A vehicle body proxy model construction method based on an improved neural network

Abstract

The application relates to a vehicle body proxy model construction method based on an improved neural network. After determining the initial sample quantity of model data and the input data dimension of the model, the initial sample of the model data is sampled, and the model data is normalized. Then, a meta-heuristic algorithm with strong global search performance is used to optimize the neural network parameters once, and a Levy flight method is used to disturb the optimal parameters in the meta-heuristic algorithm optimization. Then, a gradient descent method is used to optimize the neural network parameters optimized by the meta-heuristic algorithm twice, and an adaptive step factor is introduced in the secondary optimization process. With the increase of the iteration number of the gradient descent method, the step factor gradually decreases. The method is small in calculation amount, fast in convergence speed, and suitable for the construction of proxy models in various large vehicle body structure designs.

Description

Technical Field

[0001] This invention relates to the field of vehicle body structure, and in particular to a method for constructing a vehicle body proxy model based on an improved neural network. Background Technology

[0002] In the vehicle body concept design phase, it is typically necessary to perform simulation analysis on the overall vehicle frame performance and optimize key performance indicators. Directly using a high-precision finite element model for analysis would result in a significant waste of computational resources and would be difficult to implement in engineering. To improve simulation design efficiency, a surrogate model can be constructed by collecting multiple sample points and then used in place of the high-precision finite element model during the optimization process. The surrogate model is computationally fast and can handle the time-consuming vehicle body frame optimization design problem.

[0003] Currently, common methods for constructing surrogate models can be categorized into the following types: response surface methodology, neural network methods, and Kriging models. Response surface methodology and Kriging models are suitable for models with low dimensionality; however, as the model dimensionality increases, the computational cost of these two methods grows exponentially. In the process of vehicle body structure design, there are many variables and output performance to consider, resulting in a large model dimensionality. Therefore, response surface methodology and Kriging models consume significant computational resources in practical applications. Neural network methods have significant advantages in handling nonlinear and high-dimensional problems. However, when using neural networks to construct surrogate models, the following problems exist: First, the convergence accuracy of neural network methods is greatly affected by the initial values ​​of each parameter. If the initial values ​​of the neural network parameters are not properly selected, it can easily lead to slow convergence or even training failure. Second, when optimizing parameters, neural network methods tend to obtain locally optimal parameters rather than globally optimal parameters, severely affecting the accuracy of the surrogate model.

[0004] To address the above issues, this invention patent proposes a method for constructing a vehicle body proxy model based on an improved neural network. This method not only improves the convergence efficiency of the neural network method and saves computational resources, but also enhances the accuracy of the vehicle body proxy model. Summary of the Invention

[0005] This invention addresses the shortcomings of existing technologies by proposing a method for constructing a vehicle body proxy model based on an improved neural network. This method not only enhances the convergence efficiency of the neural network method and saves computational resources, but also improves the accuracy of the vehicle body proxy model.

[0006] One of the above-mentioned objectives of the present invention is achieved by the following technical solution:

[0007] A method for constructing a vehicle body proxy model based on an improved neural network includes the following steps:

[0008] S1: Determine the dimensions of the model input data, the dimensions of the model output data, and the initial number of model data samples;

[0009] S2: The initial sample of the model data is sampled using the Latin hypercube sampling method;

[0010] S3: Normalize the model data;

[0011] S4: Determine the number of input layers, hidden layers, and output layers in the neural network;

[0012] S5: Determine the initial number of samples for neural network parameters;

[0013] S6: Determine the maximum number of iterations for the metaheuristic algorithm and the maximum number of iterations for the gradient descent method;

[0014] S7: Optimize the parameters in the neural network using meta-heuristic algorithms;

[0015] S8: Perturb the currently generated optimal parameters using the Lévy flight method;

[0016] S9: Determine whether the current metaheuristic algorithm iteration count is greater than the maximum metaheuristic algorithm iteration count. If the current metaheuristic algorithm iteration count is greater than the maximum metaheuristic algorithm iteration count, proceed to step S10; otherwise, return to step S7.

[0017] S10: Use the optimal neural network parameters output from step S9 as input, and perform secondary optimization using gradient descent.

[0018] S11: Determine whether the current number of gradient descent iterations is greater than the maximum number of gradient descent iterations. If the current number of gradient descent iterations is greater than the maximum number of gradient descent iterations, proceed to step S12; otherwise, return to step S10.

[0019] S12: Output the neural network parameters to complete the construction of the surrogate model.

[0020] Further, in step S1, the initial number of model data samples N is determined by the following formula:

[0021] N = 2k(ub - lb) + k

[0022] In the formula, ub is the upper limit of the input variable; lb is the lower limit of the input variable; k is the dimension of the model input data; the dimension k of the model input data is determined according to the actual situation.

