Towards a single-loop Gaussian process regression based-active learning method for time-dependent reliability analysis

Time-dependent reliability analysis has received increasing attention for assessing the performance and safety of engineered components and systems subject to both random and time-varying dynamic factors. However, many existing methods may prove insufficient when applied to real-world problems, particularly in terms of applicability, efficiency and accuracy. This paper presents a novel time-dependent reliability analysis method called ‘single-loop Gaussian process regression based-active learning’ (SL-GPR-AL). In this method, a GPR model is trained as a global response surrogate model for the time-dependent performance function in an active learning fashion. A new stopping criterion is proposed to assess the convergence of the GPR model in estimating the time-dependent failure probability. Additionally, two new learning functions are introduced to identify the best next point for further refining the GPR model if the stopping criterion is not met. Finally, the well-trained GPR model in conjunction with Monte Carlo simulation provides the time-dependent failure probability over a specified time interval, along with the time-dependent failure probability function as a byproduct. Four numerical examples are analyzed to demonstrate the performance of the proposed method. The results indicate that our approach provides an alternative, efficient and accurate means for computationally expensive time-dependent reliability analysis.