Multiobjective optimization for crash safety design of vehicles using stepwise regression model

In automotive industry, structural optimization for crashworthiness criteria is of special importance. Due to the high nonlinearities, however, there exists substantial difficulty to obtain accurate continuum or discrete sensitivities. For this reason, metamodel or surrogate model methods have been extensively employed in vehicle design with industry interest. This paper presents a multiobjective optimization procedure for the vehicle design, where the weight, acceleration characteristics and toe-board intrusion are considered as the design objectives. The response surface method with linear and quadratic basis functions is employed to formulate these objectives, in which optimal Latin hypercube sampling and stepwise regression techniques are implemented. In this study, a nondominated sorting genetic algorithm is employed to search for Pareto solution to a full-scale vehicle design problem that undergoes both the full frontal and 40% offset-frontal crashes. The results demonstrate the capability and potential of this procedure in solving the crashworthiness design of vehicles.     

Multivariable crashworthiness optimization of vehicle body by unreplicated saturated factorial design

Crashworthiness, influenced unequally by disparate factors such as the structural dimensions and the material parameters, represents a natural benchmark criterion to judge the passive safety quality of the automobile design. The unreplicated saturated factorial design has enjoyed a remarkable success in the factor screening of different industrial regions due to its huge benefits in the efficiency and accuracy. In order to single out the active factors which pose a profound impact on the crashworthiness, this paper introduces an unreplicated saturated factorial design to tackle the obstacle from the factor screening during the multivariable crashworthiness optimization design of the whole vehicle body. Three unreplicated saturated factorial design methods, including the normal or half-normal probability plot method, Dong93 method, and PSZ method, are employed to capture the active factors while D-optimal design is presented to obtain the design sampling points and to construct the response surface model for the crashworthiness optimization problem. Finally, multi-island genetic algorithm (MIGA) and sequential quadratic programming (SQP)-NLPQL are utilized to obtain the Pareto set of the optimal solution for the multivariable crashworthiness optimization design of the vehicle body under the full-scale frontal impact loading.     

Time-based metamodeling technique for vehicle crashworthiness optimization

In automotive industry, structural optimization for crashworthiness criteria is of special importance in the early design stage. To reduce the vehicle design cycle, metamodeling techniques have become so widespread... In this study, a time-based metamodeling technique is proposed for the vehicle design. The characteristics of the proposed method are the construction of a time-based objective function and establishment of a metamodel by support vector regression (SVR). Compared with other popular metamodel-based optimization methods, the design space of the proposed method is expanded to time domain. Thus, more information and features can be extracted in the expanded time domain. To validate the performance of the time-based metamodeling technique, cylinder impacting and full vehicle frontal collision are optimized by the proposed method. The results demonstrate that the proposed method has potential capability to solve the crashworthiness vehicle design.     

Factor screening and multivariable crashworthiness optimization for vehicle side impact by factorial design

This paper demonstrates the application of factor screening to multivariable crashworthiness design of the vehicle body subjected to the side impact loading. Crashworthiness, influenced unequally by disparate factors such as the structural dimensions and material parameters, represents a natural benchmark criterion to judge the passive safety quality of the automobile design. In order to single out the active factors which pose a profound influence on the crashworthiness of vehicle bodies subjected to the side impact loading, the unreplicated saturated factorial design is adopted to tackle the obstacle from the factor screening due to its huge benefits in the efficiency and accuracy. In this paper, two different kinds of vehicles are analyzed by the unreplicated saturated factorial design for multivariable crashworthiness and the optimization results enhance the crashworthiness of vehicle. This method overcomes the limitations of design variables selection which depends on experience, and solves the in-efficiency problems caused by the direct optimization design without the selection of variables. It will shorten the design cycles, decrease the development costs and will have a certain reference value for the improvement of the vehicle’s crashworthiness performance.     

