Extreme value analysis of multivariate Gaussian processes with wave-passage effects.

• Extreme analysis of multivariate Gaussian processes considering wave passage effect. • Wave passage is common and results in clump of upcrossings in the maximum process. • Analytical method for clump size to remove conservatism in Poisson approximation. • Proposed method is fast, accurate and applicable to high-dimensional problems. • Monte Carlo simulations performed to verify the accuracy of proposed method. Extreme value analysis is a central aspect of random vibration applications. Most studies focus on a univariate process. System reliability necessitates the extreme value across multiple correlated processes, but analytical methods are scarce and confined to low-dimensional problems. Recently, the authors proposed an analytical method for the extreme analysis of multivariate Gaussian processes. The exact upcrossing rate is derived for the maximum process representing the instantaneous maxima over all processes, and the extreme value distribution is obtained from the Poisson approximation. Nevertheless, for applications involving the wave-passage effect that is commonplace in random vibration, the upcrossings manifest in clumps, rendering the Poisson approximation conservative. The clumping from wave-passage is a complex novel phenomenon, differing from the clumping in narrowband processes. This paper extends the prior work by developing an analytical method for predicting the clump size, thereby providing an accurate prediction of the multivariate extreme value while accounting for the wave-passage effect. The method is powerful as it is fast and amenable to high-dimensional problems. Two examples include the propagation of ocean waves and a multi-span bridge subjected to propagating ground motions. The proposed method is shown to accurately predict the clumping factor and the probability of failure, compared to numerical simulations. In contrast, the Poisson approximation using the exact upcrossing rate noticeably overestimates the failure probability. [ABSTRACT FROM AUTHOR]