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 randomexcitation is addressed. Under the assumption of independent up-crossings of a specified threshold, an efficient procedure forthe evaluation of the bounds of the interval reliability function of the generic response process is presented. The first step of theproposed approach is to derive approximate expressions of the interval mean-value and spectral moments of the response along withthe associated bounds. To this aim, the improved interval analysis via extra unitary interval is applied in conjunction with a novelseries 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 ofthe interval mean-value and spectral moments of the response. Two numerical examples are provided to demonstrate the accuracyof the proposed procedure and its usefulness in view of decision-making in engineering practice.