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Quantitative model validation techniques: New insights

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  • Ling, You
  • Mahadevan, Sankaran

Abstract

This paper develops new insights into quantitative methods for the validation of computational model prediction. Four types of methods are investigated, namely classical and Bayesian hypothesis testing, a reliability-based method, and an area metric-based method. Traditional Bayesian hypothesis testing is extended based on interval hypotheses on distribution parameters and equality hypotheses on probability distributions, in order to validate models with deterministic/stochastic output for given inputs. Formulations and implementation details are outlined for both equality and interval hypotheses. Two types of validation experiments are considered—fully characterized (all the model/experimental inputs are measured and reported as point values) and partially characterized (some of the model/experimental inputs are not measured or are reported as intervals). Bayesian hypothesis testing can minimize the risk in model selection by properly choosing the model acceptance threshold, and its results can be used in model averaging to avoid Type I /II errors. It is shown that Bayesian interval hypothesis testing, the reliability-based method, and the area metric-based method can account for the existence of directional bias, where the mean predictions of a numerical model may be consistently below or above the corresponding experimental observations. It is also found that under some specific conditions, the Bayes factor metric in Bayesian equality hypothesis testing and the reliability-based metric can both be mathematically related to the p-value metric in classical hypothesis testing. Numerical studies are conducted to apply the above validation methods to gas damping prediction for radio frequency (RF) micro-electro-mechanical-system (MEMS) switches. The model of interest is a general polynomial chaos (gPC) surrogate model constructed based on expensive runs of a physics-based simulation model, and validation data are collected from fully characterized experiments.

Suggested Citation

  • Ling, You & Mahadevan, Sankaran, 2013. "Quantitative model validation techniques: New insights," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 217-231.
  • Handle: RePEc:eee:reensy:v:111:y:2013:i:c:p:217-231
    DOI: 10.1016/j.ress.2012.11.011
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    References listed on IDEAS

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    1. Rebba, Ramesh & Mahadevan, Sankaran, 2006. "Validation of models with multivariate output," Reliability Engineering and System Safety, Elsevier, vol. 91(8), pages 861-871.
    2. Rebba, Ramesh & Mahadevan, Sankaran, 2008. "Computational methods for model reliability assessment," Reliability Engineering and System Safety, Elsevier, vol. 93(8), pages 1197-1207.
    3. Sankararaman, Shankar & Mahadevan, Sankaran, 2011. "Likelihood-based representation of epistemic uncertainty due to sparse point data and/or interval data," Reliability Engineering and System Safety, Elsevier, vol. 96(7), pages 814-824.
    4. Rebba, Ramesh & Mahadevan, Sankaran & Huang, Shuping, 2006. "Validation and error estimation of computational models," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1390-1397.
    5. Jiang, Xiaomo & Mahadevan, Sankaran, 2007. "Bayesian risk-based decision method for model validation under uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 707-718.
    6. Scott Ferson & William L. Oberkampf, 2009. "Validation of imprecise probability models," International Journal of Reliability and Safety, Inderscience Enterprises Ltd, vol. 3(1/2/3), pages 3-22.
    7. Sankararaman, Shankar & Mahadevan, Sankaran, 2011. "Model validation under epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1232-1241.
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    4. An, Dawn & Kim, Nam H. & Choi, Joo-Ho, 2015. "Practical options for selecting data-driven or physics-based prognostics algorithms with reviews," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 223-236.
    5. Ao, Dan & Hu, Zhen & Mahadevan, Sankaran, 2017. "Design of validation experiments for life prediction models," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 22-33.
    6. Wang, Chong & Matthies, Hermann G., 2019. "Novel model calibration method via non-probabilistic interval characterization and Bayesian theory," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 84-92.
    7. McKeand, Austin M. & Gorguluarslan, Recep M. & Choi, Seung-Kyum, 2021. "Stochastic analysis and validation under aleatory and epistemic uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 205(C).

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