Structural optimization of the cross-beam of a gantry machine tool based on grey relational analysis

Crossbeam structural design of gantry machine tool is a multi-level, multi-index and multi-scheme decision-making problem. In order to solve the above problem, the optimum seeking model of crossbeam structure was built through using the grey relational analysis and Analytic Hierarchy Process. The finite element analysis of the static and dynamic performance parameters for four kinds of crossbeam structural schemes designed had been done, and the optimal design scheme was selected by using the optimum seeking model. After conducting sensitivity analysis for the optimal crossbeam selected, the reasonable design variables were obtained, and the dynamic optimization design model of crossbeam was established. Six groups of non-inferior solutions were obtained after solving the optimization design model. The optimal solution was selected from the non-inferior solution set through using the crossbeam structural optimization method based on grey relational analysis again, which makes the crossbeam’s dynamic performance improving greatly. The dynamic experiments on the crossbeams before and after optimization design were conducted, then the experimental results show that the first four order natural frequencies of the crossbeam increase 17.56 %, 19.36 %, 17.04 % and 19.58 % respectively, which proves that the structural optimization design method based on grey relational analysis proposed in this paper is reasonable and practicable.     

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.     

基于灰色综合关联分析的多目标优化方法

针对现有多目标优化方法存在的搜索性能弱、效率低等问题,提出一种基于灰色综合关联分析的多目标优化方法.该多目标优化方法采用单目标优化算法构建高质量的参考序列,计算参考序列与优化解的目标函数值序列之间的灰色综合关联度,定义基于灰色综合关联度的解支配关系准则,将灰色综合关联度作为多目标优化算法的适应度值.以带顺序相关调整时间的多目标流水车间调度问题作为应用对象,建立总生产成本、最大完工时间、平均流程时间及机器平均闲置时间的多目标函数优化模型.提出基于灰色关联分析的多目标烟花算法,对所建立的多目标优化模型进行优化求解.仿真实验表明,所提出多目标烟花算法的性能优于3种基于不同多目标优化方法的烟花算法及两种经典多目标算法,验证了所提出的多目标优化方法及多目标算法的可行性和有效性.     

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.     

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 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 %.     

基于显式有限元技术的梁截面抗撞性优化

本文基于显式有限元技术,采用响应面法,以结构的比吸能为优化函数,以提高吸能原件的抗撞性为目的,对正方形截面的金属薄壁梁进行了形状优化．经过数值分析,得出了正方形截面梁的比吸能关于壁厚和截面边长的变化规律,这些规律可以用于实际吸能原件的设计,并为进一步研究奠定了基础．     

An early software-quality classification based on improved grey relational classifier

The inherent uncertainty and incomplete information of the software development process presents particular challenges for identifying fault-prone modules and providing a preferred model early enough in a development cycle in order to guide software enhancement efforts effectively. Grey relational analysis (GRA) of grey system theory is a well known approach that is utilized for generalizing estimates under small sample and uncertain conditions. This paper examines the potential benefits for providing an early software-quality classification based on improved grey relational classifier. The particle swarm optimization (PSO) approach is adopted to explore the best fit of weights on software metrics in the GRA approach for deriving a classifier with preferred balance of misclassification rates. We have demonstrated our approach by using the data from the medical information system dataset. Empirical results show that the proposed approach provides a preferred balance of misclassification rates than the grey relational classifiers without using PSO. It also outperforms the widely used classifiers of classification and regression trees (CART) and C4.5 approaches.     

基于隐式参数化的车身多学科轻量化设计

为实现整车综合性能的快速方案验证和优化设计,在新车型设计阶段构建车身隐式参数化模型,并对其进行模态、刚度和安全等综合性能计算,验证参数化模型的有效性。基于灵敏度分析、试验设计（design of experiments, DOE）方法和近似模型优化等策略,对某白车身进行多学科轻量化设计。优化设计结果表明,白车身的模态、刚度和安全性能均满足设计要求。     

基于灰关联度的面板数据聚类方法及在空气污染分析中的应用

针对面板数据的三维特征、正负相关性以及灰色关联模型缺乏有效检验等问题,构建面板数据灰色关联模型,拓展了面板数据聚类方法;引入灰熵,提出灰色关联聚类的检验模型.研究发现,灰色关联度模型能够反映面板数据的正、负相关关系,且具有对称性、唯一性和可比性.通过在苏南4市空气质量区域划分中的应用,表明基于面板数据灰关联模型的聚类方法具有良好的效果,各类别的灰色关联度差异明显,层次清晰.     

Synergetic use of different evaluation,parameterization and search tools within a multilevel optimization platform

This paper presents the synergetic use of different evaluation tools, parameterization schemes and search methods on the levels of a multilevel optimization platform to efficiently solve single- and multi-objective computationally demanding optimization problems. The platform is formed by a number of levels which concurrently search for optimal solutions, by regularly exchanging promising individual solutions. Each level is associated with a problem-specific evaluation tool with its own accuracy and computational cost, a parameterization scheme which determines the design variables and their mapping to generate individual solutions and a search algorithm which is either a metamodel-assisted evolutionary algorithm or a gradient-based method. The use of the multilevel platform with only one of the aforementioned features changing from level to level was presented in a previous paper by the authors. The present paper shows that the combined use of hierarchical evaluation, hierarchical parameterization and hierarchical search decreases further the computational cost by increasing the efficiency of the optimization method. This is demonstrated on function minimization and aerodynamic shape optimization problems; though only two levels are used herein, this is not a restriction and the optimization platform may accommodate any number of them.     

