Title: Parametric modeling — The identifiability problem
Abstract: In the case of structural models, but not of input/output models, it is necessary to assess if the designed experiment has enough information to estimate all the unknown parameters of the postulated model structure. This assessment can be made by resorting to a data-independent test that is called a priori identifiability. A priori identifiability is a key step in the formulation of a structural model whose parameters are going to be estimated from a set of data. Only if the model is a priori identifiable is it meaningful to use the techniques to estimate the numerical values of the parameters from the data. If the model is a priori nonidentifiable, a number of strategies can be considered. One would be to enhance the information content of the experiment by adding, when feasible, inputs and/or measurements. Another possibility would be to reduce the complexity of the model by simplifying its model structure, e.g., by lowering the model order, or by aggregating some parameters. This chapter explores the nature of the identifiability problem in relation to parametric models and discusses methods that are available for addressing it. In essence this involves asking the question as to whether or not it is theoretically possible to make unique estimates of all the unknown model parameters on the basis of data obtained from particular input/output experiments. This is an exercise that needs to be undertaken prior to performing any actual experiment, thereby avoiding unnecessary resource expenditure that would be ineffective in terms of securing useful parameter estimates. The various approaches to addressing the problem are illustrated by a number of examples.
Publication Year: 2008
Publication Date: 2008-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 1
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