Discretization Analysis Method of Hybrid Reliability Based on Evidence Theory

Abstract

Aiming at the problem that various types of uncertainties, such as randomness, fuzziness, and interval, coexist in structure reliability analysis, a discretization analysis method of hybrid reliability for uncertain structures is proposed based on evidence theory (ET) in this article. Firstly, in order to establish a hybrid reliability model based on ET, a generalized density method (GDM) is developed to transform the fuzzy variables into equivalent random variables on the basis of the entropy equivalent method (EEM). Based on the discrete property of the basic probability assignment (BPA) in evidence theory, the random variables and fuzzy variables (equivalent random variables) are both discretized into subintervals according to six-sigma rule. Then, the BPA of each subinterval is solved and all focal elements are assigned BPA, so the evidence structure characterization of random and fuzzy variables is realized. Secondly, using Fmincon function based on the sequential quadratic programming (SQP) algorithm in MATLAB, the minimum and maximum values of performance function over each focal element can be acquired directly. Meanwhile, the production rules are used to judge the belonging of focal elements and classify them, so the numerical calculation of belief measure and plausibility measure is also realized. Finally, combined with the Monte Carlo Simulation (MCS) method, an engineering example is provided to demonstrate the feasibility and accuracy of the proposed method.

A Multisource Uncertainty Fusion Reliability Evaluation Method for the Control Rod Drive Mechanism of Nuclear Power Plants

“…In [43], fuzzy variables and random variables were transformed into interval variables and then solved by an iterative first-order reliability method. In [44], random variables and fuzzy variables (equivalent to random variables) were discretized into subintervals, and finally, the reliability analysis was completed by using evidence theory. Based on the cut set optimization theory, Zhang et al [45] converted fuzzy variables Equivalent probability density function Guo et al [20] Equivalent probability density function Valdebenito et al [21] Approximate calculation You et al [22] Envelope distribution Zhang et al [23] Information entropy…”

“…An et al [43] Iterative first-order reliability method Tang et al [44] Subintervals and evidence theory Zhang et al [45] Uniformity variable conversion 3 International Journal of Energy Research into random variables and interval variables into random variables by the uniformity method and then used the FORM method to solve the structural reliability.…”

“…When the structure of the Bayesian network is determined, the Bayesian network can act as a probabilistic surrogate that inference each node's probability based on posterior knowledge, i.e., the evidence. The basic algorithm of Bayesian network inference is the variable elimination algorithm [44].…”

Research on Reliability Modelling for Heavy CNC Machine Tools under Uncertain Variables Based on Universal Generating Function

“…Wang [10] transformed fuzzy variables into interval variables and established a reliability model containing random variables and fuzzy variables. Tang [11] proposed a mixed reliability discretization analysis method of uncertain structures based on evidence theory to solve the coexistence of random, fuzzy, and other uncertainties in structural reliability analysis. It can be seen that many methods have been applied to uncertainty quantification.…”