基于随机克里金模型的元建模序贯试验设计  

Sequential experimental design for metamodeling based on stochastic Kriging

作　　者：苗致远 霍鑫[1] 马杰[1] 张凯[2] 郑小鹏[2] MIAO Zhi-yuan;HUO Xin;MA Jie;ZHANG Kai;ZHENG Xiao-peng(Control and Simulation Center,Harbin Institute of Technology,Harbin 150080,China;China Academy of Launch Vehicle Technology,Beijing 100076,China)

机构地区：[1]哈尔滨工业大学控制与仿真中心,哈尔滨150080 [2]中国运载火箭技术研究院,北京100076

出　　处：《控制与决策》2024年第10期3405-3412,共8页Control and Decision

基　　金：国家自然科学基金项目(62373128);国家自然科学基金基础中心项目(62188101);黑龙江省自然科学基金项目(LH2021F025)。

摘　　要：在复杂系统的试验评估中,受制于时间和成本,试验次数有限,需要对试验的试验点和样本量进行设计.序贯设计适用于高成本试验,但设计效果取决于使用的准则和方法.针对这一问题,基于随机克里金模型研究序贯设计方法.在试验点设计上,对期望预测误差的组成成分分别进行估计,引入中心化L2偏差平衡探索和开发,构建一种试验点设计准则;在样本量分配上,以积分均方误差准则为目标函数构造整数规划并转化为多阶段决策过程,利用松弛问题的解构造近似代价函数,提出一种基于近似动态规划的求解方法.最后,将所提出序贯设计方法分别应用于数值仿真实验和实际飞行仿真转台实验以验证方法的有效性.In test and evaluation of complex systems,the number of tests is limited due to constraints in time and cost.Thus,proper designs are needed for test point and sample size.Sequential design is suitable for high-cost tests but its performance is determined by the design criterion and method utilized.To address this problem,a sequential design strategy is proposed based on the stochastic Kriging.For test point design,a design criterion is established by estimating components of the expected prediction error while centered-L2 discrepancy is introduced to balance exploration and exploitation.For sample size allocation,an integer programming problem with an integrated mean squared error as an objective function is converted into a multistep decision process,and an approximate-dynamic-programming-based solving method is proposed with the value function approximated based on the solution of the slack problem.Finally,the proposed sequential design method is applied to a numerical simulation and a real-world flight simulation turntable experiment respectively to verify its validity.

关 键 词：序贯设计 随机克里金 元建模 试验设计 代理模型 近似动态规划 

分 类 号：TB114[理学—概率论与数理统计]