Model completion and validation using inversion of grey box models

Abstract

A grey box model uses some theoretical structure that is not complete and it is thus necessary to complete the model using data. Unfortunately, as the models are generally nonlinear, the efficient linear methods of selecting regression terms were not available for the completion of these models. However, the method of model inversion converts the unknown parts within a nonlinear model into an approximate linear model such that efficient linear term selection methods can be applied. In addition to completing grey box models, the inversion technique can be used to test if the model adequately describes the available data. References

• Bohlin, T. P., Practical grey-box process identification, Theory and applications (Advances in industrial control, Springer (London), 2006. ISBN: 978-1-846-28402-1.
• Draper, N. R., and Smith, H., Applied regression analysis, Wiley (New York), 1998. ISBN: 978-0-471-17082-2.
• Gustafsson, F., and Hjalmarsson, H., Twenty-one ML estimators for model selection, Automatica, 31(10) 1377--1392, 1995. doi:10.1016/0005-1098(95)00058-5
• Kojovic, T., The davelopment and application of Model--an automated model builder for mineral processing, PhD thesis, The University of Queensland, 1989.
• Kojovic, T., and Whiten W. J., Evaluation of the quality of simulation models, Innovations in mineral processing, (Lauretian University, Sudbury) p437--446, 1994. ISBN: 088667025X.
• Konishi, S., and Kitagawa, G., Information criteria and statistical Modeling, Springer (New York) 2010. ISBN 978-1-441-92456-8
• Lawson, C. L., and Hanson, R. J., Solving least squares problems, SIAM (Philadelphia), 1995. ISBN: 978-0-898-71356-5.
• Napier--Munn, T. J., Morrell, S., Morrison, R. D. and Kojovic, T., Mineral comminution circuits--their operation and optimisation, Julius Kruttschnitt Mineral Research Centre (Brisbane), 1996.
• Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., Numerical recipes, Cambridge (New York), 2007. ISBN: 978-0-521-88068-8.
• Tran, V., Improved calibration techniques for nuclear analysers, PhD thesis, The University of Queensland, 1998.
• Weisburg, S., Applied linear regression, Wiley-Interscience (Hoboken, N.J.), 2005. ISBN: 978-0-471-66379-9.
• Whiten, W. J., Model building techniques applied to mineral treatment processes, Symp. on Automatic Control Systems in Mineral Processing Plants, (Australas. Inst. Min. Metall., S. Queensland Branch, Brisbane), 129--148, 1971.
• Whiten, W.J., A matrix theory of comminution machines, Chem. Eng. Sci., 29, 589-599., 1974. doi:10.1016/0009-2509(74)80070-9.
• Whiten, W. J., Determination of parameter relations within non-linear models, SIGNUM Newsletter, 29(3--4), 2--5, 1994. doi:10.1145/192527.192535.
• Xiao, J., Extensions of model building techniques and their applications in mineral processing, PhD thesis, The University of Queensland, 1998.