Dynamic reliability evaluation considering the stochastic evolving process based on extreme characteristics of system responses

The randomness of high-frequency system responses in engineering, such as vibration, stress, and displacement, poses a significant challenge to system reliability and can potentially lead to system failure. This study proposes a novel stochastic evolving process that directly incorporates random extreme values and their occurrence times, enabling the characterization of the spatial distribution and temporal evolution of dynamic system responses. By integrating the saddle-point approximation and renewal process, the proposed approach effectively captures the statistical properties and variation patterns of extreme responses. Additionally, a convolution technique is explored to handle both known and unknown process parameters. A general reliability model is formulated with rigorous theoretical reasoning to assess dynamic system performance. The unified probabilistic framework is developed that systematically integrates dynamic response evolution and different random characteristics for reliability evaluation in stochastic environments. Specifically, an analytical approach is developed for systems with memoryless properties, while a general numerical method, based on the Laplace transform, is introduced to evaluate equipment reliability under stochastic conditions in both the complex frequency and time domains. The proposed method is validated through three engineering case studies, analyzing the impact of mean values and standard deviations on system reliability. The results demonstrate strong consistency and accuracy, aligning well with Monte Carlo simulations, thereby confirming the validity and practical applicability of the approach.