the other is not, the feasible solution automatically wins;

[0120] If both solutions are infeasible, the solution with the less severe constraint violation should be chosen.

[0121] When two infeasible solutions have the same number of constraint violations, the solution with the smaller number of constraint violations is selected as the better solution.

[0122] The objective function and constraints are as follows, within the rules to be followed:

[0123] ,

[0124] ,

[0125] In the above formula, It is about maximizing the objective function of the individual potential assessment criteria. It is the objective function of the individual potential assessment criteria. This represents the candidate individual vector of the candidate frame set. This represents the set of candidate vehicle frames. Denotes the neighbor solution set of the candidate vehicle frame set. Represents the set of advantageous objectives. It is the first The neighbor solutions are constructed using a Chebyshev aggregation function based on an ideal reference vector. It is the Chebyshev aggregation function constructed from the candidate individual vectors based on the ideal reference vector. Indicates the first solution in the neighbor set A neighbor explained. Indicates the reference vector at the th The weight of each goal This indicates that the ideal reference vector in the dataset is at the th . Minimum value on each objective Indicates constraints. This represents the set of disadvantaged targets. It is the first The neighbor solutions are constructed using Chebyshev aggregation functions based on the nadir reference vector. It is a Chebyshev aggregation function constructed from candidate individual vectors based on the nadir reference vector. Indicates the reference vector at the th The weight of each goal This indicates that the nadir reference vector in the dataset is at the [missing information] th [missing information]. The maximum value on each target.

[0126] (5) Obtain the target values ​​of the optimal candidate frame, update the dataset and radial basis function model, return to step (3) until all targets are met, and output the optimal parameter values.

[0127] Step (5) specifically includes the following steps:

[0128] The first step is to use a simulation model of the front subframe weight, first-order natural frequency, strength and stiffness to simulate and evaluate the optimal candidate frame, and obtain the target values ​​corresponding to the optimal candidate frame, namely the front subframe weight, first-order natural frequency, strength and stiffness.

[0129] The second step is to store the optimal candidate chassis and its corresponding target values ​​into the dataset, and update the radial basis function model based on all individual vectors in the dataset.

[0130] The third step is to verify whether the four objectives of weight, first natural frequency, strength and stiffness corresponding to the current optimal candidate frame meet the requirements respectively; if they do, output the optimal parameter values; otherwise, return to step (3) to continue iterative optimization until all objectives meet the requirements and output the optimal parameter values.

[0131] Example 1 illustrates the optimization performance of the proposed MaOP method for a front subframe structure based on TPT using the benchmark test function DTLZ6. The expression of the benchmark test function DTLZ6, which has four optimization objectives, is as follows:

[0132] ,

[0133] ,

[0134] ,

[0135] ,

[0136] ,

[0137] In the above formula, , , and These are the first objective function, the second objective function, the third objective function, and the fourth objective function, respectively. It is an auxiliary constructor. It is the first One design parameter, It is the first design parameter. It is the second design parameter. It is the third design parameter. These are the remaining design parameters within the design space, excluding the first, second, and third design parameters.

[0138] To further illustrate the superiority of the method in this embodiment, a MaOP method for the front subframe structure based on TPT in this embodiment is compared with another classic and excellent Kriging-assisted reference vector guided evolutionary algorithm. The maximum number of simulation evaluations in this embodiment is set to 300, and the number of design parameters is set to 10. The average backward generation distance (hereinafter referred to as average IGD) of 30 rounds of optimization is compared. The results are shown in Table 1. The results show that under the same number of simulation evaluations, the method in this embodiment is significantly better than the Kriging-assisted reference vector guided evolutionary algorithm. It can be considered that the method in this embodiment can effectively solve the multi-objective design optimization problem of weight, modality, strength and stiffness of the front subframe structure.

[0139] Table 1. Comparison of optimization results of different methods

[0140]

[0141] This invention provides a front subframe structure MaOP method based on TPT, which improves the efficiency and accuracy of MaOP for optimizing the weight, modal, strength and stiffness of the front subframe structure, and provides a systematic solution for MaOP design for optimizing the weight, modal, strength and stiffness of the front subframe structure.

