Inverse reliability analysis using high dimensional model representation

Reliability analysis is one of the major concerns at the design stage since the occurrence of failures in engineering systems may lead to catastrophic consequences. Therefore, the expectation of higher reliability and lower environmental impact has become imperative. Hence the inverse reliability problem arises when one is seeking to determine the unknown design parameters such that prescribed reliability indices are attained. The inverse reliability problems with implicit response functions require the evaluation of the derivatives of the response functions with respect to the random variables. When these functions are implicit functions of the random variables, derivatives of these response functions are not readily available. Moreover in many engineering systems, due to unavailability of sufficient statistical information, some uncertain variables cannot be modelled as random variables. In this paper High Dimensional Model Representation (HDMR) based inverse reliability analysis method is presented for the determination of the design parameters in the presence of mixed uncertain variables. The method involves HDMR approximation of the limit state function, transformation technique to obtain the contribution of the fuzzy variables to the convolution integral, and fast Fourier transform techniques to evaluate the convolution integral for solving the inverse reliability problem. The accuracy and efficiency of the proposed method is demonstrated through two numerical examples