REIF: A novel active-learning function toward adaptive Kriging surrogate models for structural reliability analysis

2019 ◽  
Vol 185 ◽  
pp. 440-454 ◽  
Author(s):  
Xufang Zhang ◽  
Lei Wang ◽  
John Dalsgaard Sørensen
Author(s):  
Xiongxiong You ◽  
Mengya Zhang ◽  
Diyin Tang ◽  
Zhanwen Niu

Reducing the surrogate model-based method computation without loss of prediction accuracy remains a significant challenge in structural reliability analysis. The unbalanced probability density, important information in critical region and information redundancy of added sample points are ignored in most of traditional surrogate-based methods, resulting in heavy computational burden. In this work, an active learning combining adaptive Kriging method and weighted penalty (AK-WP) is proposed to analyze the reliability of engineering structures. Firstly, an active learning and weighted penalty function (WPLF) is the result of integrating active learning method, weighted function and penalty function, which is proposed to find the most probable point (MPP). Meanwhile, to avoid redundant information, the best suitable MPP is determined by a proposed distance law established between the found MPP and the existing design of experiment (DoE). Secondly, the Kriging model is refined according to best suitable MPP in each iteration. Thirdly, the failure probability is estimated by the Monte Carlo sample points from the n-ball domain until the convergence condition is satisfied. The accuracy and efficiency of the proposed method are demonstrated by some numerical examples including the highly nonlinear, the small probability problems and implicit function, as well as a real engineering application.


Author(s):  
Wellison J. S. Gomes

Abstract Surrogate models are efficient tools which have been successfully applied in structural reliability analysis, as an attempt to keep the computational costs acceptable. Among the surrogate models available in the literature, Artificial Neural Networks (ANNs) have been attracting research interest for many years. However, the ANNs used in structural reliability analysis are usually the shallow ones, based on an architecture consisting of neurons organized in three layers, the so-called input, hidden and output layers. On the other hand, with the advent of deep learning, ANNs with one input, one output, and several hidden layers, known as deep neural networks, have been increasingly applied in engineering and other areas. Considering that many recent publications have shown advantages of deep over shallow ANNs, the present paper aims at comparing these types of neural networks in the context of structural reliability. By applying shallow and deep ANNs in the solution of four benchmark structural reliability problems from the literature, employing Monte Carlo simulation and adaptive experimental designs, it is shown that, although good results are obtained for both types of ANNs, deep ANNs usually outperform the shallow ones.


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