To read the full version of this content please select one of the options below:

Efficient uncertainty propagation for MAPOD via polynomial chaos-based Kriging

Xiaosong Du (Department of Aerospace Engineering, Iowa State University, Ames, Iowa, USA)
Leifur Leifsson (Department of Aerospace Engineering, Iowa State University, Ames, Iowa, USA)

Engineering Computations

ISSN: 0264-4401

Article publication date: 13 August 2019

Issue publication date: 16 January 2020



Model-assisted probability of detection (MAPOD) is an important approach used as part of assessing the reliability of nondestructive testing systems. The purpose of this paper is to apply the polynomial chaos-based Kriging (PCK) metamodeling method to MAPOD for the first time to enable efficient uncertainty propagation, which is currently a major bottleneck when using accurate physics-based models.


In this paper, the state-of-the-art Kriging, polynomial chaos expansions (PCE) and PCK are applied to “a^ vs a”-based MAPOD of ultrasonic testing (UT) benchmark problems. In particular, Kriging interpolation matches the observations well, while PCE is capable of capturing the global trend accurately. The proposed UP approach for MAPOD using PCK adopts the PCE bases as the trend function of the universal Kriging model, aiming at combining advantages of both metamodels.


To reach a pre-set accuracy threshold, the PCK method requires 50 per cent fewer training points than the PCE method, and around one order of magnitude fewer than Kriging for the test cases considered. The relative differences on the key MAPOD metrics compared with those from the physics-based models are controlled within 1 per cent.


The contributions of this work are the first application of PCK metamodel for MAPOD analysis, the first comparison between PCK with the current state-of-the-art metamodels for MAPOD and new MAPOD results for the UT benchmark cases.



The authors gratefully acknowledge the support of the Center for Nondestructive Evaluation Industry/University Cooperative Research Program at Iowa State University. The authors would also like to thank Prof Jiming Song at Iowa State University for providing them with the physics-based ultrasonic testing models.


Du, X. and Leifsson, L. (2020), "Efficient uncertainty propagation for MAPOD via polynomial chaos-based Kriging", Engineering Computations, Vol. 37 No. 1, pp. 73-92.



Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited