Reliability-based design optimization for vehicle body crashworthiness based on copula functions

ABSTRACT Vehicle body crashworthiness is crucial in a traffic accident. It can protect passengers from serious injury or death and reduce vehicle damage. To provide a more effective design framework for ensuring crash safety, a reliability-based design optimization (RBDO) method for vehicle body crashworthiness considering complex parametric correlation is developed by integrating copula functions. An RBDO model is formulated for the vehicle body crashworthiness problem based on a finite element model of a vehicle crash. Taking into account the correlation of random parameters, the optimal copula function is selected by the Bayesian method to model parametric correlation and build the joint probability distribution function. An efficient solution strategy is provided to perform the reliability analysis and optimization design of crashworthiness. The results demonstrate that the proposed method is reliable and has a high accuracy for crashworthiness design.

[1]  M. Rosenblatt Remarks on a Multivariate Transformation , 1952 .

[2]  Pan Wang,et al.  Efficient structural reliability analysis method based on advanced Kriging model , 2015 .

[3]  Hu Lin,et al.  Reliability-based optimization design of structure subjected to vehicle frontal impact based on probability-convex hybrid model , 2016 .

[4]  M. Sklar Fonctions de repartition a n dimensions et leurs marges , 1959 .

[5]  Dian-Qing Li,et al.  Bivariate distribution models using copulas for reliability analysis , 2013 .

[6]  Kyung K. Choi,et al.  A NEW STUDY ON RELIABILITY-BASED DESIGN OPTIMIZATION , 1999 .

[7]  Qing Li,et al.  A Comparative study on multiobjective reliable and robust optimization for crashworthiness design of vehicle structure , 2013 .

[8]  Jianwei Lu,et al.  Reliability-based robust assessment for multiobjective optimization design of improving occupant restraint system performance , 2014, Comput. Ind..

[9]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[10]  R. Yang,et al.  Large-Scale Reliability Based Design Optimization For Vehicle Crash Safety , 2002 .

[11]  B. Y. Ni,et al.  A Vine-Copula-Based Reliability Analysis Method for Structures With Multidimensional Correlation , 2015 .

[12]  Guangyao Li,et al.  Reliability-based multiobjective optimisation of vehicle bumper structure holes for the pedestrian flexible legform impact , 2016 .

[13]  Lei Shi,et al.  A new RBDO method using adaptive response surface and first-order score function for crashworthiness design , 2016, Reliab. Eng. Syst. Saf..

[14]  Kyung K. Choi,et al.  Identification of marginal and joint CDFs using Bayesian method for RBDO , 2009 .

[15]  Masoud Rais-Rohani,et al.  Shape and sizing optimisation of automotive structures with deterministic and probabilistic design constraints , 2010 .

[16]  Jianwei Lu,et al.  Reliability-based design optimization for vehicle occupant protection system based on ensemble of metamodels , 2015 .

[17]  Baoding Liu Uncertain Risk Analysis and Uncertain Reliability Analysis , 2010 .

[18]  Kaushik Sinha,et al.  Reliability-based multiobjective optimization for automotive crashworthiness and occupant safety , 2007 .

[19]  M. Kendall A NEW MEASURE OF RANK CORRELATION , 1938 .

[20]  Liang Xia,et al.  A system methodology for optimization design of the structural crashworthiness of a vehicle subjected to a high-speed frontal crash , 2017 .

[21]  H. Akaike A new look at the statistical model identification , 1974 .

[22]  Byeng D. Youn,et al.  Adaptive-sparse polynomial chaos expansion for reliability analysis and design of complex engineering systems , 2011 .

[23]  Byeng D. Youn,et al.  Reliability-Based Multidisciplinary Design Optimization of a Full Vehicle System , 2002 .

[24]  B. Youn,et al.  Reliability-based robust design optimization using the eigenvector dimension reduction (EDR) method , 2009 .

[25]  Yu Zhang,et al.  Metamodeling development for reliability-based design optimization of automotive body structure , 2011, Comput. Ind..

[26]  A. Kiureghian,et al.  Multivariate distribution models with prescribed marginals and covariances , 1986 .

[27]  Kyung K. Choi,et al.  Reliability-based design optimization for crashworthiness of vehicle side impact , 2004 .

[28]  Guangyao Li,et al.  Reliable optimisation design of vehicle structure crashworthiness under multiple impact cases , 2017 .

[29]  Pol D. Spanos,et al.  Probabilistic engineering mechanics , 1992 .

[30]  Kiran Solanki,et al.  System reliability based vehicle design for crashworthiness and effects of various uncertainty reduction measures , 2009 .

[31]  C. Jiang,et al.  Reliability-based design optimization for problems with interval distribution parameters , 2016, Structural and Multidisciplinary Optimization.

[32]  Bill Ravens,et al.  An Introduction to Copulas , 2000, Technometrics.

[33]  Liu Weiguo,et al.  Reliability design optimization of vehicle front-end structure for pedestrian lower extremity protection under multiple impact cases , 2015 .

[34]  John Dalsgaard Sørensen,et al.  Reliability-Based Optimization in Structural Engineering , 1994 .

[35]  Qing Li,et al.  Radial basis functional model for multi-objective sheet metal forming optimization , 2011 .

[36]  André T. Beck,et al.  System reliability-based design optimization and risk-based optimization: a benchmark example considering progressive collapse , 2018, Engineering Optimization.

[37]  Byeng D. Youn,et al.  Reliability-Based Design Optimization , 2018, Springer Series in Reliability Engineering.

[38]  Wei Chen,et al.  Application of conservative surrogate to reliability based vehicle design for crashworthiness , 2013 .

[39]  Katsuichiro Goda,et al.  Statistical modeling of joint probability distribution using copula: Application to peak and permanent displacement seismic demands , 2010 .

[40]  R. Lebrun,et al.  An innovating analysis of the Nataf transformation from the copula viewpoint , 2009 .

[41]  Anne-Catherine Favre,et al.  Bayesian copula selection , 2006, Comput. Stat. Data Anal..

[42]  Yang Ji-kuang Reliability Optimization of Occupant Restraint System in Side Impact Tests , 2011 .