[0023] Further, in step S3, the model data is mainly divided into model input data and model output data. The model input data is a matrix composed of vehicle body parameters, and the model output parameters are mainly a matrix composed of vehicle body performance. The model input data is generated by sampling in step S2. The model input data is imported into the Hypermesh software for calculation to obtain the corresponding model output data. The i-th dimension model input data P i =(p i1 ,p i2 ,p i3 ,p i4 ,...,p iN Normalization is performed using the following formula:

[0024]

[0025] P′ i =(p′) i1 ,p′ i2 ,p′ i3 ,p′ i4 ,...,p′ iN )

[0026] In the formula, p′ ij Input data P for the i-th dimension model i =(p i1 ,p i2 ,p i3 ,p i4 ,...,p iN The normalized result of the j-th element of ); min{P i} is the input data P for the i-th dimension model i =(p i1 ,p i2 ,p i3 ,p i4 ,...,p iN The minimum value in ); max{P i} is the input data P for the i-th dimension model i =(p i1 ,p i2 ,p i3 ,p i4 ,...,p iN The maximum value in )

[0027] The r-th dimension model outputs data Q. r =(q r1 ,q r2 ,q r3 ,q r4 ,...,q rN Normalization is performed using the following formula:

[0028]

[0029] Q′ r =(q′) r1 ,q′ r2 ,q′ r3 ,q′ r4 ,...,q′ rN )

[0030] In the formula, q′ rj Output data Q for the r-th dimension model r =(q r1 ,q r2 ,q r3 ,q r4 ,...,q rN The normalized result of the j-th element of ); min{Q r} Output data Q for the r-th dimension model r =(q r1 ,q r2 ,q r3 ,q r4 ,...,q rN The minimum value in ); max{Q r} Output data Q for the r-th dimension model r =(q r1 ,q r2 ,q r3 ,q r4 ,...,q rN The maximum value in ).

[0031] Further, in step S4, the number of input layers of the neural network is equal to the dimension of the model input data; the number of output layers of the neural network is equal to the dimension of the model output data; the number of hidden layers of the neural network is determined by the following formula:

[0032]

[0033] In the formula, k is the dimension of the model input data; m is the dimension of the model output data; and n is the number of hidden layers in the neural network.

[0034] Furthermore, in step S5, the initial number of samples for the neural network parameters is determined using the following formula:

[0035] M = 200(n·k+m·n+k·m)

[0036] In the formula, k is the dimension of the model input data; m is the dimension of the model output data; n is the number of hidden layers in the neural network; and M is the initial number of samples for the neural network parameters.

[0037] Furthermore, in step S6, the maximum number of iterations for the metaheuristic algorithm ranges from 100 to 500; the maximum number of iterations for the gradient descent method (maxiter2) and the maximum number of iterations for the metaheuristic algorithm (maxiter1) satisfy the following relationship:

[0038] maxiter2 = 100·maxiter1

[0039] In the formula, maxiter1 is the maximum number of iterations of the metaheuristic algorithm; maxiter2 is the maximum number of iterations of the gradient descent method.

[0040] Furthermore, in step S7, the design variables are the parameters in the neural network, which mainly consist of four parts: the first weight coefficient W, the second weight coefficient E, the first bias coefficient B, and the second bias coefficient D; the total number of neural network parameters is determined by the following formula:

[0041] T = n·k+m·n+m+n

[0042] In the formula, T is the total number of parameters in the neural network; k is the dimension of the model input data; m is the dimension of the model output data; and n is the number of hidden layers in the neural network.

[0043] The i-th design variable vector is:

[0044] The i-th design variable vector can be written as Z i =[W i E i B i D i ],in, Combine all design variables into a single variable:

[0045]

[0046] In step S7, the fitness of the i-th group of neural network parameters obj i Calculated using the following formula:

[0047] obj i =∑∑|F i -Q′|

[0048]

[0049] In the formula, Q′ represents the normalized model output data; F i The output data for the i-th set of neural network parameters is F; i It can be obtained using the following formula:

[0050]

[0051] In the formula, W i E is the first weighting coefficient of the i-th group; i B is the second weighting coefficient of the i-th group; i D is the first bias coefficient of the i-th group; i is the second bias coefficient of the i-th group; P′ is the normalized model input data;

[0052] logsig is the activation function of the neural network, and its expression is as follows:

[0053]

[0054] In the formula, e is the natural constant, with a value of 2.71828;

[0055] In step S7, the update formula in the metaheuristic algorithm is as follows:

[0056]

[0057] In the formula, a represents the number of iterations of the metaheuristic algorithm; These are the parameters of the i-th group of neural networks in the (a+1)-th iteration; is the overall optimal parameter for the a-th iteration; TA, TS, and TB are random vectors (1×T) in the range [0,1]; sum(TS) is the sum of all elements in TS; wt is a random value generated in the range [-5,5]; rnd is a random value generated in the range [0,1]; coe is a random value generated in the range [0,0.17]; T is the total number of parameters in the neural network; maxiter1 is the maximum number of iterations of the meta-heuristic algorithm.

[0058] Furthermore, in step S8, the Levy flight method perturbs the optimal parameters using the following formula:

[0059]

[0060] In the formula, β is a fixed variable with a value of 1.8; lfu and lfv are random vectors (1×T) in the range [0,1]; Γ is the gamma function; These are the optimal parameters in the iteration of the a-th heuristic algorithm. Let be the parameter vector after perturbation by the Lévy flight method for the optimal parameters in the a-th dimension heuristic algorithm iteration; if the parameter vector after perturbation by the Lévy flight method... Better than the original parameter vector Then use replace Otherwise, no replacement is needed.

