Principal Component Analysis of Spectra

This paper discusses principal component analysis (PCA) of integral transforms (spectra and autocovariance functions) of time-domain signals. It is illustrated using acoustic emissions from mechanical equipment. It was found that acoustic signals from different stages of operation appeared as distinct clusters in the PCA analysis. The clusters moved when machinery faults were present and the modelling errors also increased under fault conditions, thus each type of fault had a distinctive signature and could be diagnosed. PCA using autocovariance functions that were derived from the full power spectrum had better performance than spectral PCA using averaged periodograms, and both gave a significant improvement over time domain PCA.