Metamodeling development for reliability-based design optimization of automotive body structure

Metamodels are commonly used in reliability-based design optimization (RBDO) due to the enormously expensive computation cost of numerical simulations. However, for large-scale design optimization of automotive body structure, with the increasing number of design variable and enhanced nonlinearity degree of structural performance, polynomial response surface which is commonly used for vehicle design optimization often suffers exponentially increased computation burden and serious loss of approximation accuracy. In this paper, support vector regression, along with other four complex metamodeling techniques including moving least square, artificial neural network, radial basis function and Kriging, is investigated for approximating frontal crashworthiness performance which is one of the most highly nonlinear performances. It aims at testing support vector regression and providing advanced metamodeling technique for RBDO of automotive body structure. Approximation results are compared in both accuracy and computational efficiency. Based on the frontal crashworthiness example, it is found that support vector regression and moving least square are preferable techniques to approximate structural performances with good accuracy. But support vector regression is recommended for its computational efficiency and better approximation potential. Moreover, the ensemble of support vector regression, moving least square, Kriging and artificial neural network is an effective alternative and is proved, in the RBDO example for the lightweight design of front body structure, to outperform any other single metamodel. The remarkable predominance indicates that the ensemble of support vector regression, moving least square, Kriging and artificial neural network holds great potential in approximating highly nonlinear performances for RBDO of automotive body structure.     

Optimizing the design of automotive S-rail using grey relational analysis coupled with grey entropy measurement to improve crashworthiness

The optimization of the crashworthiness and lightweight design of S-rail extracted from the frontal body in white was studied in this paper. A physical test was conducted to verify the validity of S-rail model and then an implicit parameterization model was built based on the S-rail model using the software SFE-CONCEPT. Based on the implicit parameterization modeling, a steel-aluminum S-rail was designed to reduce the peak collision force (PCF) and increase the specific energy absorption (SEA) under the condition that the total weight (M) of S-rail does not increase. L₁₆ (4⁵) Taguchi array was used to collect sample points which will be prepared for the optimization design. The experimental results were analyzed through grey relational analysis (GRA) coupled with grey entropy measurement method. The multi-objective optimization was then converted into a single objective optimization problem based on the grey relational grade. The optimal combination of design parameters for S-rail was obtained using the proposed method. Meanwhile, a comparison was presented between the proposed method and other extensively used methods (i.e. NSGA-II, MOPSO, and ASA), and the proposed method reduces the PCF and M to 26.81% and 46.01% respectively, and increases the corresponding SEA by 176.06%. Moreover the computational cost can be reduced by 143.5% at least when compared with other extensively used methods. Therefore, the hybrid method can efficiently improve the crashworthiness and reduce the computational cost during the design process of S-rail.     

基于响应面法的汽车前防撞梁轻量化分析

将原来的汽车前防撞横梁材料替换成超高强度钢后,在确保低速碰撞性能基础上,利用响应面法进行轻量化分析.建立前防撞梁有限元模型,用LS-DYNA进行低速碰撞仿真.在此基础上以横梁和吸能盒的厚度作为变量进行试验设计.构建各项碰撞性能的2阶多项式响应面模型,并验证模型的有效性.以质量和吸能作为优化目标,建立多目标优化模型.与原设计相比,求出的优化方案在保证低速碰撞性能的基础上实现前防撞梁减重36%.     

Crashworthiness design of vehicle by using multiobjective robust optimization

Although deterministic optimization has to a considerable extent been successfully applied in various crashworthiness designs to improve passenger safety and reduce vehicle cost, the design could become less meaningful or even unacceptable when considering the perturbations of design variables and noises of system parameters. To overcome this drawback, we present a multiobjective robust optimization methodology to address the effects of parametric uncertainties on multiple crashworthiness criteria, where several different sigma criteria are adopted to measure the variations. As an example, a full front impact of vehicle is considered with increase in energy absorption and reduction of structural weight as the design objectives, and peak deceleration as the constraint. A multiobjective particle swarm optimization is applied to generate robust Pareto solution, which no longer requires formulating a single cost function by using weighting factors or other means. From the example, a clear compromise between the Pareto deterministic and robust designs can be observed. The results demonstrate the advantages of using multiobjective robust optimization, with not only the increase in the energy absorption and decrease in structural weight from a baseline design, but also a significant improvement in the robustness of optimum.     

