Abstract
This study is focused on a novel approach for calculating structural fuzzy reliability by using the classical reliability theory. In order to handle the structural fuzzy reliability problem, the formulae for establishing normal random variables equivalent to symmetric triangular fuzzy number are presented. From these equivalent random ones, the original problem is converted to the basic structural reliability problems, then the methods of the classical reliability theory should be applied to calculate. Moreover, this study proposes two notions in terms of central fuzzy reliability and standard deviation of fuzzy reliability as well as a calculation procedure to define them. Lastly, the ultimate fuzzy reliability of the proposed method is established and utilized to compare the allowable reliability in the design codes. Numerical results are supervised to verify the accuracy of the proposed method.
Highlights
In engineering structures, most of the input data, such as load characteristics, material properties, boundary conditions, geometric dimensions, load-carrying capacities, contain non-deterministic quantities, which are described as uncertainty variables
The terminologies are named the fuzzy reliability later.This fuzzy reliability can be classified into three classes: the resistance function R and the load effect S are fuzzy numbers, the resistance R is a random parameter and the load effect S is a fuzzy number, the resistance R is a fuzzy number and the load effect S is a random parameter
For the transformation from standardized symmetric triangular fuzzy number (Fig. 4) into random quantity, the error of probability measure between equivalent probability density function p(x) of standardized symmetric triangular fuzzy number got by the principle of insufficient reason and normal random variable p1(x) is expressed by the following formula (P(A)-P1(A))2 → min ∀x ∈[-1,0)
Summary
Most of the input data, such as load characteristics, material properties, boundary conditions, geometric dimensions, load-carrying capacities, contain non-deterministic quantities, which are described as uncertainty variables. We only consider that the epistemic ones are represented as fuzzy numbers, which are always interested in the reality problems In this case, the structural reliability had the different names, such as the safety possibility of structures [6], the fuzzy reliability index [7, 8], the fuzzy reliability [9, 10, 11]. The terminologies are named the fuzzy reliability later.This fuzzy reliability can be classified into three classes: the resistance function R and the load effect S are fuzzy numbers, the resistance R is a random parameter and the load effect S is a fuzzy number, the resistance R is a fuzzy number and the load effect S is a random parameter These approaches [5÷12] for the fuzzy reliability are detailed analyzed below
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