一种改进的约束域拉丁方抽样算法及工程应用

Formulation and Engineering Application of an Improved Constrained Domain Latin Hypercube Sampling Algorithm

提出一种改进的约束域拉丁方抽样算法(ICD-LHS)。该算法分为2个阶段:第一阶段利用聚类算法获取满足约束条件的样本特征点;第二阶段通过差分进化算法优化样本点位置,得到满足约束条件的均匀分布样本点。选取3个标准测试函数,将该算法与传统抽样算法进行对比,结果表明:ICD-LHS算法具有较好的均匀性及通用性。最后,以汽车防撞梁截面形状的样本抽样为典型案例,利用ICD-LHS算法产生指定数量的、并在不规则设计区域内满足制造约束条件的防撞梁截面样本,该截面样本具有较好的均匀性,对后续的截面优化设计具有指导意义。

An improved constrained domain Latin hypercube sampling algorithm(ICD-LHS)is proposed.The algorithm is divided into two stages.The first stage uses the clustering algorithm to obtain the sample feature points that satisfy the constraints.In the second stage,the differential evolution algorithm is used to optimize the sample point position,and the uniformly distributed sample points satisfying the constraint conditions are obtained.Three standard test functions are selected,and the algorithm is compared with the traditional sampling algorithm.The results show that the ICD-LHS algorithm has good uniformity and versatility.Finally,taking the sample sampling of the cross-section shape of automobile bumper beam as a typical case,the ICD-LHS algorithm is used to generate a specified number of cross-section samples of bumper beam which meet the manufacturing constraints in the irregular design area.The proposed cross-section samples have good uniformity,which has a good guiding significance for section optimization design.