First Excursion Probability Sensitivity Estimation by means of Multidomain Line Sampling

Abstract

The first excursion probability offers the means for measuring the chances that one or more dynamic responses of a structural system subject to stochastic loading exceed a prescribed threshold level within a certain time duration. Such probability allows quantifying the level of safety and is dependent on the properties of the structure, such as dimensions of structural elements. The sensitivity of that probability with respect to such properties offers valuable information for optimal design under uncertain conditions and for pinpointing influential parameters. Nonetheless, the calculation of both first excursion probability and its sensitivity remains a challenging issue, as they must be estimated by means of simulation approaches for cases of practical interest, which can become numerically demanding. Thus, this contribution proposes a framework for calculating the first excursion probability and its sensitivity (in terms of a gradient) of a class of structural dynamical systems, namely linear structures subject to Gaussian loading. The framework is developed within the context of multidomain Line Sampling, which allows estimating first excursion probabilities with a reduced number of samples. Moreover, the sought sensitivity is obtained as a byproduct of the reliability analysis, and its numerical evaluation demands performing a sensitivity analysis of the mode shapes and natural frequencies.