Multiscale PCA with Application to Multivariate Statistical Process Monitoring

Multiscale Principal Component Analysis (MSPCA) combines the ability of PCA to decorrelate the variables by extracting a linear relationship, with that of wavelet analysis to extract deterministic features and approximately decorrelate autocorrelated measurements. MSPCA computes the PCA of the wavelet coefficients at each scale, followed by combining the results at relevant scales. Due to its multiscale nature, MSPCA is appropriate for modeling of data containing contributions from events whose behavior changes over time and frequency. Process monitoring by MSPCA involves combining only those scales where significant events are detected, and is equivalent to adaptively filtering the scores and residuals, and adjusting the detection limits for easiest detection of deterministic changes in the measurements. Approximate decorrelation of wavelet coefficients also makes MSPCA effective for monitoring autocorrelated measurements without matrix augmentation or time-series modeling. In addition to improving the ability to detect deterministic changes, monitoring by MSPCA also simultaneously extracts those features that represent abnormal operation. The superior performance of MSPCA for process monitoring is illustrated by several examples.