[0061] Furthermore, in step S10, when using the gradient descent method, the optimal neural network parameters Z output in step S9 are... u Divide it into four parts according to the following method: Gradient descent, first weight coefficient W u Gradient descent second weight coefficient E u Gradient descent first bias coefficient B u and the second bias coefficient D of gradient descent u ;

[0062]

[0063]

[0064] Further, in step S10, the gradient descent method updates the first weight coefficient W of gradient descent using the following formula. u Gradient descent second weight coefficient E u Gradient descent first bias coefficient B u and the second bias coefficient D of gradient descent u :

[0065]

[0066] In the formula, This represents the first weight coefficient of gradient descent in the (y+1)th iteration of the gradient algorithm; This refers to the first weight coefficient of gradient descent in the y-th iteration of the gradient algorithm; This refers to the second weight coefficient of gradient descent in the (y+1)th iteration of the gradient algorithm; This refers to the second weighting coefficient of the gradient descent algorithm in the y-th iteration. This refers to the first bias coefficient of gradient descent in the (y+1)th iteration of the gradient algorithm; Let y be the first bias coefficient of gradient descent in the y-th iteration of the gradient algorithm; This refers to the second bias coefficient of gradient descent in the (y+1)th iteration of the gradient algorithm; `learnrate` is the second bias coefficient of gradient descent in the `y`th iteration of the gradient algorithm. (y) This is the step size factor in the y-th iteration of the gradient algorithm; This represents the increment of the first weight coefficient in the gradient descent during the y-th iteration of the gradient algorithm; This represents the increment of the second weight coefficient in the gradient descent during the y-th iteration of the gradient algorithm; This represents the increment of the first bias coefficient in the gradient descent during the y-th iteration of the gradient algorithm. This represents the increment of the second bias coefficient in the gradient descent during the y-th iteration of the gradient algorithm;

[0067] The increment of the first weight coefficient in the gradient descent during the y-th iteration of the gradient algorithm The increment of the second weight coefficient in the gradient descent during the y-th iteration of the gradient algorithm The increment of the first bias coefficient in the gradient descent during the y-th iteration of the gradient algorithm The increment of the second bias coefficient in the gradient descent during the y-th iteration of the gradient algorithm It can be obtained using the following formula:

[0068]

[0069] In the formula, delta1 (y) delta2 is the first updated parameter in the y-th iteration of the gradient algorithm. (y) is the second update parameter in the y-th iteration of the gradient algorithm; P′ is the normalized model input data; This refers to the first weight coefficient of gradient descent in the y-th iteration of the gradient algorithm; Let y be the first bias coefficient of gradient descent in the y-th iteration of the gradient algorithm;

[0070] The first update parameter delta1 in the y-th iteration of the gradient algorithm (y) And the second update parameter delta2 in the y-th iteration of the gradient algorithm (y) The calculation is performed using the following formula:

[0071]

[0072] In the formula, Q′ represents the normalized model output data; This refers to the second weighting coefficient of the gradient descent algorithm in the y-th iteration. P' represents the first weight coefficient of gradient descent in the y-th iteration of the gradient algorithm; P' represents the normalized model input data. Let y be the first bias coefficient of gradient descent in the y-th iteration of the gradient algorithm; The neural network parameter output data in the y-th iteration of the gradient algorithm can be obtained using the following formula:

[0073]

[0074] In the formula, This refers to the second weighting coefficient of the gradient descent algorithm in the y-th iteration. P' represents the first weight coefficient of gradient descent in the y-th iteration of the gradient algorithm; P' represents the normalized model input data. Let y be the first bias coefficient of gradient descent in the y-th iteration of the gradient algorithm; is the second bias coefficient of gradient descent in the y-th iteration of the gradient algorithm; logsig is the activation function of the neural network, which is the same as the activation function of the neural network mentioned above;

[0075] The step size factor learnrate in the y-th iteration of the gradient algorithm (y) It can be obtained using the following formula:

[0076]

[0077] In the formula, y is the number of iterations of the gradient algorithm; maxiter2 is the maximum number of iterations of the gradient descent method.

[0078] The advantages and positive effects of this invention are as follows:

[0079] 1. This invention first proposes a metaheuristic algorithm with strong global search performance to optimize the neural network parameters, which can effectively reduce the influence of the initial value of the neural network on the final result. In order to avoid getting trapped in local optima during the parameter optimization process and improve the accuracy of the vehicle body proxy model, this invention uses the Levy fly method to perturb the optimal parameters in the metaheuristic algorithm optimization.

[0080] 2. When optimizing neural network parameters using the gradient descent method, this invention introduces an adaptive step size factor. As the number of iterations of the gradient descent method increases, the step size factor gradually decreases, effectively reducing the optimization convergence time and avoiding oscillations in the iteration results.

[0081] 3. This invention first uses a metaheuristic algorithm to optimize the neural network parameters once, and then uses gradient descent to optimize the neural network parameters optimized by the metaheuristic algorithm a second time. This method has low computational cost and fast convergence speed, and is suitable for the construction of surrogate models in the design of various large vehicle body structures. Attached Figure Description

[0082] Figure 1 This is a flowchart of the method for constructing a vehicle body proxy model based on an improved neural network according to the present invention;

[0083] Figure 2 This is an isometric view of the vehicle body frame according to an embodiment of the present invention;

[0084] Figure 3 This is a top view of the vehicle body frame according to an embodiment of the present invention;

[0085] Figure 4 This is the iterative convergence curve of an embodiment of the present invention. Detailed Implementation

[0086] The technical solution of the present invention will be described in more detail below with reference to the accompanying drawings. The present invention includes, but is not limited to, the following embodiments.

