Comparative study of metamodeling techniques for reliability analysis using evidence theory

Different from classical probability theory, evidence theory has been proposed to handle uncertainties with incomplete or imprecise information. Evidence theory has a flexible framework to represent different types of uncertainties, and has been introduced to perform reliability analysis and design. However, its application for reliability analysis is still a challenging problem due to excessive computational cost. The coupling of the discontinuous nature of uncertainty representation in evidence theory with practical complex problem makes the computational cost extremely prohibitive. To improve its practical utility, metamodels are always used to replace the actual limit-state function to reduce the computational cost. In this paper, we systematically compare three selected metamodeling techniques - quadratic polynomial without cross terms (termed as polynomial approach), radial basis function (RBF), high-dimensional model representation combined with moving least square (HDMR-MLS) - to test the average analysis accuracy and robustness using six representative reliability problems. The objective of this research is to study applicability of different metamodeling techniques for reliability analysis using evidence theory, conclude their overall performances under different test cases, and further investigate their advantages and disadvantages for predicting low failure-probability problems.