Confidence-based adaptive extreme response surface for time-variant reliability analysis under random excitation

Time-variant reliability analysis aims at revealing the time evolution of the reliability of an engineered system under time-dependent uncertainties that are best described by random processes. In practice, it is still a grand challenge to handle random process in time-variant reliability analysis due to the extremely high computational cost. In this work, a new adaptive extreme response surface (AERS) approach is proposed for time-variant reliability problems. With AERS, the dimensionality of a random process is first reduced to a set of standard normal variables and corresponding deterministic orthogonal functions based on spectral decomposition. As a result, the limit state function is reformulated as a function of only random variables and time. Next, Gaussian process (GP) models are constructed as surrogate models for predicting the value of limit state function at all discretized time nodes to approximate the extreme response surface. The accuracy of GP surrogate models is quantified by a confidence level measure and continuously improved through the sequential adaptive sampling. Using the GP surrogate models, time-dependent reliability is computed via Monte Carlo simulations (MCS). Two case studies are used to demonstrate the effectiveness of the AERS method for time-variant reliability analysis.