Kriging Model for Time-Dependent Reliability: Accuracy Measure and Efficient Time-Dependent Reliability Analysis Method

As the performance function of a mechanical structure is usually based on time-consuming computer codes, predicting time-dependent reliability analysis requires a large number of costly simulations in engineering. To reduce the number of evaluations of time-consuming models and enhance efficiency of time-dependent reliability analysis, Kriging is employed as a surrogate of original performance function. Firstly, a quantitative measure of the error of Kriging-based estimation of time-dependent failure probability is obtained by derivation. Dividing the quantitative measure by the Kriging-based estimation, the associated relative error is approximately estimated. Secondly, to construct an accurate Kriging model using fewer samples, a DoE (the design of experiments) strategy is developed. The idea is to adaptively refresh Kriging model with the best next sample that could enhance Kriging model the most with regard to expectation. Finally, a Kriging-based time-dependent reliability analysis method is constructed. In the method, Kriging model is adaptively refreshed according to the proposed DoE strategy, until the relative error of estimated probability of failure below a given threshold. The threshold could be quantitatively adjusted to accuracy requirement of reliability analysis. The proposed method can predict the evolution of failure probability over time. Its advantage is validated by three numerical examples.