RESEARCH PAPERS: Experimental Techniques

Model Validation: Model Parameter and Measurement Uncertainty

[+] Author and Article Information
Richard G. Hills

Department of Mechanical Engineering,  New Mexico State University, Las Cruces, NM 88003rhills@nmsu.edu

J. Heat Transfer 128(4), 339-351 (Oct 17, 2005) (13 pages) doi:10.1115/1.2164849 History: Received April 22, 2004; Revised October 17, 2005

Our increased dependence on complex models for engineering design, coupled with our decreased dependence on experimental observation, leads to the question: How does one know that a model is valid? As models become more complex (i.e., multiphysics models), the ability to test models over the full range of possible applications becomes more difficult. This difficulty is compounded by the uncertainty that is invariably present in the experimental data used to test the model; the uncertainties in the parameters that are incorporated into the model; and the uncertainties in the model structure itself. Here, the issues associated with model validation are discussed and methodology is presented to incorporate measurement and model parameter uncertainty in a metric for model validation through a weighted r2 norm. The methodology is based on first-order sensitivity analysis coupled with the use of statistical models for uncertainty. The result of this methodology is compared to results obtained from the more computationally expensive Monte Carlo method. The methodology was demonstrated for the nonlinear Burgers’ equation, the convective-dispersive equation, and for conduction heat transfer with contact resistance. Simulated experimental data was used for the first two cases, and true experimental data was used for the third. The results from the sensitivity analysis approach compared well with those for the Monte Carlo method. The results show that the metric presented can discriminate between valid and invalid models. The metric has the advantage that it can be applied to multivariate, correlated data.

Copyright © 2006 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 1

Experimental observations and model predictions

Grahic Jump Location
Figure 2

Uncertainty in the measurements and the model predictions

Grahic Jump Location
Figure 3

Combined uncertainty

Grahic Jump Location
Figure 4

Simulated experimental measurements; X_mean– prediction based on mean model parameters; X_exp_1, X_exp_2– simulated experimental data for realizations 1 and 2, respectively

Grahic Jump Location
Figure 5

PDF quantiles for front location at various times; 25%, 50%, 75%, 95% quantiles; sensitivity analysis represent by dashed lines; Monte Carlo analysis represented by solid lines; X_exp_1 and X_exp_2 measurements indicated by a circle and square respectively

Grahic Jump Location
Figure 6

Calibrated convective dispersion equation; X_exp_cal, X_exp_val – simulated experimental data used for calibration and validation respectively; X_exp_2 – experiment 2 simulated data; X_cal – calibrated model

Grahic Jump Location
Figure 7

Heat conduction apparatus and computational domain




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In