Quantification of margins and mixed uncertainties using evidence theory and stochastic expansions

Shah, Harsheel R.; Hosder, Serhat; Winter, Tyler

doi:10.1016/j.ress.2015.01.012

Cited by 43 publications

(5 citation statements)

References 55 publications

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“…Polynomial chaos expansion is a powerful technique to provide a functional approximation of a computational model through its spectral representation on a suitably built basis of polynomial function [46][47][48][49]. Consider a random vector n XR  with independent components, the polynomial chaos expansion of () M X is defined as: Theoretically, the number of terms of polynomial chaos expansion should be infinite [30,50]. It is straightforward to define a "standard truncation scheme" given as:…”

Section: Two-phase Mcs/nipc Methods For Mixed Uncertainty Quantificmentioning

confidence: 99%

“…Based on the characterization of uncertainty in system performance boundaries, the quantification of margins and uncertainties (QMU) have been used as one of the tools to facilitate analysis and communication of confidence for certification of complex systems [30]. An accurate QMU is crucial for the analysis of aeroelastic system which is highdemanding in performance requirement, and the uncertainty propagation process plays an important role in the procedures of the QMU.…”

Section: Introductionmentioning

confidence: 99%

“…Thomas et al [38] presented a practical QMU for complex spacecraft systems in which uncertainty exists in both the operating region and the performance requirement. Harsheel et al [30] implemented Dempster-Shafer Theory of Evidence in the presence of mixed uncertainties in the reliability and performance assessment of complex engineering systems through the use of the QMU methodology. Xie et al [39] proposed to use the QMU for simulation-based structural analysis of a pressure vessel with corrosion damage.…”

Section: Introductionmentioning

confidence: 99%

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A Two-Phase Monte Carlo Simulation/Non-Intrusive Polynomial Chaos (MSC/NIPC) Method for Quantification of Margins and Mixed Uncertainties (QMMU) in Flutter Analysis

Zhang

Yang

2020

IEEE Access

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A two-phase Monte Carlo Simulation/Non-intrusive Polynomial Chaos (MCS/NIPC) method for quantification of margins and mixed uncertainties (aleatory and epistemic uncertainties) is proposed in this paper for the flutter speed boundary analysis. Compared with the traditional MCS/MCS method which needs lots of numerical simulations, the MCS/NIPC method can reduce the computational cost without losing accuracy due to the use of point collocation non-intrusive polynomial chaos in the inner loop. Based on the results of uncertainty quantification, a novel practical quantification of margins and mixed uncertainties (QMMU) framework is proposed considering both aleatory and epistemic uncertainties such as the parametric uncertainties in complicated models. A two-dimensional airfoil and a three-dimensional benchmark wing, the AGARD 445.6 wing, are both employed to illustrate the practical application of the proposed methods for flutter speed computation in the presence of mixed uncertainties arising from the material properties and flight conditions. Within the analysis, aleatory and mixed uncertainty quantification are conducted to prove the effectiveness and efficiency of the MCS/NIPC method. Then the QMMU metrics are accomplished for the flutter speed boundary analysis of the two airfoil models. The results demonstrate the potential of the proposed QMMU framework to analyze the stability of engineering systems. INDEX TERMS Flutter, non-intrusive polynomial chaos, probability bounds, quantification of margins and mixed uncertainties, uncertainty quantification

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Section: Two-phase Mcs/nipc Methods For Mixed Uncertainty Quantificmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Two-Phase Monte Carlo Simulation/Non-Intrusive Polynomial Chaos (MSC/NIPC) Method for Quantification of Margins and Mixed Uncertainties (QMMU) in Flutter Analysis

Zhang

Yang

2020

IEEE Access

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“…Researchers such as Du et al [11] transformed random variables into fuzzy variables according to the principle of probability possibility consistency and the most conservative condition. Shah et al [12] used evidence theory and random expansion method to study the uncertainty of implicit state when random variables and interval variables exist at the same time. While, "analysis type" refers to the analysis of system reliability by different uncertainty quantification theories without any transformation for the mixed uncertainties.…”

