Mathematical modelling of chemical processes—obtaining the best model predictions and parameter estimates using identifiability and estimability procedures

Chemical engineers who develop fundamental models often have difficulties estimating all model parameters due to problems with parameter identifiability and estimability. These two concepts are reviewed, as are techniques for assessing identifiability and estimability. When some parameters are not estimable from the data, modellers must decide whether to conduct new experiments, change the model structure, or to estimate only a subset of the parameters and leave the others at fixed values. Estimating a reduced number of parameters can lead to better model predictions with lower mean squared error (MSE). MSE-based techniques for parameter subset selection are discussed and compared. © 2011 Canadian Society for Chemical Engineering

[1]  Gilles Clermont,et al.  An ensemble of models of the acute inflammatory response to bacterial lipopolysaccharide in rats: results from parameter space reduction. , 2008, Journal of theoretical biology.

[2]  L. John Schreiner,et al.  Mathematical Modeling of PAG‐ and NIPAM‐Based Polymer Gel Dosimeters Contaminated by Oxygen and Inhibitor , 2009 .

[3]  David W. Bacon,et al.  Modeling Ethylene/Butene Copolymerization with Multi‐site Catalysts: Parameter Estimability and Experimental Design , 2003 .

[4]  H. Rabitz,et al.  Similarity transformation approach to identifiability analysis of nonlinear compartmental models. , 1989, Mathematical biosciences.

[5]  Haihong Zhu,et al.  Parameter Identifiability and Estimation of HIV/AIDS Dynamic Models , 2008, Bulletin of mathematical biology.

[6]  Gheorghe Maria,et al.  Note concerning two tecniques for complex kinetic pathway analysis , 1993 .

[7]  P. James McLellan,et al.  Parameter Estimation in a Simplified MWD Model for HDPE Produced by a Ziegler‐Natta Catalyst , 2009 .

[8]  Gheorghe Maria,et al.  A Review of Algorithms and Trends in Kinetic Model Identification for Chemical and Biochemical Systems , 2004 .

[9]  Amos Ben-Zvi,et al.  Identifiability Study of a Liquid-Liquid Phase-Transfer Catalyzed Reaction System , 2004 .

[10]  J. Babary,et al.  Theoretical and practical identifiability of a reduced order model in an activated sludge process doing nitrification and denitrification , 1998 .

[11]  Bernt Lie,et al.  Validation of a compartmental population balance model of an industrial leaching process: The Silgrain® process , 2006 .

[12]  John F. MacGregor,et al.  Jackknife and bootstrap methods in the identification of dynamic models , 2001 .

[13]  K. Glover,et al.  Identifiability of linear and nonlinear dynamical systems , 1976 .

[14]  Amos Ben-Zvi,et al.  Identifiability and estimability study for a dynamic solid oxide fuel cell model , 2009, Comput. Chem. Eng..

[15]  Peter A. Vanrolleghem,et al.  Practical Identifiability of a Biokinetic Model of Activated-sludge Respiration , 1995 .

[16]  K. McAuley,et al.  A Kinetic Model for Non‐Oxidative Thermal Degradation of Nylon 66 , 2012 .

[17]  Bjarne A. Foss,et al.  Parameter ranking by orthogonalization - Applied to nonlinear mechanistic models , 2008, Autom..

[18]  K R Godfrey,et al.  Structural identifiability of the parameters of a nonlinear batch reactor model. , 1992, Mathematical biosciences.

[19]  Tian Zhang,et al.  Evaluating the structural identifiability of the parameters of the EBPR sub-model in ASM2d by the differential algebra method. , 2010, Water research.

[20]  Peter Reichert,et al.  Practical identifiability of ASM2d parameters--systematic selection and tuning of parameter subsets. , 2002, Water research.

[21]  D J W De Pauw,et al.  Identifiability analysis and improvement of a tree water flow and storage model. , 2008, Mathematical biosciences.

[22]  P. Reichert,et al.  Identifiability and uncertainty analysis of the river water quality model no. 1 (RWQM1). , 2001, Water science and technology : a journal of the International Association on Water Pollution Research.

[23]  Eric Walter,et al.  Identifiability of State Space Models , 1982 .

