Sequential Experimental Design for Model Discrimination

Based on alternative assumptions about the mechanism of the process under investigation, one often comes up with a set of alternative mathematical models that could potentially describe the behavior of the system. Of course, it is expected that only one of them is the correct model and the rest should prove to be inadequate under certain operating conditions. Let us assume that we have conducted a set of preliminary experiments and we have fitted several rival models that could potentially describe the system. The problem we are attempting to solve is  

What are the best conditions to perform the next experiment so that with the additional information we will maximize our ability to discriminate among the rival models  

Obviously, it is very important that the next experiment has maximum discriminating power. Let us illustrate this point with a very simple example where simple common sense arguments can lead us to a satisfactory design. Assume that we have the following two rival single-response models, each with two parameters and one independent variable  

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Buzzi-Ferraris, G., P. Forzatti, G. Emig and H. Hofmann, "Sequential Experimental Design for Model Discrimination in the Case of Multiple Responses", Chem. Eng. Sci., 39(1), 81-85 (1984). 

Procedures on how to make inferences on the parameters and the response variables are introduced in Chapter 11. The design of experiments has a direct impact on the quality of the estimated parameters and is presented in Chapter 12. The emphasis is on sequential experimental design for parameter estimation and for model discrimination. Recursive least squares estimation, used for on-line data analysis, is briefly covered in Chapter 13. 

The rate equations were determined by Dumez and Froment by means of sequentially designed experimental programs for model discrimination and... 

Fig. 11. Structure of a sequential experimental design for discrimination between rivaling models.

The sequential experimental design can be made either for precise parameter estimation or for model discrimination purposes. 

The text reviews the methodology of kinetic analysis for simple as well as complex reactions. Attention is focused on the differential and integral methods of kinetic modelling. The statistical testing of the model and the parameter estimates required by the stochastic character of experimental data is described in detail and illustrated by several practical examples. Sequential experimental design procedures for discrimination between rival models and for obtaining parameter estimates with the greatest attainable precision are developed and applied to real cases. 

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