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Research Papers

# A Mixed-Kernel-Based Support Vector Regression Model for Automotive Body Design Optimization Under Uncertainty

[+] Author and Article Information
Yudong Fang

State Key Laboratory
of Mechanical Transmission,
Chongqing University,
Chongqing 400044, China
e-mail: yudongfang@cqu.edu.cn

Zhenfei Zhan

State Key Laboratory
of Mechanical Transmission,
Chongqing University,
Chongqing 400044, China
e-mail: zhenfeizhan@cqu.edu.cn

Junqi Yang

State Key Laboratory
of Mechanical Transmission,
Chongqing University,
Chongqing 400044, China
e-mail: yangjunqi_cqu@foxmail.com

Xu Liu

College of Automotive Engineering,
Chongqing University,
Chongqing 400044, China
e-mail: liuxu931027@hotmail.com

Manuscript received February 27, 2017; final manuscript received May 22, 2017; published online June 28, 2017. Assoc. Editor: Alba Sofi.

ASME J. Risk Uncertainty Part B 3(4), 041008 (Jun 28, 2017) (9 pages) Paper No: RISK-17-1037; doi: 10.1115/1.4036990 History: Received February 27, 2017; Revised May 22, 2017

## Abstract

Finite element (FE) models are commonly used for automotive body design. However, even with increasing speed of computers, the FE-based simulation models are still too time-consuming when the models are complex. To improve the computational efficiency, support vector regression (SVR) model, a potential approximate model, has been widely used as the surrogate of FE model for crashworthiness optimization design. Generally, in the traditional SVR, when dealing with nonlinear data, the single kernel function-based projection cannot fully cover data distribution characteristics. In order to eliminate the application limitations of single kernel SVR, a method for reliability-based design optimization (RBDO) based on mixed-kernel-based SVR (MKSVR) is proposed in this research. The mixed kernel is constructed based on the linear combination of radial basis kernel function and polynomial kernel function. Through the particle swarm optimization (PSO) algorithm, the parameters of the mixed kernel SVR are optimized. The proposed method is demonstrated through a representative analytical RBDO problem and a vehicle lightweight design problem. And the comparitive studies for SVR and MKSVR in application indicate that MKSVR surpasses SVR in model accuracy.

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## References

Yang, R. J. , Akkerman, A. , and Anderson, D. F. , 2000, “ Robustness Optimization for Vehicular Crash Simulations,” Comput. Sci. Eng., 2(6), pp. 8–13.
Zhan, Z. , Fu, Y. , Yang, R. J. , and Peng, Y. H. , 2011, “ An Automatic Model Calibration Method for Occupant Restraint Systems,” Struct. Multidiscip. Optim., 44(6), pp. 815–822.
Gu, X. , Sun, G. , Li, G. , Huang, X. , Li, Y. , and Li, Q. , 2013, “ Multiobjective Optimization Design for Vehicle Occupant Restraint System Under Frontal Impact,” Struct. Multidiscip. Optim., 47(3), pp. 465–477.
Viana, F. A. C. , Haftka, R. T. , and Steffen, V., Jr. , 2009, “ Multiple Surrogates: How Cross-Validation Errors Can Help us to Obtain the Best Predictor,” Struct. Multidiscip. Optim., 39(4), pp. 439–457.
Simpson, T. W. , Poplinski, J. D. , Koch, P. N. , and Allen, J. K. , 2001, “ Metamodels for Computer-Based Engineering Design: Survey and Recommendations,” Eng. Comput., 17(2), pp. 129–150.
Wang, G. G. , and Shan, S. , 2006, “ Review of Metamodeling Techniques in Support of Engineering Design Optimization,” ASME J. Mech. Des., 129(4), pp. 370–380.
Vapnik, V. , Golowich, S. E. , and Smola, A. , 1997, “ Support Vector Method for Function Approximation, Regression Estimation, and Signal Processing,” Adv. Neural Inf. Process. Syst., 9(3), pp. 281–287.
Rafiq, M. Y. , Bugmann, G. , and Easterbrook, D. J. , 2001, “ Neural Network Design for Engineering Applications,” Comput. Struct., 79(17), pp. 1541–1552.
Jin, R. , Chen, W. , and Simpson, T. W. , 2001, “ Comparative Studies of Metamodeling Techniques Under Multiple Modelling Criteria,” Struct. Multidiscip. Optim., 23(1), pp. 1–13.
Clarke, S. M. , Griebsch, J. H. , and Simpson, T. W. , 2005, “ Analysis of Support Vector Regression for Approximation of Complex Engineering Analyses,” ASME J. Mech. Des., 127(6), pp. 1077–1087.
Guoqi, X. , and Dagui, H. , 2010, “ A Metamodeling Method Based on Support Vector Regression for Robust Optimization,” Chin. J. Mech. Eng., 23(2), pp. 242–251.
Zhu, P. , Pan, F. , Chen, W. , and Zhang, S. , 2012, “ Use of Support Vector Regression in Structural Optimization: Application to Vehicle Crashworthiness Design,” Math. Comput. Simul., 86(3), pp. 21–31.
Drucker, H. , Burges, C. J. C. , Kaufman, L. , Smola, A. , and Vapnik, V. , 1997, “ Support Vector Regression Machines,” Adv. Neural Inf. Process. Syst., 9, pp. 155–161.
Chapelle, O. , Vapnik, V. , and Bousquet, O. , 2002, “ Choosing Multiple Parameters for Support Vector Machines,” Mach. Learn., 46(1–3), pp. 131–159.
Kennedy, J. , and Eberhart, R. , 2002, “ Particle Swarm Optimization,” IEEE Int. Conf. Neural Networks., 4(8), pp. 1942–1948.
Sano, N. , Higashinaka, K. , and Suzuki, T. , 2014, “ Efficient Parameter Selection for Support Vector Regression Using Orthogonal Array,” IEEE International Conference on Systems, Man, and Cybernetics (SMC), San Diego, CA, Oct. 5–8, pp. 2256–2261.
Kim, C. , 2008, “ Reliability-Based Design Optimization Using Response Surface Method With Prediction Interval Estimation,” ASME J. Mech. Des., 130(12), p. 121401.
Yang, J. , Zhan, Z. , Zheng, K. , Hu, J. , and Zheng, L. , 2016, “ Enhanced Similarity-Based Metamodel Updating Strategy for Reliability-Based Design Optimization,” Eng. Optim., 48(12), pp. 2026–2045.

## Figures

Fig. 1

Flowchart of reliability-based design optimization based on MKSVR model

Fig. 2

Formulation of the employed reliability-based design optimization problem

Fig. 3

Reliability evaluation for the design obtained by optimization based on: (a) the SVR and (b) the MKSVR

Fig. 4

Comparison of global deformation for Taurus in NCAP test and simulation

Fig. 5

Design variables in the front structures of body-in-white

Fig. 6

Comparison of MKSVR with SVR in prediction for ACC and CD

Fig. 7

Reliability evaluation for the design obtained by using SVR: (a) the reliability evaluation for CD and (b) the reliability evaluation for ACC

Fig. 8

Reliability evaluation for the design obtained by using MKSVR: (a) the reliability evaluation for CD and (b) the reliability evaluation for ACC

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