Hybrid probabilistic fuzzy and non-probabilistic model of structural reliability

Ni, Zao; Qiu, Zhiping

doi:10.1016/j.cie.2009.11.005

Cited by 39 publications

(21 citation statements)

References 18 publications

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“…The interval parameters i Y , i=1,2,…,m can be described as the following equations: In the limit state function Z , the random variables as well as interval variables are included. The random (3) he availability engineering ables may not ation. These in other words, ic and interval oblems.…”

Section: Probability-interval Hybrid Reliabi-lity Theorymentioning

confidence: 99%

“…Fig. 4 Reliability index of the HU reliabilit , j=1, 2, ..., m, where σ Xi is the standard deviation of X i and Y j r is the radius of Y j , κ x and κ y are two sampling coefficients and generally between [1,3] can provide good computational results.…”

Section: Neural Networkmentioning

confidence: 99%

“…In the training process, training samples for neural network is important. This paper uses the improved axial experimental design method [31] to obtain samples points of X and Y, the initial sample point is selected as (μ X , Y C ),where μ X is the mean vector of the random variables X and Y C is the midpoint vector of the interval variables Y, the samples of input variables will be updated in subsequent iterations, the remaining 2n+2m samples points will be obtained through κ and y κ are two sampling coefficients and generally between [1,3] can provide…”

Section: Reliability Analysis Based Hu-bp Neural Networkmentioning

confidence: 99%

“…These variables are known with certain intervals, in other words, the hybrid uncertain model with probabilistic and interval widely exists in the practical engineering problems. Some researches make some assumptions for random distributions when using probability approach to perform the reliability analysis [1][2][3], and these methods bring a problem of confidence. Other techniques [4][5][6][7][8] also are proposed to deal with this problem.…”

Section: Introductionmentioning

confidence: 99%

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The hybrid uncertain neural network method for mechanical reliability analysis

Peng¹,

Zhang²,

You³

2015

International Journal of Aeronautical and Space Sciences

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Concerning the issue of high-dimensions, hybrid uncertainties of randomness and intervals including implicit and highly nonlinear limit state function, reliability analysis based on the hybrid uncertainty reliability mode combining with back propagation neural network (HU-BP neural network) is proposed in this paper. Random variables and interval variables are as input layer of the neural network, after the training and approximation of the neural network, the response variables are obtained through the output layer. Reliability index is calculated by solving the optimization model of the most probable point (MPP) searching in the limit state band. Two numerical cases are used to demonstrate the method proposed in this paper, and finally the method is employed to solving an engineering problem of the aerospace friction plate. For this high nonlinear, small failure probability problem with interval variables, this method could achieve a good analysis result.

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Section: Probability-interval Hybrid Reliabi-lity Theorymentioning

confidence: 99%

Section: Neural Networkmentioning

confidence: 99%

Section: Reliability Analysis Based Hu-bp Neural Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The hybrid uncertain neural network method for mechanical reliability analysis

Peng¹,

Zhang²,

You³

2015

International Journal of Aeronautical and Space Sciences

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“…An et al [35] presented a new hybrid reliability index and its solving method based on random-fuzzy-interval model. Ni et al [36] established a new hybrid reliability model which contains randomness, fuzziness, and nonprobabilistic uncertainties based on the structural fuzzy random reliability and nonprobabilistic setbased models. Wang et al [37] proposed a new reliability analysis method based on convex models for uncertain structures which may contain randomness, fuzziness, and nonprobabilistic uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Discretization Analysis Method of Hybrid Reliability Based on Evidence Theory

Tang

2018

Mathematical Problems in Engineering

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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.

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Fuzzy interval perturbation method for uncertain heat conduction problem with interval and fuzzy parameters

Wang

Qiu

2015

Int. J. Numer. Meth. Engng

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SUMMARYThis paper proposes a fuzzy interval perturbation method (FIPM) and a modified fuzzy interval perturbation method (MFIPM) for the hybrid uncertain temperature field prediction involving both interval and fuzzy parameters in material properties and boundary conditions. Interval variables are used to quantify the non-probabilistic uncertainty with limited information, whereas fuzzy variables are used to represent the uncertainty associated with the expert opinions. The level-cut method is introduced to decompose the fuzzy parameters into interval variables. FIPM approximates the interval matrix inverse by the first-order Neumann series, while MFIPM improves the accuracy by considering higher-order terms of the Neumann series. The membership functions of the interval temperature field are eventually derived using the fuzzy decomposition theorem. Three numerical examples are provided to demonstrate the feasibility and effectiveness of the proposed methods for solving heat conduction problems with hybrid uncertain parameters, pure interval parameters, and pure fuzzy parameters, respectively.

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Hybrid probabilistic fuzzy and non-probabilistic model of structural reliability

Cited by 39 publications

References 18 publications

The hybrid uncertain neural network method for mechanical reliability analysis

The hybrid uncertain neural network method for mechanical reliability analysis

Discretization Analysis Method of Hybrid Reliability Based on Evidence Theory

Fuzzy interval perturbation method for uncertain heat conduction problem with interval and fuzzy parameters

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