A method for establishing an approximate model for parametric design of vehicle body structure

Abstract

The present invention relates to a method for establishing an approximate model for parametric design of a vehicle body structure, comprising: step 1, forming an initial training sample set according to an optimization design problem; step 2, establishing multiple approximate models to form a unit model library; step 3, making unit model decisions and constructing an ideal unit model set suitable for the current training sample; step 4, calculating the weight coefficients of each unit model and establishing an integrated approximate model; step 5, correcting the current integrated approximate model; step 6, judging whether the convergence criterion is met, if so, completing the design, otherwise executing step 7; step 7, using incremental learning technology to add new training samples to the training sample set generated in step 1, and executing steps 2 to 6 in sequence. The present invention eliminates the dependence of the approximate model on the response characteristics, ensures the technical versatility, improves the prediction robustness, improves the prediction reliability, and improves the prediction accuracy of the integrated approximate model.

Description

Technical Field

[0001] The invention relates to the field of vehicle structure design, and in particular to an approximate model establishment method for parametric design of vehicle body structure. Background Art

[0002] Parametric design is an important means of forward design of vehicle body structure. By establishing an implicit parametric vehicle body model and optimizing the vehicle body structure based on full-scale parameter transformation and efficient optimization algorithms, it can meet multidisciplinary design requirements, reduce repeated trial and error work, and shorten the design and development cycle.

[0003] Whether it is based on gradient algorithm or evolutionary algorithm, optimization design method requires a lot of structural performance response evaluation, while the performance response evaluation based on finite element simulation is expensive, resulting in problems such as excessive calculation and slow convergence. For example, a collision simulation usually takes dozens of hours, which is obviously impossible to achieve if finite element simulation is used for hundreds or thousands of iterations. Therefore, in order to reduce the calculation time of structural performance response and improve the efficiency of optimization design, approximate modeling methods are usually used instead of finite element simulation for structural optimization design in engineering practice.

[0004] Although the optimization method based on approximate model is considered to be one of the most effective ways to achieve parametric design of vehicle body structure, it still has some shortcomings, mainly manifested in: 1. Vehicle body structure design is a multidisciplinary optimization design method that meets the requirements of multiple response indicators. At present, there are many types of approximate models, but there is no universal approximate modeling technology that has outstanding advantages for different types of responses; 2. Crashworthiness is one of the important performances that must be considered in the process of vehicle body structure design, and crashworthiness response is a typical strong nonlinear structural response. The existing approximate modeling technology has poor prediction accuracy for crashworthiness response; 3. Since approximate modeling is a mathematical approximation of complex physical systems, any approximate model inevitably has prediction uncertainty. The establishment and application of approximate models is one of the important influencing factors for achieving structural optimization. As far as the currently disclosed technology is concerned, there is no approximate modeling method that meets both the requirements of reliable accuracy and robust performance in the crashworthiness design of vehicle body structure. Summary of the invention

[0005] The purpose of the present invention is to provide an approximate model building method for parametric design of vehicle body structure, so as to alleviate or eliminate the above-mentioned technical problems.

[0006] The method for establishing an approximate model for parametric design of a vehicle body structure according to the present invention comprises the following steps:

[0007] Step 1: According to the optimization design problem, the optimized Latin square sampling technique is used to generate N = 3 × Ndv groups of initial experimental designs, where Ndv is the number of design variables. Finite element simulation is called to obtain the true response value y corresponding to each group of experimental designs. i (i=1, 2, ..., N), constituting the initial training sample set;

[0008] Step 2: define a unit model library based on the training sample set, and use existing approximate modeling technology to establish multiple approximate models to form a unit model library;

[0009] Step 3: Use model screening technology to make unit model decisions, remove redundant approximate models from the unit model library, and build an ideal unit model set suitable for the current training sample;

[0010] Step 4: According to Calculate the weight coefficients of each unit model and establish an integrated approximate model HM, where E i is the sum of squares of the prediction residuals of the i-th unit model, and M is the number of approximate models in the unit model set;

[0011] Step 5: Use model updating technology to correct the current integrated approximate model;

[0012] Step 6: Determine whether the convergence criterion is met:

[0013]

[0014] If satisfied, the design is completed, otherwise proceed to step 7. is the sum of squares of the prediction residuals of the integrated approximate model in the kth period;

[0015] Step 7: Use incremental learning technology to add new training samples to the training sample set generated in step 1, and execute steps 2 to 6 in sequence.

