A New Numerical Method for General Failure Probability with Fuzzy Failure Region

摘要

For general reliability analysis with fuzzy failure region F , the general failure probability P_F is defined as the integral of product of μ_F[g(y)], the membership of performance function g(y) to F, and joint Probability Density Function (PDF) f(y) over Ω, the total variable space, i.e. P_F = ∫· · ·∫ _Ω μ_Ff[g(y)]f(y)dy . On the basis of line sampling, an efficient method for random failure probability analysis with clear failure region, a new numerical method is presented to calculate P_F . In the presented method, the total integral region Ω is split into m clear sub-regions F, in a way that the value of g(y) in F_i can be approximately viewed as g_i, a constant independent of y, and the value of μ_F[g(y)] in F_i can be viewed as a constant μ_F(g_i) subsequently. Due to the closely invariant property of μ_F[g(x)] in F_i and Ω = F_1∩F_2 ∩· · ·∩F_m, P_F is transformed into the sum of μ_(g_i) ∫ · · ·∫F_i f(y) dy, where ∫ · · ·∫ _(F_i) f(y)dy is the random failure probability with the clear failure region F_i and can be obtained by line sampling. The high efficiency of the presented method resulted from that of the line sampling is demonstrated by the illustration.