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.     

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.     

A new approach for optimizing automotive crashworthiness: concurrent usage of ANFIS and Taguchi method

Design optimization is presented for the crashworthiness improvement of an automotive body structure. The optimization objective was to improve automotive crashworthiness conditions according to the defined criterion (occupant chest deceleration) during a full frontal impact. The controllable factors used in this study consisted of six internal parts of the vehicle’s frontal structure in a condition that their thickness was the “design parameter”. First using the Taguchi method, this study analyzed the optimum conditions in discontinuous design area and impact factors and their optimal levels of design objectives were obtained by analyzing the experimental results. Next to model a precise understanding of the explicit mathematical input–output relationship, fuzzy logic is utilized which make use of full factorial design set of experimental test cases resulted from Taguchi predicting formulations. Interestingly, the optimum conditions for automotive crashworthiness occurred with 2.72 % improvement in the defined crashworthiness criterion in comparison with the baseline design while selected structural parts experienced mass reduction by 8.23 %.     

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.     

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.     

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.     

Reliability-based design optimization for crashworthiness of vehicle side impact

With the advent of powerful computers, vehicle safety issues have recently been addressed using computational methods of vehicle crashworthiness, resulting in reductions in cost and time for new vehicle development. Vehicle design demands multidisciplinary optimization coupled with a computational crashworthiness analysis. However, simulation-based optimization generates deterministic optimum designs, which are frequently pushed to the limits of design constraint boundaries, leaving little or no room for tolerances (uncertainty) in modeling, simulation uncertainties, and/or manufacturing imperfections. Consequently, deterministic optimum designs that are obtained without consideration of uncertainty may result in unreliable designs, indicating the need for Reliability-Based Design Optimization (RBDO).Recent development in RBDO allows evaluations of probabilistic constraints in two alternative ways: using the Reliability Index Approach (RIA) and the Performance Measure Approach (PMA). The PMA using the Hybrid Mean Value (HMV) method is shown to be robust and efficient in the RBDO process, whereas RIA yields instability for some problems. This paper presents an application of PMA and HMV for RBDO for the crashworthiness of a large-scale vehicle side impact. It is shown that the proposed RBDO approach is very effective in obtaining a reliability-based optimum design.     

Crashworthiness design for functionally graded foam-filled bumper beam

Automotive bumper beam is an important component to protect passenger and vehicle from injury and damage induced by severe collapse. Recent studies showed that foam-filled structures have significant advantages in light weight and high energy absorption. In this paper, a novel bumper beam filled with functionally graded foam (FGF) is considered here to explore its crashworthiness. To validate the FGF bumper beam model, the experiments at both component and full vehicle levels are conducted. Parametric study shows that gradient exponential parameter m that controls the variation of foam density has significant effect on bumper beam’s crashworthiness; and the crashworthiness of FGF-filled bumper beam is found much better than that of uniform foam (UF) filled and hollow bumper beam. The multiobjective optimization of FGF-filled bumper beam is also performed by considering specific energy absorption (SEA) and peak impact force as the design objectives, and the wall thickness t, foam densities ρ_f1 and ρ_f2 (foam densities at the end and at mid cross section, respectively) and gradient exponential parameter m as design variables. The Kriging surrogate modeling technique and multiobjective particle swarm optimization (MOPSO) algorithm were implemented to optimize the FGF-filled bumper beam. The optimized FGF-filled bumper beam is of great advantages and it can avoid the harmful local bending behavior and absorb more energy than UF filled and hollow bumper beam. Finally, the optimized FGF-filled bumper beam is installed to a passenger car model, and the results demonstrate that the FGF-filled bumper beam ensures the crashworthiness performance of the passenger car while reduces weight about 14.4% compared with baseline bumper beam.     

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.     

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.     

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.     

Simulation analysis with group screening

Simulation of systems involve a number of factors or variables which act and interact to produce an output. When these factors are small in number the experimenter can control them effectively to obtain an optimal output, but when the number of factors increases then efforts to control all the factors effectively also increases and leads to wastage of resources and away from optimality. Very often in a system where a number of factors are involved only a few of them actively involve in producing the output. Therefore it is the interest of the researcher to detect those active factors, and experimental design is frequently applied. The detecting process is called as screening. Screening can done by factorial designs such as 2^K (full factorial design) or by 2^k-p (fractional factorial design). Even by the fractional factorial method, one might still need to run too many experiments. It is desired to accomplish the screening process in as few number of runs as possible using random balance design, super saturated design or group-screening. Of these methods group-screening has been identified by researchers such as Mauro, Smith, etc. as the most efficient tool. In this research we study the usage of group-screening method as a simulation analysis tool while improving the method from earlier researches. Performance and results are studied and provided in form of response surface figures and tables.     