[0016] Further, the model screening technique in step 3 includes the following steps:

[0017] Step 3-1: Use N-1 sample points to build M approximate models And use these M approximate models to evaluate the predicted values ​​at the remaining sample points Repeat this process until the cross-validation prediction values ​​of all training sample points are obtained;

[0018] Step 3-2: Reconstruct a new training sample set

[0019] Step 3-3: Based on the newly constructed training sample set, a linear regression model Y=Zβ+ε is established, where Y=(y1, y2, ..., y N )T , coefficient β=(β1, β2,...,β N ) T , Z is a matrix;

[0020] Step 3-4: Use the formula Calculate the significance index of each unit model, where b i is the regression coefficient of the partial least squares regression model, vector 1 i is a special vector whose i-th component is 1 and the rest are 0. W is the transformation matrix from linear regression model to partial least squares regression;

[0021] Step 3-5: Remove the approximate model with the smallest ΔE value from the current unit model library, update the training samples and unit model set in step 3-2, re-establish the integrated approximate model and calculate its prediction residual sum of squares E HM ;

[0022] Step 3-6: Repeat the decision-making process from step 3-2 to step 3-5 until E HM Start to rise, and then execute the decision process twice in succession. If both are E HM As the value increases, convergence is confirmed.

[0023] Further, the model updating technique in step 5 includes the following steps:

[0024] Step 5-1: Select the prediction data of each unit model in the current integrated approximate model Establish a normal prior distribution of the hyperparameter μ0 of the deviation information Δ(x)~N(μ0,σ0), where y i is the true response value of the designed experiment for the i-th group, is the predicted value of the corresponding ensemble approximate model;

[0025] Step 5-2: Combined with the overall sample information, Bayesian inference is used to calculate the conjugate posterior probability distribution N(μ1, σ1) of the deviation mean μ0, and Gaussian process is used to establish an approximate model of the hyperparameter posterior μ1 and σ1. The approximate model of the hyperparameter is consistent with the experimental design space of the original uncorrected integrated approximate model;

[0026] Step 5-3: Unknown experimental design point x a The prediction value of the ensemble approximate model at is

[0027] Further, the incremental learning technique in step 7 includes the following steps:

[0028] Step 7-1: Combined variance indicator based on response quantity As the optimization target, the maximum in is the predicted value of the current approximate model, which is built based on all training samples, is the leave-one-out cross-validation prediction value; the space filling index based on Euclidean distance Define an optimization problem for the constraints, where γ i =min j≠i |x i -x j |, N i is the total number of samples in the current cycle, C is the number of samples added in each cycle, x is the design variable, x i is the i-th design variable, x j is the jth design variable;

[0029] Step 7-2, using a genetic algorithm to solve the optimization problem defined in step 7-1;

[0030] Step 7-3: Use the optimized solution obtained in step 7-2 as a new experimental design, calculate its corresponding true response value, and add it to the training samples of the previous cycle.

[0031] The approximate model establishment method of the present invention eliminates the dependence of the approximate model on the response characteristics through an integrated learning strategy, thereby ensuring the versatility of the technology; avoids the influence of inaccurate or inappropriate unit models on the final prediction results through model screening, thereby improving the prediction robustness; corrects the prediction uncertainty of the approximate model through model updating, thereby improving the prediction reliability; improves the influence of the experimental design on the model fitting effect through incremental learning, thereby further improving the prediction accuracy of the integrated approximate model. In addition, the approximate model establishment method of the present invention does not involve the selection of empirical parameters, is flexible to use, and has strong scalability. By changing the incremental learning technology of step 7 to multi-objective optimization, it can be applied to the approximate modeling of multi-response systems. The present invention is used in the crashworthiness design of the vehicle body structure to meet both the requirements of reliable accuracy and robust performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a flow chart of the method for establishing an approximate model for parametric design of vehicle body structure;

[0033] Figure 2 is a flow chart of the model screening technique;

[0034] Figure 3 is a flow chart of the model updating technique;

[0035] Figure 4 is a flow chart of the incremental learning technique;

[0036] Figure 5Schematic diagram of design variables and structural response indicators of an embodiment of the present invention. DETAILED DESCRIPTION

[0037] The present invention will be further described below by taking the front end structure of Ford Taurus 2001 composed of eight parts (including symmetrical structures) as an example, but the protection scope of the present invention is not limited to the following example.