[0142] In a second aspect, the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the MaOP method for a front subframe structure based on TPT as described in the foregoing embodiments.

[0143] The memory can be volatile or non-volatile, or a combination of both. Non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. Volatile memory can be random access memory (RAM), used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). The memory of this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0144] The processor can be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in this invention. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in this invention can be directly embodied in the execution of a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method.

[0145] The method steps of this invention can be implemented in hardware, software, firmware, middleware, microcode, or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), general-purpose processors, controllers, microcontrollers, microprocessors, other electronic units for performing the functions described in this application, or combinations thereof.

[0146] Software implementation can be achieved by executing functional modules (such as procedures, functions, etc.). Software code can be stored in memory and executed by the processor. Memory can be implemented in the processor or outside the processor.

[0147] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of a front subframe structure MaOP method based on TPT as described in the foregoing embodiments.

[0148] Computer storage media can include various media that can store program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0149] Fourthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the steps of a TPT-based front subframe structure MaOP method according to the foregoing embodiments.

[0150] Specifically, computer program products include: data signals and data signals embodied in a carrier wave.

[0151] It should be noted that the technical solutions described in this invention can be combined arbitrarily without conflict.

[0152] Those skilled in the art will readily understand that the above are merely 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 within the scope of protection of the present invention.

Claims

1. A TPT-based front subframe structure MaOP method, characterized by, The method comprises the steps of: (1) based on the geometric characteristics of the front subframe longitudinal beam, taking the thickness, length and width of each longitudinal beam of the front subframe as design parameters, and combining static load analysis, a MaOP design model capable of simultaneously optimizing four optimization objectives of weight, modal, strength and stiffness is constructed; (2) combining the design parameter value range to construct a design space, based on the diversity criterion and Latin hypercube to generate an elite population, simulating and evaluating the elite population to obtain each target value, establishing a data set, and constructing a radial basis function model; (3) according to the potential of each target of the elite population, selecting a potential advantage individual set and a potential disadvantage individual set from the data set, and using a co-evolution operation to generate a candidate frame set; (4) based on the candidate frame set, the radial basis function model selects an advantage and disadvantage target set, which is used to construct an individual potential evaluation criterion, and the optimal candidate frame is screened; (5) obtaining the target values of the optimal candidate frame, updating the data set and the radial basis function model, returning to step (3) until all targets meet the requirements, and outputting the optimal parameter value.

2. The method of claim 1, wherein, Step (1) specifically comprises the following steps: First step, according to the geometric characteristics of the front subframe longitudinal beam, taking the thickness, length and width of the first longitudinal beam, the thickness, length and width of the second longitudinal beam as design parameters; Second step, combining the stress condition of the front subframe structure and the selected material, constructing a three-dimensional model in a three-dimensional modeling software and parameterizing it to obtain a parameterized model; Third step, importing the parameterized model, the stress condition of the front subframe and the key boundary conditions into a finite element analysis pre-processing software for finite element analysis to obtain a finite element analysis model; Fourth step, using the solver of a structure optimization and multi-physical field simulation software to perform static load analysis on the finite element analysis model to obtain a modal, strength and stiffness simulation model of the front subframe, and constructing a weight extraction interface based on the solver; Fifth step, based on the weight, modal, strength and stiffness simulation model of the front subframe, taking the four optimization objectives of weight, modal, strength and stiffness to construct a MaOP design model of the front subframe, and the specific expression is as follows: ， ， ， In the above formula, Find represents finding the optimal solution for the design parameters. This indicates the design parameters of the front subframe. This indicates the thickness of the first longitudinal beam. Indicates the length of the first longitudinal beam. This indicates the width of the first longitudinal beam. This indicates the thickness of the second longitudinal beam. Indicates the length of the second longitudinal beam. This represents the width of the second longitudinal beam, and Min represents minimizing the total weight and first natural frequency of the front subframe. This indicates the total weight of the front subframe. Indicates design parameters The front subframe was divided into N The total mass function of the front subframe obtained by summing the components. This indicates the density of the front subframe. Indicates design parameters The corresponding volume of the front subframe, This indicates the front subframe's design parameters. The corresponding first natural frequency, This indicates the front subframe's design parameters. The corresponding first-order natural frequency function is given by Max, which represents maximizing the strength and stiffness of the front subframe. This indicates the front subframe's design parameters. The corresponding intensity at that time This indicates the front subframe's design parameters. The corresponding intensity function at time, This indicates the front subframe's design parameters. The corresponding stiffness, This indicates the front subframe's design parameters. The stiffness function corresponding to the time.

