Optimization method, device, medium, and program product based on neural network model

Abstract

The application discloses an optimization method, device, medium and program product based on a neural network model, and the method comprises the following steps: (1) modeling an automobile rear subframe based on SFE-Concept, constructing a first-order modal maximization mathematical model according to an adaptive penalty function, generating an optimization population based on a Latin hypercube, and performing first-order modal and stiffness simulation analysis on the optimization population in an Isight multidisciplinary optimization design platform; (2) generating an optimal candidate subpopulation and a successful design variable vector by differential evolution based on a cubic kernel radial basis function machine learning model; (3) training a Dropout neural network model to obtain an evolution parameter; (4) updating the evolution parameter based on the Dropout neural network model; (5) updating the optimization population based on the evolution parameter, and if a convergence condition is reached, outputting an optimal rear subframe, or else returning to step (2). According to the Dropout neural network model, the evolution parameter is adaptively adjusted, and the method has strong adaptability to the modal optimization problem of the automobile rear subframe.

Description

Technical Field

[0001] This invention relates to the fields of artificial intelligence and automobile manufacturing technology, and more specifically, to an optimization method, device, medium, and program product based on a neural network model. Background Technology

[0002] In automotive engineering, the rear subframe, as a key load-bearing component of the chassis system, directly impacts the vehicle's NVH (Noise, Vibration, and Harshness) performance. If the first-order mode of the rear subframe is close to the frequency of excitation from the engine, transmission system, or road surface, resonance may occur, leading to increased structural fatigue, decreased ride comfort, and even safety hazards. Therefore, optimizing the design to improve the first-order mode of the rear subframe while meeting stiffness constraints is one of the core issues in improving overall vehicle performance.

[0003] Traditional methods rely on evolutionary algorithms combined with finite element simulation models for iterative design. However, their core drawback lies in the fact that the evolutionary parameters in these algorithms typically need to be manually preset and fixed throughout the process. This makes it difficult to adapt to the dynamic requirements of different optimization stages in high-dimensional design spaces, especially when the geometric complexity of the rear subframe leads to design variables encompassing multiple dimensions such as position, shape, and curvature. In the initial stage of wide-area exploration, fixed parameters result in low search efficiency; in later, localized development, parameter mismatch can easily cause the evolutionary algorithm to get stuck in local optima. Furthermore, the penalty function method used in traditional methods applies constraints to the objective function through static weights, failing to accurately reflect the correlation between the degree of constraint violation and the optimization process. This often leads to excessive penalties or constraint relaxation, causing the objective function to become disconnected from engineering requirements.

[0004] Existing technologies attempt to incorporate machine learning models to assist optimization, such as using surrogate models to reduce simulation computation. However, traditional neural networks are prone to overfitting due to limited training data and noise interference, exhibiting significant prediction biases for new design variables and failing to reliably guide optimization. Furthermore, these models often focus on target prediction and are not deeply coupled with evolutionary parameter adjustment mechanisms. The evolutionary process remains constrained by fixed rules, making it impossible to extract dynamic parameter adjustment patterns from historical data, resulting in wasted computational resources and low knowledge transfer efficiency. Summary of the Invention

[0005] To address the limitations of existing technologies or the need for improved technologies, this invention proposes an optimization method, device, medium, and program product based on a neural network model. This method, based on the geometric complexity of the automotive rear subframe, the low adaptability of evolutionary parameters in traditional evolutionary algorithms, and the design requirement of first-order mode enhancement under stiffness constraints, researches and designs a solution based on a neural network model. The method adaptively adjusts evolutionary parameters through a Dropout neural network model and precisely coordinates the conflict between first-order mode enhancement and stiffness constraints through an adaptive penalty function, thereby improving the adaptability to the automotive rear subframe modal optimization problem.

[0006] To achieve the above objectives, in a first aspect, the present invention provides an optimization method based on a neural network model, the method comprising the following steps:

[0007] (1) A finite element model of the rear subframe of the automobile was established using SFE-Concept software, and the position, shape, and curvature parameters of the parts were recorded using the proportional vector method to construct the design variable vector. The fitness function of the first-order mode with stiffness constraint as the penalty term was constructed using the adaptive penalty function as the objective function to construct the mathematical model of maximizing the first-order mode of the rear subframe of the automobile. The range of values ​​of the design variable vector was determined in combination with the actual conditions of the rear subframe structure. The design variable vector was used to form an optimization population based on Latin hypercube sampling in the multidimensional design space composed of the design variable vector. Each design variable vector corresponds to an individual vector in the optimization population. The first-order modal simulation and stiffness simulation analysis of the optimization population were performed using the Isight multidisciplinary optimization design platform to obtain the values ​​of the first-order mode and stiffness of all individual vectors in the optimization population. The optimization population and its corresponding first-order mode and stiffness values ​​were stored in the historical database.