[0087] A method for constructing a vehicle body proxy model based on an improved neural network, see [link to relevant documentation]. Figure 1 Its inventive point is: including the following steps:

[0088] S1: Determine the dimensions of the model input data, the dimensions of the model output data, and the initial number of model data samples;

[0089] S2: The initial sample of the model data is sampled using the Latin hypercube sampling method;

[0090] S3: Normalize the model data;

[0091] S4: Determine the number of input layers, hidden layers, and output layers in the neural network;

[0092] S5: Determine the initial number of samples for neural network parameters;

[0093] S6: Determine the maximum number of iterations for the metaheuristic algorithm and the maximum number of iterations for the gradient descent method;

[0094] S7: Optimize the parameters in the neural network using meta-heuristic algorithms;

[0095] S8: Perturb the currently generated optimal parameters using the Lévy flight method;

[0096] S9: Determine whether the current metaheuristic algorithm iteration count is greater than the maximum metaheuristic algorithm iteration count. If the current metaheuristic algorithm iteration count is greater than the maximum metaheuristic algorithm iteration count, proceed to step S10; otherwise, return to step S7.

[0097] S10: Use the optimal neural network parameters output from step S9 as input, and perform secondary optimization using gradient descent.

[0098] S11: Determine whether the current number of gradient descent iterations is greater than the maximum number of gradient descent iterations. If the current number of gradient descent iterations is greater than the maximum number of gradient descent iterations, proceed to step S12; otherwise, return to step S10.

[0099] S12: Output the neural network parameters to complete the construction of the surrogate model.

[0100] In step S1, the initial number of model data samples N is determined by the following formula:

[0101] N = 2k(ub - lb) + k

[0102] In the formula, ub is the upper limit of the input variable; lb is the lower limit of the input variable; k is the dimension of the model input data; the dimension k of the model input data is determined according to the actual situation.

[0103] In step S2, the hypercubic Latin sampling method is a sampling method built into the MATLAB software.

[0104] In step S3, the model data is mainly divided into model input data and model output data. The model input data is a matrix composed of vehicle body parameters, and the model output parameters are mainly a matrix composed of vehicle body performance parameters. The model input data is generated through sampling in step S2. The model input data is then imported into the Hypermesh software for calculation to obtain the corresponding model output data. The i-th dimension model input data P i =(p i1 ,p i2 ,p i3 ,p i4 ,...,p iN Normalization is performed using the following formula:

[0105]

[0106] P′ i =(p′) i1 ,p′ i2 ,p′ i3 ,p′ i4 ,...,p′ iN )

[0107] In the formula, p′ ij Input data P for the i-th dimension model i =(p i1 ,p i2 ,p i3 ,p i4 ,...,p iN The normalized result of the j-th element of ); min{P i} is the input data P for the i-th dimension model i =(p i1 ,p i2 ,p i3 ,p i4 ,...,p iN The minimum value in ); max{P i} is the input data P for the i-th dimension model i =(p i1 ,p i2 ,p i3 ,p i4 ,...,p iN The maximum value in ).

[0108] The r-th dimension model outputs data Q. r =(q r1 ,q r2 ,q r3 ,q r4 ,...,q rN Normalization is performed using the following formula:

[0109]

[0110] Q′ r =(q′) r1 ,q′ r2 ,q′ r3 ,q′ r4 ,...,q′ rN )

[0111] In the formula, q′ rj Output data Q for the r-th dimension model r =(q r1 ,q r2 ,q r3 ,q r4 ,...,q rN The normalized result of the j-th element of ); min{Q r} Output data Q for the r-th dimension model r =(q r1 ,q r2 ,q r3 ,q r4 ,...,q rN The minimum value in ); max{Q r} Output data Q for the r-th dimension model r =(q r1 ,q r2 ,q r3 ,q r4 ,...,q rN The maximum value in ).

[0112] In step S4, the number of input layers in the neural network is equal to the dimension of the model input data; the number of output layers in the neural network is equal to the dimension of the model output data; the number of hidden layers in the neural network is determined by the following formula:

[0113]

[0114] In the formula, k is the dimension of the model input data; m is the dimension of the model output data; and n is the number of hidden layers in the neural network. The number of hidden layers in the neural network is an integer, and the calculated value needs to be rounded up.

[0115] The model input data dimension is equal to the total number of design variables of the vehicle body, and the model output data dimension is equal to the number of vehicle body performance indicators of interest.

[0116] In step S5, the initial number of samples for the neural network parameters is determined by the following formula:

[0117] M = 200(n·k+m·n+k·m)

[0118] In the formula, k is the dimension of the model input data; m is the dimension of the model output data; n is the number of hidden layers in the neural network; and M is the initial number of samples for the neural network parameters.

[0119] In step S6, the maximum number of iterations for the metaheuristic algorithm ranges from 100 to 500. The maximum number of iterations for gradient descent (maxiter2) and the maximum number of iterations for the metaheuristic algorithm (maxiter1) satisfy the following relationship:

[0120] maxiter2 = 100·maxiter1

[0121] In the formula, maxiter1 is the maximum number of iterations of the metaheuristic algorithm; maxiter2 is the maximum number of iterations of the gradient descent method.