3. The method of claim 1, wherein, Step (2) specifically comprises the following steps: First step, combining the material strength and design requirements to determine the value range of the design parameters, and then constructing a design space based on the value range; Second step, generating multiple candidate populations in the design space using Latin hypercube; Third step, calculating the score value of each candidate population according to the diversity criterion, and taking the candidate population with the maximum score value as the elite population; Fourth step, generating uniformly distributed reference vectors in the target space composed of the four optimization objectives of weight, first-order natural frequency, strength and stiffness using the simplex method, and using the total mass function, first-order natural frequency function, strength function and stiffness function of the front subframe to simulate and evaluate the elite population to obtain the total mass, first-order natural frequency, strength and stiffness of the front subframe as real sample data to establish a data set; Step 5, the radial basis function model for the total mass function, the first order natural frequency function, the strength function and the stiffness function is established by using all the population individual vectors in the data set.

4. The method of claim 3, wherein, The specific calculation steps of the score value are as follows: The dispersion of each candidate population set from the mass center is calculated, and the calculation formula is as follows: ， ， In the above formula, is the dispersion of the candidate population ensemble from the mass center, denotes the dispersion function of the candidate population ensemble from the mass center, denotes the number of individual vectors of the candidate population, denotes the number of design parameters, denotes the value of the i-th design parameter of the j-th individual vector, denotes the value of the i-th design parameter of the j-th individual vector, denotes the value of the i-th design parameter of the j-th individual vector, denotes the mass center of the candidate population; The dispersion of each candidate population set from the mass center is taken as the score value of each candidate population.

5. The method of claim 1, wherein, Step (3) specifically includes the following steps: Step 1, according to the target values of the elite population, for each optimization target, all individual vectors are sorted in ascending order, and the targets corresponding to the individual vectors ranked in the top 50% are selected as the dominant targets, and the targets corresponding to the individual vectors ranked in the last 50% are selected as the inferior targets; Step 2, select the individual vectors ranked in the last 50% in ascending order on the dominant target from the data set to form a potential dominant individual set, and select the individual vectors ranked in the last 50% in ascending order on the inferior target from the data set to form a potential inferior individual set; Step 3, the TPT driven co-evolution operation is performed on each individual vector in the elite population to generate the temporary selected offspring individual vector, and the formula of the co-evolution operation is as follows: ， In the above formula, represents the individual vector of the first elite population, represents the individual vector of the first elite population, represents the first mutation factor, represents the first individual vector randomly selected from the potential disadvantage individual set, represents the first individual vector randomly selected from the potential advantage individual set, represents the second mutation factor, represents the second individual vector randomly selected from the potential disadvantage individual set, represents the second individual vector randomly selected from the potential advantage individual set. Step 4, the radial basis function model is used to predict the weight, the first order natural frequency, the strength and the stiffness of all the temporary selected offspring individual vectors, and the target values of all the temporary selected offspring individual vectors are obtained; Step 5, the Chebyshev aggregation function is constructed according to the ideal reference vector and the nadir reference vector, the fitness values of all the temporary selected offspring individual vectors are calculated, the non-dominated ranking level of all the temporary selected offspring individual vectors is obtained according to the target values and the fitness values of the temporary selected offspring individual vectors; The Chebyshev aggregation functions constructed based on the ideal reference vector and the nadir reference vector respectively are as follows: ， ， In the above formula, It is a Chebyshev aggregation function constructed based on an ideal reference vector. It is a Chebyshev aggregation function constructed based on the nadir reference vector. It is a reference vector. It is a temporary candidate offspring individual vector. Indicates the reference vector at the th The weight of each goal The temporary candidate offspring individual vector is in the th... The target value on each target, This indicates that the ideal reference vector in the dataset is at the th . Minimum value on each objective This indicates that the nadir reference vector in the dataset is at the [missing information] th [missing information]. The maximum value on each target; Step 6, combined with the obtained non-dominated ranking level, the temporary selected offspring individual vectors are selected to form the temporary selected population according to the ascending order principle and the calculated fitness values as the screening index; Step 7, combined with the uniform distribution random number, a temporary selected offspring individual vector is selected as the reference point from the temporary selected population, and the candidate offspring individual vectors are generated by using the DPM evolution strategy to form the candidate frame set.

