A new active learning method based on the learning function U of the AK-MCS reliability analysis method

2017 ◽  
Vol 148 ◽  
pp. 185-194 ◽  
Author(s):  
Zheng Peijuan ◽  
Wang Chien Ming ◽  
Zong Zhouhong ◽  
Wang Liqi
Keyword(s):  
Active Learning ◽  
Reliability Analysis ◽  
Learning Method ◽  
Analysis Method ◽  
Learning Function ◽  
Active Learning Method

AK-PDF: An active learning method combining kriging and probability density function for efficient reliability analysis

2019 ◽  
Vol 234 (3) ◽  
pp. 536-549 ◽  
Author(s):  
Chengning Zhou ◽  
Ning-Cong Xiao ◽  
Ming J Zuo ◽  
Xiaoxu Huang
Keyword(s):  
Probability Density Function ◽  
Active Learning ◽  
Probability Density ◽  
Reliability Analysis ◽  
Density Function ◽  
State Function ◽  
Learning Method ◽  
Learning Function ◽  
Reliability Method ◽  
Active Learning Method

An important challenge in structural reliability is to reduce the number of calls to evaluate the performance function, especially the complex implicit performance functions. To reduce the computational burden and improve the reliability analysis efficiency, a new active learning method is developed to consider the probability density function of samples based on the learning function U in an active learning reliability method that combines the kriging and Monte Carlo simulation. In the proposed method, the proposed active learning function contains two parts: part A is based on function U, and part B is based on the probability density function and function U. By changing the weights of parts A and B, the sample points close the limit-state function, and those in the region with a higher probability density function have more weight to be selected compared to the others. Subsequently, the kriging model can be constructed more effectively. The proposed method avoids a large number of time-consuming function evaluations, and the recommended weight is also reported. The performance of the proposed method is evaluated through three numerical examples and one engineering example. The results demonstrate the efficiency and accuracy of the proposed method.

An improved active learning method combing with the weight information entropy and Monte Carlo simulation of efficient structural reliability analysis

2020 ◽  
pp. 095440622097323
Author(s):  
Jingkui Li ◽  
Bomin Wang ◽  
Zhandong Li ◽  
Ying Wang
Keyword(s):  
Active Learning ◽  
Reliability Analysis ◽  
Information Entropy ◽  
Structural Reliability ◽  
Limit State ◽  
State Function ◽  
Learning Method ◽  
Learning Function ◽  
Active Learning Method ◽  
Variable Space

A significant challenge of surrogate model-based structural reliability analysis (SRA) is to construct an accurate approximated model of the nonlinear limit state function (LSF) with high order and high dimension effectively. As one of the sequential update-strategies of design of experiment (DoE), the active learning method is more attractive in recent years due to greatly reduces the burden of reliability analysis. Although the active learning method based on information entropy learning function H and the line simulation (AK-LS) is a powerful tool of SRA, the computational burden from the iterative algorithm is still large during the learning process. In this research, an improved learning criterion, named the weight information entropy function (WH), is developed to update the DoE of Kriging-based reliability analysis. The WH learning function consists of the information entropy function and an adaptive weight function (W). Locations in the variable space and probability densities of the samples are taken accounted into the WH learning function, which is the most important difference from the H learning function. The samples that are closer to the LSF and has a greater probability density can be preferentially selected into the DoE comparing to others by changing the weight of information entropy during the learning process. The WH learning function can efficiently match the limit state function in an important domain rather than the entire variable space. Consequently, the approximated model of LSF via Kriging interpolation can be constructed more effectively. The new active learning method is developed based on Kriging model, in which WH learning function and Monte Carlo simulation (MCS) are employed. Finally, several engineering examples with high non-linearity are analyzed. Results shown that the new method are very efficient when dealing with intractable problems of SRA.

An active learning method combining adaptive kriging and weighted penalty for structural reliability analysis

2021 ◽  
pp. 1748006X2110161
Author(s):  
Xiongxiong You ◽  
Mengya Zhang ◽  
Diyin Tang ◽  
Zhanwen Niu
Keyword(s):  
Active Learning ◽  
Reliability Analysis ◽  
Penalty Function ◽  
Structural Reliability ◽  
Learning Method ◽  
Structural Reliability Analysis ◽  
Highly Nonlinear ◽  
Active Learning Method ◽  
Sample Points ◽  
Adaptive Kriging

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.

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