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Evidence-based quantification of uncertainties induced via simulation-based modeling

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  • Riley, Matthew E.

Abstract

The quantification of uncertainties in simulation-based modeling traditionally focuses upon quantifying uncertainties in the parameters input into the model, referred to as parametric uncertainties. Often neglected in such an approach are the uncertainties induced by the modeling process itself. This deficiency is often due to a lack of information regarding the problem or the models considered, which could theoretically be reduced through the introduction of additional data. Because of the nature of this epistemic uncertainty, traditional probabilistic frameworks utilized for the quantification of uncertainties are not necessarily applicable to quantify the uncertainties induced in the modeling process itself. This work develops and utilizes a methodology – incorporating aspects of Dempster–Shafer Theory and Bayesian model averaging – to quantify uncertainties of all forms for simulation-based modeling problems. The approach expands upon classical parametric uncertainty approaches, allowing for the quantification of modeling-induced uncertainties as well, ultimately providing bounds on classical probability without the loss of epistemic generality. The approach is demonstrated on two different simulation-based modeling problems: the computation of the natural frequency of a simple two degree of freedom non-linear spring mass system and the calculation of the flutter velocity coefficient for the AGARD 445.6 wing given a subset of commercially available modeling choices.

Suggested Citation

  • Riley, Matthew E., 2015. "Evidence-based quantification of uncertainties induced via simulation-based modeling," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 79-86.
  • Handle: RePEc:eee:reensy:v:133:y:2015:i:c:p:79-86
    DOI: 10.1016/j.ress.2014.08.016
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    References listed on IDEAS

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    1. Eldred, M.S. & Swiler, L.P. & Tang, G., 2011. "Mixed aleatory-epistemic uncertainty quantification with stochastic expansions and optimization-based interval estimation," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1092-1113.
    2. He, Ji-Huan, 2007. "Variational approach for nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1430-1439.
    3. Park, Inseok & Amarchinta, Hemanth K. & Grandhi, Ramana V., 2010. "A Bayesian approach for quantification of model uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 95(7), pages 777-785.
    4. Marc C. Kennedy & Anthony O'Hagan, 2001. "Bayesian calibration of computer models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 425-464.
    5. Helton, Jon C., 2011. "Quantification of margins and uncertainties: Conceptual and computational basis," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 976-1013.
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    1. Liu, Di & Wang, Shaoping & Zhang, Chao & Tomovic, Mileta, 2018. "Bayesian model averaging based reliability analysis method for monotonic degradation dataset based on inverse Gaussian process and Gamma process," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 25-38.

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