USE OF PRESS FOR PROCESS MODEL SELECTION

This section illustrates application of the PRESS statistic for process model structure selection. Ljung (1987) used data collected from a laboratory-scale Process Trainer to illustrate various identification techniques and examined the sum of squared conventional residuals and Akaike s information theoretic criterion (AIC) for model structure selection. Two sets of input-output data collected from this process are available within MATLAB. We use the entire first set of data M = 1000), called DRYER2 in MATLAB, for this study. Two different model structures are examined here, namely the ARX and FIR model structures, with the objective to find the model within a pcurtic-ular structure that produces the smallest PRESS. 

For a linear, time invariamt system, the regressor associated with the ARX model is chosen to have the following form 

For this model, the time delay d and model order ni must be determined in addition to estimation of the parameter vector 6. 

Prom the results presented in Table 3.1, our conclusion is that the best ARX model, in terms of predictive capability, for the Process Trainer is either a 14th order model (28 model terms) with d = 1 or a. IZth order model (26 model terms) with d — 2. The reason such high order models were selected is that, with low order ARX models, there must exist a mismatch between the assumed and actual noise structures. Evidence for this statement can be found in Ljung (1987) where the addition of a noise model was found to give improvement in terms of the AIC. In a similar situation, Kosut and Anderson (1994) have fit least squares ARX models using cross validation for model order selection and have found that high order ARX models are often necessary. 

If the model structure must be restricted, the above results also indicate 

---