Data-driven time-variant reliability analysis using deep Gaussian processes

Time-variant reliability analysis (TRA) is critical for assessing the dynamic risk of engineering systems under evolving conditions, such as material degradation and random external forces. However, conventional methods often assume that the statistical properties of all stochastic inputs are precisely known. In practice, these properties must be inferred from limited and often non-stationary measured data, introducing significant epistemic uncertainty. This paper presents a comprehensive, data-driven TRA framework designed to address this challenge. The proposed method integrates multivariate kernel density estimation (KDE) with bootstrapping to non-parametrically model correlated random variables and their epistemic uncertainty. Simultaneously, it employs deep Gaussian processes (DGP) as a probabilistic model for complex, non-stationary random processes, where the epistemic uncertainty is quantified through latent functions. A key contribution of this framework is its ability to systematically quantify and propagate the epistemic uncertainty from input modeling to the reliability prediction, yielding the full probability distribution of the reliability. The effectiveness of the proposed approach is validated through numerical studies by comparing its performance with existing methods. The results demonstrate that the proposed framework provides accurate probabilistic predictions, particularly in scenarios with complex non-stationarity and sparse data, thereby enabling more informed risk assessment and decision-making.