[0038] like Figure 1 As shown, the present embodiment relates to a method for establishing an approximate model for parametric design of a vehicle body structure, comprising the following steps:

[0039] Step 1: According to the optimization design problem, the optimized Latin square sampling technique is used to generate N = 3 × Ndv groups of initial experimental designs, where Ndv is the number of design variables. Finite element simulation is called to obtain the true response value y corresponding to each group of experimental designs. i (i=1, 2, ..., N), constituting the initial training sample set;

[0040] In the specific implementation, according to the variable ranges of the eight components shown in Table 1, 24 groups of initial test designs were generated using the optimized Latin square sampling technology, and the LS-DYNA solver was called for finite element simulation to obtain the performance indicators corresponding to each group of test designs.

[0041] Table 1 Detailed information of design variables

[0042] Design variable number Description of design variables Lower limit mm Upper limit value mm x1 Rail_inner 1.50 2.30 x2 Rail_outer_front 1.50 2.30 x3 Rail_outer_rear 2.00 3.00 x4 Rail_reinf_front 1.90 2.90 x5 Rail_reinf_rear 2.00 3.10 x6 Sunframe_arm 1.80 2.70 x7 Subframe_front 1.80 2.70 x8 Shot_gun 1.20 1.80

[0043] like Figure 5 As shown, the finite element simulation refers to: according to the C-NCAP (China New Car Assessment Program) standard, the car has a 100% frontal collision with a rigid wall at an initial speed of 50km / h, and the simulation time lasts for 120ms. The calculation time required using 32 CPUs on a high-performance parallel processor is about 4.5 hours. The performance indicator is the maximum value of the vehicle acceleration signal near the B-pillar, hereinafter referred to as ACC.

[0044] like Figure 1 As shown, step 2 to step 7 are an iterative process. The following takes the 15th cycle (when the iteration reaches the 15th cycle, the total number of training samples is 39 groups) as an example for further explanation. In this embodiment, only one new training sample is added in each learning cycle.

[0045] Step 2. Define a unit model library based on the training sample set, and use existing approximate modeling technology to establish multiple approximate models to form a unit model library. This embodiment uses a second-order polynomial, and the regression functions are linear, thin plate spline, and Kriging of radial basis functions. A total of 7 modeling technologies, including multi-quadratic radial basis functions, thin plate spline radial basis functions, and Gaussian radial basis functions, are used to define the unit model library, which are hereinafter referred to as PRS, MR, TR, GR, LK, EK, and RK.

[0046] Step 3: Use model screening technology to make unit model decisions, remove redundant approximate models from the unit model library, and build an ideal unit model set suitable for the current training sample; Figure 2 As shown, the model screening technique in step 3 includes the following steps 3-1 to 3-6

[0047] Step 3-1: Refer to the following steps to obtain the cross-validation prediction information for all 39 groups of sample points

[0048] Select 38 groups of sample points other than a certain group (e.g., group 12) in the training sample Build 7 cross-validation approximate models Use these 7 approximate models to evaluate the approximate model prediction value of the 12th group of sample points

[0049] Step 3-2: Combine cross-validation predictions Construct a new training sample set based on the actual ACC values ​​corresponding to each group of experimental designs:

[0050]

[0051] Step 3-3: Based on the newly constructed training sample set, a linear regression model Y=Zβ+ε is established, where Y=(y1, y2, ..., y N ) T , coefficient β=(β1, β2,...,β N ) T , The linear regression model established in step 3-3 is as follows:

[0052]

[0053] Step 3-4: Use the formula Calculate the significance index of each unit model, where b i is the regression coefficient of the partial least squares regression model, vector 1 iis a special vector whose i-th component is 1 and the rest are 0. W is the transformation matrix from the linear regression model to the partial least squares regression. Steps 3-4 calculated the normalized significance index ΔE of the seven approximate models: 0.815, 0.906, 0.127, 0.913, 0.632, 0.097, 0.278;

[0054] Step 3-5: Remove the approximate model with the smallest ΔE value (0.097) from the current unit model library Reconstruct the training sample set in step 3-2 And establish an integrated approximate model, the prediction residual sum of squares E HM =2.355;

[0055] Step 3-6: Repeat steps 3-2 to 3-5. After the second iteration, E HM =2.728, E after the third iteration HM =2.602, E after the 4th iteration HM =2.685, E HM Start to increase, and then perform steps 3-2 to 3-5 twice in succession. HM are 2.697 and 2.713 respectively, so it can be confirmed that the third iteration converges. At this time, the unit model set is

[0056] Step 4: According to Calculate the weight coefficients of each unit model and establish an integrated approximate model HM, where E i is the prediction residual sum of squares of the i-th unit model, and M is the number of approximate models in the unit model set. The integrated approximate model HM established in this embodiment is:

[0057]

[0058] Step 5: Use model updating technology to correct the current integrated approximate model; Figure 3 As shown, the model updating technique includes steps 5-1 to 5-3.

