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.     

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.     

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.     

Configurational optimization of multi-cell topologies for multiple oblique loads

Multi-cell thin-walled structures exhibit significant advantages in maximizing energy absorption and minimizing mass during vehicle crashes. Since the topological distribution of wall members has an appreciable effect on the crashworthiness, their design signifies an important area of research. As a major energy absorber, multi-cell tubes are more commonly encounter oblique loading in real life. Thus, this study aimed to optimize multi-cell cross-sectional configuration of tubal structures for multiple oblique loading cases. An integer coded genetic algorithm (ICGA) is introduced here to optimize topological distribution of multi-celled web members for single/multiple oblique impacting conditions. Specifically, material distribution in a form of allocating web wall thickness, starting from zero, is considered as design variables and maximization of energy absorption (EA) as the design objective under the predefined peak crushing force and structural mass constraints. The optimization allows generating uniform or non-uniform thickness distribution in different web wall configurations to maximize usage efficiency of material. Compared with the baseline structure, the optimized configurations largely improved the energy absorption in both single and multiple load cases. The examples demonstrate that the proposed ICGA-based design method not only provides a useful approach to searching for novel crashworthy structures in a systematic fashion, but also develops a series of novel multi-cell topologies for multiple oblique loading cases.     

Using surrogate models and response surfaces in structural optimization – with application to crashworthiness design and sheet metal forming

The aim of this paper is to determine if the Space Mapping technique using surrogate models together with response surfaces is useful in the optimization of crashworthiness and sheet metal forming. In addition, the efficiency of optimization using Space Mapping will be compared to traditional structural optimization using the Response Surface Methodology (RSM). Five examples are used to study the algorithm: one optimization of an analytic function and four structural optimization problems. All examples are constrained optimization problems. In all examples, the algorithm converged to an improved design with all constraints fulfilled, even when a conventional RSM optimization failed to converge. For the crashworthiness design problems, the total computing time for convergence was reduced by 53% using Space Mapping compared to conventional RSM. For the sheet metal forming problems the total computing time was reduced by 63%. The conclusions are that optimization using Space Mapping and surrogate models can be used for optimization in crashworthiness design and sheet metal forming applications with a significant reduction in computing time.     

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.     

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.     

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.     

Topology optimization for crashworthiness of thin-walled structures under axial impact using hybrid cellular automata

Although topology optimization is well established in most engineering fields, it is still in its infancy concerning highly non-linear structural applications like vehicular crashworthiness. One of the approaches recently proposed and based on Hybrid Cellular Automata is modified here such that it can be applied for the first time to thin-walled structures. Classical methods based on voxel techniques, i.e., on solid three-dimensional volume elements, cannot derive structures made from thin metal sheets where the main energy absorption mode is related to plastic buckling, folding and failure. Because the main components of car structures are made from such thin-walled beams and panels, a special approach using SFE CONCEPT was developed, which is presented in this paper.     

A review of optimization of structures subjected to transient loads

Various aspects of structural optimization techniques under transient loads are extensively reviewed. The main themes of the paper are treatment of time-dependent constraints, calculation of design sensitivity, and approximation. Each subject is reviewed with corresponding papers that have been published since the 1970s. The treatment of time-dependent constraints in both the direct method and the transformation method is discussed. Two ways of calculating design sensitivity of a structure under transient loads are discussed—direct differentiation method and adjoint variable method. The approximation concept mainly focuses on the response surface method in crashworthiness and local approximation with the intermediate variables. Especially, a method using the equivalent static load is discussed as an approximation method. It takes advantage of the well-established static response optimization. The structural optimization in flexible multibody dynamic systems is reviewed in the viewpoint of the above three themes.     

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.     

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.     

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.     

不同复合材料蒙皮机身段的适坠性研究

基于典型客机机身结构建立了三框两跨机身段有限元模型,模拟了金属蒙皮机身段和复合材料蒙皮机身段的坠撞过程,分析了机身结构变形、加速度响应、能量变化趋势和各结构吸能特征,研究了蒙皮对机身段适坠性的影响。结果表明,抗剪切能力较差的复合材料蒙皮会导致结构破坏不够充分引发较大的坠撞加速度进而对乘员安全造成威胁。复合材料蒙皮刚度较大会导致"三角区域"产生加速度过载。蒙皮作为飞机坠撞时的重要吸能结构之一,不仅会影响自身的吸能特性,还会显著影响各个结构的吸能特性和整个机身段的适坠性。     

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.     

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 %.     

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.     

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.     

Bi-directional Evolutionary Structural Optimization on Advanced Structures and Materials: A Comprehensive Review

The evolutionary structural optimization (ESO) method developed by Xie and Steven (Comput Struct 49(5):885–896, 162), an important branch of topology optimization, has undergone tremendous development over the past decades. Among all its variants, the convergent and mesh-independent bi-directional evolutionary structural optimization (BESO) method developed by Huang and Xie (Finite Elem Anal Des 43(14):1039–1049, 48) allowing both material removal and addition, has become a widely adopted design methodology for both academic research and engineering applications because of its efficiency and robustness. This paper intends to present a comprehensive review on the development of ESO-type methods, in particular the latest convergent and mesh-independent BESO method is highlighted. Recent applications of the BESO method to the design of advanced structures and materials are summarized. Compact Malab codes using the BESO method for benchmark structural and material microstructural designs are also provided.