Reliability assessment of interval uncertain structural systems subjected to spectrum compatible seismic excitations

The present paper deals with reliability assessment of linear structures with uncertain parameters subjected to seismic excitations modeled as stationary spectrum compatible random Gaussian processes. Structural uncertainties are described by applying the interval model, stemming from the interval analysis. Under the Vanmarcke assumption that the upcrossings of a specified threshold occur in clumps, an efficient procedure for the evaluation of the bounds of the interval reliability function of the generic response process is presented. The key idea is to consider the interval reliability function as depending on the zero-, first- and second-order interval spectral moments of the stationary response rather than on the interval structural parameters. This allows to determine the bounds of the interval reliability function for a given barrier level as the minimum and maximum among the values pertaining to the eight combinations of the bounds of the interval spectral moments of the response. The effectiveness of the proposed approach lies in the evaluation of the bounds of the interval spectral moments of the response in approximate explicit form. To this aim, the so-called Interval Rational Series Expansion is applied in conjunction with the improved interval analysis. For validation purposes, numerical results concerning the region of the interval reliability function of a spatial structure with interval stiffness properties subjected to stationary spectrum compatible seismic excitation are presented.