Perturbation principle-based fuzzy reliability analysis method

Abstract

The invention discloses a perturbation principle-based fuzzy reliability calculation method containing a fuzzy random variable, and is applied to the field of reliability. The objective of the invention is to solve the problem of structural function non-linear fuzzy random reliability. A perturbation theory and a fuzzy decomposition theory are used for carrying out perturbation quantization on fuzzy random variables, fuzzy characteristic parameters of the fuzzy random variables of the structure are expressed as the sum of true values and fuzzy perturbation microscale of the fuzzy characteristic parameters, the fuzzy characteristic parameters are decomposed into a series of interval quantities under horizontal truncation, the interval quantities are equivalent to random variables, and a mean value and a standard deviation are obtained through calculation. And meanwhile, equivalent selection is carried out on perturbation microscale. Secondly, decomposing the fuzzy probability density function and the fuzzy function function of the structure into interval quantities under a series of horizontal truncation sets, and performing Taylor series expansion on upper and lower limit values ofthe interval quantities to obtain perturbation values of the joint probability density function and the structure function; And finally, according to the definition of the structure reliability, introducing a sigmoid function as a step function by using a direct integration method, and solving to obtain a fuzzy reliability interval. Compared with a traditional convex set method, the reliability interval obtained through calculation is narrower under the same confidence level, and engineering application is more convenient.

Description

technical field [0001] The invention belongs to the field of reliability, in particular to a calculation method of structural reliability with fuzzy random variables. Background technique [0002] There are a lot of uncertainties in practical engineering problems, including random uncertainties and cognitive uncertainties. For structural analysis problems with fuzzy uncertainties, it is very difficult to describe them using conventional reliability theories and methods, and even improper use of conventional reliability analysis methods may cause the calculated results to be completely inconsistent with the actual situation The situation 0 appears. Therefore, it has certain practical significance to study the fuzzy reliability of structures by applying fuzzy reliability analysis theory and method. Especially for the structure containing fuzzy random variables, when its function function and probability density function are nonlinear, the convex set method usually used in fu...

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Problems solved by technology

Especially for the structure containing fuzzy random variables, when its function function and probability density function are nonlinear, the convex set method often used in fuzzy reliability analysis methods is not suitable, and the obtained reliability interval is relatively fuzzy

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