[24]  Isidoro García-García,et al.  Optimization of biotechnological processes. The acetic acid fermentation. Part II: Practical identifiability analysis and parameter estimation. , 2009 .

[25]  K. McAuley,et al.  Application of Parameter Selection and Estimation Techniques in a Thermal Styrene Polymerization Model , 2011 .

[26]  Xiaohua Xia,et al.  On Identifiability of Nonlinear ODE Models and Applications in Viral Dynamics , 2011, SIAM Rev..

[27]  Thomas J. Harris,et al.  SELECTION OF SIMPLIFIED MODELS: II. DEVELOPMENT OF A MODEL SELECTION CRITERION BASED ON MEAN SQUARED ERROR , 2011 .

[28]  Eric Walter,et al.  On the identifiability and distinguishability of nonlinear parametric models , 1996 .

[29]  R. R. Hocking.  The analysis and selection of variables in linear regression , 1976 .

[30]  Lorenz T. Biegler,et al.  Nonlinear parameter estimation: A case study comparison , 1986 .

[31]  Amos Ben-Zvi,et al.  Identifiability of non-linear differential algebraic systems via a linearization approach , 2008 .

[32]  Denis Dochain,et al.  A simplified method to assess structurally identifiable parameters in Monod-based activated sludge models. , 2003, Water research.

[33]  Thomas J. Harris,et al.  Selection of optimal parameter set using estimability analysis and MSE-based model-selection criterion , 2011 .

[34]  Kevin A. P. McLean.  OBTAINING THE BEST MODEL PREDICTIONS AND PARAMETER ESTIMATES USING LIMITED DATA , 2011 .

[35]  P. Huck,et al.  Parameter estimation for biofilm processes in biological water treatment , 1996 .

[36]  Rudiyanto Gunawan,et al.  Parameter identifiability of power-law biochemical system models. , 2010, Journal of biotechnology.

[37]  Lorenz T. Biegler,et al.  Modeling and optimization of a seeded suspension polymerization process , 2010 .

[38]  Javier Lafuente,et al.  Systematic identifiability study based on the Fisher Information Matrix for reducing the number of parameters calibration of an activated sludge model , 2009, Environ. Model. Softw..

[39]  Peter Reichert,et al.  The use of AQUASIM for estimating parameters of activated sludge models , 1995 .

[40]  Thomas J. Harris,et al.  The use of simplified or misspecified models : Linear case , 2008 .

[41]  Steven P. Asprey,et al.  A coupled single cell-population-balance model for mammalian cell cultures , 2006 .

[42]  Andrew J Daugulis,et al.  Model for a solid-liquid stirred tank two-phase partitioning bioscrubber for the treatment of BTEX. , 2010, Journal of hazardous materials.

[43]  Zuyi Huang,et al.  Improving prediction capabilities of complex dynamic models via parameter selection and estimation , 2009 .

[44]  Jorge E Jiménez-Hornero,et al.  Structural identifiability of a model for the acetic acid fermentation process. , 2008, Mathematical biosciences.

[45]  Eric Walter,et al.  QUALITATIVE AND QUANTITATIVE IDENTIFIABILITY ANALYSIS OF NONLINEAR CHEMICAL KINETIC MODELS , 1989 .

[46]  Jj Jan Kok,et al.  Parameter identifiablity in the IAWQ Model No. 1 for modelling activated sludge plants for enhanced nitrogen removal , 1996 .

[47]  Victor M. Zavala,et al.  Interior-point decomposition approaches for parallel solution of large-scale nonlinear parameter estimation problems , 2008 .

[48]  Ralf Takors,et al.  Sensitivity analysis for the reduction of complex metabolism models , 2004 .

[49]  P A Vanrolleghem,et al.  Practical identifiability of model parameters by combined respirometric-titrimetric measurements. , 2001, Water science and technology : a journal of the International Association on Water Pollution Research.

[50]  E. Walter,et al.  Global approaches to identifiability testing for linear and nonlinear state space models , 1982 .

[51]  Juergen Hahn,et al.  Parameter Set Selection via Clustering of Parameters into Pairwise Indistinguishable Groups of Parameters , 2009 .

