Choosing the right model: Case studies on the use of statistical modeldiscrimination experiments

Abstract

Statistical model discrimination methods were developed to efficiently and reliably choose the 'best' model for a system from a set of candidate models. Three promising model discrimination techniques are compared using three chemical engineering examples in this paper. The examples were studied via computer simulations in which experimental data were generated using a known model. The use of a computer simulation allowed factors such as error magnitude to be studied at different levels in repeat runs of the program. The results indicated the exact entropy method is the best method for use with non-nested nonlinear models, while the Buzzi-Ferraris and Forzatti (1983) method is best for use with nonlinear nested models.On a mis au point des methodes de Keywords: model discrimination, reaction kinetics, copolymerization. n science and engineering, it is often necessary to develop a I mechanistic model which explains the underlying phenomena governing a process. However, there are often several models which seem reasonable based on theory or existing data. The models are typically nonlinear in the parameters and may or may not be nested. The problem then, is how to determine whether one of the models provides a significantly better description of the process given the needs of the particular project and the available resources.Statistical model discrimination methods were designed specifically to address this problem. They describe how to design experiments which should provide the maximum amount of information on the strengths and weaknesses of competing models. They also describe how to rigorously analyze data to determine whether any of the models is significantly better than the others. Statistical model discrimination methods are typically sequential methods. This allows models to be compared and the value of further experimentation to be assessed after each experiment.Model discrimination methods that contain both design and analysis steps were introduced by Hunter and Reiner ( 1965), Roth ( 1965), Box and Hill ( I 967) and Reilly (1 970). However, they have not been extensively evaluated or systematically examined for their sensitivity to factors such as experimental error level or the quality of initial parameter estimates. For this reason, three of the most promising model discrimination methods were chosen for extensive comparison.The methods chosen were the Buzzi-Ferraris and Forzatti method (Buzzi-Ferraris and Forzatti, 1983;Buzzi-Ferraris et al., 1984, 1990, the exact entropy method (Reilly, 1970), and the Hsiang and Reilly (1971) method. These three ?Present address: Novacor Research and Technology Corporation, 2928-*Author to whom correspondence should be addressed. E-mail address:16th St. N.E., Calgary, AB T2E 7K7, Canada.penlidis@cape.uwaterloo.ca methods are described in the first section of this paper as part of an overview of model discrimination methods.The overview is followed by three examples. For each example, computer simulations were used to study the application of the three model discr...

Model-based experimental analysis of enzyme kinetics in aqueous–organic biphasic systems

“…For this purpose, the model is used to simulate data which are subsequently disturbed with white noise. In silico experiments are useful to check the identifiability of kinetic parameters, to compare different regularization strategies (Santos and Bassrei, 2007), to determine the discriminability between model variants (Burke et al, 1997;Kremling et al, 2004), to validate new model identification approaches (Brendel et al, 2006), or to evaluate the precision of analysis programs (Straathof, 2001). …”

“…The principle is to determine experimental conditions under which the difference between the predictions of alternative model variants is maximized. Later on, this concept was further improved and investigated in detail (Asprey and Macchietto, 2000;Fedorov, 1975a, 1975b;Burke et al, 1997;Draper and Hunter, 1966;Hill, 1978;Kremling et al, 2004;Walter and Pronzato, 1990). In all cases OED requires interactions between modeler and experimenter since a compromise between maximum information content and practical feasibility has to be achieved (Cappuyns et al, 2007).…”

“…In silico experiments, which are simulations with subsequent noising of the data, are useful to check the identifiability of kinetic parameters, to determine the discriminability between model variants (Burke et al, 1997;Kremling et al, 2004), to validate new model identification approaches (Brendel et al, 2006), or to evaluate the precision of computer programs (Straathof, 2001). The advantage of in silico experiments is that in contrast to experimental data it can easily be checked if the parameter estimation yields the correct values.…”

Discrimination of Chain Branching Models in Addition Diene Polymerizations

“…In another work, Burke et al25 compared the same three previous statistical model discrimination methods to a set of competing models. The first example involved theoretical reactions (A to B) and the models presented different reaction orders; the second example involved mechanisms for the steady‐state oxidation of ferrous iron; and the last example involved nested kinetic models used to describe the copolymerization of styrene and acrylonitrile.…”

“…Their results were in agreement with previous simulation investigations. [19,23] In another work, Burke et al [25] compared the same three previous statistical model discrimination methods to a set of competing models. The first example involved theoretical reactions (A to B) and the models presented different reaction orders;The present work analyzes whether discrimination of chain branching models is possible in addition diene polymerizations, based solely on average molecular weights and monomer conversions monitored during the reaction course, as usually performed in most quality control labs of industrial plants.…”