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

Abstract

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. INDEX TERMS Time-dependent reliability analysis, Kriging, Monte Carlo simulation, the best next sample.

An active learning Bayesian ensemble surrogate model for structural reliability analysis

“…The adaptive sampling method starts from a small experimental design and then sequentially adds the new sample points that contribute the most to the approximate model, thus significantly reducing some unnecessary sample points in the one‐shot experimental design. In the existing surrogate‐based reliability analysis combined with adaptive sampling design, several surrogate models, such as Kriging, 10,11 polynomial chaos expansion (PCE), 12,13 and support vector regression (SVR), 14,15 are frequently used. Kriging is the most popular surrogate model due to its attractive characteristic which can provide both the predicted mean value and variance of unsampled points 16–18 .…”

A Multilevel Simulation Method for Time-Variant Reliability Analysis

“…Next, the cumulative probability of failure is estimated by a random sampling method. The strategies of determining the set of training samples are of the utmost importance for the accuracy and efficiency of surrogate model-based methods, on which a number of studies can be found [36,37]. For example, Jiang et al [38] proposed an active failure-pursuing Kriging method to identify the most valuable samples for improving the accuracy of the Kriging model; Wang et al [37] developed two methods based on projection outline adaptive Kriging to handle time-variant problems with random and interval uncertainties.…”

Importance Sampling for Time-Variant Reliability Analysis

“…Compared with time-independent reliability analysis, timevariant reliability analysis [17] is more in line with the actual situation because the performance of a practical structure or system generally degrades with time. In time-variant reliability analysis, stochastic processes (e.g.…”