Integrated design technique for materials and structures of vehicle body under crash safety considerations

With the rapid development of the vehicle industry, crashworthiness has become a crucial aspect in vehicle body design. In fact, crashworthiness is a multivariable optimization design problem for a vehicle body, regardless of structure or material. However, when crashworthiness involves a large number of design variables, including both material and structure variables, it is more difficult to deal with. In this paper, an integrated design technique for materials and structures of vehicle body under crash safety consideration is suggested. First, a finite element model of the vehicle body is established according to relevant vehicle safety standards. Then, the material parameters of the vehicle body are set as analytical factors for factor screening. Next, significant factors are obtained using a three-level saturated design integrated with multi-index comprehensive balance analysis and the MaxUr ⁽³⁾ method, with an improved evaluation method. These screened material parameters along with the corresponding continuous variables of the structure, are considered as the design variables of the integrated design of the vehicle body. Both the weight and the crashworthiness properties are set as the design objectives. Optimal Latin hypercube sampling and radius basis functions are utilized to construct highly accurate surrogate models. Furthermore, the non-dominated sorting genetic algorithm II is implemented to seek the optimal solutions. Finally, two cases considering the roof module and the frontal module of a vehicle body are analyzed to verify the proposed method.     

Using the response surface methodology and the D-optimality criterion in crashworthiness related problems

The aim of this paper is to determine the efficient number of experimental points when using the response surface methodology in crashworthiness problems. The D-optimality criterion is used as experimental design method. Two application models have been studied, one square tube and one front rail from Saab Automobile AB. Both models were fully parameterized in the preprocessor LS-INGRID but only two design variables were used. The optimization package LS-OPT was used to determine the design of experiments using the D-optimality criterion. Both models were subjected to an impact into a rigid wall and the simulations were carried out using LS-DYNA. A general recommendation is to to use 1.5 times the minimum number of experimental points. A more specialized recommendation is for linear surfaces 1.5, elliptic surfaces 2.2 and for quadratic surfaces 1.6 times the minimum number of experimental points.     

Robust optimization of foam-filled thin-walled structure based on sequential Kriging metamodel

Deterministic optimization has been successfully applied to a range of design problems involving foam-filled thin-walled structures, and to some extent gained significant confidence for the applications of such structures in automotive, aerospace, transportation and defense industries. However, the conventional deterministic design could become less meaningful or even unacceptable when considering the perturbations of design variables and noises of system parameters. To overcome this drawback, a robust design methodology is presented in this paper to address the effects of parametric uncertainties of foam-filled thin-walled structure on design optimization, in which different sigma criteria are adopted to measure the variations. The Kriging modeling technique is used to construct the corresponding surrogate models of mean and standard deviation for different crashworthiness criteria. A sequential sampling approach is introduced to improve the fitness accuracy of these surrogate models. Finally, a gradient-based sequential quadratic program (SQP) method is employed from 20 different initial points to obtain a quasi-global robust optimum solution. The optimal solutions were verified by using the Monte Carlo simulation. The results show that the presented robust optimization method is fairly effective and efficient, the crashworthiness and robustness of the foam-filled thin-walled structure can be improved significantly.     

Structural optimization with crashworthiness constraints

An automated structural design methodology has been devised which simultaneously considers design criteria associated with both linear elastic and crashworthiness loading conditions. This method is developed within the context of a nonlinear mathematical programming based structural optimization capability using an efficient two-phased crashworthiness analysis technique. Specially constructed nonlinear approximations for the crashworthiness constraints are employed to further reduce the computational burden during the optimization process. This methodology is demonstrated on an automobile structural design problem. It is shown that more mass efficient designs can be obtained by simultaneously considering elastic and crashworthiness design criteria as compared to a sequential approach in which the structure is first designed for the elastic loads and then modified to satisfy the crashworthiness criteria.     

