Discretization Analysis Method of Hybrid Reliability Based on Evidence Theory

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.