Reliability analysis of randomly vibrating structures with parameter uncertainties

The problem of reliability analysis of randomly driven, stochastically parametered, vibrating structures is considered. The excitation components are assumed to be jointly stationary, Gaussian random processes. The randomness in structural parameters is modelled through a vector of mutually correlated, non-Gaussian random variables. The structure is defined to be safe if a set of response quantities remain within prescribed thresholds over a given duration of time. An approximation for the failure probability, conditioned on structure randomness, is first formulated in terms of recently developed multivariate extreme value distributions. An estimate of the unconditional failure probability is subsequently obtained using a method based on Taylor series expansion. This has involved the evaluation of gradients of the multivariate extreme value distribution, conditioned on structure random variables, with respect to the basic variables. Analytical and numerical techniques for computing these gradients have been discussed. Issues related to the accuracy of the proposed method have been examined. The proposed method has applications in reliability analysis of vibrating structural series systems, where different failure modes are mutually dependent. Illustrative examples presented include the seismic fragility analysis of a piping network in a nuclear power plant.