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First-passage reliability of single-degree-of-freedom nonlinear systems excited by combined Gaussian and Poisson white noise based on extreme value process
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DOI：10.1016/j.probengmech.2026.103976.png)
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Abstract
En 中文
Complex engineering dynamic systems are often subject to combined stochastic excitations, making reliability a core design and optimization concern. Existing reliability analysis methods incur high computational costs with varying safety thresholds, as they must reset the absorbing boundaries and recalculate the reliability. To overcome this limitation, this paper develops a method based on the system response’s extreme value process (EVP) for reliability analysis of single-degree-of-freedom (SDOF) nonlinear systems under combined Gaussian and Poisson white noise. First, for systems under combined noise, the time-varying EVP combined with its underlying response process (forming the Augmented Markov Vector, AMV) is proven to be a Markov vector. Subsequently, the probability evolution equation for the AMV is derived and iterative formulas based on the path integral (PI) method are developed to solve it for both continuous and discrete Poisson jump amplitude distributions. This extends the AMV framework for solving the transient probability density function (PDF) of the time-varying EVP, allowing the analysis of the reliability of the system. Three typical SDOF nonlinear systems are analyzed to demonstrate the method’s application and effectiveness in reliability analysis. Comparisons with the PI method based on absorbing boundary condition are reported under the tested systems and discretization settings. The main practical advantage of the proposed method is that one computed extreme-value distribution can be reused when the safety threshold changes, thereby avoiding repeated absorbing-boundary calculations. The results demonstrate that the proposed approach effectively captures the dynamic behavior of the systems, offering novel methodological support for reliability analysis of engineering systems under combined noise excitations.
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