A reliability-based multidisciplinary design optimization procedure based on combined probability and evidence theory

Yao, Wen; Chen, Xiaoqian; Ouyang, Qiubao; Tooren, Michel van

doi:10.1007/s00158-013-0901-1

Cited by 62 publications

(21 citation statements)

References 47 publications

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“…To obtain engineering products with high reliability, it is indispensable and very important to quantify, control, and manage all kinds of uncertainties (Du and Chen 2000;Guo and Du 2007). For this reason, recently, reliability analysis under uncertainty has been paid a lot of attentions Jiang et al 2013;Yao et al 2013). part of all the focal elements.…”

Section: Introductionmentioning

confidence: 99%

An efficient method for reliability analysis under epistemic uncertainty based on evidence theory and support vector regression

Xiao

Gao

Xiong

et al. 2015

Journal of Engineering Design

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With a great capability of dealing with epistemic uncertainty, evidence theory has been utilised to conduct reliability analysis for engineering systems recently. Unfortunately, the discontinuous nature of uncertainty quantification using evidence theory incurs a huge computational cost. This paper proposes an efficient method to improve the computational efficiency of evidence theory for reliability analysis. In this method, evidence variables are transformed into random variables. Support vector regression is used to construct the approximation model of the limit-state function. The most probable point (MPP) of the approximate reliability problem with only random variables is searched out. Based on the MPP, the most probable focal element (MPFE) of the original problem with evidence variables is identified. According to the MPFE and the monotonicity of the limit-state function, contributions of some focal elements to belief and plausibility in evidence theory can be judged directly. Hence, the number of focal elements involved in the calculation of extreme values of the limit-state function is reduced. Four numerical examples are utilised to test the performance of the proposed method. Results indicate that the proposed method can reduce the computational cost on reliability analysis under epistemic uncertainty while ensuring the high accuracy of reliability analysis results.

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Section: Introductionmentioning

confidence: 99%

An efficient method for reliability analysis under epistemic uncertainty based on evidence theory and support vector regression

Xiao

Gao

Xiong

et al. 2015

Journal of Engineering Design

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show abstract

“…Besides, some available theories, e.g. evidence theory, probabilistic graphs, have been leveraged to address the uncertainty arising in various optimization problems (Jensen and Nielsen 2013;Jiang et al 2016a, b;Ning et al 2016;Yao et al 2013).…”

Section: Introductionmentioning

confidence: 99%

Physarum solver: a bio-inspired method for sustainable supply chain network design problem

et al. 2017

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A supplier of products and services aims to minimize the capacity investment cost and the operational cost incurred by unwanted byproducts, e.g. carbon dioxide emission. In this paper, we consider a sustainable supply chain network design problem, where the capacity and the product flow along each link are design variables. We formulate it as a multi-criteria optimization problem. A bio-inspired algorithm is developed to tackle this problem. We illustrate how to design a sustainable supply chain network in three steps. First, we develop a generalized model inspired by the foraging behaviour of slime mould Physarum polycephalum to handle the network optimization with multiple sinks. Second, we propose a strategy to update the link cost iteratively, thus making the Physarum model to converge to a user equilibrium. Third, we perform an equivalent operation to transform a system optimum problem into a corresponding user equilibrium problem so that it is solvable in the Physarum model. The efficiency of the proposed algorithm is illustrated with numerical examples.

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“…Sankararaman et al [5,6] utilized Bayesian statistics to solve the presence of incomplete information in actual design situations. Yao et al [7] presented a RBMDO procedure based on combined probability and evidence theory to solve the problem under aleatory and epistemic uncertainties. Jiang et al [8] proposed a spatial-random-process (SRP) based on multidisciplinary uncertainty analysis (MUA) method to address both aleatory and epistemic uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Reliability-Based Multidisciplinary Design Optimization under Correlated Uncertainties

Wang

et al. 2017

Mathematical Problems in Engineering

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Complex mechanical system is usually composed of several subsystems, which are often coupled with each other. Reliabilitybased multidisciplinary design optimization (RBMDO) is an efficient method to design such complex system under uncertainties. However, the present RBMDO methods ignored the correlations between uncertainties. In this paper, through combining the ellipsoidal set theory and first-order reliability method (FORM) for multidisciplinary design optimization (MDO), characteristics of correlated uncertainties are investigated. Furthermore, to improve computational efficiency, the sequential optimization and reliability assessment (SORA) strategy is utilized to obtain the optimization result. Both a mathematical example and a case study of an engineering system are provided to illustrate the feasibility and validity of the proposed method.

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A reliability-based multidisciplinary design optimization procedure based on combined probability and evidence theory

Cited by 62 publications

References 47 publications

An efficient method for reliability analysis under epistemic uncertainty based on evidence theory and support vector regression

An efficient method for reliability analysis under epistemic uncertainty based on evidence theory and support vector regression

Physarum solver: a bio-inspired method for sustainable supply chain network design problem

Reliability-Based Multidisciplinary Design Optimization under Correlated Uncertainties

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