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.     

Automotive door design with the ULSAB concept. using structural optimization

Weight reduction for an automobile body is sought to achieve fuel efficiency and energy conservation. Recently, the UltraLight Steel Auto Body (ULSAB) concept is suggested using a few methods. ULSAB pursues a lightweight automotive with steel structure. Tailor welded blank (TWB) is one of the ULSAB methods and TWB can be utilized for an automobile door. Optimization technology is applied to the inner panel of a door which is made by TWB. A design process is appropriately defined for the inner panel. The design starts from an existing component. At first, the inner reinforcements are removed to use TWB technology. In the conceptual design stage, topology optimization is conducted to find the distribution of the variable thickness. The number of parts and the welding lines are determined from the topology design. In the detailed design process, size optimization is carried out to find thickness while the stiffness constraints are satisfied. Size optimization is performed based on the welding lines determined from topology optimization. The final parting lines are tuned by shape optimization. The results from size optimization are considered constant in shape optimization. A commercial optimization software GENESIS is utilized for the optimization processes. Received November 10, 2000     

Crashworthiness optimization of foam-filled tapered thin-walled structure using multiple surrogate models

Despite the rapid growth of computing power and continuing advancements in numerical techniques, significant complexity exists when applying traditional sensitivity based optimization to such highly nonlinear problems as crashworthiness design. As a major alternative, surrogate modeling techniques have proven considerably effective. However the challenge remains how to determine the most suitable surrogate scheme for modeling nonlinear responses and conducting optimization. This paper presents a comparative study on the different surrogate models, such as polynomial response surface (PRS), Kriging (KRG), support vector regression (SVR) and radial basis function (RBF), which have been widely used for a variety of engineering problems, thereby gaining insights into their relative performance and features in computational modeling and design. In this study, a foam-filled tapered thin-walled structure is exemplified. Both the gradient and non-gradient algorithms, specifically sequential quadratic programming (SQP) and particle swarm optimization (PSO), are used for these abovementioned four surrogate models, respectively. The design results demonstrate that simultaneous use of different surrogate models can be essential for both gradient and non-gradient optimization algorithms because they may generate different outcomes in the crashworthiness design.     

Nonlinear channel equalizer design using directional evolutionary multi-objective optimization

In this paper, a new equalizer learning scheme is introduced based on the algorithm of the directional evolutionary multi-objective optimization (EMOO). Whilst nonlinear channel equalizers such as the radial basis function (RBF) equalizers have been widely studied to combat the linear and nonlinear distortions in the modern communication systems, most of them do not take into account the equalizers’ generalization capabilities. In this paper, equalizers are designed aiming at improving their generalization capabilities. It is proposed that this objective can be achieved by treating the equalizer design problem as a multi-objective optimization (MOO) problem, with each objective based on one of several training sets, followed by deriving equalizers with good capabilities of recovering the signals for all the training sets. Conventional EMOO which is widely applied in the MOO problems suffers from disadvantages such as slow convergence speed. Directional EMOO improves the computational efficiency of the conventional EMOO by explicitly making use of the directional information. The new equalizer learning scheme based on the directional EMOO is applied to the RBF equalizer design. Computer simulation demonstrates that the new scheme can be used to derive RBF equalizers with good generalization capabilities, i.e., good performance on predicting the unseen samples.     

An intelligent sampling approach for metamodel-based multi-objective optimization with guidance of the adaptive weighted-sum method

In order to reduce the computational cost of multi-objective optimization (MOO) with expensive black-box simulation models, an intelligent sampling approach (ISA) is proposed with the guidance of the adaptive weighted-sum method (AWS) to construct a metamodel for MOO gradually. The initial metamodel is built by using radial basis function (RBF) with Latin Hypercube Sampling (LHS) to distribute samples over the design space. An adaptive weighted-sum method is then employed to obtain the Pareto Frontier (POF) efficiently based on the metamodel constructed. The design variables related to extreme points on the frontier and an extra point interpolated between the maximal-minimal-distance point along the frontier and the nearest boundary point are selected as the concerned points to update the metamodel, which could improve the metamodel accuracy gradually. This iterative updating strategy is performed until the optimization problem is converged. A series of representative mathematical examples are systematically investigated to demonstrate the effectiveness of the proposed method, and finally it is employed for the design of a bus body frame.     

Adaptive heuristic search algorithm for discrete variables based multi-objective optimization

Although metamodel technique has been successfully used to enhance the efficiency of the multi-objective optimization (MOO) with black-box objective functions, the metamodel could become less accurate or even unavailable when the design variables are discrete. In order to overcome the bottleneck, this work proposes a novel random search algorithm for discrete variables based multi-objective optimization with black-box functions, named as k-mean cluster based heuristic sampling with Utopia-Pareto directing adaptive strategy (KCHS-UPDA). This method constructs a few adaptive sampling sets in the solution space and draws samples according to a heuristic probability model. Several benchmark problems are supplied to test the performance of KCHS-UPDA including closeness, diversity, efficiency and robustness. It is verified that KCHS-UPDA can generally converge to the Pareto frontier with a small quantity of number of function evaluations. Finally, a vehicle frontal member crashworthiness optimization is successfully solved by KCHS-UPDA.     

基于PSO-RBF无线传感器网络入侵检测技术研究

针对无线传感器网络自身特性,提出了基于粒子群优化(PSO)径向基函数(RBF)神经网络的轻量级入侵检测方案,该方案结合PSO算法与RBF神经网络分别在全局搜索和局部搜索的优势,使用PSO优化RBF的中心、宽度及权值.仿真实验表明:基于PSO-RBF的入侵检测算法可以有效、可靠地运用于无线传感器入侵检测系统中.     

