A journal paper, titled “Probability-Adaptive Kriging in n-Ball (PAK-Bn) for reliability analysis” was recently published in Structural Safety. The paper was co-authored by a PhD student at SSRG, Mr. Jungho Kim and Prof. Junho Song.
The permanent link via DOI number of the paper is https://doi.org/10.1016/j.strusafe.2020.101924. The full reference information is as follows.
Kim, J., and J. Song* (2020). Probability-Adaptive Kriging in n-Ball (PAK-Bn) for reliability analysis. Structural Safety. Vol. 85, 101924.
Structural reliability analysis aims to assess the failure probability of engineering systems. Although many methods have been developed to quantify the reliability of structures, their applications to practical problems were often hampered by huge computational costs from a large number of simulations of complex engineering systems. Kriging-based reliability methods, which replace the original performance (limit-state) function with approximate Kriging surrogates to increase the computational efficiency of reliability analysis have gained significant attention recently.
Echard et al. (2011) proposed an adaptive Kriging method that can efficiently estimate the failure probability by combining Kriging and Monte Carlo simulation, termed AK-MCS. However, it still remains challenging to assess the structural reliability problem that has small failure probability and/or complex (system) failure domains. To this end, it is important to explore critical domains such as areas including the design point with a priority. Thus, adaptive refinement focusing on such critical domains is desired.
In order to address these issues in reliability analysis, a new adaptive Kriging method, termed Probability-Adaptive Kriging method based on sampling in n-Ball (PAK-Bn), is developed in this paper. The proposed method introduces a new learning function to find the best simulation point in terms of not only enrichment of design of experiment but also its influence on the estimation of the failure probability. The proposed adaptive Kriging framework also uses alternative sampling in n-Ball instead of brute force MCS samples, and has an adaptive scheme to identify a proper radius of the n-Ball that achieves efficient convergence to an accurate estimate. The PAK-Bn framework achieves computational efficiency and feasibility, and thus can deal with challenging benchmark problems in reliability analysis. The supporting source code and data are available for download at https://github.com/Jungh0Kim/PAK-Bn.
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-Bn) 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.
Structural System Reliability Group 