[0008] (2) Generate the optimal candidate subpopulation and successful design variable vector through differential evolution operation based on the cubic kernel radial basis function machine learning model, and store the successful design variable vector and the corresponding evolutionary parameters into the success database;

[0009] (3) Construct a Dropout neural network model, using the successful design variable vector in the success database as input, its corresponding evolution parameters as the target, the mean squared error function as the loss function, and setting the hyperparameters of the optimizer, learning rate, and training cycle to train the Dropout neural network model until convergence;

[0010] (4) Adjust and optimize the evolutionary parameters of the population based on the output of the trained Dropout neural network model;

[0011] (5) Update and optimize the population based on the adjusted evolutionary parameters. If the machine learning model based on the cubic kernel radial basis function reaches the convergence condition, output the optimal rear subframe scheme; otherwise, return to step (2) until the convergence condition is reached.

[0012] Furthermore, step (1) specifically includes:

[0013] The first step is to establish a finite element model of the automotive rear subframe using SFE-Concept software and then use the proportional vector method to record the position, shape, and curvature parameters of the parts to construct the design variable vector. The coordinate transformation formula for the proportional vector method is as follows:

[0014]

[0015] In the above formula, the angle The scaling direction and scaling value are used to control the scaling of the control point. FV Controls the scaling ratio along a specified direction. The transformed y-axis The transformed z-axis;

[0016] The specific recording method for designing variable vectors is as follows:

[0017] Record the angle of the scale vector for each control point on multiple sections. and scaling value FV These two parameters serve as the part's shape parameters;

[0018] Record the X / Y / Z coordinates of the base point as part position parameters;

[0019] Record the tangent direction or weight parameters of the baseline control points as part curvature parameters;

[0020] The second step involves constructing a fitness function for the first-order modes with stiffness constraints as the penalty term, using an adaptive penalty function as the objective function, and then building a mathematical model for maximizing the first-order modes of the vehicle's rear subframe. The specific expression is as follows:

[0021]

[0022] In the above formula, x This represents the design variable vector for the rear subframe of a car. Indicates the part position parameters. Indicates the shape parameters of the part. This represents the curvature parameters of the part, where the number of part position parameters is... p The number of shape parameters of the part is qp The number of curvature parameters of the part is nq Find indicates the vector of design variables to be optimized, Min indicates that the optimization direction is minimization, and St indicates the constraints on the vector of design variables. Let the fitness function be defined with stiffness constraints as the penalty function. The design variable vector for the rear subframe of the car is... xThe first-order mode of time, Here is the stiffness constraint function. This represents the multidimensional design space formed by the design variable vectors of the rear subframe of a car. For the first g The adaptive penalty factor of the generation is updated using the following formula:

[0023]

[0024] In the above formula, g Let the current iteration algebra be... cp The update rate of the penalty factor is controlled, and its value ranges from 2 to 10. To control the number of iterations, the value range is 0.1. Up to 0.8 ,in It is the maximum number of iterations;

[0025] The third step is to construct a multi-dimensional design space composed of design variable vectors for part shape, position, and curvature, where the dimension of the design space is consistent with the dimension of the design variable vectors; and to determine the number of design variable vectors to be sampled based on the dimension of the multi-dimensional design space and computational resources. N Within the multidimensional design space, based on Latin hypercube sampling, the design space will... Each individual is used as the optimization population, and each design variable vector corresponds to an individual vector in the optimization population.

[0026] The fourth step involves using the Isight multidisciplinary optimization design platform, which integrates finite element model automatic reconstruction software and finite element analysis programs, to perform first-order modal simulation and stiffness simulation analysis on the optimization population. This yields the first-order modal and stiffness values ​​for all individual vectors in the optimization population. The optimization population and its corresponding first-order modal and stiffness values ​​are then stored in a historical database. The steps for the first-order modal simulation and stiffness simulation analysis are as follows:

[0027] The first step is to set up software for automatic reconstruction of the finite element model, which automatically reconstructs the finite element model based on the optimized population.

[0028] The second step is to define the physical parameters of the material and inject them into the finite element model in batches via a script to ensure that the optimized population can be accurately mapped to the finite element model generated by the automatic reconstruction software.

[0029] The third step is to call the finite element analysis program to perform modal simulation analysis on the optimized population to obtain the first-order modes;

[0030] The fourth step is to call the finite element analysis program to perform stiffness simulation analysis on the optimized population and quantify the stiffness of each point on the rear subframe of the car.