一种基于改进灰色关联分析的变量选择算法

针对灰色绝对关联度模型和灰色相似关联度模型存在的问题,提出一种基于相对变化面积的改进灰色关联度模型.以序列几何形状的相似程度为基础,构建反应折线相似程度的相对变化面积,并以此作为关联系数的计算依据,同时以局部关联度的平均值度量整体的相似性,定义灰色关联度模型.此外,根据关联度计算结果,提出一种基于集合思想的变量选择算法,有效去除变量间的无关和冗余变量.仿真结果验证了所提出算法的有效性和合理性.     

基于灰色准指数律的灰色生成速率关联模型的构建及应用

现有灰色关联模型都是直接考察原始数据,没有考虑需要经过数据处理才能显现的规律。对此,构建基于灰色准指数律的生成速率关联分析模型。首先,对原始数据进行累加灰色生成,构造生成速率序列,进而用生成速率序列的接近性表征原序列的动态变化趋势的相似性;然后,对生成速率关联分析模型的性质进行研究;最后,将所构建的关联度模型应用于全国交通拥堵度相关因素的识别,结果验证了所提出模型的实用性和有效性。     

灰色关联分析和粒子群优化算法相融合的合作伙伴选择

针对目前解决云服务商合作伙伴选择问题方法均存在如搜索速度变慢、实用性差、难以获得完全合理的选择方案等不足,提出了一种灰色关联分析和粒子群优化(PSO)算法相融合的合作伙伴选择方法。首先采用灰色关联法对云服务商的评价指标进行筛选,并计算每一种指标的权重值;然后建立云环境下服务商合作伙伴选择问题的数学模型,并采用粒子群算法对其进行求解,找到云服务商合作伙伴选择的最佳方案。具体应用实例性能测试结果验证了方法的有效性和合理性,它可以选择出最佳的合作伙伴。     

Particle swarm optimization with grey evolutionary analysis

Based on grey relational analysis, this study attempts to propose a grey evolutionary analysis (GEA) to analyze the population distribution of particle swarm optimization (PSO) during the evolutionary process. Then two GEA-based parameter automation approaches are developed. One is for the inertia weight and the other is for the acceleration coefficients. With the help of the GEA technique, the proposed parameter automation approaches would enable the inertia weight and acceleration coefficients to adapt to the evolutionary state. Such parameter automation behaviour also makes an attempt on the GEA-based PSO to perform a global search over the search space with faster convergence speed. In addition, the proposed PSO is applied to solve the optimization problems of twelve unimodal and multimodal benchmark functions for illustration. Simulation results show that the proposed GEA-based PSO could outperform the adaptive PSO, the grey PSO, and two well-known PSO variants on most of the test functions.     

Aerodynamic shape optimization using efficient evolutionary algorithms and unstructured CFD solver

An efficient evolutionary algorithm is presented for shape optimization of transonic airfoils. Several techniques have been used to improve the efficiency and convergence rate of the optimization Genetic Algorithm (GA). A new airfoil shape parameterization method is used which is capable of producing more efficient shapes at viscous flow conditions. A Real-Coded Population Dispersion (PD) Genetic Algorithm is developed in order to increase the robustness and convergence rate of the Genetic Algorithm. A Multi-Layer Perceptron Neural Network (NN) is utilized to reduce the huge computational cost of the objective function evaluation. Further improvement in the performance of NN is obtained by using dynamic retraining and normal distribution of the training data to determine well trained parts of the design space to NN. Using the above techniques, the total computational time of optimization algorithm is reduced up to 60% compared with the conventional GA.     

武器系统研制方案的多层次灰关联综合评价

为了更好地解决多层次多目标的综合评价问题,文中将层次分析法和灰关联综合评估法两种系统评价方法结合起来,提出一种多目标多层次加权灰关联综合评估方法。先建立综合评估模型,再通过多层次灰关联评估,获取了加权灰关联度。根据关联度大小,对三种武器系统研制方案进行了优劣排序。实例应用结果证明,该方法综合了两种方法的优点,使用简便,切实可行,适合于解决多方案的优选问题。     

A virtual punching method for shape optimization of openings on curved panels using CAD-based Boolean operations

This paper aims at developing new methodologies for shape optimization of openings on three-dimensional curved panels that are used widely in aeronautical and aerospace engineering. To circumvent the difficulties associated with the hole boundary shape parameterization, a virtual punching method that exploits Boolean operations of the CAD modeler is proposed for the definition of shape design variables. Compared with the parametric mapping method developed previously, the virtual punching method is shown to be an implicit boundary representation for this specific kind of structure. Instead, the parametric mapping method is based on the explicit boundary representation.A zero-order genetic algorithm (GA) is correspondingly implemented into the design procedure of the virtual punching method to execute the optimization process for two reasons. First, it makes it possible to avoid sensitivity analysis that is relatively difficult due to the implicit boundary representation formulation and the use of an unstructured mesh. Second, the computing cost of the GA is practically affordable in shape optimization because often only a small number of design variables are involved. Numerical tests are carried out for typical examples of the stress concentration minimization around openings on the curved panels.     

基于灰熵并行分析法的多目标作业车间调度优化

提出利用信息熵理论与灰色关联分析法并行地处理多目标优化问题,将多目标优化的目标值构成数据序列,挖掘序列关系实现多目标优化。首先,并行的对目标值序列计算灰关联系数以及熵值权重,之后将信息熵与灰关联系数结合计算灰熵并行关联度,建立灰熵并行分析法。最终,利用灰熵并行关联度作为优化算法的适应值计算策略,以该策略引导智能优化算法进化。建立作业车间调度问题的三目标优化模型,以灰熵并行分析法为基础,分别应用差分算法、遗传算法解决三目标作业车间调度问题,验证新方法的可行性。实验表明：新方法均能使两算法收敛且得到分布均匀的 Pareto 前端,表明其有效和可靠。同时,差分算法得到的解较遗传算法的解具有明显的优势。     

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.