Dynamic Principal Component Analysis Using Integral Transforms

The paper describes an approach to dynamic multivariate analysis in which principal component analysis (PCA) is combined with integral transform techniques. The aim was to detect correlations when process dynamics cause lags or time delays. The techniques give a signature that characterises the correlated measurements. Tools for Fourier and wavelet PCA have been developed and tested. They have been demonstrated through the analysis of acoustic signals captured in a pilot plant using a multichannel acoustic instrument purpose-built for the project. A highlight of the work was the demonstration using the acoustic emissions from a stirred tank reactor of an instance where dynamic PCA in the time domain failed and Fourier PCA succeeded in showing that three acoustic channels were correlated, having a spectral signature at several frequencies in the low audio range.