[0031] The fifth step is to analyze and calculate the stiffness of each point on the rear subframe of the vehicle based on the results of the stiffness analysis module.

[0032] Step 6: Rename the result analysis files according to the sample number in a regularized manner.

[0033] Furthermore, the specific steps of step (2) are as follows:

[0034] The first step is to use differential evolution to generate vectors for each individual in the optimization population. N There are candidate mutant individuals, where the differential evolution operation formula is as follows:

[0035]

[0036] In the above formula, Represents the generation of the first individual vector. j One candidate variant individual, This represents the top [rankings] of all individuals in the optimized population after ranking according to the feasibility rules. p A vector of an individual randomly selected from % individuals. Represents the current individual vector. and This represents two individuals randomly selected from the optimized population; F This represents the scaling factor, which controls the magnitude of individual variation;

[0037] The second step involves optimizing the vector of each individual in the population by generating a binary crossover operation. N One candidate offspring individual;

[0038] The third step involves constructing machine learning models based on cubic kernel radial basis functions using all individual vectors from the historical database and their corresponding stiffness and first-order modal values.

[0039] The fourth step involves using a machine learning model based on cubic kernel radial basis functions to predict the corresponding vector for each individual vector. N The first-order modes and stiffness values ​​of each candidate offspring individual are determined, and the optimal candidate offspring individual and the successful design variable vector corresponding to each individual vector are selected using feasibility rules.

[0040] The fifth step is to input the optimal candidate offspring individuals into the Isight multidisciplinary optimization design platform for modal analysis and stiffness analysis to obtain the first-order mode and stiffness values ​​of each optimal candidate offspring individual, and calculate the fitness of the optimal candidate offspring individual based on the fitness function.

[0041] The sixth step is to store the successfully designed variable vector, its corresponding scaling factor and crossover probability as evolutionary parameters in the success database.

[0042] Furthermore, step (3) specifically includes:

[0043] The first step is to build a Dropout neural network model to learn from the data in the success database, as follows:

[0044] The successfully designed variable vector is first processed by a batch normalization layer for data standardization before being input into the Dropout neural network model.

[0045] Subsequently, a 32-node fully connected layer is added to achieve dimensionality-up mapping of the feature space, and non-linear feature representation capability is introduced through the ReLU activation function;

[0046] Configure a Dropout layer with a probability of 0.5 to enhance model generalization;

[0047] Subsequently, a 16-node fully connected layer is used for feature compression, and the ReLU activation function is used to introduce non-linear feature representation capabilities;

[0048] The fully connected layer with 8 nodes continues to compress features, and the ReLU activation function is used to introduce non-linear feature representation capabilities;

[0049] Evolutionary parameters are output using a 2-node fully connected layer in conjunction with a Sigmoid activation function;

[0050] The second step is to select the mean squared error function as the loss function and set the hyperparameters of the optimizer, learning rate, and training cycle.

[0051] The third step is to use the successful design variable vectors in the success database as input to the Dropout neural network model, and use their corresponding scaling factors and crossover probabilities as targets to construct the dataset for the Dropout neural network model to learn.

[0052] The fourth step is to train the Dropout neural network model using the constructed dataset and check its convergence. If it does not converge, return to the second step to adjust the hyperparameters until the Dropout neural network model converges.

[0053] Furthermore, the specific steps of step (4) are as follows:

[0054] The first step is to input the individual vectors of the optimized population into the trained Dropout neural network model to obtain the updated scaling factor and crossover probability evolution parameters.

[0055] The second step is to match the individual vectors of the optimized population with the corresponding updated scaling factors and crossover probability evolutionary parameters, and then save them.

[0056] Further, step (5) specifically includes:

[0057] The first step is to update and optimize the population based on the scaling factor and crossover probability evolutionary parameters updated by the Dropout neural network model;

[0058] The second step is to input the updated optimized population into the Isight multidisciplinary optimization design platform to perform stiffness simulation analysis and first-order modal simulation analysis to obtain the values ​​of stiffness and first-order modes, and calculate the fitness of each individual vector through the fitness function.

[0059] The third step is to determine whether the first-order mode and stiffness of the individual vector with the smallest fitness and the design variable vector meet the design index of the actual working condition of the rear subframe of the car. If the design index is met, the design variable vector is output as the optimal rear subframe scheme. Otherwise, return to step (2) to enter the next iteration loop until the design index is met.

[0060] In a second aspect, the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the aforementioned optimization method based on a neural network model.

[0061] 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 the aforementioned optimization method based on a neural network model.