Section: Introductionmentioning

confidence: 99%

A Decoupling Strategy for Reliability Analysis of Multidisciplinary System with Aleatory and Epistemic Uncertainties

Liu

2021

Applied Sciences

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In reliability-based multidisciplinary design optimization, both aleatory and epistemic uncertainties may exist in multidisciplinary systems simultaneously. The uncertainty propagation through coupled subsystems makes multidisciplinary reliability analysis computationally expensive. In order to improve the efficiency of multidisciplinary reliability analysis under aleatory and epistemic uncertainties, a comprehensive reliability index that has clear geometric meaning under multisource uncertainties is proposed. Based on the comprehensive reliability index, a sequential multidisciplinary reliability analysis method is presented. The method provides a decoupling strategy based on performance measure approach (PMA), probability theory and convex model. In this strategy, the probabilistic analysis and convex analysis are decoupled from each other and performed sequentially. The probabilistic reliability analysis is implemented sequentially based on the concurrent subspace optimization (CSSO) and PMA, and the non-probabilistic reliability analysis is replaced by convex model extreme value analysis, which improves the efficiency of multidisciplinary reliability analysis with aleatory and epistemic uncertainties. A mathematical example and an engineering application are demonstrated to verify the effectiveness of the proposed method.

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“…The uncertainty resulted from the lack of knowledge or imperfect of information is called epistemic uncertainty. Various theories have been introduced to deal with epistemic uncertainty, including probability-box [13] [15], interval theory [16], [17] possibility theory [18], fuzzy set theory [19], [20], [21] Bayesian method [22], Dempster-Shafer evidence theory [23], [24], [25] etc. The fuzzy set theory has been intensively implemented in the reliability engineering as it can be constructed on the basis of expert vague attitudes/judgements rather than a large amount of objective information.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Reliability Assessment of Safety Instrumented Systems Accounting for Common Cause Failure

Zhao

2020

IEEE Access

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Reliability of safety instrumented systems (SISs) is a critical measure to ensure production safety of many industries. This paper focus on low-demand SISs. The reliability of these SISs is quantified by evaluating their probability of failure on demand (PFD). However, due to lack of knowledge, and/or vague judgments from experts, epistemic uncertainty associated with the parameters of components' degradation models is inevitable. Meanwhile, common cause failure (CCF) of two or more components caused by shared environments, often exists in SISs, reliability assessment for a SIS, therefore, becomes a challenging task. In this paper, fuzzy reliability assessment for SISs is conducted by taking account of the CCF among components of a SIS. The fuzzy Markov model is utilized to characterize the degradation process of components under fuzzy environment. The fuzzy state probability distribution of components is, then, calculated by formulating a set of constrained optimization models. Based on the fault tree of a SIS, the fuzzy PFD of the entire SIS with CCFs is formulated by using the  -factor to quantify the CCFs. The fuzzy PFD at any  -cut level is, therefore, computed by a constrained optimization model. According to the optimization of parameters of SIS, the lower bound and upper bound of fuzzy PFD of SIS can be determined. Finally, we can quantify the effectiveness of CCF event for assessing the fuzzy PFD of SIS.

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Quantification of margins and mixed uncertainties using evidence theory and stochastic expansions

Cited by 43 publications

References 55 publications

A Two-Phase Monte Carlo Simulation/Non-Intrusive Polynomial Chaos (MSC/NIPC) Method for Quantification of Margins and Mixed Uncertainties (QMMU) in Flutter Analysis

A Two-Phase Monte Carlo Simulation/Non-Intrusive Polynomial Chaos (MSC/NIPC) Method for Quantification of Margins and Mixed Uncertainties (QMMU) in Flutter Analysis

A Decoupling Strategy for Reliability Analysis of Multidisciplinary System with Aleatory and Epistemic Uncertainties

Fuzzy Reliability Assessment of Safety Instrumented Systems Accounting for Common Cause Failure

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