Reliability analysis of structures with interval uncertainties under stationary stochastic excitations

Reliability analysis of linear discretized structural systems with interval uncertainties subjected to stationary Gaussian random excitation is addressed. Under the assumption of independent up-crossings of a specified threshold, an efficient procedure for the evaluation of the bounds of the interval reliability function of the generic response process is presented. The first step of the proposed approach is to derive approximate expressions of the interval mean-value and spectral moments of the response along with the associated bounds. To this aim, the improved interval analysis via extra unitary interval is applied in conjunction with a novel series expansion of the inverse of an interval matrix with modifications, called Interval Rational Series Expansion (IRSE). Then, the lower bound and upper bounds of the interval reliability function are readily evaluated by properly combining the bounds of the interval mean-value and spectral moments of the response. Two numerical examples are provided to demonstrate the accuracy of the proposed procedure and its usefulness in view of decision-making in engineering practice.