[0062] Fourthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the aforementioned optimization method based on a neural network model.

[0063] In summary, the optimization method based on a neural network model provided by this invention has the following improvements over the limitations of existing technologies:

[0064] 1. Considering that the evolutionary parameters of traditional evolutionary algorithms need to be manually preset and fixed throughout the process, which cannot adapt to the dynamic requirements of different optimization stages in the high-dimensional design space of the automotive rear subframe, this invention uses the Dropout neural network model to autonomously learn parameter mapping rules from a successful database to achieve dynamic adjustment of evolutionary parameters.

[0065] 2. An adaptive penalty function is used to dynamically correlate the adaptive penalty factor with the number of iterations. In the early stages of optimization, the adaptive penalty factor is relaxed to explore high-potential regions, and in the later stages, the adaptive penalty factor is strengthened to guide towards a feasible solution, effectively alleviating the contradiction between excessive penalty and constraint relaxation in multi-objective optimization.

[0066] 3. Introducing a Dropout layer enhances the robustness of the Dropout neural network model and reduces interference from noisy data. Combined with a batch normalization layer, the Dropout neural network model significantly improves its generalization ability for automotive rear subframe optimization problems, ensuring consistency between the evolutionary direction and the actual performance target.

[0067] 4. Constructing a closed-loop framework of "simulation-learning-optimization": The Dropout neural network model continuously extracts the parameter mapping patterns between successful design variable vectors and evolutionary parameters from the successful database, dynamically updates the evolutionary strategy, and dynamically adjusts the adaptive penalty factor under the guidance of the adaptive penalty function. This mechanism enables the algorithm to autonomously respond to changes in the design space, improving the quality of the solution set while reducing the number of simulations, and providing a scalable paradigm for complex engineering optimization. Attached Figure Description

[0068] Figure 1 The flowchart illustrates an optimization method based on a neural network model provided by this invention. Detailed Implementation

[0069] To more clearly illustrate the objectives, technical solutions, and advantages of this invention, a detailed description will be provided 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.

[0070] Please see Figure 1 This invention provides an optimization method based on a neural network model, which is applicable to the modal optimization problem of the rear subframe of an automobile. Specifically, the method mainly includes steps (1) to (5).

[0071] Step (1): Establish a finite element model of the rear subframe of the automobile using SFE-Concept software and record the position, shape, and curvature parameters of the parts using the proportional vector method to construct design variable vectors. Construct a fitness function of the first-order mode with stiffness constraint as the penalty term using an adaptive penalty function as the objective function to build a mathematical model for maximizing the first-order mode of the rear subframe of the automobile. Determine the range of values ​​for the design variable vectors based on the actual conditions of the rear subframe structure. In the multidimensional design space composed of design variable vectors, form an optimization population based on Latin hypercube sampling, with each design variable vector corresponding to an individual vector in the optimization population. Use the Isight multidisciplinary optimization design platform to perform first-order modal simulation and stiffness simulation analysis on the optimization population to obtain the values ​​of the first-order mode and stiffness of all individual vectors in the optimization population. Store the optimization population and its corresponding first-order mode and stiffness values ​​in the historical database.

[0072] Step (1) specifically includes:

[0073] The first step is to establish a finite element model of the automotive rear subframe using SFE-Concept software and then use the proportional vector method to record the position, shape, and curvature parameters of the parts to construct the design variable vector. The coordinate transformation formula for the proportional vector method is as follows:

[0074]

[0075] In the above formula, the angle The scaling direction and scaling value are used to control the scaling of the control point. FV Controls the scaling ratio along a specified direction. The transformed y-axis The transformed z-axis;

[0076] The specific recording method for designing variable vectors is as follows:

[0077] Record the angle of the scale vector for each control point on multiple sections. and scaling value FV These two parameters serve as the part's shape parameters;

[0078] Record the X / Y / Z coordinates of the base point as part position parameters;

[0079] Record the tangent direction or weight parameters of the baseline control points as part curvature parameters;

[0080] The second step involves constructing a fitness function for the first-order modes with stiffness constraints as the penalty term, using an adaptive penalty function as the objective function, and then building a mathematical model for maximizing the first-order modes of the vehicle's rear subframe. The specific expression is as follows:

[0081]

[0082] In the above formula, x This represents the design variable vector for the rear subframe of a car. Indicates the part position parameters. Indicates the shape parameters of the part. This represents the curvature parameters of the part, where the number of part position parameters is... p The number of shape parameters of the part is qp The number of curvature parameters of the part is nq Find indicates the vector of design variables to be optimized, Min indicates that the optimization direction is minimization, and St indicates the constraints on the vector of design variables. Let the fitness function be defined with stiffness constraints as the penalty function. The design variable vector for the rear subframe of the car is... x The first-order mode of time, Here is the stiffness constraint function. This represents the multidimensional design space formed by the design variable vectors of the rear subframe of a car. For the first g The adaptive penalty factor of the generation is updated using the following formula:

