Reliability Function for the Interval Stress Process of Randomly Excited Structures

This paper deals with reliability analysis of linear discretized structures with interval parameters subjected to stationary Gaussian multi-correlated random excitation. Within the interval framework, the range of the interval reliability function for the critical stress process may be significantly overestimated by the classical interval analysis due to the so-called dependency phenomenon which is particularly insidious for stress-related quantities. To limit the dangerous effects of this phenomenon, a novel sensitivity-based procedure relying on a combination of the Interval Rational Series Expansion and the Improved Interval Analysis via Extra Unitary Interval is proposed. This procedure allows us to detect the combinations of the bounds of the uncertain parameters which yield the lower bound and upper bound of the interval reliability function for the selected stress process. Furthermore, sensitivity analysis enables to identify the most influential parameters on structural reliability. A numerical application is presented to demonstrate the accuracy of the proposed procedure and its usefulness in view of decision-making in engineering practice.