Improved Grey Relational Analysis for Model Validation

  • Ke FangEmail author
  • Yuchen Zhou
  • Ju Huo
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1094)


GRA (Grey Relational Analysis) is a typical time series similarity analysis method. However in model validation, it cannot satisfy the feature of monotonicity, and the result is lack of precision. Based on several similarity measurement criteria of time series data, traditional GRA method is developed and modified to satisfy normalization, symmetry and monotonicity. Case study shows that, improved GRA can produce a better similarity analysis result, which is in accordance with the result of TIC (Theil’s Inequality Coefficient).


Improved grey relational analysis Model validation Similarity analysis Monotonicity TIC 


  1. 1.
    Mullins, J., Ling, Y., Mahadevan, S., et al.: Separation of aleatory and epistemic uncertainty in probabilistic model validation. Reliab. Eng. Syst. Saf. 147, 49–59 (2016)CrossRefGoogle Scholar
  2. 2.
    Ling, Y., Mahadevan, S.: Quantitative model validation techniques: new insights. Reliab. Eng. Syst. Saf. 111, 217–231 (2013)CrossRefGoogle Scholar
  3. 3.
    Jiang, X., Mahadevan, S.: Wavelet spectrum analysis approach to model validation of dynamic systems. Mech. Syst. Signal Process. 25(2), 575–590 (2011)CrossRefGoogle Scholar
  4. 4.
    Liu, W., Hong, L., Qi, Z.: Model validation method of radar signal model based on spectrum estimation. Microcomput. Inf. 28(5), 161–163 (2012)Google Scholar
  5. 5.
    Min, F., Yang, M., Wang, Z.: Knowledge-based method for the validation of complex simulation models. Simul. Model. Pract. Theory 18(5), 500–515 (2010)CrossRefGoogle Scholar
  6. 6.
    Ahn, J., Weck, O., Steele, M.: Credibility assessment of models and simulations based on NASA’s models and simulation standard using the Delphi method. Syst. Eng. 17(2), 237–248 (2014)CrossRefGoogle Scholar
  7. 7.
    Crochemore, L., Perrin, C., Andreassian, V., et al.: Comparing expert judgement and numerical criteria for hydrograph evaluation. Hydrol. Sci. J. 60(3), 402–423 (2015)CrossRefGoogle Scholar
  8. 8.
    Hauduc, H., Neumann, M.B., Muschalla, D., et al.: Efficiency criteria for environmental model quality assessment: a review and its application to wastewater treatment. Environ. Model. Softw. 68, 196–204 (2015)CrossRefGoogle Scholar
  9. 9.
    Consonni, V., Ballabio, D., Todeschini, R.: Evaluation of model predictive ability by external validation techniques. J. Chemom. 24, 194–201 (2010)CrossRefGoogle Scholar
  10. 10.
    Kheir, N.A., Holmes, W.M.: On validating simulation models of missile systems. Simulation 30(4), 117–128 (1978)CrossRefGoogle Scholar
  11. 11.
    Dorobantu, A., Balas, G.J., Georgiou, T.T.: Validating aircraft models in the gap metric. J. Aircr. 51(6), 1665–1672 (2014)CrossRefGoogle Scholar
  12. 12.
    Zhou, Y., Fang, K., Ma, P., Yang, M.: Complex simulation model validation method based on ensemble learning. Syst. Eng. Electron. 40(9), 2124–2130 (2018)Google Scholar
  13. 13.
    Wei, H., Li, Z.: Grey relational analysis and its application to the validation of computet simulation models for missile systems. Syst. Eng. Electron. 2, 55–61 (1997)Google Scholar
  14. 14.
    Ning, X.L., Wu, Y.X., Yu, T.P., et al.: Research on comprehensive validation of simulation models based on improved grey relational analysis. Acta Armamentarii 37(3), 338–347 (2016)Google Scholar
  15. 15.
    Ma, P., Zhou, Y., Shang, X., Yang, M.: Firing accuracy evaluation of electromagnetic railgun based on multicriteria optimal Latin Hypercube design. IEEE Trans. Plasma Sci. 45(7), 1503–1511 (2017)CrossRefGoogle Scholar
  16. 16.
    Hundertmark, S., Lancelle, D.: A scenario for a future European shipboard railgun. IEEE Trans. Plasma Sci. 43(5), 1194–1197 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Harbin Institute of TechnologyHarbinChina

Personalised recommendations