An efficient hybrid reliability analysis method based on active learning Kriging model and multimodal‐optimization‐based importance sampling

Abstract

A novel method is proposed, which aims to solve rare‐event hybrid reliability problems with random and interval variables, where the performance function has various failure zones. It combines the active learning Kriging (ALK) model with importance sampling (IS) and evolutionary multimodal‐based multiobjective optimization (EMO‐MMO). The surrogate limit state surfaces (LSS) for the upper and lower failure probability bounds are respectively defined considering the Kriging variance. Failure candidate solutions located in different failure regions are generated by the EMO‐MMO method. Subsequently, all the most probable failure points (MPPs) are identified from those candidate solutions. The IS samples are simulated around the MPPs using the MPP‐based IS method. The IS samples located in unimportant regions are removed in order to improve the efficiency of approximating the surrogate LSSs. The optimal training points are selected from the truncated IS samples to update the Kriging model. After several training iterations, the surrogate LSSs are convergent. Ultimately, a reliable and unbiased estimation of the upper and lower failure probability bounds is provided. The performance of the ALK‐EMO‐IS‐HRA approach is verified through five application examples.

Application of Evolutionary Artificial Intelligence. An Exploratory Literature Review

“…They did not aim to simplify the multi-objective task; rather, they developed a method for finding solutions in parallel. The complex model of rare events can be solved by the complex model proposed by Wang et al [18], known as evolutionary multimodal-based multiobjective optimization (EMO-MMO), which recognizes the most probable failure points. For antenna engineers, alignment can be greatly simplified using the methodology proposed by De Melo et al [19], which incorporates the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective evolutionary algorithm based on decomposition (MOEA / D) to easily reconcile several objectives.…”

The adaptive weight learning function for reliability analysis and its application to multiple active learning methods

“…The aim of the structural reliability analysis is to obtain failure probabilities while taking into account the randomness of input variables 1–3 . The first‐order and second‐order reliability methods (FORM, SORM) have wide applications in reliability analysis 4,5 .…”

A novel method for reliability analysis with interval parameters based on active learning Kriging and adaptive radial‐based importance sampling

“…For engineering practice, sufficient experimental data is not always available or sometimes very expensive to obtain, thus the probability distributions are difficult to be obtained precisely, which is represented by the epistemic uncertainty. Recent years, several classical models have been proposed to account for this type of uncertainty, including stochastic model, 7 fuzzy set model 8,9 and interval model 10,11 . Also, several researchers have made comparisons for the selection of those models and applied them into geotechnical engineering, 12 aeronautical engineering, 13 environment engineering 14 and so forth.…”

“…Recent years, several classical models have been proposed to account for this type of uncertainty, including stochastic model, 7 fuzzy set model 8,9 and interval model. 10,11 Also, several researchers have made comparisons for the selection of those models and applied them into geotechnical engineering, 12 aeronautical engineering, 13 environment engineering 14 and so forth.…”