Taguchi Method–GONNS integration: Complete procedure covering from experimental design to complex optimization

Determination of the optimal operating conditions from the experimental data without fitting any analytical or empirical models is very convenient for manufacturing applications. In this paper, integration of Taguchi Method and Genetically Optimized Neural Networks (GONNS) is proposed. The proposed procedure covers all the steps from experimental design to complex optimization. The feasibility of the approach was evaluated by estimating the optimal cutting conditions for the milling of Ti6Al4V titanium alloy with PVD coated inserts. The test conditions were determined by the Taguchi Method. The optimal cutting condition and influences of the cutting speed, feed rate and cutting depth on the surface roughness were analyzed with the same method. GONNS estimated that the optimal cutting conditions were very close to the Taguchi Method when the same criterion was used. GONNS was also capable to minimize or maximize one of the output parameters while the others were kept within the desired range. Study demonstrated that Taguchi Method and GONNS complement each other for creation of a robust procedure for determination of the test conditions, analysis of the quality of the collected data, estimation of the influence of each parameter on the output(s) and estimation of optimal conditions with complex optimization objective functions.     

Reliability-based multiobjective optimization for automotive crashworthiness and occupant safety

This paper presents a methodology for reliability-based multiobjective optimization of large-scale engineering systems. This methodology is applied to the vehicle crashworthiness design optimization for side impact, considering both structural crashworthiness and occupant safety, with structural weight and front door velocity under side impact as objectives. Uncertainty quantification is performed using two first order reliability method-based techniques: approximate moment approach and reliability index approach. Genetic algorithm-based multiobjective optimization software GDOT, developed in-house, is used to come up with an optimal pareto front in all cases. The technique employed in this study treats multiple objective functions separately without combining them in any form. It shows that the vehicle weight can be reduced significantly from the baseline design and at the same time reduce the door velocity. The obtained pareto front brings out useful inferences about optimal design regions. A decision-making criterion is subsequently invoked to select the “best” subset of solutions from the obtained nondominated pareto optimal solutions. The reliability, thus computed, is also checked with Monte Carlo simulations. The optimal solution indicated by knee point on the optimal pareto front is verified with LS-DYNA simulation results.     

Improved hybrid cellular automata for crashworthiness optimization of thin-walled structures

Thin-walled structures are of great importance in automotive crashworthiness design, because of their high crash energy absorption capability and their high potential for light weighting. To identify the best compromise between these two requirements, numerical optimization is needed. Size and shape optimization is relatively well explored while topology optimization for crash is still an open issue. Hence, this paper proposes an approach based on hybrid cellular automata (HCA) for crashworthiness topology optimization with a special focus on thin-walled structures. First approaches have been published, e.g. Duddeck et al. (Struct Multidiscip Optim 54(3):415–428, 2016), using a simple rule to define the target mass for the inner loop of the HCA. To improve the performance, a modified scheme is proposed here for the outer optimization loop, which is based on a bi-section search with limited length. In the inner loop, hybrid updating rules are used to redistribute the mass and a mass correction technique is proposed to make the real mass converge to the target mass strictly. The efficiency and correctness of the proposed method is compared with LS-OPT for axial crash case. Two different methods of defining the target mass in the outer loop are studied, the proposed bi-section search with limited length shows its advantage in two types of three-point bending crash optimization cases. Another advantage of this method is that it requires no significantly increasing number of evaluations when the number of design variables increases. This is demonstrated by applying this method to a crashworthiness optimization problem with 380 design variables.     

A Comparative study on multiobjective reliable and robust optimization for crashworthiness design of vehicle structure

Design optimization without considering uncertainties of system variables and parameters can be problematic in real life. In order to take into account the effect of uncertainties, reliable and robust design schemes have proven effective, but limited studies have been reported to compare their difference in a multiobjective framework. This paper takes a typical vehicle structure subject to offset frontal crashing scenario as an example to compare reliable and robust designs with their deterministic counterpart. The thicknesses of some key components of vehicle frontal structures were selected as design variables, the vehicle weight and energy absorption as the objectives, deceleration and firewall intrusion as the constraints. The deterministic multiobjective optimization problem was first solved by adopting Design of Experimental (DOE), metamodels and Non-dominated Sorting Genetic Algorithm II (NSGA-II). Take into account the uncertainties, a Monte Carlo Simulation (MCS) is adopted to generate random distributions of the objective and constraint functions for each design. For the reliability-based optimization the desired reliabilities of 90 %, 95 % and 99 % are considered, respectively. For the robustness-based optimization, two different formulation strategies are adopted. The optimization showed that the reliable and robust Pareto fronts are shifted away from their deterministic counterpart due to uncertainties. The different Pareto fronts yielded from the deterministic, reliable and robust designs are compared to provide some quantitative insights into how to apply these different design schemes for resolving uncertainty problems. It is shown that, compared with the baseline design, the optimizations enhance the crashworthiness of vehicle, though more conservative solutions could have been generated from the reliable and robust optimizations.     