[0059] Step 5-1: According to the prediction error data of each unit model in the current integrated approximate model:

[0060]

[0061] Establish bias information for each set of experimental designs The prior distribution of the hyperparameters of i is the true response value of the designed experiment for the i-th group, Predict the value for the corresponding ensemble approximate model;

[0062] Step 5-2: Combine the training sample information added after executing step 6 and use Bayesian inference to calculate the mean deviation The posterior probability distribution of And use Gaussian process to establish the approximate model of hyperparameter posterior μ1 and σ1 and The approximate model of hyperparameters remains consistent with the experimental design space of the original uncorrected ensemble approximate model;

[0063] Step 5-3: According to the formula Calculate the unknown experimental design point x a The predicted value of the integrated approximate model at ;

[0064] Step 6: ε=0.1082>0.01 in the current cycle, which does not meet the convergence condition, and proceed to step 7;

[0065] Step 7: Use incremental learning technology to add new training samples to the training sample set generated in step 1, and execute steps 2 to 6 in sequence. Figure 4 The incremental learning technique shown includes steps 7-1 to 7-3.

[0066] Step 7-1: Combined variance indicator based on response quantity As the optimization target, the maximum

[0067] in is the predicted value of the current approximate model, which is built based on all training samples, is the leave-one-out cross-validation prediction value; the space filling index based on Euclidean distance Define an optimization problem for the constraints, where γ i =min j≠i |x i -x j |, N i is the total number of samples in the current cycle, C is the number of samples added in each cycle, x is the design variable, x i is the i-th design variable, x j is the jth design variable. In this embodiment, step 7-1 defines the optimization problem as:

[0068]

[0069] Step 7-2, using a genetic algorithm to solve the optimization problem defined in step 7-1;

[0070] Step 7-3: Use the optimized solution obtained in step 7-2 as a new experimental design, call LS-DYNA to calculate the corresponding ACC value, and add it to the current 39 groups of training samples.

[0071] Repeat steps 3 to 7. In the 74th cycle, ε=0.0089<0.01, which meets the convergence criterion, the loop is terminated, and the approximate modeling process is completed. At this time, the total number of training samples is 98 groups.

[0072] An additional 15 test designs were randomly generated, and the LS-DYNA solver was used for finite element simulation to obtain the ACC value of each test design as a validation sample point. To verify the technical advantages of the present invention, y i The actual ACC values ​​of 15 groups of verification sample points, is the corresponding approximate model prediction value;

[0073] According to all 98 sets of training samples generated from step 1 to step 7, 7 single approximate models are established using the modeling technology described in step 2. The RMSE of the 7 single approximate models and the integrated approximate model established by the present invention are calculated respectively, and the results are shown in Table 2.

[0074] Table 2 RMSE values ​​of various modeling techniques

[0075] Modeling techniques PRS MR TR GR LK EK R The present invention RMSE 2.025 1.795 1.323 1.284 1.205 1.197 1.384 1.035

[0076] To further verify the technical advantages of the present invention, the optimized Latin square sampling technology is used to directly generate 98 groups, 102 groups, 106 groups, 110 groups, 114 groups, 118 groups, 122 groups, and 126 groups of experimental designs, and the LS-DYNA solver is called for finite element simulation to obtain the performance index of each group of experimental designs as training sample points. According to the above 8 groups of experimental designs, 8 integrated approximate models are established using the modeling technology described in step 2 and the coefficient calculation method in step 4. The RMSE of the 8 integrated approximate models is calculated, and the results are shown in Table 3.

[0077] Table 3 RMSE values ​​of ensemble approximate models based on different training samples

[0078] Sample size 98 102 106 110 114 118 122 126 RMSE 1.184 1.167 1.141 1.133 1.115 1.062 1.032 1.031

[0079] It can be seen from Table 2 that, under the same computing resource conditions, the approximate model building method proposed in the present invention can obtain better prediction performance. Table 3 verifies the technical advantage of the present invention from another perspective: although the integrated approximate modeling method is also adopted, the traditional direct modeling technology requires 122 sets of training samples to reach (or exceed) the performance of the present invention, that is, the present invention can achieve a given prediction accuracy with fewer training samples.