[0122] In step S7, the design variables are the parameters in the neural network, mainly composed of four parts: the first weight coefficient W, the second weight coefficient E, the first bias coefficient B, and the second bias coefficient D. The total number of neural network parameters is determined by the following formula:

[0123] T = n·k+m·n+m+n

[0124] In the formula, T is the total number of parameters in the neural network; k is the dimension of the model input data; m is the dimension of the model output data; and n is the number of hidden layers in the neural network.

[0125] The i-th design variable vector is

[0126] For ease of subsequent calculations, the i-th design variable vector can be written as Z. i =[W i E i B i D i ],in, Combine all design variables into a single variable:

[0127]

[0128] In step S7, the fitness of the i-th group of neural network parameters obj i Calculated using the following formula:

[0129] obj i =∑∑|F i -Q′|

[0130]

[0131] In the formula, Q′ represents the normalized model output data; F iThe output data for the i-th set of neural network parameters is F. i It can be obtained using the following formula:

[0132]

[0133] In the formula, W i E is the first weighting coefficient of the i-th group; i B is the second weighting coefficient of the i-th group; i D is the first bias coefficient of the i-th group; i is the second bias coefficient of the i-th group; P′ is the normalized model input data.

[0134] logsig is the activation function of the neural network, and its expression is as follows:

[0135]

[0136] In the formula, e is the natural constant, with a value of 2.71828.

[0137] In step S7, the update formula in the metaheuristic algorithm is as follows:

[0138]

[0139] In the formula, a represents the number of iterations of the meta-heuristic algorithm; These are the parameters of the i-th group of neural networks in the (a+1)-th iteration; is the overall optimal parameter for the a-th iteration; TA, TS, and TB are random vectors (1×T) in the range [0,1]; sum(TS) is the sum of all elements in TS; wt is a random value generated in the range [-5,5]; rnd is a random value generated in the range [0,1]; coe is a random value generated in the range [0,0.17]; T is the total number of parameters in the neural network; maxiter1 is the maximum number of iterations of the meta-heuristic algorithm.

[0140] In step S8, the Levy flight method perturbs the optimal parameters using the following formula:

[0141]

[0142] In the formula, β is a fixed variable with a value of 1.8; lfu and lfv are random vectors (1×T) in the range [0,1]; Γ is the gamma function; These are the optimal parameters in the iteration of the a-th heuristic algorithm. Let be the parameter vector after perturbation using the Lévy flight method for the optimal parameters in the a-th heuristic algorithm iteration. If the parameter vector after perturbation using the Lévy flight method... Better than the original parameter vector Then use replace Otherwise, no replacement is needed.

[0143] In step S10, when using the gradient descent method, the optimal neural network parameters Z output in step S9 are... u Divide it into four parts according to the following method: Gradient descent, first weight coefficient W u Gradient descent second weight coefficient E u Gradient descent first bias coefficient B u and the second bias coefficient D of gradient descent u .

[0144]

[0145] In step S10, the gradient descent method updates the first weight coefficient W of gradient descent using the following formula. u Gradient descent second weight coefficient E u Gradient descent first bias coefficient B u and the second bias coefficient D of gradient descent u :

[0146]

[0147] In the formula, This represents the first weight coefficient of gradient descent in the (y+1)th iteration of the gradient algorithm; This refers to the first weight coefficient of gradient descent in the y-th iteration of the gradient algorithm; This refers to the second weight coefficient of gradient descent in the (y+1)th iteration of the gradient algorithm; This refers to the second weighting coefficient of the gradient descent algorithm in the y-th iteration. This refers to the first bias coefficient of gradient descent in the (y+1)th iteration of the gradient algorithm; Let y be the first bias coefficient of gradient descent in the y-th iteration of the gradient algorithm; This refers to the second bias coefficient of gradient descent in the (y+1)th iteration of the gradient algorithm; `learnrate` is the second bias coefficient of gradient descent in the `y`th iteration of the gradient algorithm. (y) This is the step size factor in the y-th iteration of the gradient algorithm; This represents the increment of the first weight coefficient in the gradient descent during the y-th iteration of the gradient algorithm; This represents the increment of the second weight coefficient in the gradient descent during the y-th iteration of the gradient algorithm; This represents the increment of the first bias coefficient in the gradient descent during the y-th iteration of the gradient algorithm. This represents the increment of the second bias coefficient in the gradient descent during the y-th iteration of the gradient algorithm.

[0148] The increment of the first weight coefficient in the gradient descent during the y-th iteration of the gradient algorithm The increment of the second weight coefficient in the gradient descent during the y-th iteration of the gradient algorithm The increment of the first bias coefficient in the gradient descent during the y-th iteration of the gradient algorithm The increment of the second bias coefficient in the gradient descent during the y-th iteration of the gradient algorithm It can be obtained using the following formula:

[0149]

[0150] In the formula, delta1 (y) delta2 is the first updated parameter in the y-th iteration of the gradient algorithm. (y) is the second update parameter in the y-th iteration of the gradient algorithm; P′ is the normalized model input data; This refers to the first weight coefficient of gradient descent in the y-th iteration of the gradient algorithm; Let y be the first bias coefficient of gradient descent in the y-th iteration of the gradient algorithm.

