Model Validation in Process Identification

Once the model parameters have been determined, it is necessary to validate the model. As before, three different components need to be considered (1) testing the residuals, (2) testing the adequacy of the model, and (3) taking corrective action. The general details of these components are the same as for regression analysis (see Sect. 3.3.5 Model Validation). However, some specific details are needed for model validation in process system identification. 

The first system identification-specific detail is that the goal of most such models is to predict future values. Therefore, the model validation tests are often performed on a separate set of data that was not used for model parameter estimation. This is one major difference from standard regression analysis where the same data set is used for both cases. This means that the data set is split into two parts one is used for model parameter estimation and one is used for model validation. In general, the model creation part will consist of A of the data, while the model validation part will consist of % of the data. 

It is possible to test model adequacy using various indices. These indices seek to take into consideration the trade-off between the overall model fit as measured using the variance of the residuals and the number of parameters used. The two most common indices are  

Akaike s Irtformation Criterion (AIC) Akaike s information criterion seeks to find the global minimum between the variance and the number of parameters. It is defined as 

Final Prediction Error Criterion (FPE) The final prediction error criterion seeks to minimise the variance of the prediction errors with future data. It is defined as 

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