Optimal shape design of functionally graded thickness inversion tubes subjected to oblique loading

This paper aims to understand and optimize the crush response of Functionally Graded Thickness (FGT) tubes with various thickness distributions subjected to oblique loading using multi-objective optimization method. Hence, finite element (FE) models are established and their results are validated by experimental tests. Two objective functions (specific energy absorption and peak load) are approximated by four different multi-objective optimization models: the weighted average, multi-design optimization (MDO) technique, constrained single-objective optimization, and geometrical average methods. The optimum design results demonstrate that the selection of appropriate inversion tube parameters such as the die radius, the coefficient of friction between the die and tube, and thickness distribution function have significant roles in the crashworthiness design. The results give new ideas to improve the crashworthiness performance of inversion tubes under oblique loading conditions.     

Structural design and global sensitivity analysis of the composite B-pillar with ply drop-off

Vehicle lightweight and safety design becomes an increasingly critical issue nowadays. In order to improve the crashworthiness of side impact and roof crush with the consideration of the manufacturing process, a new composite B-pillar structure with ply drop-off is proposed in this paper. It improves the crashworthiness by changing the section thickness of structure and reduces the weight of B-pillar. The ply drop-off regions on the outer part and inner part of B-pillar are divided into three sub-laminates respectively, named as thick panel, taper panel and thin panel. The thickness of the panel are determined by the number of lay-up. Based on traditional sensitivity analysis, this paper derives some new equations and clearly evaluates and quantifies the importance of uncertainty design parameters. Finally, the comprehensive performance of the lightweight and crashworthiness for the composite B-pillar with ply drop-off is improved through structural optimization.     

Crashworthiness design of multi-component tailor-welded blank (TWB) structures

Crashworthiness of tailor-welded blank (TWB) structures signifies an increasing concern in lightweight design of vehicle. Although multiobjective optimization (MOO) has to a considerable extent been successfully applied to enhance crashworthiness of vehicular structures, majority of existing designs were restricted to single or uniform thin-walled components. Limited attention has been paid to such non-uniform components as TWB structures. In this paper, MOO of a multi-component TWB structure that involves both the B-pillar and inner door system subjected to a side impact, is proposed by considering the structural weight, intrusive displacements and velocity of the B-pillar component as objectives, and the thickness in different positions and the height of welding line of B-pillar as the design variables. The MOO problem is formulated by using a range of different metamodeling techniques, including response surface methodology (RSM), artificial neural network (ANN), radial basis functions (RBF), and Kriging (KRG), to approximate the sophisticated nonlinear responses. By comparison, it is found that the constructed metamodels based upon the radial basis function (RBF, especially multi-quadric model, namely RBF-MQ) fit to the design of experiment (DoE) checking points well and are employed to carry out the design optimization. The performance of the TWB B-pillar and indoor panel system can be improved by optimizing the thickness of the different parts and height of the welding line. This study demonstrated that the multi-component TWB structure can be optimized to further enhance the crashworthiness and reduce the weight, offering a new class of structural/material configuration for lightweight design.     

微型客车正面碰撞特性建模及仿真研究

该文利用Pam—Crash对某微型客车及乘员约束系统进行了建模及仿真研究，全面研究了该微型客车的正面碰撞特性，包括结构耐撞性和乘员安全性。整个建模过程分三个阶段：白车身建模；整车建模；整车及乘员约束系统建模，每个阶段都参照相应的试验条件进行了仿真计算，所得计算结果与试验结果基本吻合，表明所建立的微型客车及乘员约束系统模型是可信的、采用的建模和计算方法是正确的。这些仿真方法可为企业改善汽车的碰撞安全性或开发新产品提供参考。