First excursion probability sensitivity in stochastic linear dynamics by means of multidomain line sampling

This contribution presents a novel framework for estimating the sensitivity of first excursion probabilities. The focus is on linear dynamic systems with non-proportional damping subject to stationary or non-stationary Gaussian excitation. The sensitivity is estimated with respect to structural parameters of the system, including material properties and geometric dimensions of the elements. In dynamical systems, calculating both the first excursion probability and its sensitivity is done in a high-dimensional space, making the task challenging and computationally expensive. In this regard, the multidomain Line Sampling framework exploits linearity to obtain sensitivity estimates as a byproduct of the first excursion probability evaluation. The results show that the presented technique is highly efficient compared to different methods in the literature, as demonstrated through two numerical examples involving small- and large-scale models.