摘要An approximate model can be used to replace the real model to reduce the computing time and guarantee the feasibility of optimization. However, the approximate model must meet the required accuracy. The higher the accuracy of the approximate model, the higher the reliability of optimization results. In this study, a finite element model for the 40% offset impact of minibus was established, with the thickness of 10 plates in the front of the car body as the design variable and peak acceleration of B pillar lower end, the total mass, and the intrusion volume of dashboard beam, steering column hole, and clutch pedal as the response values. We obtained 70 sample points by the Latin hypercube experimental design method and built approximate models of design variables and the response. Then, we compared the relative error scatter, mean relative error, and decision coefficient of the response surface approximate model, radial basis function network approximate model, kriging approximate model, and orthogonal polynomial approximate model. Results show that the prediction accuracy of the response surface approximate model and radial basis function network approximate model in the peak acceleration of B pillar lower end and the intrusion volume of the steering column hole and clutch pedal does not meet the requirement. The orthogonal polynomial approximate model has a high prediction accuracy in total mass, but its prediction accuracy in other responses does not meet the requirement. In addition, all three approximate models are obviously influenced by the linear relationship between the response and the variables. The kriging approximate model meets the required prediction accuracy of the four responses and is less affected by the linear relationship. Thus, the kriging approximate model is suitable to replace the original model. Then, particle swarm optimization can be performed to optimize the kriging approximate model. This study shows that the kriging approximate model has high fitting precision, and the optimization results reach the expected aim.
Abstract:An approximate model can be used to replace the real model to reduce the computing time and guarantee the feasibility of optimization. However, the approximate model must meet the required accuracy. The higher the accuracy of the approximate model, the higher the reliability of optimization results. In this study, a finite element model for the 40% offset impact of minibus was established, with the thickness of 10 plates in the front of the car body as the design variable and peak acceleration of B pillar lower end, the total mass, and the intrusion volume of dashboard beam, steering column hole, and clutch pedal as the response values. We obtained 70 sample points by the Latin hypercube experimental design method and built approximate models of design variables and the response. Then, we compared the relative error scatter, mean relative error, and decision coefficient of the response surface approximate model, radial basis function network approximate model, kriging approximate model, and orthogonal polynomial approximate model. Results show that the prediction accuracy of the response surface approximate model and radial basis function network approximate model in the peak acceleration of B pillar lower end and the intrusion volume of the steering column hole and clutch pedal does not meet the requirement. The orthogonal polynomial approximate model has a high prediction accuracy in total mass, but its prediction accuracy in other responses does not meet the requirement. In addition, all three approximate models are obviously influenced by the linear relationship between the response and the variables. The kriging approximate model meets the required prediction accuracy of the four responses and is less affected by the linear relationship. Thus, the kriging approximate model is suitable to replace the original model. Then, particle swarm optimization can be performed to optimize the kriging approximate model. This study shows that the kriging approximate model has high fitting precision, and the optimization results reach the expected aim.
基金资助:Supported by the the National Natural Science Foundation of China (No.51305269);the Shanghai Automotive Industry Technology Development Foundation (No.1744)
通讯作者:
GAO Da-wei
E-mail: gddwww1999@163.com
引用本文:
高大威, 郑腾飞. 基于微型客车碰撞的近似模型预测精度研究[J]. Journal of Highway and Transportation Research and Development, 2019, 13(1): 94-103.
GAO Da-wei, ZHENG Teng-fei. Prediction Accuracy of Collision Indicators for Mini-bus Based on an Approximate Model. Journal of Highway and Transportation Research and Development, 2019, 13(1): 94-103.
[1] WU He-quan,CAO Li-bo,MIAO Run-lu. Study on Bus Crash Safety Based on Reliability Optimal Design[J].Journal of Highway and Transportation Research and Development,2016,33(10):142-147. (in Chinese)
[2] ZHANG Yong. Optimization Design Method of Vehicle Lightweight Based on Approximate Model[D].Changsha:Hunan University,2009. (in Chinese)
[3] WANG Da-zhi,KONG Fan-zhong,HUANG Shi-lin et. Improvenent Design of Minibus's Frame Structure in Frontal Impact[J].Journal of Highway and Transportation Research and Development,2004,21(2):119-122. (in Chinese)
[4] XIAO Mi. Research on Approximation Models and Decomposition Strategies in Multidisciplinary Design Optimization[D]. Wuhan:Huazhong University of Science and Technology,2012. (in Chinese)
[5] CAO Yan-chao. Numerical Simulation of Vehicle Crash by Finite Element Method[D].Jinan:Shandong University,2014. (in Chinese)
[6] WU He-quan,XIN Yong,HU Hong-wei. Parameters Optimization of S-shaped Rail for Crashworthiness Analysis[J].Journal of Highway and Transportation Research and Development,2009,26(12):131-136. (in Chinese)
[7] WANG Fan,ZHU Hui,YANG Zhi-gang. Aerodynamic Shape Optimization of Automotive Body Based on Approximation Model[J].Computer Aided Engineering,2016,25(6):34-41. (in Chinese)
[8] HAN Ding,ZHENG Jian-rong. A Survey of Metamodeling Techniques in Engineering Optimization[J].Journal of East China University of Science and Technology:Natural Science Edition,2012,38(6):762-768. (in Chinese)
[9] YE Li-yu,WANG Chao,SUN Wen-lin et. Application of Approximate Model Method in Optimization Design of Marine Propeller[J].Journal of Shanghai Jiao Tong University,2016,50(8):1173-1179,1185. (in Chinese)
[10] REN Yuan,BAI Guang-chen. Approximation Model Method in Optimization Design of Vehicle Suspension and Its Application[J].Automobile Technology,2009,(3):35-38,60. (in Chinese)
[11] ZHENG Gang,LI Guang-yao,SUN Guang-yong et. Geometrical Parameter Inverse Problem for Drawbeads Based on the Approximate Model[J].China Mechanical Engineering,2006,17(19):1988-1992. (in Chinese)
[12] LIU, Yu-cheng. Crashworthiness Design of Thin-walled Curved Beams with Box and Channel Cross Sections[J]. International Journal of Crashworthiness,2010,15(1):413-423.
[13] XIE Hui,CHEN Long,LI Fan. Application on Variable Complexity Models for Vehicle Safety Based on RBF Meta-modeling Technique[J].Mechanical Science and Technology for Aerospace Engineering,2016,35(10):1624-1628(in Chinese)
[14] XIE Yan-min,YU Hu-ping,CHEN Jia-jun et. The Reliability Estimation Based on Kriging Model[J].Journal of Shanghai Jiao Tong University,2007,41(2):177-180,193. (in Chinese)
[15] FORRESTER A I J, KEANE A J. Recent Advances in Surrogate-based Optimization[J].Progress in Aerospace Sciences,2009,45(1/2/3:50-79.
[16] LIU Yu-cheng. Development and Evaluation of A Finite Element Truck Chassis Crash Model[J].International Journal of Crashworthiness,2010,15(1):107-113.
[17] MASCHIO C,SCHIOZER D J. Probabilistic History Matching Using Discrete Latin Hypercube Sampling and Nonparametric Density Estimation[J].Journal of Petroleum Science and Engineering,2016,147:98-115.
[18] GAO Da-wei,DENG You-zhi,GAO Yun-kai. Multidisciplinary Optimal Design for Ultra-high-strength Steel Side Impact Bar[J].Journal of Highway and Transportation Research and Development, 2012,29(6):144-149,158. (in Chinese)
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