基于Stochastic Kriging模型的不确定性序贯试验设计方法

摘要

不确定性研究中需要计算大量重复样本，这无疑对计算量较大的数值模拟提出了巨大的挑战。通过试验设计方法可以有效地减少不确定性研究中的计算量，然而，目前考虑不确定性的试验设计方法研究大多仍专注于传统试验设计方法。针对这一问题，为了通过更为合理的计算资源分配得到更精准的不确定性评估，基于有限样本的Stochastic Kriging模型提出了针对不确定性问题的三阶段序贯试验设计方法。首先，通过特定位置的采样对 IMSE进行简化，构建了预选步进信息选取策略，通过预选增量样本总个数以及各取样位置处的分布信息，达到随机代理模型目标精度要求；同时，基于 IMSE构建了基于步进信息的单轮选点试验设计准则，以同时考虑设计变量的取样位置及其分布信息。由算例与传统方法的对比分析可知，所建立方法通过等量的采样得到了精度更高的随机代理模型，验证了其在不确定性问题中的可行性和优势。%The research on uncertainty requires many duplications and undoubtedly it puts forward a giant challenge to numerical simulations which is time-consuming.The amount of computation in the study of uncertainty can be effectively reduced through design of experiment method,but the current researches on design of experiment method about uncertainty mainly concentrate on traditional methods.Aiming at the problem,in order to address the problem and attain an accu-rate uncertainty assessment through reasonably allocating computational resources,the sequential design of experiment method with three stages was constructed based on the Stochastic Kriging metamodel with finite sampling.At the beginning,the criterion to choose the predetermined number and distribution of samples to attain certain accuracy of stochastic metamodel was pro-posed through the simplification of IMSE at specific sampling states.In addition,the criterion to obtain the optimum based on the predetermined information was also derived to simultaneously take the state and distribution of samples into account.Moreover,traditional methods were used to do the comparison with the proposed method,and the feasibility and advantages of proposed method were verified by examples with uncertainty,in which stochastic metamodel with more ac-curacy was achieved by using the same amount of sampling as traditional methods.