Linear Model Creation and Validation

The first step will be to create a linear model of the system and validate it. This procedure will be split into three steps time delay estimation, model creation, and model validation. The last two steps are iterative, in that if the model validation fails, a new model structure may be created and then fit. This procedure is repeated until a sufficiently good model is obtained. For the purpose of this section, the initial model and the final model will be presented, as well as any intermediate steps that present any special challenges. 

Unless there is additional information about the process, it is useful to always start with the simplest model and work one s way up. A good recommended initial guess is a first-order Box-Jenkins model and then, based on the fit, to advance to more complex models until the fit becomes good or the model order is too large. 

For the initial, first-order Box-Jenkins model, the parameter estimates and their standard deviation are  

The auto- and cross-correlation plots are shown in Fig. 6.12. A comparison between the predicted and actual levels is shown in Fig. 6.13. Both figures use the validation data set for testing the model. From Fig. 6.12, it is clear that the residuals are not uncorrelated with each other or the inputs. Therefore, the initial model needs to be improved. Since there is a suggestion that the process model is incorrectly specified, it will first be changed. The best approach is to increase the order of the numerator and denominator (of the B- and F-polynomials) until either the cross-correlation plot shows the desired behaviour or the confidence intervals for the parameters cover zero. If the second case is reached, then this could be a suggestion that a linear model is insufficient/inappropriate for the given data set. Furthermore, the fit between the predicted and measured levels is not great (55.4%). 

6 Modelling Dynamic Processes Using System Identification Methods 

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