The reliability analysis of probabilistic and interval hybrid structural system

Wang, Jun; Qiu, Zhiping

doi:10.1016/j.apm.2010.03.015

Cited by 58 publications

(17 citation statements)

References 19 publications

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“…The former can be treated as random variables and given precise probability distribution functions; while the latter can only be given intervals since lacking sufficient information. So far some work (Penmetsa and Grandhi 2002;Guo and Lu 2002;Cheng et al 2005;Du 2007;Luo et al 2008;Wang and Qiu 2010;Fang et al 2014;Alibrandi and Koh 2015;Guo and Du 2009) has been carried out for this uncertain model. (Penmetsa and Grandhi 2002) developed a probability-interval hybrid reliability assessment method based on an approximate model.…”

Section: Introductionmentioning

confidence: 99%

“…(Luo et al 2008) used a quantified measure for the non-probabilistic reliability based on the multi-ellipsoid convex model. (Wang and Qiu 2010) evaluated the reliability of the probability and interval mixed uncertain structural system and established the mathematical model of reliability analysis. (Alibrandi and Koh 2015) presented a novel procedure based on FORM; and the probability-interval hybrid reliability problem was decoupled to several reliability problems in which the limit state functions were defined only in terms of the random variables.…”

Section: Introductionmentioning

confidence: 99%

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Reliability-based design optimization for problems with interval distribution parameters

Huang

Zhou

Zheng

et al. 2016

Struct Multidisc Optim

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Traditional reliability-based design optimization (RBDO) generally describes uncertain variables using random distributions, while some crucial distribution parameters in practical engineering problems can only be given intervals rather than precise values due to the limited information. Then, an important probability-interval hybrid reliability problem emerged. For uncertain problems in which interval variables are included in probability distribution functions of the random parameters, this paper establishes a hybrid reliability optimization design model and the corresponding efficient decoupling algorithm, which aims to provide an effective computational tool for reliability design of many complex structures. The reliability of an inner constraint is an interval since the interval distribution parameters are involved; this paper thus establishes the probability constraint using the lower bound of the reliability degree which ensures a safety design of the structure. An approximate reliability analysis method is given to avoid the time-consuming multivariable optimization of the inner hybrid reliability analysis. By using an incremental shifting vector (ISV) technique, the nested optimization problem involved in RBDO is converted into an efficient sequential iterative process of the deterministic design optimization and the hybrid reliability analysis. Three numerical examples are presented to verify the proposed method, which include one simple problem with explicit expression and two complex practical applications.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reliability-based design optimization for problems with interval distribution parameters

Huang

Zhou

Zheng

et al. 2016

Struct Multidisc Optim

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“…These in other words, ic and interval oblems. Some for random ach to perform thods bring a [4][5][6][7][8] also are ure [8] analyze ough a twoesign method ability is also ore studies on val can refer model above ion. However, are implicit.…”

Section: Probability-interval Hybrid Reliabi-lity Theorymentioning

confidence: 99%

“…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. Literature [8] analyze the hybrid reliability of linear problems through a two-stage limit state function.…”

Section: Introductionmentioning

confidence: 99%

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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“…Qiu et al [30] investigated the reliability analysis problems of random-interval structural system based on the combination of the classical reliability theory and the interval analysis. Wang et al [31] evaluated the reliability of a probabilistic and interval hybrid structural system based on the interval reliability model and probabilistic operation. Mourelatos et al [32] proposed an efficient reliability-based design optimization (RBDO) method based on ET to handle a mixture of aleatory and epistemic 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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The reliability analysis of probabilistic and interval hybrid structural system

Cited by 58 publications

References 19 publications

Reliability-based design optimization for problems with interval distribution parameters

Reliability-based design optimization for problems with interval distribution parameters

The hybrid uncertain neural network method for mechanical reliability analysis

Discretization Analysis Method of Hybrid Reliability Based on Evidence Theory

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