[0083]

[0084] In the above formula, g Let the current iteration algebra be... cp The update rate of the penalty factor is controlled, and its value ranges from 2 to 10. To control the number of iterations, the value range is 0.1. Up to 0.8 ,in It is the maximum number of iterations;

[0085] The third step is to construct a multi-dimensional design space composed of design variable vectors for part shape, position, and curvature, where the dimension of the design space is consistent with the dimension of the design variable vectors; and to determine the number of design variable vectors to be sampled based on the dimension of the multi-dimensional design space and computational resources. N Within the multidimensional design space, based on Latin hypercube sampling, the design space will... Each individual is used as the optimization population, and each design variable vector corresponds to an individual vector in the optimization population.

[0086] The fourth step involves using the Isight multidisciplinary optimization design platform, which integrates finite element model automatic reconstruction software and finite element analysis programs, to perform first-order modal simulation and stiffness simulation analysis on the optimization population. This yields the first-order modal and stiffness values ​​for all individual vectors in the optimization population. The optimization population and its corresponding first-order modal and stiffness values ​​are then stored in a historical database. The steps for the first-order modal simulation and stiffness simulation analysis are as follows:

[0087] The first step is to set up software for automatic reconstruction of the finite element model, which automatically reconstructs the finite element model based on the optimized population.

[0088] The second step is to define the physical parameters of the material and inject them into the finite element model in batches via a script to ensure that the optimized population can be accurately mapped to the finite element model generated by the automatic reconstruction software.

[0089] The third step is to call the finite element analysis program to perform modal simulation analysis on the optimized population to obtain the first-order modes;

[0090] The fourth step is to call the finite element analysis program to perform stiffness simulation analysis on the optimized population and quantify the stiffness of each point on the rear subframe of the car.

[0091] The fifth step is to analyze and calculate the stiffness of each point on the rear subframe of the vehicle based on the results of the stiffness analysis module.

[0092] Step 6: Rename the result analysis files according to the sample number in a regularized manner.

[0093] Step (2): Generate the optimal candidate subpopulation and successful design variable vector through differential evolution operation based on the cubic kernel radial basis function machine learning model, and store the successful design variable vector and the corresponding evolution parameters into the success database.

[0094] The specific steps of step (2) are as follows:

[0095] The first step is to use differential evolution to generate vectors for each individual in the optimization population. N There are candidate mutant individuals, where the differential evolution operation formula is as follows:

[0096]

[0097] In the above formula, Represents the generation of the first individual vector. j One candidate variant individual, This represents the top [rankings] of all individuals in the optimized population after ranking according to the feasibility rules. p A vector of an individual randomly selected from % individuals. Represents the current individual vector. and This represents two individuals randomly selected from the optimized population; F This represents the scaling factor, which controls the magnitude of individual variation;

[0098] The second step involves optimizing the vector of each individual in the population by generating a binary crossover operation. N One candidate offspring individual;

[0099] The third step involves constructing machine learning models based on cubic kernel radial basis functions using all individual vectors from the historical database and their corresponding stiffness and first-order modal values.

[0100] The fourth step involves using a machine learning model based on cubic kernel radial basis functions to predict the corresponding vector for each individual vector. N The first-order modes and stiffness values ​​of each candidate offspring individual are determined, and the optimal candidate offspring individual and the successful design variable vector corresponding to each individual vector are selected using feasibility rules.

[0101] The fifth step is to input the optimal candidate offspring individuals into the Isight multidisciplinary optimization design platform for modal analysis and stiffness analysis to obtain the first-order mode and stiffness values ​​of each optimal candidate offspring individual, and calculate the fitness of the optimal candidate offspring individual based on the fitness function.

[0102] The sixth step is to store the successfully designed variable vector, its corresponding scaling factor and crossover probability as evolutionary parameters in the success database.

[0103] Step (3): Construct a Dropout neural network model, using the successful design variable vectors in the success database as input, their corresponding evolutionary parameters as targets, the mean squared error function as the loss function, and setting the hyperparameters of the optimizer, learning rate, and training cycle to train the Dropout neural network model until convergence.

[0104] Step (3) specifically includes:

[0105] The first step is to build a Dropout neural network model to learn from the data in the success database, as follows:

[0106] The successfully designed variable vector is first processed by a batch normalization layer for data standardization before being input into the Dropout neural network model.

