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Multicut-HDMR based reliability bounds estimation under mixed uncertainties

Reliability analysis taking into account the uncertainties involved in a structural system plays an important role in the analysis and design of structures. Due to the complexity of structural systems, the information about the functioning of various structural components has different sources and the failure of systems is usually governed by multiple failure criteria, all of which are to be taken into consideration for reliability estimation. In this paper High Dimensional Model Representation (HDMR) based uncertain analysis method is presented for estimating the bounds on the reliability of structural systems involving multiple design points in the presence of mixed uncertain variables. The method involves HDMR approximation of the limit state function, weight function to identify multiple design points, 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 estimation of the membership function of reliability. The proposed effort in evaluating the failure probability involves calculating conditional responses at a selected input determined by sample points. Three numerical examples have been presented, and comparisons have been made with direct MCS method to evaluate the accuracy and the computational efficiency of the present method.