Selecting scale factor of Bayesian multi-fidelity surrogate by minimizing posterior variance  

作　　者：Hongyan BU Liming SONG Zhendong GUO Jun LI 

机构地区：[1]Institute of Turbomachinery,School of Energy&Power Engineering,Xi'an Jiaotong University,Xi'an 710049,China

出　　处：《Chinese Journal of Aeronautics》2022年第11期59-73,共15页中国航空学报（英文版）

基　　金：the financial support from the National Science and Technology Major Project,China(No.2019-Ⅱ-0008-0028);Key Program of National Natural Science Foundation of China(No.51936008)。

摘　　要：The Bayesian Multi-Fidelity Surrogate(MFS)proposed by Kennedy and O’Hagan(KOH model)has been widely employed in engineering design,which builds the approximation by decomposing the high-fidelity function into a scaled low-fidelity model plus a discrepancy function.The scale factor before the low-fidelity function,ρ,plays a crucial role in the KOH model.This scale factor is always tuned by the Maximum Likelihood Estimation(MLE).However,recent studies reported that the MLE may sometimes result in MFS of bad accuracy.In this paper,we first present a detailed analysis of why MLE sometimes can lead to MFS of bad accuracy.This is because,the MLE overly emphasizes the variation of discrepancy function but ignores the function waviness when selectingρ.To address the above issue,we propose an alternative approach that choosesρby minimizing the posterior variance of the discrepancy function.Through tests on a one-dimensional function,two high-dimensional functions,and a turbine blade design problem,the proposed approach shows better accuracy than or comparable accuracy to MLE,and the proposed approach is more robust than MLE.Additionally,through a comparative test on the design optimization of a turbine endwall cooling layout,the advantage of the proposed approach is further validated.

关 键 词：CO-KRIGING Gaussian process regression Multi-fidelity surrogate OPTIMIZATION Scale factor 

分 类 号：V23[航空宇航科学与技术—航空宇航推进理论与工程]