Probability-Adaptive Kriging in n-Ball (PAK-Bn) for reliability analysis. (July 2020)

• Record Type: Journal Article
• Authors: Kim, Jungho; Song, Junho
• Is Part Of: Structural safety. Volume 85(2020)
• Publication Date: 2020-07
• Subjects: Adaptive Kriging -- Design of experiment -- Kriging -- Learning function -- Multiple failure regions -- Structural reliability -- Surrogate model; Structural stability -- Periodicals; Safety factor in engineering -- Periodicals; Reliability (Engineering) -- Periodicals; Constructions -- Stabilité -- Périodiques; Coefficient de sécurité en ingénierie -- Périodiques; Fiabilité -- Périodiques; 620.86
• DOI: 10.1016/j.strusafe.2020.101924
• Languages: English
• ISSNs: 0167-4730

Abstract

Highlights: A new adaptive Kriging method is developed for efficient reliability analysis. The method enriches the experimental designs from reliability analysis standpoint. The probability-adaptive learning function guides simulations to critical regions. PAK-B n uses an alternative sampling in n -Ball whose radius is adaptively determined. The proposed method is successfully demonstrated by benchmark reliability problems. Abstract: Complexity of today's engineering systems inevitably makes the computational simulation of their performance challenging and time-consuming. Since structural reliability analysis methods generally repeat such computational simulations, it is essential to reduce the number of function evaluations required to achieve reliable estimates. In research efforts to fulfill this aim, adaptive Kriging methods have gained significant interest because of desirable properties and accuracy of the surrogate model. A new adaptive Kriging approach proposed in this paper improves the efficiency of reliability analysis by incorporating the probabilistic density of the random variable space into the adaptive procedure of identifying the surrogate limit-state surface. In addition, samples distributed uniformly inside the n -ball domain are used as the candidate points to enrich the experimental design, and the best candidate for simulation is determined in terms of influence on the failure probability estimation. The efficiency and accuracy of the proposed Probability-Adaptive Kriging in n -Ball (PAK-B n ) method are demonstrated by several reliability examples characterized by highly non-linear limit-state functions, small failure probability and multiple design points. The results confirm that the method facilitates convergence to the failure probability with a smaller number of function evaluations. The supporting source codes are available for download at https://github.com/Jungh0Kim/PAK-Bn .