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Figure 6.37. Comparison of average pH profiles. Solid curve is obtained after alignment by landmark registration.

that, instead of using one variable to determine process landmarks a combination of three variables is used in this example. The landmark location information from the inflection point of biomass concentration, the instant when base flow reaches zero after about 100 h and the instant when acid flow controller takes action after base flow decreases to zero are gathered in a landmark location vector, respectively.

Alignment of variable profiles in reference batches using landmark registration

Given the locations of landmarks in the reference batches, variable profiles are 'registered' so that similar events will be aligned with respect to mean landmarks. Mean landmark locations can be calculated from £m and used for the alignment to be performed around the average landmark locations. This is an arbitrary choice. A vector of landmark locations that belong to a reference batch could also be chosen. The aforementioned curve registration technique is implemented to all variable trajectories by using the mean landmarks vector and the matrix tm of landmarks in reference batches.

Comparison of cross-sectional mean trajectories prior to alignment and structural means after alignment illustrates the affects of trajectory alignment. The average pH profile (dashed curve) that is the cross-sectional mean of the reference profiles before alignment (Figure 6.37), resembles the reference profiles shown in Figure 6.38(a) but differ in the amplitudes

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