Figure 6.55. Comparison of local and overall models performances on explained variance.
Two local models for phase 1 and phase 2, and one overall model, are developed using MPCA technique and compared. Variance plots can be useful for comparing different models and investigating the changing variance structure in overall data. The variance explained is higher (45.67% more) for the local model of phase 1 than the overall model, whereas variances explained are much closer but still higher (4.22% more) for the local model of phase 2 (Fig. 6.55). This is expected, since the same event occurs in the second phase (Fig. 6.53). Local models explain more information (17.98% more for the whole process) based on computations of sum of squared errors and data lengths in each phase.
Process monitoring stage: A new batch with a small drift in impeller speed introduced at 0.5 min (10th observation in phase 1 of stage 1) was monitored after its completion. Note that the fault starts early in the first phase. Both SPE and T2 plots for local and overall models in Figure 6.56 indicated that there is a deviation from the NO. Since overall model performance is not high in the first phase, the early departure is caught later with monitoring based on the overall model than with the local model (Figure 6.56b), and many false alarms are observed in the SPE plot (Figure 6.56a). The advantages of using the local model for phase 1 are:
1. The false alarms observed with the overall model for phase 1 in the
SPE plot are eliminated.
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