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Bayesian risk-based decision method for model validation under uncertainty

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  • Jiang, Xiaomo
  • Mahadevan, Sankaran

Abstract

This paper develops a decision-making methodology for computational model validation, considering the risk of using the current model, data support for the current model, and cost of acquiring new information to improve the model. A Bayesian decision theory-based method is developed for this purpose, using a likelihood ratio as the validation metric for model assessment. An expected risk or cost function is defined as a function of the decision costs, and the likelihood and prior of each hypothesis. The risk is minimized through correctly assigning experimental data to two decision regions based on the comparison of the likelihood ratio with a decision threshold. A Bayesian validation metric is derived based on the risk minimization criterion. Two types of validation tests are considered: pass/fail tests and system response value measurement tests. The methodology is illustrated for the validation of reliability prediction models in a tension bar and an engine blade subjected to high cycle fatigue. The proposed method can effectively integrate optimal experimental design into model validation to simultaneously reduce the cost and improve the accuracy of reliability model assessment.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:92:y:2007:i:6:p:707-718
    DOI: 10.1016/j.ress.2006.03.006
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    Citations

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    Cited by:

    1. Urbina, Angel & Mahadevan, Sankaran & Paez, Thomas L., 2011. "Quantification of margins and uncertainties of complex systems in the presence of aleatoric and epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1114-1125.
    2. Ling, You & Mahadevan, Sankaran, 2013. "Quantitative model validation techniques: New insights," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 217-231.
    3. Park, Chan Y. & Kim, Nam H. & Haftka, Raphael T., 2014. "How coupon and element tests reduce conservativeness in element failure prediction," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 123-136.
    4. 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.
    5. Sankararaman, Shankar & Mahadevan, Sankaran, 2011. "Model validation under epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1232-1241.
    6. Enrique López Droguett & Ali Mosleh, 2013. "Integrated treatment of model and parameter uncertainties through a Bayesian approach," Journal of Risk and Reliability, , vol. 227(1), pages 41-54, February.
    7. Jiang, Xiaomo & Mahadevan, Sankaran, 2009. "Bayesian structural equation modeling method for hierarchical model validation," Reliability Engineering and System Safety, Elsevier, vol. 94(4), pages 796-809.
    8. Enrique López Droguett & Ali Mosleh, 2008. "Bayesian Methodology for Model Uncertainty Using Model Performance Data," Risk Analysis, John Wiley & Sons, vol. 28(5), pages 1457-1476, October.
    9. 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.
    10. Bodda, Saran Srikanth & Gupta, Abhinav & Dinh, Nam, 2020. "Enhancement of risk informed validation framework for external hazard scenario," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    11. Sankararaman, Shankar & Mahadevan, Sankaran, 2015. "Integration of model verification, validation, and calibration for uncertainty quantification in engineering systems," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 194-209.
    12. Muhammad Zubair & Gyunyoung Heo, 2013. "Advancement in living probabilistic safety assessment to increase safety of nuclear power plants," Journal of Risk and Reliability, , vol. 227(5), pages 534-539, October.
    13. Jiang, Xiaomo & Yuan, Yong & Liu, Xian, 2013. "Bayesian inference method for stochastic damage accumulation modeling," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 126-138.
    14. Kwag, Shinyoung & Gupta, Abhinav & Dinh, Nam, 2018. "Probabilistic risk assessment based model validation method using Bayesian network," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 380-393.
    15. Teferra, Kirubel & Shields, Michael D. & Hapij, Adam & Daddazio, Raymond P., 2014. "Mapping model validation metrics to subject matter expert scores for model adequacy assessment," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 9-19.

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