USE OF PRESS FOR MODEL STRUCTURE SELECTION IN PROCESS IDENTIFICATION

2 USE OF PRESS FOR MODEL STRUCTURE SELECTION IN PROCESS IDENTIFICATION 

When working with regression-based techniques for process model identification, one of the challenging tasks is to determine the most appropriate process model structure. In a linear model context, this would be information such as the number of poles and zeros to be included in the transfer function description. If the structure of the system being identified is known in advance, then the problem reduces to a much simpler parameter estimation problem. 

There is another way to generate the prediction errors without actually having to split the data set. The idea is to set aside each data point, estimate a model using the rest of the data, and then evaluate the prediction error at the point that was removed. This concept is well known as the PRESS statistic in the statistical community (Myers, 1990) and is used as a technique for model validation of general regression models. However, to our knowledge, the system identification literature has not suggested the use of the PRESS for model structure selection. 

Chapter 3 presents the development of the PRESS statistic as a criterion for structure selection of dynamic process models which are linear-in-the-parameters. Computation of the PRESS statistic is based on the orthogonal decomposition algorithm proposed by Korenberg et al. (1988) and can be viewed as a by-product of their algorithm since very little additional computation is required. We also show how the PRESS statistic can be used as an efficient technique for noise model development directly fi-om time series data. 

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