Dynamic reliability analysis of systems under combined Gaussian and Poisson white noise by time-varying extreme value process

The analysis of system reliability under combined Gaussian and Poisson white noise constitutes a significant research interest in engineering. However, existing methods face computational inefficiency when addressing reliability analysis for systems under such combined noise excitation with varying safety domain thresholds. Building upon the time-varying extreme value process (EVP), this paper proposes a method called AMV-PIS that combines the augmented Markov vector (AMV) process and the path integral solution (PIS) for systems subjected to combined Gaussian and Poisson white noises. In this method, an AMV process is first defined by combining the system response and its EVP. Leveraging the Markov property of this AMV process, the PIS for the probability density function (PDF) of system response and its AMV under different is derived in detail when Poisson jump magnitudes follow continuous or discrete distributions. This derivation subsequently yields the PDFs governing both the system response and its associated EVP. The system reliability is then obtained by integrating the PDF of the EVP over the safety domain. Finally, we demonstrate the application of the proposed method using both linear and nonlinear systems. To validate its efficiency and accuracy, comparisons were made against results obtained via the Monte Carlo Simulation (MCS) method and the path integral (PI) method. The results show excellent agreement between the AMV-PIS method and the other two methods, confirming its accuracy. Crucially, the AMV-PIS method demonstrates superior computational efficiency for reliability analysis involving varying safety domains.