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.     

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.     

Reliability-based design optimization using probabilistic sufficiency factor

A probabilistic sufficiency factor approach is proposed that combines safety factor and probability of failure. The probabilistic sufficiency factor approach represents a factor of safety relative to a target probability of failure. It provides a measure of safety that can be used more readily than the probability of failure or the safety index by designers to estimate the required weight increase to reach a target safety level. The probabilistic sufficiency factor can be calculated from the results of Monte Carlo simulation with little extra computation. The paper presents the use of probabilistic sufficiency factor with a design response surface approximation, which fits it as a function of design variables. It is shown that the design response surface approximation for the probabilistic sufficiency factor is more accurate than that for the probability of failure or for the safety index. Unlike the probability of failure or the safety index, the probabilistic sufficiency factor does not suffer from accuracy problems in regions of low probability of failure when calculated by Monte Carlo simulation. The use of the probabilistic sufficiency factor accelerates the convergence of reliability-based design optimization.     

Reliability-based design optimization of aeroelastic structures

Aeroelastic phenomena are most often either ignored or roughly approximated when uncertainties are considered in the design optimization process of structures subject to aerodynamic loading, affecting the quality of the optimization results. Therefore, a design methodology is proposed that combines reliability-based design optimization and high-fidelity aeroelastic simulations for the analysis and design of aeroelastic structures. To account for uncertainties in design and operating conditions, a first-order reliability method (FORM) is employed to approximate the system reliability. To limit model uncertainties while accounting for the effects of given uncertainties, a high-fidelity nonlinear aeroelastic simulation method is used. The structure is modelled by a finite element method, and the aerodynamic loads are predicted by a finite volume discretization of a nonlinear Euler flow. The usefulness of the employed reliability analysis in both describing the effects of uncertainties on a particular design and as a design tool in the optimization process is illustrated. Though computationally more expensive than a deterministic optimum, due to the necessity of solving additional optimization problems for reliability analysis within each step of the broader design optimization procedure, a reliability-based optimum is shown to be an improved design. Conventional deterministic aeroelastic tailoring, which exploits the aeroelastic nature of the structure to enhance performance, is shown to often produce designs that are sensitive to variations in system or operational parameters.     

System reliability based vehicle design for crashworthiness and effects of various uncertainty reduction measures

Reliability-based design optimization of automobile structures for crashworthiness has been studied by many researchers by using either single component probabilistic constraints or single failure mode based probabilistic constraints, while system reliability considerations are mostly disregarded. In this paper, we perform system reliability based design optimization (SRBDO) of an automobile for crashworthiness and analyze the effect of reliability allocation in different failure modes. In addition, effects of various uncertainty reduction measures (e.g., reducing variability in material properties, reducing error of finite element analysis) are investigated and tradeoff plots of uncertainty reduction, system reliability and structural weight are generated. These types of tradeoff plots can be used by a company manager to decide whether to allocate the company resources for employing uncertainty reduction measures or allocating the resources for the excess weight to protect against the unreduced uncertainties. Furthermore, relative importance of automobile structural members in different crash scenarios is quantified. Submitted for publication in the Structural and Multidisciplinary Optimization (SMO).     

Multidisciplinary design optimization of a vehicle system in a scalable, high performance computing environment

Multidisciplinary Design Optimization of a vehicle system for safety, NVH (noise, vibration and harshness) and weight, in a scalable HPC environment, is addressed. High performance computing, utilizing several hundred processors in conjunction with approximation methods, formal MDO strategies and engineering judgement are effectively used to obtain superior design solutions with significantly reduced elapsed computing times. The increased computational complexity in this MDO work is due to addressing multiple safety modes including frontal crash, offset crash, side impact and roof crush, in addition to the NVH discipline, all with detailed, high fidelity models and analysis tools. The reduction in large-scale MDO solution times through HPC is significant in that it now makes it possible for such technologies to impact the vehicle design cycle and improve the engineering productivity.     

Extensions of design potential concept for reliability-based design optimization to nonsmooth and extreme cases

The reliability-based design optimization (RBDO) can be described by the design potential concept in a unified system space, where the probabilistic constraint is identified by the design potential surface of the reliability target that is obtained analytically from the first-order reliability method (FORM). This paper extends the design potential concept to treat nonsmooth probabilistic constraints and extreme case design in RBDO. In addition, refinement of the design potential surface, which yields better optimum design, can be obtained using more accurate second-order reliability method (SORM). By integrating performance probability analysis into the iterative design optimization process, the design potential concept leads to a very effective design potential method (DPM) for robust system parameter design. It can also be applied effectively to extreme case design (ECD) by directly representing a probabilistic constraint in terms of the system performance function. Received July 25, 2000     

Reliability-based structural optimization of frame structures for multiple failure criteria using topology optimization techniques

Topology optimization methods using discrete elements such as frame elements can provide useful insights into the underlying mechanics principles of products; however, the majority of such optimizations are performed under deterministic conditions. To avoid performance reductions due to later-stage environmental changes, variations of several design parameters are considered during the topology optimization. This paper concerns a reliability-based topology optimization method for frame structures that considers uncertainties in applied loads and nonstructural mass at the early conceptual design stage. The effects that multiple criteria, namely, stiffness and eigenfrequency, have upon system reliability are evaluated by regarding them as a series system, where mode reliabilities can be evaluated using first-order reliability methods. Through numerical calculations, reliability-based topology designs of typical two- or three-dimensional frames are obtained. The importance of considering uncertainties is then demonstrated by comparing the results obtained by the proposed method with deterministic optimal designs.     

