Numerical Method for Fuzzy Reliability Analysis

Tang, Zhangchun; Lü, Zhenzhou; Xia, Yanjun

doi:10.2514/1.c031817

Cited by 11 publications

(4 citation statements)

References 17 publications

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“…In this study, 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.…”

Section: Introductionmentioning

confidence: 99%

“…Figure 2: The method [6,7] where μM(x) is the membership function of fuzzy number MF igure 3: The interference model [10,11] The formula ( 5) is approriate for the geometrical definition of probabiliy in [16]. Nevertheless, it should be realized that the membership functions in the fuzzy sets theory and the density distribution functions in the probability theory are not equivalent representations of uncertainty.…”

Section: Introductionmentioning

confidence: 99%

“…In order to overcome this drawback, Jiang and Chen [10] supposed that the α-cuts of a fuzzy number were the linear distributions, then computed the conventional probability at various α-cuts and the fuzzy reliability was the average of the reliabilities at the α-cuts. Tang et al [11] also utilized this assumption and computed the fuzzy failure probability by applying the Gauss-Legendre quadrature formula. However, it should be seen that different distribution assumptions of the α-cuts lead to totally different fuzzy reliability results.…”

Section: Introductionmentioning

confidence: 99%

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Structural fuzzy reliability analysis using the classical reliability theory

Nguyen¹,

Le²

2021

J Appl Eng Science

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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 formulas 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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Structural fuzzy reliability analysis using the classical reliability theory

Nguyen¹,

Le²

2021

J Appl Eng Science

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“…For the structure with randomness and fuzziness, an effective method for determining the membership function was established by constructing the membership function, and a structural fuzzy reliability analysis method for fuzzy security state was proposed. Tang et al [15] proposed an effective numerical estimation method for fuzzy failure probability based on mathematical transformation from fuzzy probability to random probability. Li et al [16] uniformly distributed the membership degrees of different fuzzy variables as independent criteria and proposed a new fuzzy reliability model to measure the security of fuzzy variable structures.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Reliability Analysis With Fuzzy Random Variables Based on Perturbation Principle

Nie

2019

IEEE Access

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In structural reliability calculation, there are fuzzy uncertainties in the distribution parameters of random variables, which bring the problem of large computation and poor precision. In order to improve accuracy and efficiency of structural reliability, a novel structural reliability calculation method with fuzzy random variables is proposed from the perspective of perturbation principle. First, the fuzzy characteristic parameters of the structural fuzzy random variables are expressed as the sums of their true values and fuzzy perturbations. At the same time, the perturbations are equivalently selected. Second, the probability density function and the performance function are decomposed into a series of intervals under different level cut sets, and the Taylor series is expanded on the upper and lower limits of the intervals. Finally, according to the definition of structural reliability, based on the direct integration method, the sigmoid function is introduced into the reliability function to approximate the step function, and the fuzzy reliability is obtained. The simulation results show the effectiveness and accuracy of the proposed method, and it provides a feasible way for structural reliability analysis with fuzzy variables or fuzzy random variables. INDEX TERMS Fuzzy reliability, fuzzy random variable, perturbation principle, direct integration method.

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