A novel active learning Gaussian process modeling-based method for time-dependent reliability analysis considering mixed variables

The purpose of time-dependent reliability analysis is evaluating the reliability of a system or component within a specified timeframe. Several approaches have been suggested for addressing time-dependent reliability challenges, including analytical methods and methods based on response surrogate models. As a representative of Machine Learning methods, the Active Learning Gaussian process model has gained more and more popularity in time-dependent reliability analysis. In practical applications, certain uncertainties may not be adequately represented by random variables following deterministic distributions. In contrast, these uncertainties can be easily described by interval variables. This article introduces an innovative method based on Active Learning Gaussian process modeling for time-dependent reliability analysis, encompassing both random and interval variables. The initial step involves transforming stochastic processes into random parameters through spectral decomposition. Moreover, a new sampling strategy to manage mixed uncertainties is proposed, where the candidate samples of mixed variables with positive maximum extreme responses and negative minimum extreme responses are identified. These samples are utilized to construct and renew an extreme Gaussian process model. Lastly, we present an improved confidence-based learning function to accelerate the learning process, which is designed to locate the optimal random input and interval input for updating the extreme Gaussian process model. One mathematical example and two engineering examples are conducted to verify the performance of the proposed method. Results illustrate that our method offers high accuracy while reducing the evaluations of true performance functions in addressing time-dependent reliability issues under mixed uncertainties.