[0151] The first update parameter delta1 in the y-th iteration of the gradient algorithm (y) And the second update parameter delta2 in the y-th iteration of the gradient algorithm (y) The calculation is performed using the following formula:

[0152]

[0153] In the formula, Q′ represents the normalized model output data; This refers to the second weighting coefficient of the gradient descent algorithm in the y-th iteration. P' represents the first weight coefficient of gradient descent in the y-th iteration of the gradient algorithm; P' represents the normalized model input data. Let y be the first bias coefficient of gradient descent in the y-th iteration of the gradient algorithm; The neural network parameter output data in the y-th iteration of the gradient algorithm can be obtained using the following formula:

[0154]

[0155] In the formula, This refers to the second weighting coefficient of the gradient descent algorithm in the y-th iteration. P' represents the first weight coefficient of gradient descent in the y-th iteration of the gradient algorithm; P' represents the normalized model input data. Let y be the first bias coefficient of gradient descent in the y-th iteration of the gradient algorithm; is the second bias coefficient of gradient descent in the y-th iteration of the gradient algorithm; logsig is the activation function of the neural network, which is the same as the activation function of the neural network mentioned above.

[0156] The step size factor learnrate in the y-th iteration of the gradient algorithm (y) It can be obtained using the following formula:

[0157]

[0158] In the formula, y is the number of iterations of the gradient algorithm; maxiter2 is the maximum number of iterations of the gradient descent method.

[0159] Example:

[0160] This embodiment uses the body frame structure of a six-wheeled unmanned support vehicle as an example. The isometric view of the body frame is shown below. Figure 2 As shown, the top view of the vehicle body frame is as follows: Figure 3 As shown. Based on symmetry and manufacturing constraints, the six-wheeled unmanned support vehicle's body frame structure can be divided into 19 parts, as shown in the attached diagram. Figure 2 and 3 The data is labeled with numbers 1-19, and the thickness of each part is used as a design variable, i.e., the model input data dimension k=19. The thickness of the six-wheeled unmanned support vehicle's body frame structure ranges from 1mm to 4mm, i.e., lb=1, ub=4. The initial sample size of the model data can be obtained through the following calculation formula:

[0161] N=2k(ub-lb)+k=2×19×(4-1)+19=133

[0162] In this embodiment, the vehicle body performance of interest includes the first-order modal frequency, second-order modal frequency, maximum displacement under static load, and mass. Therefore, the model output data dimension m = 4. The sampling results of the initial model data using the Latin hypercube sampling method are shown in Appendix Tables 1-1 and 1-2. Importing the model input data into Hypermesh software yields the corresponding model output data, as shown in Appendix Table 2.

[0163] The model input data in Appendix 1 are normalized according to the following formula:

[0164]

[0165] P′ i =(p′) i1 ,p′ i2 ,p′ i3 ,p′ i4 ,...,p′ iN )

[0166] In the formula, p′ ij Input data P for the i-th dimension model i =(p i1 ,p i2 ,p i3,p i4 ,...,p iN The normalized result of the j-th element of ); min{P i} is the input data P for the i-th dimension model i =(p i1 ,p i2 ,p i3 ,p i4 ,...,p iN The minimum value in ); max{P i} is the input data P for the i-th dimension model i =(p i1 ,p i2 ,p i3 ,p i4 ,...,p iN The maximum value in the model input data is shown in Appendix Tables 3-1 and 3-2.

[0167] The model output data in Appendix 2 is normalized according to the following formula:

[0168]

[0169] Q′ r =(q′) r1 ,q′ r2 ,q′ r3 ,q′ r4 ,...,q′ rN )

[0170] In the formula, q′ rj Output data Q for the r-th dimension model r =(q r1 ,q r2 ,q r3 ,q r4 ,...,q rN The normalized result of the j-th element of ); min{Q r} Output data Q for the r-th dimension model r =(q r1 ,q r2 ,q r3 ,q r4 ,...,q rN The minimum value in ); max{Q r} Output data Q for the r-th dimension model r =(q r1 ,q r2 ,q r3 ,q r4 ,...,q rN The maximum value in the model output data is shown in Appendix Table 4.

[0171] The number of hidden layers, n, in a neural network can be determined using the following formula:

[0172]

[0173] The initial number of samples for neural network parameters can be determined using the following formula:

[0174] M=200(n·k+m·n+k·m)=200×(10×19+4×10+19×4)=61200

[0175] The maximum number of iterations (maxiter1) for the metaheuristic algorithm is 600. The maximum number of iterations (maxiter2) for the gradient descent method can be calculated using the following formula:

[0176] maxiter2=100·maxiter1=100×600=60000

[0177] Iterative convergence curve as shown Figure 4 As shown, the error between the predicted and actual values ​​of the vehicle body performance indicators decreases with increasing iteration count. Through iterative calculation, the first weighting coefficient W of gradient descent is obtained. u Gradient descent second weight coefficient E u Gradient descent first bias coefficient B u and the second bias coefficient D of gradient descent u as follows:

[0178]

[0179] To verify the effectiveness of the proposed vehicle body proxy model, multiple sets of data were randomly generated for validation. The generated validation set data is shown in Appendix Table 5. Appendix Table 6 shows the actual performance calculated in Hypermesh and the predicted performance using the proposed vehicle body proxy model. The tables show that the errors between the predicted and actual first-order modal frequencies, second-order modal frequencies, maximum displacement, and mass of each validation set are all within 5%, 10%, 10%, and 10%, respectively. This comparison demonstrates that the proposed vehicle body proxy model construction method has good prediction accuracy and can be used in engineering simulation applications.

