Abstract
Models are frequently used to make predictions in regions where experimental testing is difficult. This often involves extrapolating to regions far from where the model was validated. In this paper an example is shown where, despite using a Bayesian analysis to quantify parameter estimation uncertainties, such an extrapolation performs poorly. It is then demonstrated that, in the presence of measurement noise, treating a system’s parameters as being time-variant (even if this is not believed to be true) can reveal fundamental flaws in a model. Finally, existing methods which can be used to quantify model error—the inevitable discrepancies that arise because of approximations made during model development—are extended towards dynamical systems.
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Notes
- 1.
The methodology described in [9] is actually more detailed than this, and also takes account of the scenario where one’s model is emulated using a Gaussian process. This is not considered in the current paper.
References
Hemez, F., Atamturktur, S., Unal, C.: Defining predictive maturity for validated numerical simulations. Comput. Struct. 88 (7), 497–505 (2010)
Atamturktur, S., Hemez, F., Williams, B., Tome, C., Unal, C.: A forecasting metric for predictive modeling. Comput. Struct. 89 (23), 2377–2387 (2011)
Jaynes, E.T.: Probability Theory: The Logic of Science. Cambridge University Press, Cambridge (2003)
Ching, J., Chen, Y.C.: Transitional Markov chain Monte Carlo method for Bayesian model updating, model class selection, and model averaging. J. Eng. Mech. 133 (7), 816–832 (2007)
Arulampalam, M.S., Maskell, S., Gordon, N., Clapp, T.: A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans. Signal Process. 50 (2), 174–188 (2002)
Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, New York (2006)
MacKay, D.J.C.: Information Theory, Inference and Learning Algorithms. Cambridge University Press, Cambridge (2003)
Ching, J., Beck, J.L., Porter, K.A.: Bayesian state and parameter estimation of uncertain dynamical systems. Probab. Eng. Mech. 21 (1), 81–96 (2006)
Kennedy, M.C., O’Hagan, A.: Bayesian calibration of computer models. J. R. Stat. Soc. Ser. B Stat. Methodol. 63 (3), 425–464 (2001)
Higdon, D., Gattiker, J., Williams, B., Rightley, M.: Computer model calibration using high-dimensional output. J. Am. Stat. Assoc. 103 (482), 570–583 (2008)
Worden, K., Manson, G., Cross, E.J.: On Gaussian process NARX models and their higher-order frequency response functions. In: Solving Computationally Expensive Engineering Problems, pp. 315–335. Springer, Cham (2014)
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© 2016 The Society for Experimental Mechanics, Inc.
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Green, P.L. (2016). Towards the Diagnosis and Simulation of Discrepancies in Dynamical Models. In: Atamturktur, S., Schoenherr, T., Moaveni, B., Papadimitriou, C. (eds) Model Validation and Uncertainty Quantification, Volume 3. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-29754-5_27
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DOI: https://doi.org/10.1007/978-3-319-29754-5_27
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