[0107] Subsequently, a 32-node fully connected layer is added to achieve dimensionality-up mapping of the feature space, and non-linear feature representation capability is introduced through the ReLU activation function;

[0108] Configure a Dropout layer with a probability of 0.5 to enhance model generalization;

[0109] Subsequently, a 16-node fully connected layer is used for feature compression, and the ReLU activation function is used to introduce non-linear feature representation capabilities;

[0110] The fully connected layer with 8 nodes continues to compress features, and the ReLU activation function is used to introduce non-linear feature representation capabilities;

[0111] Evolutionary parameters are output using a 2-node fully connected layer in conjunction with a Sigmoid activation function;

[0112] The second step is to select the mean squared error function as the loss function and set the hyperparameters of the optimizer, learning rate, and training cycle.

[0113] The third step is to use the successful design variable vectors in the success database as input to the Dropout neural network model, and use their corresponding scaling factors and crossover probabilities as targets to construct the dataset for the Dropout neural network model to learn.

[0114] The fourth step is to train the Dropout neural network model using the constructed dataset and check its convergence. If it does not converge, return to the second step to adjust the hyperparameters until the Dropout neural network model converges.

[0115] Step (4): Adjust and optimize the evolutionary parameters of the population based on the output of the trained Dropout neural network model.

[0116] The specific steps of step (4) are as follows:

[0117] The first step is to input the individual vectors of the optimized population into the trained Dropout neural network model to obtain the updated scaling factor and crossover probability evolution parameters.

[0118] The second step is to match the individual vectors of the optimized population with the corresponding updated scaling factors and crossover probability evolutionary parameters, and then save them.

[0119] Step (5): Update and optimize the population based on the adjusted evolutionary parameters. If the machine learning model based on the cubic kernel radial basis function reaches the convergence condition, output the optimal rear subframe scheme; otherwise, return to step (2) until the convergence condition is reached.

[0120] Step (5) specifically includes:

[0121] The first step is to update and optimize the population based on the scaling factor and crossover probability evolutionary parameters updated by the Dropout neural network model;

[0122] The second step is to input the updated optimized population into the Isight multidisciplinary optimization design platform to perform stiffness simulation analysis and first-order modal simulation analysis to obtain the values ​​of stiffness and first-order modes, and calculate the fitness of each individual vector through the fitness function.

[0123] The third step is to determine whether the first-order mode and stiffness of the individual vector with the smallest fitness and the design variable vector meet the design index of the actual working condition of the rear subframe of the car. If the design index is met, the design variable vector is output as the optimal rear subframe scheme. Otherwise, return to step (2) to enter the next iteration loop until the design index is met.

[0124] This embodiment uses the benchmark function in the CEC2010 test suite to illustrate the optimization performance of the neural network model-based optimization method provided in this embodiment. The expression of the benchmark function in the CEC2010 test suite is as follows:

[0125] ,

[0126] In this embodiment It is the objective function. For constraint functions, Indicates the first i One design variable, It is the first i The offset value of each design variable. The values ​​of are shown in Table 1 below.

[0127] Table 1 Value table

[0128]

[0129] To illustrate this embodiment in more detail, an optimization method based on a neural network model is compared with the classic differential evolution algorithm. The classic differential evolution algorithm uses feasibility rules as its constraint handling mechanism. In this embodiment, the maximum number of simulation evaluations is set to 1000, the number of design variable vectors is set to 40, the optimizer is the Adam optimizer, the learning rate is 0.001, and the training period is 40. The experimental results are shown in Table 2. The comparison method used is the average, standard deviation, and minimum value of 20 independent runs. With the same number of simulations, the method in this embodiment significantly outperforms the classic differential evolution algorithm. Therefore, it can be considered that the method in this embodiment can effectively solve the modal optimization problem of the automotive rear subframe.

[0130] Table 2 Comparison of Optimization Results of Different Methods

[0131]

[0132] This invention provides an optimization method based on a neural network model. The method adaptively adjusts the evolution parameters through a Dropout neural network model and precisely coordinates the conflict between first-order modal enhancement and stiffness constraints through an adaptive penalty function, providing a systematic solution to the modal optimization problem of automotive rear subframes.

[0133] In a second aspect, the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the aforementioned optimization method based on a neural network model.

[0134] 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 the aforementioned optimization method based on a neural network model.

[0135] Fourthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the aforementioned optimization method steps based on a neural network model.

