A mathematical programming framework for optimal model selection/validation of process data

Abstract This work considers the use of information indices for optimal model selection and validation of process data. The approach followed assumes the existence of a set of fundamental process models associated with possible, although distinct, operating regions. A 2-phase mathematical programming algorithm for the assessment of structural changes and optimal fitting of local models in data series is proposed. This approach is used to determine the kinetic parameters of the gelation reaction of chitosan with genipin, employing dynamical elastic modulus data.

[1]  D. Andrews Tests for Parameter Instability and Structural Change with Unknown Change Point , 1993 .

[2]  Leo Breiman,et al.  Hinging hyperplanes for regression, classification, and function approximation , 1993, IEEE Trans. Inf. Theory.

[3]  M. Avrami Kinetics of Phase Change. I General Theory , 1939 .

[4]  Tyler A. Soderstrom,et al.  A mixed integer optimization approach for simultaneous data reconciliation and identification of measurement bias , 2000 .

[5]  Alberto Bemporad,et al.  Identification of piecewise affine systems via mixed-integer programming , 2004, Autom..

[6]  Bruce E. Hansen,et al.  Testing for parameter instability in linear models , 1992 .

[7]  Robert C. Bolles,et al.  Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography , 1981, CACM.

[8]  G. Franks,et al.  Chitosan tissue scaffolds by emulsion templating , 2006, Journal of biomaterials science. Polymer edition.

[9]  Russell Beale,et al.  Handbook of Neural Computation , 1996 .

[10]  S. Leyffer,et al.  Comparison of certain MINLP algorithms when applied to a model structure determination and parameter estimation problem , 1998 .

[11]  Detection of gross errors using mixed integer optimization approach in process industry , 2007 .

[12]  K. Kadota,et al.  Detection of genes with tissue-specific expression patterns using Akaike's information criterion procedure. , 2003, Physiological genomics.

[13]  Stefan Van Aelst,et al.  Building a robust linear model with forward selection and stepwise procedures , 2007, Comput. Stat. Data Anal..

[14]  J. Friedman Multivariate adaptive regression splines , 1990 .

[15]  Alan Parker,et al.  Gelation Kinetics of Gelatin: A Master Curve and Network Modeling , 2000 .

[16]  Nikolaos V. Sahinidis,et al.  Simultaneous parameter estimation and model structure determination in FTIR spectroscopy by global MINLP optimization , 2003, Comput. Chem. Eng..

[17]  L. Biegler,et al.  Redescending estimators for data reconciliation and parameter estimation , 2001 .