Multiscale PCA with application to multivariate statistical process monitoring

TLDR

Multiscale PCA (MSPCA) merges PCA’s linear decorrelation with wavelet analysis to extract deterministic features and decorrelate autocorrelated measurements, making it suitable for data whose behavior varies across time and frequency. MSPCA performs PCA on wavelet coefficients at each scale, then combines the results from relevant scales, effectively adaptively filtering scores and residuals and adjusting detection limits to highlight deterministic changes. MSPCA improves monitoring of autocorrelated data without matrix augmentation, enhances detection of deterministic changes, simultaneously extracts abnormal operation features, and demonstrates superior performance in several examples.

Abstract

Abstract 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 wavelet coefficients at each scale and then combines the results at relevant scales. Due to its multiscale nature, MSPCA is appropriate for the 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.