Claims

1. A method for establishing an approximate model for parametric design of a vehicle body structure, characterized in that: The following steps are involved: Step 1: According to the optimization design problem, the optimized Latin square sampling technique is used to generate N = 3 × Ndv groups of initial experimental designs, where Ndv is the number of design variables. Finite element simulation is called to obtain the true response value y corresponding to each group of experimental designs. i , where i = 1, 2, ..., N, constitutes the initial training sample set; Step 2: define a unit model library based on the training sample set, and use existing approximate modeling technology to establish multiple approximate models to form a unit model library; Step 3: Use model screening technology to make unit model decisions, remove redundant approximate models from the unit model library, and build an ideal unit model set suitable for the current training sample; Step 4: According to Calculate the weight coefficients of each unit model and establish an integrated approximate model HM, where E i is the sum of squares of the prediction residuals of the i-th unit model, and M is the number of approximate models in the unit model set; Step 5: Use model updating technology to correct the current integrated approximate model; Step 6: Determine whether the convergence criterion is met: If satisfied, the design is completed, otherwise proceed to step 7. is the sum of squares of the prediction residuals of the integrated approximate model in the kth period; Step 7: Use incremental learning technology to add new training samples to the training sample set generated in step 1, and execute steps 2 to 6 in sequence; The model screening technique in step 3 includes the following steps: Step 3-1: Use N-1 sample points to build M approximate models Where i = 1, 2, ..., M, and use these M approximate models to evaluate the predicted values ​​at the remaining sample points Where i = 1, 2, ..., M, j = 1, 2, ..., N, and the process is repeated until the cross-validation prediction values ​​of all training sample points are obtained; Step 3-2: Reconstruct a new training sample set Where j = 1, 2, ..., N; Step 3-3: Based on the newly constructed training sample set, a linear regression model Y=Zβ+ε is established, where Y=(y1, y2, ..., y N ) T , coefficient β=(β1, β2,...,β N ) T , Z is a matrix; Step 3-4: Use the formula Calculate the significance index of each unit model, where b i is the regression coefficient of the partial least squares regression model, vector 1 i is a special vector whose i-th component is 1 and the other components are 0, and W is the transformation matrix from the linear regression model to the partial least squares regression; Step 3-5: Remove the approximate model with the smallest ΔE value from the current unit model library, update the training samples and unit model set in step 3-2, re-establish the integrated approximate model and calculate its prediction residual sum of squares E HM ; Step 3-6: Repeat the decision-making process from step 3-2 to step 3-5 until E HM Start to rise, and then execute the decision process twice in succession. If both are E HM As the value increases, convergence is confirmed; The incremental learning technique in step 7 includes the following steps: Step 7-1: Combined variance indicator based on response quantity As the optimization target, the maximum in is the predicted value of the current approximate model, which is built based on all training samples, is the leave-one-out cross-validation prediction value; the space filling index based on Euclidean distance Define an optimization problem for the constraints, where γ i =min j≠i |x i -x j |,N i is the total number of samples in the current cycle, C is the number of samples added in each cycle, x is the design variable, x i is the i-th design variable, x j is the jth design variable; Step 7-2, using a genetic algorithm to solve the optimization problem defined in step 7-1; Step 7-3: Use the optimized solution obtained in step 7-2 as a new experimental design, calculate its corresponding true response value, and add it to the training samples of the previous cycle.

2. The method for establishing an approximate model for parametric design of a vehicle body structure according to claim 1, characterized in that: The model updating technique in step 5 comprises the following steps: Step 5-1: Select the prediction data of each unit model in the current integrated approximate model Establish a normal prior distribution of the hyperparameter μ0 of the deviation information Δ(x)~N(μ0,σ0), where y i is the true response value of the designed experiment for the i-th group, is the predicted value of the corresponding ensemble approximate model; Step 5-2: Combined with the overall sample information, Bayesian inference is used to calculate the conjugate posterior probability distribution N(μ1, σ1) of the deviation mean μ0, and Gaussian process is used to establish an approximate model of the hyperparameter posterior μ1 and σ1. The approximate model of the hyperparameter is consistent with the experimental design space of the original uncorrected integrated approximate model; Step 5-3: Unknown experimental design point x a The prediction value of the ensemble approximate model at is

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