Coupled principal component analysis.

Multivariate and multiscale monitoring of wastewater treatment operation.

In this work extensions to principal component analysis (PCA) for wastewater treatment (WWT) process monitoring are discussed. Conventional PCA has some limitations when used for WWT monitoring. Firstly, PCA assumes that data are stationary, which is normally not the case in WWT monitoring. Secondly, PCA is most suitable for monitoring data that display events in one time-scale. However, in WWT operation. disturbances and events occur in different time-scales. These two limitations make conventional PCA unsuitable for WWT monitoring. The first limitation can be overcome by use of adaptive PCA. In adaptive PCA. the PCA model is continuously updated using an exponential memory function. Variable mean, variance and co-variance are thus adapted to the changing conditions. The second problem can be solved by time-scale decomposition of data prior to analysis. The time-scale decomposition methodology involves wavelets and multiresolution analysis (MRA) in combination with PCA. MRA provides a tool for investigation and monitoring of process measurement at different time-scales by decomposing measurement data into separate frequency bands. Time-scale decomposition increases the sensitivity of the monitoring, which makes it possible to detect small but significant events in data displaying large variations. Moreover, time-scale information is sometimes important in the interpretation of a disturbance to determine its physical cause. Also, by decomposing data, the problem of changing process conditions is partly solved. All the presented methods are illustrated with examples using real WWT process data.