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Validation of models with multivariate output

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  • Rebba, Ramesh
  • Mahadevan, Sankaran

Abstract

This paper develops metrics for validating computational models with experimental data, considering uncertainties in both. A computational model may generate multiple response quantities and the validation experiment might yield corresponding measured values. Alternatively, a single response quantity may be predicted and observed at different spatial and temporal points. Model validation in such cases involves comparison of multiple correlated quantities. Multiple univariate comparisons may give conflicting inferences. Therefore, aggregate validation metrics are developed in this paper. Both classical and Bayesian hypothesis testing are investigated for this purpose, using multivariate analysis. Since, commonly used statistical significance tests are based on normality assumptions, appropriate transformations are investigated in the case of non-normal data. The methodology is implemented to validate an empirical model for energy dissipation in lap joints under dynamic loading.

Suggested Citation

  • Rebba, Ramesh & Mahadevan, Sankaran, 2006. "Validation of models with multivariate output," Reliability Engineering and System Safety, Elsevier, vol. 91(8), pages 861-871.
    • Handle: RePEc:eee:reensy:v:91:y:2006:i:8:p:861-871
    DOI: 10.1016/j.ress.2005.09.004
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    References listed on IDEAS

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    1. Srivastava, M. S. & Hui, T. K., 1987. "On assessing multivariate normality based on shapiro-wilk W statistic," Statistics & Probability Letters, Elsevier, vol. 5(1), pages 15-18, January.
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    Cited by:

    1. Ling, You & Mahadevan, Sankaran, 2013. "Quantitative model validation techniques: New insights," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 217-231.
    2. Li, Luyi & Lu, Zhenzhou, 2018. "A new method for model validation with multivariate output," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 579-592.
    3. Ming-Na Tong & Fu-Qiang Shen & Chen-Xing Cui, 2022. "The Inverse Transformation of L-Hermite Model and Its Application in Structural Reliability Analysis," Mathematics, MDPI, vol. 10(22), pages 1-15, November.
    4. 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.
    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. Zhao, Lufeng & Lu, Zhenzhou & Yun, Wanying & Wang, Wenjin, 2017. "Validation metric based on Mahalanobis distance for models with multiple correlated responses," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 80-89.
    7. Li, Wei & Chen, Wei & Jiang, Zhen & Lu, Zhenzhou & Liu, Yu, 2014. "New validation metrics for models with multiple correlated responses," Reliability Engineering and System Safety, Elsevier, vol. 127(C), pages 1-11.
    8. Mullins, Joshua & Ling, You & Mahadevan, Sankaran & Sun, Lin & Strachan, Alejandro, 2016. "Separation of aleatory and epistemic uncertainty in probabilistic model validation," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 49-59.
    9. 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.

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