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.     

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.     

Multi-objective optimization for bus body with strength and rollover safety constraints based on surrogate models

It is important to consider the performances of lightweight, stiffness, strength and rollover safety when designing a bus body. In this paper, the finite element (FE) analysis models including strength, stiffness and rollover crashworthiness of a bus body are first built and then validated by physical tests. Based on the FE models, the design of experiment is implemented and multiple surrogate models are created with response surface method and hybrid radial basis function according to the experimental data. After that, a multi-objective optimization problem (MOP) of the bus body is formulated in which the objective is to minimize the weight and maximize the torsional stiffness of the bus body under the constraints of strength and rollover safety. The MOP is solved by employing multi-objective evolutionary algorithms to obtain the Pareto optimal set. Finally, an optimal solution of the set is chosen as the final design and compared with the original design.     

On design optimization for structural crashworthiness and its state of the art

Optimization for structural crashworthiness and energy absorption has become an important topic of research attributable to its proven benefits to public safety and social economy. This paper provides a comprehensive review of the important studies on design optimization for structural crashworthiness and energy absorption. First, the design criteria used in crashworthiness and energy absorption are reviewed and the surrogate modeling to evaluate these criteria is discussed. Second, multiobjective optimization, optimization under uncertainties and topology optimization are reviewed from concepts, algorithms to applications in relation to crashworthiness. Third, the crashworthy structures are summarized, from generically novel structural configurations to industrial applications. Finally, some conclusions and recommendations are provided to enable academia and industry to become more aware of the available capabilities and recent developments in design optimization for structural crashworthiness and energy absorption.

     

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 %.     

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.     

Optimization design of corrugated beam guardrail based on RBF-MQ surrogate model and collision safety consideration

As the main safety facility on the highway, a guardrail system is very essential for the highway traffics safety. In this paper, the Finite Element (FE) models of the vehicle and the corrugated beam guardrail system were created. Two types of widely used corrugated beam semi-rigid guardrails were simulated, which were the W-beam guardrail and the Thrie-beam guardrail. The collision between the corrugated beam guardrail systems and the vehicle body was analyzed. In the collision process, the snagging effect of the post to the vehicle body was also concerned. Under the considerations of the collision safety and the mechanism of the snagging effect, the multiobjective optimization problem was defined with dimensional sizes of guardrails to be the design variables. And the radial basis function (RBF) was applied to construct the regression models of the analytical objective, which increased the accuracy of fitting. The Pareto set and the optimal solution were obtained. After the optimization design, the W-beam guardrail and Thrie-beam guardrail were both greatly improved, that increased the collision safety between the corrugated beam guardrail and the vehicle body. This kind of analytical method can also be used for the crashworthiness optimization between any other cars and guardrails.     

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%.     

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.     

Optimal design of structures subjected to time history loading by swarm intelligence and an advanced metamodel

This paper proposes a new metamodeling framework that reduces the computational burden of the structural optimization against the time history loading. In order to achieve this, two strategies are adopted. In the first strategy, a novel metamodel consisting of adaptive neuro-fuzzy inference system (ANFIS), subtractive algorithm (SA), self organizing map (SOM) and a set of radial basis function (RBF) networks is proposed to accurately predict the time history responses of structures. The metamodel proposed is called fuzzy self-organizing radial basis function (FSORBF) networks. In this study, the most influential natural periods on the dynamic behavior of structures are treated as the inputs of the neural networks. In order to find the most influential natural periods from all the involved ones, ANFIS is employed. To train the FSORBF, the input–output samples are classified by a hybrid algorithm consisting of SA and SOM clusterings, and then a RBF network is trained for each cluster by using the data located. In the second strategy, particle swarm optimization (PSO) is employed to find the optimum design. Two building frame examples are presented to illustrate the effectiveness and practicality of the proposed methodology. A plane steel shear frame and a realistic steel space frame are designed for optimal weight using exact and approximate time history analyses. The numerical results demonstrate the efficiency and computational advantages of the proposed methodology.     

Multi-objective concurrent topology optimization of thermoelastic structures composed of homogeneous porous material

The present paper studies multi-objective design of lightweight thermoelastic structure composed of homogeneous porous material. The concurrent optimization model is applied to design the topologies of light weight structures and of the material microstructure. The multi-objective optimization formulation attempts to find minimum structural compliance under only mechanical loads and minimum thermal expansion of the surfaces we are interested in under only thermo loads. The proposed optimization model is applied to a sandwich elliptically curved shell structure, an axisymmetric structure and a 3D structure. The advantage of the concurrent optimization model to single scale topology optimization model in improving the multi-objective performances of the thermoelastic structures is investigated. The influences of available material volume fraction and weighting coefficients are also discussed. Numerical examples demonstrate that the porous material is conducive to enhance the multi-objective performance of the thermoelastic structures in some cases, especially when lightweight structure is emphasized. An “optimal” material volume fraction is observed in some numerical examples.     

RBF neural network based on q-Gaussian function in function approximation

To enhance the generalization performance of radial basis function (RBF) neural networks, an RBF neural network based on a q-Gaussian function is proposed. A q-Gaussian function is chosen as the radial basis function of the RBF neural network, and a particle swarm optimization algorithm is employed to select the parameters of the network. The non-extensive entropic index q is encoded in the particle and adjusted adaptively in the evolutionary process of population. Simulation results of the function approximation indicate that an RBF neural network based on q-Gaussian function achieves the best generalization performance.