Prof. Faes gives talk at ISRERM 2022
This paper presents a highly efficient and effective approach to bound the first excursion probability of linear stochastic FE models subjected to imprecise stochastic excitations. In previous work, some of the authors proposed a highly efficient approach based on the operator norm framework to bound such first excursion probabilities without having to resort to double-loop problems [1]. However very efficient, the approach presented in [1] is limited to deterministic models, or models containing epistemic uncertainty. In this paper, the classic operator norm approach is augmented by linearizing the stochastic FE model around the mean of the aleatory uncertain parameter. This allows for determining those values of the epistemically uncertain parameters that yield an extremum in the first excursion probability without solving the associated reliability problem. Hence, the double loop that is typically associated to this type of problems is effectively broken. A case study is included to show the effectiveness and efficiency of the proposed method.
[1] Faes, MGR, Valdebenito, MA, Moens, D., & Beer, M. (2021). Operator norm theory as an efficient tool to propagate hybrid uncertainties and calculate imprecise probabilities. Mechanical Systems and Signal Processing, 152, 107482. doi.org/10.1016/j.ymssp.2020.107482