[52]  J. Jacquez,et al.  Numerical parameter identifiability and estimability: Integrating identifiability, estimability, and optimal sampling design , 1985 .

[53]  C K Yoo,et al.  A new statistical framework for parameter subset selection and optimal parameter estimation in the activated sludge model. , 2010, Journal of hazardous materials.

[54]  David W. Bacon,et al.  Mathematical Model and Parameter Estimation for Gas-Phase Ethylene Homopolymerization with Supported Metallocene Catalyst , 2005 .

[55]  Claudio Cobelli,et al.  Global identifiability of nonlinear models of biological systems , 2001, IEEE Transactions on Biomedical Engineering.

[56]  Klaus Schittkowski,et al.  Experimental Design Tools for Ordinary and Algebraic Differential Equations , 2007 .

[57]  H. Künsch,et al.  Practical identifiability analysis of large environmental simulation models , 2001 .

[58]  Mark A. Kramer,et al.  The simultaneous solution and sensitivity analysis of systems described by ordinary differential equations , 1988, TOMS.

[59]  Bjarne A. Foss,et al.  A field study of the industrial modeling process , 1998 .

[60]  Denis Dochain,et al.  Structural Identifiability of Biokinetic Models of Activated-sludge Respiration , 1995 .

[61]  Xiaohua Xia,et al.  Identifiability of nonlinear systems with application to HIV/AIDS models , 2003, IEEE Trans. Autom. Control..

[62]  Hong Wang,et al.  Insights into the behaviour of systems biology models from dynamic sensitivity and identifiability analysis: a case study of an NF-kappaB signalling pathway. , 2006, Molecular bioSystems.

[63]  Dirk De Pauw,et al.  Optimal experimental design for calibration of bioprocess models: a validated software toolbox , 2005 .

[64]  R. Bellman,et al.  On structural identifiability , 1970 .

[65]  Alexandre Sedoglavic.  A Probabilistic Algorithm to Test Local Algebraic Observability in Polynomial Time , 2002, J. Symb. Comput..

[66]  Lennart Ljung,et al.  On global identifiability for arbitrary model parametrizations , 1994, Autom..

[67]  H. Pohjanpalo.  System identifiability based on the power series expansion of the solution , 1978 .

[68]  Ursula Klingmüller,et al.  Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood , 2009, Bioinform..

[69]  I. E. Nikerel,et al.  Model reduction and a priori kinetic parameter identifiability analysis using metabolome time series for metabolic reaction networks with linlog kinetics. , 2009, Metabolic engineering.

[70]  David W. Bacon,et al.  Mathematical Model and Parameter Estimation for Gas-Phase Ethylene/Hexene Copolymerization With Metallocene Catalyst , 2005 .

[71]  P. James McLellan,et al.  Design of Optimal Sequential Experiments to Improve Model Predictions from a Polyethylene Molecular Weight Distribution Model , 2010 .

[72]  Stefan Weijers,et al.  A procedure for selecting best identifiable parameters in calibrating activated sludge model no. 1 to full-scale plant data , 1997 .

[73]  H. Rabitz,et al.  State isomorphism approach to global identifiability of nonlinear systems , 1989 .

[74]  Gabriele Freni,et al.  Identifiability analysis for receiving water body quality modelling , 2009, Environ. Model. Softw..

[75]  Zuyi Huang,et al.  Model simplification procedure for signal transduction pathway models: An application to IL-6 signaling , 2010 .

[76]  A. Holmberg.  On the practical identifiability of microbial growth models incorporating Michaelis-Menten type nonlinearities , 1982 .

[77]  E Morgenroth,et al.  Practical identifiability of biokinetic parameters of a model describing two‐step nitrification in biofilms , 2008, Biotechnology and bioengineering.

[78]  Maria Pia Saccomani,et al.  DAISY: A new software tool to test global identifiability of biological and physiological systems , 2007, Comput. Methods Programs Biomed..

[79]  Steven P. Asprey,et al.  Toward Global Parametric Estimability of a Large-Scale Kinetic Single-Cell Model for Mammalian Cell Cultures , 2005 .

[80]  Thomas A. Duever,et al.  Parameter Estimation in the Error‐in‐Variables Models Using the Gibbs Sampler , 2008 .