Info

Figure 6.76. Predicted local batch time for the entire process duration. The peak corresponds to switching from batch to fed-batch operation.

This model provides information about the relationship between time and the evolution of process variable trajectories. The predicted time stamp vector Zpred can then be used as an indicator variable such that process variables are re-sampled on percent increments of this derived variable. It is assumed that variable trajectories contain sufficient information to fairly predict batch time in MPLSV modeling. This assumption implies that variable trajectories somewhat linearly increase or decrease in each time region. Local batch time prediction produces weak results when there are discontinuities or there exists instances that variables have simultaneous piecewise linear dynamics during the evolution of the batch. As illustrated in Figure 6.76 with fed-batch penicillin fermentation data, predicted time shows non-increasing or decreasing behavior in the region around the discontinuity which makes it inappropriate for data alignment. Similar results were also reported for industrial data [641].

A solution is proposed to this problem by partitioning the entire process into major operational phases [606]. Two different data alignment methods are used. For the general case when batches in the reference data set are of unequal length and no appropriate indicator variable is found, an MPLSV model is developed between X and local time stamps vector z for each process phase. Process variable trajectories are then re-sampled with respect to the percent completion of predicted local batch time vector zpre<j. A vector of tmax containing predicted termination times of reference batches is used to calculate percent completion on zpred- The second type of alignment does not use MPLSV modeling. Appropriate indicator variables are chosen for aligning batch variables in each phase of operation. The discontinuity occurs in the transition from batch to fed-batch operation in penicillin fermentation (Figure 1.4). Consequently, there are two operational phases and two indicator variables are used. In this case, process termination is determined according to a maturity indicator such as a preset percent conversion level or a certain total amount of a component fed. Both cases are common in industrial operations.

Once the reference data set of good batches is aligned to give an equal number of measurements in each batch and synchronized variable profiles, an MPLSV model is developed between the aligned process variables set and predicted percent completion of the batch run, zpr€d- Model parameters from this step are used to construct MSPM charts as outlined earlier in Section 6.4.2.

Figure 6.77 shows aligned biomass concentration profiles of the reference batches in each phase of the batch run using indicator variables. As a result of the alignment procedure, temporal variation of process events is minimized so that similar events can be compared. A very useful byproduct of the alignment procedure is that the number of measurements in each batch on each variable is also equalized. zpred profiles in each phase of the reference batches are shown in Figure 6.78 along with their control limits. Zpred of a new batch can be used as a maturity indicator. It can be inferred that if its value is smaller than the observed value, the process is progressing slower than the reference batches. Limits are used to detect an unusual deviation from the expected time course of the batch.

When used as is, MPLSV modeling produces nonlinear estimated scores. Control limits can be calculated as t±3<r (6.131)

where t are average estimated scores and a their standard deviations [663]. When a new batch is monitored with the model parameters of MPLSV, estimated scores of this new batch will also be nonlinear. After proceeding with mean-centering of these scores that reduces the nonlinearity, it is possible to construct tighter control limits by using Eq. 6.95. This modification allows faster fault detection as discussed in case studies. When an out-of-control status is detected with either type of score plots, variable contributions are checked for fault diagnosis.

Online Prediction of Product Quality. It is advantageous to use MPLSV type models for online monitoring because it is not necessary to

(b) Phase 2 (The 0 on the time axis corresponds to the end of Phase 1 time).

(b) Phase 2 (The 0 on the time axis corresponds to the end of Phase 1 time).

Figure 6.77. Results of the alignment procedure for biomass concentration profiles.

Figure 6.77. Results of the alignment procedure for biomass concentration profiles.

% completion on z

Figure 6.78. Predicted local batch times (zprecj) in Phase 1 and 2 with control limits (dashed lines).

% completion on z

Figure 6.78. Predicted local batch times (zprecj) in Phase 1 and 2 with control limits (dashed lines).

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