Dynamic process monitoring using multiscale PCA

Conventional principal component analysis (PCA) is ideally suited for monitoring steady state processes based on the assumption that the measurements are time independent (uncorrelated) and normally distributed. Typically, most of the processes are in dynamic state, with various events occurring such as abrupt process changes, low drifts, bad measurements due to sensor failures, human errors, etc. Data from these processes are not only cross-correlated, but also auto-correlated. Applying conventional PCA directly to dynamic systems can raise false alarms, making it insensitive to detect and discriminate different kinds of events. Every event is associated with a certain frequency band according to its power spectrum. Wavelets are emerging tools to decompose a signal into various frequency bands providing simultaneous time-frequency domain analysis. We combine the potential of wavelets with the congeniality of PCA to monitor dynamic multivariate processes at different scales (frequencies). This multiscale monitoring strategy extends the suitability of PCA to statistically monitor processes based on auto-correlated measurements. Additionally, the resulting PCA models are more sensitive in detecting changes in a process. These ideas are illustrated by a suitable example.