Reliability analysis of uncertain dynamical systems using correlated function expansion

Reliability analysis of uncertain dynamical systems is considered. The excitations are modeled as non-stationary Gaussian processes, whereas parametric uncertainties due to structural randomness are modeled as non-Gaussian random variables. The structural responses are, therefore, non-Gaussian processes. The limit state is formulated in terms of the extreme value distribution of the response process. Developing these extreme value statistics analytically is not straightforward, which makes failure probability estimations difficult. An alternative procedure is investigated for computing exceedance probabilities. Proposed approach involves generating a full functional operational model, which approximates the original limit surface. Once the approximate form of the original limit state is defined, the failure probability can be obtained by statistical simulation. Thus, the method can be integrated with commercial finite element software, which permits uncertainty analysis of large structures with complexities that include material and geometric nonlinear behavior.