A new learning function for Kriging and its applications to solve reliability problems in engineering

Abstract

a b s t r a c tIn structural reliability, an important challenge is to reduce the number of calling the performance function, especially a finite element model in engineering problem which usually involves complex computer codes and requires time-consuming computations. To solve this problem, one of the metamodels, Kriging is then introduced as a surrogate for the original model. Kriging presents interesting characteristics such as exact interpolation and a local index of uncertainty on the prediction which can be used as an active learning method. In this paper, a new learning function based on information entropy is proposed. The new learning criterion can help select the next point effectively and add it to the design of experiments to update the metamodel. Then it is applied in a new method constructed in this paper which combines Kriging and Line Sampling to estimate the reliability of structures in a more efficient way. In the end, several examples including non-linearity, high dimensionality and engineering problems are performed to demonstrate the efficiency of the methods with the proposed learning function.

LIF: A new Kriging based learning function and its application to structural reliability analysis

“…The learning function U, proposed by Echard et al [34], focuses on the probability of misclassification made by the Kriging model on the sign of ( ) x G . Just like discussed in [41], U gives more weight to points in the vicinity of the predicted limit state rather than the Kriging variance, which is its main difference from EFF. Lv et al [41] and Yang et al [42,43] present two new learning functions which are named H and expected risk function (ERF) respectively.…”

“…An excellent strategy of DoE leads the process of reliability analysis converging quickly and provides high accuracy at the same time [31,34,[38][39][40]. Various kinds of sequential DoE based on the Kriging model have been proposed to improve the accuracy of structural reliability analysis and reduce the number of calls to the real performance function [8,29,32,38,41,42]. Kriging based sequential DoE has drawn more and more attention because it is often active and can update itself by adding new sample point based on the statistical information provided by the Kriging model.…”

Adaptive coupling of reduced basis modeling and Kriging based active learning methods for reliability analyses

“…al [21]. Other methods have also been presented to address specific problems such as small failure probabilities (rare events) estimations [3,22,23,24,25,7,26] , multiple failure regions problems [27,28,29,30] or systems failure probabilities assessment [6,31,5,2,9,32].…”

Reliability Analysis of Structures by Iterative Improved Ensemble of Surrogate Method

“…erefore, Kriging-based sequential strategies of the design of experiments (DoE) have drawn more and more attention because it is an active learning process and can update itself by adding new training point based on the statistical information provided by the Kriging model. So far, several Kriging-based reliability methods with an adaptive DoE have been proposed utilizing the Kriging variance [11][12][13].…”