[0136] 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. An optimization method based on a neural network model, characterized in that, The method includes: (1) A finite element model of the rear subframe of the automobile was established using SFE-Concept software, and the position, shape, and curvature parameters of the parts were recorded using the proportional vector method to construct the design variable vector. The fitness function of the first-order mode with stiffness constraint as the penalty term was constructed using the adaptive penalty function as the objective function to construct the mathematical model of maximizing the first-order mode of the rear subframe of the automobile. The range of values ​​of the design variable vector was determined in combination with the actual conditions of the rear subframe structure. The design variable vector was used to form an optimization population based on Latin hypercube sampling in the multidimensional design space composed of the design variable vector. Each design variable vector corresponds to an individual vector in the optimization population. The first-order modal simulation and stiffness simulation analysis of the optimization population were performed using the Isight multidisciplinary optimization design platform to obtain the values ​​of the first-order mode and stiffness of all individual vectors in the optimization population. The optimization population and its corresponding first-order mode and stiffness values ​​were stored in the historical database. (2) Generate the optimal candidate subpopulation and successful design variable vector through differential evolution operation based on the cubic kernel radial basis function machine learning model, and store the successful design variable vector and the corresponding evolution parameters into the success database; (3) Construct a Dropout neural network model, using the successful design variable vector in the success database as input, its corresponding evolution parameters as the target, the mean squared error function as the loss function, and setting the hyperparameters of the optimizer, learning rate, and training cycle to train the Dropout neural network model until convergence; (4) Adjust and optimize the evolutionary parameters of the population based on the output of the trained Dropout neural network model; (5) Update and optimize the population based on the adjusted evolutionary parameters. If the machine learning model based on the cubic kernel radial basis function reaches the convergence condition, output the optimal rear subframe scheme; otherwise, return to step (2) until the convergence condition is reached. Step (2), the specific steps are as follows: The first step is to use differential evolution to generate vectors for each individual in the optimization population. N There are candidate mutant individuals, where the differential evolution operation formula is as follows: In the above formula, Represents the generation of the first individual vector. j One candidate variant individual, This represents the top [rankings] of all individuals in the optimized population after ranking according to the feasibility rules. p A vector of an individual randomly selected from % individuals. Represents the current individual vector. and This represents two individuals randomly selected from the optimized population; F This represents the scaling factor, which controls the magnitude of individual variation; The second step involves optimizing the vector of each individual in the population by generating a binary crossover operation. N One candidate offspring individual; The third step involves constructing machine learning models based on cubic kernel radial basis functions using all individual vectors from the historical database and their corresponding stiffness and first-order modal values. The fourth step involves using a machine learning model based on cubic kernel radial basis functions to predict the corresponding vector for each individual vector. N The first-order modes and stiffness values ​​of each candidate offspring individual are determined, and the optimal candidate offspring individual and the successful design variable vector corresponding to each individual vector are selected using feasibility rules. The fifth step is to input the optimal candidate offspring individuals into the Isight multidisciplinary optimization design platform for modal analysis and stiffness analysis to obtain the first-order mode and stiffness values ​​of each optimal candidate offspring individual, and calculate the fitness of the optimal candidate offspring individual based on the fitness function. The sixth step is to store the successfully designed variable vector, its corresponding scaling factor and crossover probability as evolutionary parameters in the success database.

2. The method as described in claim 1, characterized in that, Step (1) specifically includes: The first step is to establish a finite element model of the automotive rear subframe using SFE-Concept software and then use the proportional vector method to record the position, shape, and curvature parameters of the parts to construct the design variable vector. The coordinate transformation formula for the proportional vector method is as follows: In the above formula, the angle The scaling direction and scaling value are used to control the scaling of the control point. FV Controls the scaling ratio along a specified direction. The transformed y-axis The transformed z-axis; The specific recording method for designing variable vectors is as follows: Record the angle of the scale vector for each control point on multiple sections. and scaling value FV These two parameters serve as the part's shape parameters; Record the X / Y / Z coordinates of the base point as part position parameters; Record the tangent direction or weight parameters of the baseline control points as part curvature parameters; The second step involves constructing a fitness function for the first-order modes with stiffness constraints as the penalty term, using an adaptive penalty function as the objective function, and then building a mathematical model for maximizing the first-order modes of the vehicle's rear subframe. The specific expression is as follows: In the above formula, x This represents the design variable vector for the rear subframe of a car. Indicates the part position parameters. Indicates the shape parameters of the part. This represents the curvature parameters of the part, where the number of part position parameters is... p The number of shape parameters of the part is qp The number of curvature parameters of the part is nq Find indicates the vector of design variables to be optimized, Min indicates that the optimization direction is minimization, and St indicates the constraints on the vector of design variables. Let the fitness function be defined with stiffness constraints as the penalty function. The design variable vector for the rear subframe of the car is... x The first-order mode of time, Here is the stiffness constraint function. This represents the multidimensional design space formed by the design variable vectors of the rear subframe of a car. For the first g The adaptive penalty factor of the generation is updated using the following formula: In the above formula, g Let the current iteration algebra be... cp The update rate of the penalty factor is controlled, and its value ranges from 2 to 10. To control the number of iterations, the value range is 0.

