Linking PCA and time derivatives of dynamic systems

Low dimensional approximate descriptions of the high dimensional phase space of dynamic processes are very useful. Principal component analysis (PCA) is the most used technique to find the low dimensional subspace of interest. Here, it will be shown that mean centering of the process data across time followed by PCA yields valuable information about the time derivatives of the model function underlying the data. The advantage of PCA is that it can be used when the process model is not (fully) known and enough process measurements are available. The idea is illustrated with an example of a distributed parameter system. More specifically, the binary adsorption of benzene and toluene on charcoal in a packed bed filter for air cleaning is considered. It is shown that with the information gained about time derivatives, sensor locations for monitoring this process can be found. Copyright © 2007 John Wiley & Sons, Ltd.