6. The method of claim 1, wherein, Step (4) specifically includes the following steps: Step 1, the radial basis function model is used to predict the weight, the modal, the strength and the stiffness of the candidate frame set, and the target values of the candidate frame set are sorted in ascending order for each optimization target, the targets corresponding to the candidate individual vectors ranked in the top 50% are selected to form the dominant target set, and the targets corresponding to the candidate individual vectors ranked in the last 50% are selected to form the inferior target set; Step 2, the individual potential evaluation criterion is constructed based on the dominant and inferior target sets, and the optimal candidate frame is selected by the constructed individual potential evaluation criterion; The rules followed by the individual potential evaluation criterion constructed based on the dominant and inferior target sets are as follows: If both solutions are feasible solutions, the one with the better target function value wins; If one of them is a feasible solution and the other is an infeasible solution, the feasible solution automatically wins; If both solutions are infeasible, the solution with less constraint violation is selected as the better solution; If two infeasible solutions have the same number of constraint violations, the solution with less constraint violation amount is selected as the better solution; In the followed rules, the objective function and constraints are as follows: ， ， In the above formula, It is about maximizing the objective function of the individual potential assessment criteria. It is the objective function of the individual potential assessment criteria. This represents the candidate individual vector of the candidate frame set. This represents the set of candidate vehicle frames. Denotes the neighbor solution set of the candidate vehicle frame set. Represents the set of advantageous objectives. It is the first The neighbor solutions are constructed using a Chebyshev aggregation function based on an ideal reference vector. It is the Chebyshev aggregation function constructed from the candidate individual vectors based on the ideal reference vector. Indicates the first solution in the neighbor set A neighbor explained. Indicates the reference vector at the th The weight of each goal This indicates that the ideal reference vector in the dataset is at the th . Minimum value on each objective Indicates constraints. This represents the set of disadvantaged targets. It is the first The neighbor solutions are constructed using Chebyshev aggregation functions based on the nadir reference vector. It is a Chebyshev aggregation function constructed from candidate individual vectors based on the nadir reference vector. Indicates the reference vector at the th The weight of each goal This indicates that the nadir reference vector in the dataset is at the [missing information] th [missing information]. The maximum value on each target.

7. The method of claim 1, wherein, Step (5) specifically comprises the following steps: First, the optimal candidate frame is simulated and evaluated by using the front subframe weight, the first order natural frequency, the strength and stiffness simulation model to obtain the target value corresponding to the optimal candidate frame, i.e., the front subframe weight, the first order natural frequency, the strength and stiffness; Second, the optimal candidate frame and the corresponding target values are stored in the data set, and the radial basis function model is updated according to all individual vectors in the data set; Third, it is checked whether the weight, the first order natural frequency, the strength and the stiffness corresponding to the current optimal candidate frame meet the requirements respectively; if yes, the optimal parameter value is output; otherwise, return to step (3) to continue iteration and optimization until all targets meet the requirements, and the optimal parameter value is output.

8. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that, The processor executes the computer program to implement the steps of the method of any one of claims 1-7.

9. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to implement the steps of the method of any one of claims 1-7.

10. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to implement the steps of the method of any one of claims 1-7.

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