Multifidelity Modeling by Polynomial Chaos-Based Cokriging to Enable Efficient Model-Based Reliability Analysis of NDT Systems

This work proposes a novel multifidelity metamodeling approach, the polynomial chaos-based Cokriging (PC-Cokriging). The proposed approach is used for fast uncertainty propagation in a reliability analysis of nondestructive testing systems using model-assisted probability of detection (MAPOD). In particular, PC-Cokriging is a multivariate version of polynomial chaos-based Kriging (PC-Kriging), which aims at combining the advantages of the regression-based polynomial chaos expansions and the interpolation-based Kriging metamodeling methods. Following a similar process as Cokriging, the PC-Cokriging advances PC-Kriging by enabling the incorporation of multifidelity physics information. The proposed PC-Cokriging is demonstrated on two analytical functions and three ultrasonic testing MAPOD cases. The results show that PC-Cokriging outperforms the state-of-the-art metamodeling approaches when providing the same number of training points. Specifically, PC-Cokriging reduces the high-fidelity training sample cost of the Kriging and PCE metamodels by over one order of magnitude, and the PC-Kriging and conventional Cokriging multifidelity metamodeling by up to 50%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$50\%$$\end{document} to reach the same accuracy level (defined by the root mean squared error being no greater than 1%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1\%$$\end{document} of the standard deviation of the testing points). The accuracy and robustness of the proposed method of the key MAPOD metrics versus various detection thresholds are investigated and satisfactory results are obtained.