A bounding-limit-state-surface-based active learning Kriging method for hybrid reliability analysis under random and probability-box variables

Abstract This paper presents a new method for efficient hybrid reliability analysis under both random and probability-box variables. Due to the existence of probability-box variables, the failure probability yielded by hybrid reliability analysis is an interval value. In practical engineering, numerical models are becoming more and more time-consuming, which promotes that metamodel-assisted reliability analysis methods gain considerable attention. The failure probability in hybrid reliability analysis under both random and probability-box variables can be calculated by transforming the original uncertainty space into the standard normal space. Then a limit-state band with two bounding limit-state surfaces is generated in the standard normal space. In this paper, it is determined that the lower and upper bounds of failure probability can be accurately estimated based on a Kriging metamodel as it can well describe the two bounding limit-state surfaces. Then, a new active learning strategy based on bounding limit-state surface is proposed to sequentially update Kriging metamodel by adding new update points in the vicinity of the bounding limit-state surfaces into design of experiments. Meanwhile, two error measurement functions are presented to terminate the update process by calculating the metamodel error. Combining the bounding-limit-state-surface-based active learning Kriging with interval Monte Carlo simulation, a new method for hybrid reliability analysis under both random and probability-box variables is developed. In this method, the lower and upper bounds of failure probability are estimated by interval Monte Carlo simulation based on the built Kriging metamodel. The proposed method is tested by six examples. Its comparison with some existing reliability analysis methods is provided. The high accuracy and efficiency of the proposed method are validated by comparative results.

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