Biomedical Engineering Reference
In-Depth Information
knowledge. Once the historical representative batch data set is selected, outliers
removed, missing data are treated, and data pretreatment (such as autoscaling) is
done, one may deploy PCA and PLS algorithms (when applied to batch processes,
these are also called multiway PCA and PLS [60-63]) to develop an empirical
process model that is to represent nominal behavior of the process variability and its
expected impact on output variables. This nominal model (or reference model or
baseline model) is then used in monitoring new batches by comparison. When
aforementioned MSPM charts are used (off-line or in real time) to monitor new
batch performance against this historical norm (or baseline), deviations can be
detected and responsible variables can be diagnosed within this advanced monitoring
framework. A thorough analysis and methodology on how to develop an MSPM
framework particularly in biopharmaceutical industries can be found in the literature
[64-67].
As an industrial example, two consecutive bioreactors are modeled via MPLS to
devise a real-time MSPM (RT-MSPM) framework. In this setting, historical batches are
mined from the manufacturing databases to develop nominal process models for each
bioreactor. Online quality prediction models (mathematical models predicting the end
process quality such as final titer) are also developed for providing early estimation of
quality attributes [68].
A comprehensive multivariate process monitoring and final quality estimation are
made possible in this real-time framework above. As shown in Fig. 12.9a, the time
series traces of the first score for two bioreactors (first two charts cover the batch and
fed-batch phases of a seed bioreactor, respectively, followed by the score time series
chart for a production bioreactor). These charts are useful in detecting deviations from
nominal operation by takingmany variables into account together at each time instance
(based on the data sampling frequency from the measurement systems on the
bioreactors). The red lines are 95% confidence limits indicating the multivariate
in-control region; the green curve is the mean (or average) curve, denoting the nominal
behavior when the batch is run at average trajectories. The dark colored curve of the
chart in the middle (of Fig. 12.9a, i.e., the fed-batch phase of the seed bioreactor) is for
monitoring a new batch while it is in progress and shows signs of deviation toward the
halfway of the run. The same deviation is also detected by the Hotelling's T
2
chart in
Fig. 12.9b, process maturity progress chart in Fig. 12.9c, and Squared Prediction Error
(DModX) chart in Fig. 12.9d. Once the deviation is detected, one can identify the
variable or variables that may have caused this deviation by using the contribution
plots. Interactively clicking the scores, T
2
, or DMoDX chart where the deviation point
is, respective contribution plot can be generated as shown in Fig. 12.10. Finally, we can
go into the variable level from the contribution plot interactively. In this example,
variables1and2seemedtocausethemultivariate statistics to inflate and signal a
deviation in theMVcharts in (Fig. 12.9a-d). Actual time series plots for these variables
indicate a clear deviation from their average trajectories. Root cause investigation
revealed that this deviation was due to a temporary power failure. As shown in this
example, by just monitoring a few MV charts (Fig. 12.9), engineers and scientists can
avoid having to monitor many different charts (as many as 20-30 in this example) and
quickly identify the deviations within the MV framework (Fig. 12.10).