[0180] Appendix 1-1

[0181]

[0182]

[0183]

[0184]

[0185] Appendix 1-2

[0186]

[0187]

[0188]

[0189]

[0190] Appendix 2

[0191]

[0192]

[0193]

[0194]

[0195]

[0196] Appendix 3-1

[0197]

[0198]

[0199]

[0200]

[0201] Appendix 3-2

[0202]

[0203]

[0204]

[0205]

[0206] Appendix 4

[0207]

[0208]

[0209]

[0210]

[0211] Appendix 5

[0212]

[0213] Appendix 6-1

[0214]

[0215]

[0216] Appendix 6-2

[0217]

Claims

1. A method for constructing a body proxy model based on an improved neural network, characterized in that, The method comprises the following steps: S1: determining model input data dimension, model output data dimension and model data initial sample number; S2: sampling the model data initial sample by using Latin hypercube sampling method; S3: normalizing the model data; S4: determining the number of neural network input layer, hidden layer and output layer; S5: determining the initial sample number of neural network parameters; S6: determining the maximum iteration number of meta-heuristic algorithm and the maximum iteration number of gradient descent method; S7: optimizing the parameters in the neural network by using the meta-heuristic algorithm; S8: perturbing the best parameters generated at present by using Levy flight method; S9: judging whether the current meta-heuristic algorithm iteration number is greater than the maximum iteration number of the meta-heuristic algorithm, if yes, entering step S10; Otherwise, returning to step S7; S10: taking the best neural network parameters output in step S9 as input, and optimizing them again by using the gradient descent method; S11: judging whether the current gradient descent method iteration number is greater than the maximum iteration number of the gradient descent method, if yes, entering step S12; Otherwise, returning to step S10; S12: outputting the neural network parameters and completing the construction of the proxy model; In step S7, the design variables are the parameters in the neural network, which are composed of four parts: the first weight coefficient W, the second weight coefficient E, the first bias coefficient B and the second bias coefficient D; the total number of neural network parameters is determined by the following formula: T=n·k+m·n+m+n In the formula, T is the total number of neural network parameters; k is the model input data dimension; m is the model output data dimension; n is the number of neural network hidden layers; The ith design variable vector is The i-th design variable vector is simply written as: Z i = [W i , E i , B i , D i ] wherein Grouping all design variables into a single variable: In step S7, the i-th set of neural network parameter fitness obj i is calculated by the following equation: obj i =∑∑|F i -Q′| In the formula, Q' is the normalized model output data; F i is the i-th group of neural network parameter output data; the i-th group of neural network parameter output data F i is obtained by the following formula: wherein W i is a first weight coefficient of the i-th group; E i is a second weight coefficient of the i-th group; B i is a first bias coefficient of the i-th group; D i is a second bias coefficient of the i-th group; and P' is the normalized model input data. logsig is the activation function of the neural network, and its expression is as follows: In the formula, e is a natural constant, and its value is 2.71828; In step S7, the update formula in the meta-heuristic algorithm is as follows: where a is the iteration number of the meta-heuristic algorithm; is the i-th set of neural network parameters in the a+1-th iteration; is the overall best parameter in the a-th iteration; TA, TS, and TB are random vectors in the range of [0, 1] (1 x T); sum(TS) is the sum of all elements in TS; wt is a random value generated in the range of [-5, 5]; rnd is a random value generated in the range of [0, 1]; coe is a random value generated in the range of [0, 0.17]; T is the total number of neural network parameters; and maxiterl is the maximum iteration number of the meta-heuristic algorithm.

2. The improved neural network based body proxy model construction method according to claim 1, characterized in that: In step S1, the model data initial sample number N is determined by the following formula: N=2k(ub-lb)+k In the formula, ub is the upper limit value of the input variable; lb is the lower limit value of the input variable; k is the model input data dimension; the model input data dimension k is determined according to the actual situation.

3. The method of claim 1, wherein the method further comprises: In step S3, the model data is divided into model input data and model output data, the model input data is a matrix composed of body parameters, and the model output parameters are a matrix composed of body performance; The model input data is sampled by step S2 to generate model input data, which is introduced into the Hypermesh software to calculate and obtain corresponding model output data; the i-dimensional model input data P i = (p i1 ,p i2 ,p i3 ,p i4 ,...,p iN ) is normalized by the following formula: P' i = (p' i1 ,p' i2 ,p' i3 ,p' i4 ,...,p' iN ) where p' = p / pmax ij is the i-th dimension input data P i = (p i1 , p i2 , p i3 , p i4 ,..., p iN ) normalized result of the j-th element min{P i} is the minimum value in the i-th dimension of the model input data P i = (p i1 , p i2 , p i3 , p i4 ,..., p iN ); max{P i} is the maximum value in the i-th dimension of the model input data P i = (p i1 , p i2 , p i3 , p i4 ,..., p iN ). rthdimensional model output data Q r = (q r1 ,q r2 ,q r3 ,q r4 ,...,q rN ) is normalized by the following equation: Q′ r = (q′ r1 , q′ r2 , q′ r3 , q′ r4 ,..., q′ rN ) where q' = q / max{q} and q = q / min{q} rj is the jth element of the r-dimensional model output data Q r = (q r1 , q r2 , q r3 , q r4 ,..., q rN ) normalized; min{Q r} is the minimum value in the r-dimensional model output data Q r = (q r1 , q r2 , q r3 , q r4 ,..., q rN ); and max{Q r} is the maximum value in the r-dimensional model output data Q r = (q r1 , q r2 , q r3 , q r4 ,..., q rN ).

