Abstract
When the reliability analysis of the mechanical products with high nonlinearity and time-consuming response is carried out, there will be the problems of low precision and huge computation using the traditional reliability methods. To solve these issues, the active learning reliability methods have been paid much attention in recent years. It is the key to choose an efficient learning function (such as U, EFF, and ERF). The aim of this study is to further decrease the computation and improve the accuracy of the reliability analysis. Inspired from these learning functions, a new point-selected learning function (called HPF) is proposed to update DOE, and a new point is sequentially added step by step to the DOE. The proposed learning function can consider the features like the sampling density, the probability to be wrongly predicted, and the local and global uncertainty close to the limit state. Based on the stochastic property of the Kriging model, the analytic expression of HPF is deduced by averaging a hybrid indicator throughout the real space. The efficiency of the proposed method is validated by two explicit examples. Finally, the proposed method is applied to the mechanical reliability analysis (involving time-consuming and nonlinear response). By comparing with traditional mechanical reliability methods, the results show that the proposed method can solve the problems of large computation and low precision.
Highlights
In the mechanical reliability analysis (MRA), when the joint probability density function fX(x) of the random variable vector X [X1, X2, . . ., Xn]T is known, the failure probability can be expressed asPf P(g(x) ≤ 0) fX(x)dx Ig≤0(x)fX(x)dx, F (1)where g(x) is the performance function of the mechanical system
By comparing with traditional mechanical reliability methods, the results show that the proposed method can solve the problems of large computation and low precision
Because g(x) is explicit expression, the computer can complete the calculation of the performance function g(x) at millions of sample points in a short time. erefore, Monte Carlo simulation, as the most common and robust method, is applied to reliability analysis in this paper. e failure probability can be expressed as pf where x [x1, x2, ···, xn]T is the vector of input random variables with n-dimension in the domain; fX(x) is the joint probability density function of x; nMCS is the number of random samples generated by MCS; xi, (i 1, 2, . . . , nMCS) is the ith sample in the Monte Carlo population; Ig(x) is a indicator function, and it can be defined as
Summary
In the mechanical reliability analysis (MRA), when the joint probability density function fX(x) of the random variable vector X [X1, X2, . . ., Xn]T is known, the failure probability can be expressed as. The performance function g(x) of the MRA is obtained by solving the numerical model (such as finite element method and finite different method) which is usually time-consuming and highly nonlinear For this situation, the moment reliability methods [1] are not applicable because the calculated reliability’s accuracy is very low due to ignorance of the Taylor expansion’s highorder items. Sun et al [22] proposed a learning function that considers the degree of improvement in prediction accuracy and probability density based on a dynamic point selection update strategy and established a relatively high-precision Kriging prediction model relatively quickly. A Krigingbased active learning reliability method is presented, in which an efficient point-selected learning function (called HPF) is proposed to update DOE.
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