1. Up to 0.8 ,in It is the maximum number of iterations; The third step is to construct a multi-dimensional design space composed of design variable vectors for part shape, position, and curvature, where the dimension of the design space is consistent with the dimension of the design variable vectors; and to determine the number of design variable vectors to be sampled based on the dimension of the multi-dimensional design space and computational resources. N Within the multidimensional design space, based on Latin hypercube sampling, the design space will... Each individual is used as the optimization population, and each design variable vector corresponds to an individual vector in the optimization population. The fourth step involves using the Isight multidisciplinary optimization design platform, which integrates finite element model automatic reconstruction software and finite element analysis programs, to perform first-order modal simulation and stiffness simulation analysis on the optimization population. This yields the first-order modal and stiffness values ​​for all individual vectors in the optimization population. The optimization population and its corresponding first-order modal and stiffness values ​​are then stored in a historical database. The steps for the first-order modal simulation and stiffness simulation analysis are as follows: The first step is to set up software for automatic reconstruction of the finite element model, which automatically reconstructs the finite element model based on the optimized population. The second step is to define the physical parameters of the material and inject them into the finite element model in batches via a script to ensure that the optimized population can be accurately mapped to the finite element model generated by the automatic reconstruction software. The third step is to call the finite element analysis program to perform modal simulation analysis on the optimized population to obtain the first-order modes; The fourth step is to call the finite element analysis program to perform stiffness simulation analysis on the optimized population and quantify the stiffness of each point on the rear subframe of the car. The fifth step is to analyze and calculate the stiffness of each point on the rear subframe of the vehicle based on the results of the stiffness analysis module. Step 6: Rename the result analysis files according to the sample number in a regularized manner.

3. The method as described in claim 1, characterized in that, Step (3) specifically includes: The first step is to build a Dropout neural network model to learn from the data in the success database, as follows: The successfully designed variable vector is first processed by a batch normalization layer for data standardization before being input into the Dropout neural network model. Subsequently, a 32-node fully connected layer is added to achieve dimensionality-up mapping of the feature space, and non-linear feature representation capability is introduced through the ReLU activation function; Configure a Dropout layer with a probability of 0.5 to enhance model generalization; Subsequently, a 16-node fully connected layer is used for feature compression, and the ReLU activation function is used to introduce non-linear feature representation capabilities; The fully connected layer with 8 nodes continues to compress features, and the ReLU activation function is used to introduce non-linear feature representation capabilities; Evolutionary parameters are output using a 2-node fully connected layer in conjunction with a Sigmoid activation function; The second step is to select the mean squared error function as the loss function and set the hyperparameters of the optimizer, learning rate, and training cycle. The third step is to use the successful design variable vectors in the success database as input to the Dropout neural network model, and use their corresponding scaling factors and crossover probabilities as targets to construct the dataset for the Dropout neural network model to learn. The fourth step is to train the Dropout neural network model using the constructed dataset and check its convergence. If it does not converge, return to the second step to adjust the hyperparameters until the Dropout neural network model converges.

4. The method as described in claim 1, characterized in that, Step (4), the specific steps are as follows: The first step is to input the individual vectors of the optimized population into the trained Dropout neural network model to obtain the updated scaling factor and crossover probability evolution parameters. The second step is to match the individual vectors of the optimized population with the corresponding updated scaling factors and crossover probability evolutionary parameters, and then save them.

5. The method as described in claim 4, characterized in that, Step (5) specifically includes: The first step is to update and optimize the population based on the scaling factor and crossover probability evolutionary parameters updated by the Dropout neural network model; The second step is to input the updated optimized population into the Isight multidisciplinary optimization design platform to perform stiffness simulation analysis and first-order modal simulation analysis to obtain the values ​​of stiffness and first-order modes, and calculate the fitness of each individual vector through the fitness function. The third step is to determine whether the first-order mode and stiffness of the individual vector with the smallest fitness and the design variable vector meet the design index of the actual working condition of the rear subframe of the car. If the design index is met, the design variable vector is output as the optimal rear subframe scheme. Otherwise, return to step (2) to enter the next iteration loop until the design index is met.

6. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-5.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-5.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-5.

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