Reliability-based design optimization for elastoplastic mechanical structures

In this paper, two special formulations to carry out a reliability-based design optimization of elastoplastic mechanical structures are introduced. The first approach is based on a well-known two-level method where the first level involves the optimization for the design parameters whereas the evaluation of the probabilistic constraints is carried out in a sub-optimization level. Because the evaluation of the probabilistic constraints in a sub-optimization level causes non-convergence behavior for some problems as indicated in the literature, an alternative formulation based on one-level is developed considering the optimality conditions of the β-computation by which the probabilistic constraint appears in the first level reliability-based design optimization formulation. In both approaches, an explicit parameter optimization problem is proposed for the computation of a design point for elastoplastic structures.Three examples in this paper demonstrate that the one-level reliability-based design optimization formulation is superior in terms of convergence to an optimal design than the two-level reliability-based design optimization formulation.     

Multi-objective biogeography-based optimization for supply chain network design under uncertainty

This paper proposes a new two-stage optimization method for multi-objective supply chain network design (MO-SCND) problem with uncertain transportation costs and uncertain customer demands. On the basis of risk-neutral and risk-averse criteria, we develop two objectives for our SCND problem. We introduce two solution concepts for the proposed MO-SCND problem, and use them to define the multi-objective value of fuzzy solution (MOVFS). The value of the MOVFS measures the importance of uncertainties included in the model, and helps us to understand the necessity of solving the two-stage multi-objective optimization model. When the uncertain transportation costs and customer demands have joined continuous possibility distributions, we employ an approximation approach (AA) to compute the values of two objective functions. Using the AA, the original optimization problem becomes an approximating mixed-integer multi-objective programming model. To solve the hard approximating optimization problem, we design an improved multi-objective biogeography-based optimization (MO-BBO) algorithm integrated with LINGO software. We also compare the improved MO-BBO algorithm with the multi-objective genetic algorithm (MO-GA). Finally, a realistic dairy company example is provided to demonstrate that the improved MO-BBO algorithm achieves the better performance than MO-GA in terms of solution quality.     

吸气式高超声速飞行器考虑控制约束的设计优化

为了能够获得性能卓越,可靠的吸气式高超声速飞行器(AHSV)设计,需要考虑其特殊动力学特性及控制系统的性能约束,研究面向控制系统设计的系统设计优化策略.首先,简要介绍了AHSV第1原理建模与参数化建模相关的问题与方法;其次,分析了AHSV系统模型与控制系统性能之间的约束耦合特性:系统模型的不稳定极点及其左特征向量与控制信号的饱和约束确定了反馈控制系统的零可控区域;系统模型右半平面(RHP)零极点对于反馈闭环系统灵敏度函数与补灵敏度函数具有峰值约束与带宽限制;最后,考虑系统模型与控制系统约束耦合的特性,根据选取的总体优化设计目标,介绍了系统本体与控制系统组合优化的相关策略.并简要分析了各优化策略的实用性及适用范围.对于AHSV考虑控制系统性能约束的优化设计提供了一种研究方法和设计思路.     

A multipoint version of space mapping optimization applied to vehicle crashworthiness design

In this paper, space mapping (SM) technique is combined with response surface methodology (RSM). SM is an optimization method well suited for very costly problems to find an improved design with fulfilled constraints. The SM technique use less costly models, which complements the correct models. The theory is established and compared to the corrected RSM. A multipoint version of SM is presented, where a separate evaluation is done in each iteration to improve the mapping function. Using this additional evaluation to update the mapping function, generally, the number of iterations to find the optimum solution can be reduced. Thus, the elapsed time to solve the optimization problem can be reduced if a parallel computer is utilized. Finally, one engineering optimization problem is solved to illustrate the application of SM in vehicle crashworthiness structural optimization.     

An investigation of structural optimization in crashworthiness design using a stochastic approach

In this paper the response surface methodology (RSM) and stochastic optimization (SO) are compared with regard to their efficiency and applicability in crashworthiness design. Optimization of simple analytic expressions and optimization of a front rail structure are the applications used to assess the respective qualities of both methods. A low detail vehicle structure is optimized to demonstrate the applicability of the methods in engineering practice. The investigations reveal that RSM is better compared to SO for fewer than 10–15 design variables. The convergence behaviour of SO improves compared to RSM when the number of design variables is increased. A novel zooming method is proposed which improves the convergence behaviour. A combination of both the RSM and the SO is efficient, stochastic optimization could be used in order to determine appropriate starting points for an RSM optimization, which continues the optimization. Two examples are investigated using this combined method.     

高速轨道列车防撞箱耐撞击特性仿真与优化

为了提高高速轨道列车的安全性,为其头车的主要吸能装置——防撞箱设计较为理想的结构,采用MSC Patran建立防撞箱的有限元分析模型,运用MSC Dytran仿真其耐撞击特性.通过比较分析仿真结果,对防撞箱设计方案予以多次改进,得到综合性能较为理想的方案.     

基于拓扑和形貌优化的驾驶室结构设计

为实现汽车零部件的创新设计,以某工程车驾驶室的简化有限元模型为研究对象,用HyperMesh作前处理,在OptiStruct中建立多工况条件下拓扑优化与形貌优化组合的整体优化模型,通过OSSmooth工具将优化后的结果导出后在CATIA V5中显示.拓扑和形貌组合优化技术的实践表明,该方法对产品部件的综合设计具有较好的适用性,可为设计人员提供设计思路.     

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.