An Importance Sampling Approach for Estimating First Excursion Probabilities of Linear Systems Subject to Non-Gaussian Loading

Abstract Assessing the reliability of structures subject to stochastic dynamic loading is crucial in design, construction, and the assessment of long-term system performance. To improve efficiency, many real-world systems are simplified by assuming structural linearity and/or Gaussian loading. Under these assumptions, the first excursion probability can be evaluated using efficient simulation methods that require few dynamic analyses while maintaining accuracy. However, in practical applications, system responses are often non-Gaussian. In such cases, conventional methods designed for linear systems under Gaussian loads may no longer be applicable. More general approaches, such as Monte Carlo simulation, are often required, but they come with high computational costs and lower efficiency. To address this challenge, this study introduces a new approach for estimating the first excursion probability of linear systems subjected to non-Gaussian loading. The approach is based on Importance Sampling while incorporating a Gaussian approximation of stochastic dynamic loading. In this way, computational efficiency and accuracy are balanced. The proposed method is validated through two case studies, with results compared against Monte Carlo Simulation. In addition, results obtained by the proposed method are compared to the results obtained by extended version of Directional Importance Sampling (eDIS). The findings demonstrate that the developed method provides a computationally efficient and accurate alternative for reliability assessment, making it a valuable tool for analyzing structures subjected to random loading conditions.