4. The method of claim 1, wherein the method further comprises: In step S4, the number of neural network input layer is the model input data dimension k; the number of neural network output layer is the model output data dimension m; the number of neural network hidden layer n is determined by the following formula: In the formula, k is the model input data dimension; m is the model output data dimension; n is the number of neural network hidden layers.

5. The method of claim 1, wherein: In step S5, the initial sample number of neural network parameters is determined by the following formula: M=200(n·k+m·n+k·m) In the formula, k is the model input data dimension; m is the model output data dimension; n is the number of neural network hidden layers; and M is the initial sample number of neural network parameters.

6. The method of claim 1, wherein: In step S6, the maximum iteration number of the meta-heuristic algorithm is in the range of 100-500; the maximum iteration number maxiter2 of the gradient descent method satisfies the following relationship with the maximum iteration number maxiter1 of the meta-heuristic algorithm: maxiter2 = 100 maxiter1 In the formula, maxiter1 is the maximum iteration number of the meta-heuristic algorithm; and maxiter2 is the maximum iteration number of the gradient descent method.

7. The method of claim 1, wherein: In step S8, the Levy flight method is used to perturb the optimal parameters by the following formula: where β is a constant variable with value 1.8; lfu and lfv are random vectors in the range of [0, 1] (1 x T); and Γ is the gamma function; is the best parameter in the a-th heuristic algorithm iteration; is the parameter vector after the Levy flight method is disturbed to the best parameter in the a-th heuristic algorithm iteration; if the parameter vector after the Levy flight method is disturbed to the best parameter in the a-th heuristic algorithm iteration is better than the original parameter vector is the best parameter in the a-th heuristic algorithm iteration is replaced by Otherwise, no replacement is needed. 8.The method of claim 1, wherein: In step S10, the optimal neural network parameters Z output in step S9 are updated using the gradient descent method u The four parts are divided as follows: Gradient descent first weight coefficient W u , Gradient descent second weight coefficient E u , Gradient descent first bias coefficient B u , and Gradient descent second bias coefficient D u 9.The method of claim 1, wherein: In step S10, the gradient descent method updates the gradient descent first weight coefficient W u , the gradient descent second weight coefficient E u , the gradient descent first bias coefficient B u , and the gradient descent second bias coefficient D u by the following formulas: wherein is the first weight coefficient for gradient descent in the y+1th iteration of the gradient algorithm; is the first weight coefficient for gradient descent in the yth iteration of the gradient algorithm; is the second weight coefficient for gradient descent in the y+1th iteration of the gradient algorithm; is the second weight coefficient for gradient descent in the yth iteration of the gradient algorithm; is the first bias coefficient for gradient descent in the y+1th iteration of the gradient algorithm; is the first bias coefficient for gradient descent in the yth iteration of the gradient algorithm; is the second bias coefficient for gradient descent in the y+1th iteration of the gradient algorithm; is the second bias coefficient for gradient descent in the yth iteration of the gradient algorithm;learnrate (y) is the step factor in the yth iteration of the gradient algorithm; is the increment of the first weight coefficient for gradient descent in the yth iteration of the gradient algorithm; is the increment of the second weight coefficient for gradient descent in the yth iteration of the gradient algorithm; is the increment of the first bias coefficient for gradient descent in the yth iteration of the gradient algorithm; is the increment of the second bias coefficient for gradient descent in the yth iteration of the gradient algorithm; Gradient descent first weight coefficient increment in the yth iteration of the gradient algorithm Gradient descent second weight coefficient increment in the yth iteration of the gradient algorithm Gradient descent first bias coefficient increment in the yth iteration of the gradient algorithm Gradient descent second bias coefficient increment in the yth iteration of the gradient algorithm is obtained by the following equation: where delta1 (y) is the first updated parameter in the yth iteration of the gradient algorithm; delta2 (y) is the second updated parameter in the yth iteration of the gradient algorithm; P' is the normalized model input data; is the first weight coefficient of the gradient descent in the yth iteration of the gradient algorithm; is the first bias coefficient of the gradient descent in the yth iteration of the gradient algorithm; first update parameter delta1 in the yth iteration of the gradient algorithm (y) and second update parameter delta2 in the yth iteration of the gradient algorithm (y) is calculated by the following equation: In the formula, Q' is normalized model output data; is the second weight coefficient of gradient descent in the yth iteration of the gradient algorithm; is the first weight coefficient of gradient descent in the yth iteration of the gradient algorithm; P' is the normalized model input data; is the first bias coefficient for gradient descent in the yth iteration of the gradient algorithm; is the neural network parameter output data in the yth iteration of the gradient algorithm, which is obtained by the following formula: In the formula, is the second weight coefficient of gradient descent in the yth iteration of the gradient algorithm; is the first weight coefficient of gradient descent in the yth iteration of the gradient algorithm; P' is the normalized model input data; is the first bias coefficient for the gradient descent in the yth iteration of the gradient algorithm; is the second bias coefficient for the gradient descent in the yth iteration of the gradient algorithm; and logsig is the activation function of the neural network. Step factor learnrate in the yth iteration of the gradient algorithm (y) is obtained by the following equation: In the formula, y is the iteration number of the gradient algorithm; and maxiter2 is the maximum iteration number of the gradient descent method.

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