The enhancement of stereoselectivity of a Pd-catalyzed three-component cascade reaction using parallel synthesis and multivariate analysis

Automated parallel synthesis with multivariate analysis was employed in the optimization of a Pd-catalyzed three-component cascade reaction of 7-buta-2,3-dienyl-1,3-dimethyl-3,7-dihydropurine-2,6-dione with iodobenzene and morpholine (see Scheme 1). Initially a range of reaction factors were analyzed using experimental design to optimize for selectivity, conversion, and impurity levels. Solvents and bases were screened separately as the substantial number of discrete variables involved is unsuited to the fractional factorial design used. Instead, a solvent principal component analysis (PCA) model was used in selection of solvents for screening, so gaining maximum variation in solvent properties. Similarly, tertiary amines were chosen by pKa for screening as bases alongside inorganic salts. This investigation yielded two-fold results, not only in enhancement of the reaction selectivity, but since significantly different findings were obtained on changing the solvent, the importance of the sequence of experimentation is also emphasized.     

Optimization of shock response within a military vehicle space frame

Space frames are usually used to enhance the structural strength of a vehicle while reducing its overall weight. The space frame of a military vehicle is subjected to significantly different loading than what is experienced in civilian vehicles, such as projectile impact or mine blast. In this work, a finite element (FE) model for the upper half of an armored vehicle with internal space frame is developed. The behavior of the vehicle is studied when subjected to a high impact load that simulates a projectile impact. The objective of this work is to minimize shocks at identified critical locations on the space frame while maintaining the overall structural integrity of the vehicle. Several variables that can affect shock propagation are identified including, the cross-sectional parameters of the internal space frame and outer armor. The optimization problem is solved using the Successive Heuristic Quadratic Approximation (SHQA) technique, which combines successive quadratic approximation with an adaptive random search while varying the bounds of the search space. The entire optimization process is carried out within the MATLAB environment. The results show that a significant reduction in the shock can be achieved using this approach.     

Reliability-based optimization of design variance to identify critical tolerances

Reliability-based design optimization (RBDO) is a topic of interest for research in both academia and industry. RBDO typically involves adjusting the mean values of the design variables while fixing the spread parameters, often measured as variance, in order to accomplish a given objective within the stated constraints. This paper proposes an alternate way to meet given design criteria by fixing the mean values of the statistical inputs and allowing the spread parameters to become design variables. To do this, product cost models are proposed in terms of statistical variables. By performing this type of optimization, the design changes are kept to a minimum, and the focus is instead shifted to variance control. An initial study is performed on a three-bar truss subject to static loading with material variability. A more complex example is performed involving the cost minimization of an unmanned undersea vehicle subjected to hydrostatic buckling.     

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.     

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%.     

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.     

A spreadsheet heuristic to classify random survey samples for a factorial experimental design

Industrial engineers, ergonomists, production operations managers and other field researchers may be confronted with large panels of potential respondents whose characteristics will not fit into a balanced factorial analysis design. This paper describes a microcomputer spreadsheet application that allows construction of an approximately unbiased sample in a 2ⁿ factorial design, using the Plackett-Burman reduced cell model as screening device. Binary criteria for predictor variables and binary-to-decimal conversion are used as an aid to obtain the “best” respondent selection for subsequent data analysis. Two separate studies are presented to illustrate the technique.     

地铁车辆耐撞性分析及多级能量吸收系统的验证

为研究地铁头车的耐撞性及其多级能量吸收系统设计的合理性,建立能够反映真实情况的头车用半自动车钩及其剪切装置模型.利用PAMCRASH软件,参考EN 15227标准,设定模拟运营工况,计算头车与刚性墙撞击工况,得到该车吸能结构的变形模式和最大吸能量;然后计算两头车对撞工况,从逃生空间、撞击力和加速度等方面评价车体的耐撞击性.计算结果表明该地铁头车耐撞击性能良好,多级能量吸收系统设计合理.