Research Papers

Bayesian Uncertainty Integration for Model Calibration, Validation, and Prediction

[+] Author and Article Information
Joshua Mullins

Department of Civil and
Environmental Engineering,
Vanderbilt University,
Nashville, TN 37235
e-mail: joshua.g.mullins@vanderbilt.edu

Sankaran Mahadevan

Department of Civil and
Environmental Engineering,
Vanderbilt University,
Nashville, TN 37235

Manuscript received February 25, 2015; final manuscript received December 22, 2015; published online February 19, 2016. Guest Editor: Kenneth Hu.

J. Verif. Valid. Uncert 1(1), 011006 (Feb 19, 2016) (10 pages) Paper No: VVUQ-15-1014; doi: 10.1115/1.4032371 History: Received February 25, 2015; Revised December 22, 2015

This paper proposes a comprehensive approach to prediction under uncertainty by application to the Sandia National Laboratories verification and validation challenge problem. In this problem, legacy data and experimental measurements of different levels of fidelity and complexity (e.g., coupon tests, material and fluid characterizations, and full system tests/measurements) compose a hierarchy of information where fewer observations are available at higher levels of system complexity. This paper applies a Bayesian methodology in order to incorporate information at different levels of the hierarchy and include the impact of sparse data in the prediction uncertainty for the system of interest. Since separation of aleatory and epistemic uncertainty sources is a pervasive issue in calibration and validation, maintaining this separation in order to perform these activities correctly is the primary focus of this paper. Toward this goal, a Johnson distribution family approach to calibration is proposed in order to enable epistemic and aleatory uncertainty to be separated in the posterior parameter distributions. The model reliability metric approach to validation is then applied, and a novel method of handling combined aleatory and epistemic uncertainty is introduced. The quality of the validation assessment is used to modify the parameter uncertainty and add conservatism to the prediction of interest. Finally, this prediction with its associated uncertainty is used to assess system-level reliability (a prediction goal for the challenge problem).

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Fig. 1

Combined aleatory and epistemic uncertainty represented as a family of distributions and as an unconditional density

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Fig. 2

For ϵ=2, the model reliability for the closely matching distributions Yd and Ym (r=0.86) is lower than for the deterministic observation with no measurement noise and the same distribution of Ym (r=0.95) because the probability of large bias between the uncertain deterministic prediction and observation is greater when there is more uncertainty

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Fig. 3

Idealized diagram of the tanks [28]

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Fig. 4

Diagram of workflow and data usage for the proposed solution strategy

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Fig. 5

Results of model parameter calibration

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Fig. 6

Sample computations of model reliability in the presence of combined aleatory and epistemic uncertainty. For this particular tank prediction, r=0 for X=0 and ψ=30 (left) and r=0.98 for X=0 and ψ=90 (right).

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Fig. 7

Spatial variation of model reliability averaged across four tank predictions

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Fig. 8

Expansion of parameter uncertainty to account for model form error and insufficient variability information

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Fig. 9

Reliability assessment based on the distributions of maximum predicted stress and material yield stress




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