Multi-Objective Optimization Design of Vehicle Side Crashworthiness Based on Machine Learning Point-Adding Method  
Dawei Gao  
School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China  
1  
Bufan Yao  
Correspondence: gddwww1999@163.com  
Gaoshuang Chang and Qiang Li  
School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China  
1  
Footnote 1: email: {cho  
the local optimal solution is a common dilemma in solving highly nonlinear engineering problem [7]. For this reason, it is already very difficult for the conventional mathematical surrogate models to satisfy engineering requirements. To address this problem, automobile engineers have proposed the method of using a mathematical surrogate model combined with sequential point adding [8; 9]. Additionally, they improved the accuracy of the model by continuously updating surrogate models, so as to avoid falling into the dilemma of local optimal solution and gradually approach optimal solutions. The sequential point-adding strategy optimization algorithm of these years is developing rapidly. Among all scholars, Chan Jing of Jilin University [10] discovered a Multi-Objective Particle Swarm Optimization algorithm (KMOPSO) based on the Kriging model point-adding strategy; I. Y. Kim et al. [11] proposed a double-objective optimization method having multi-objective application potential, an adaptive weighted-sum method changing the previous weighted-sum approach; Jianhua Zhou et al. [12] invented a new high-efficiency sequential multi-objective optimization method (S-MOO), in which the anchors in the design space of global variables are fully leveraged to generate a dataset of global solutions to guide the search for Pareto solutions. These sequential point-adding strategies have evident strength in solving high latitude, nonlinear multi-objective problems. Not just having fast convergence speed, they can also quickly approach Pareto front edge. Combining sequential point-adding optimization algorithm and engineering problems can increase the optimization speed of engineering problems and save computation cost significantly. As below are some applications of vehicle crashworthiness. Sun et al. [13; 14] put forwords parallel Multi-Objective Efficient Global Optimization (MOEGO) algorithm, which utilizes several local optimal strategies of \"Kriging Believe\" and EI strategies to realize parallel computation. It uses HV (hypervolume) as the indicator of beam multi-objective convergence, addresses the design of crashworthiness and tests it in practical applications, and further proves the effectiveness and accuracy of the algorithm. Fang Jianguang et al. [15] raised a new design scheme for custom welded structures of mixed materials, which applies sequential sampling strategy to establish surrogate model, realizes lightweight design on the premise of improving the rigidity of car door structure. Hangfeng Yin et al. [16] invented an adaptive radial set function method based on metamodel, which solves MOO problem well, and they applied this method to the crashworthiness optimization for a new thin-wall structure. To sum up, sequential optimization strategy has walked from theoretical level to the applications in engineering optimization problem, and it is of very good application importance in multi-objective optimization design of vehicle crashworthiness. For this reason, this paper proposed an Adaptive Radial Basis Function combined with a Machine Learning Point-Adding (ARBF-MLPA) method. In this paper, an ARBF neural network combined with MLPA is proposed. The performance of the proposed algorithm is tested by using mathematical test function, and it is applied to the engineering problem of vehicle-side crashworthiness optimization. 1.