Principal‐component analysis of multiscale data for process monitoring and fault diagnosis

Abstract An approach is presented to multivariate statistical process control (MSPC) for process monitoring and fault diagnosis based on principal‐component analysis (PCA) models of multiscale data. Process measurements, representing the cumulative effects of many underlying process phenomena, are decomposed by applying multiresolution analysis (MRA) by wavelet transformations. The decomposed process measurements are rearranged according to their scales, and PCA is applied to these multiscale data to capture process variable correlations occurring at different scales. Choosing an orthonormal mother wavelet allows each principal component to be a function of the process variables at only one scale level. The proposed method is discussed in the context of other multiscale approaches, and illustrated in detail using simulated data from a continuous stirred tank reactor (CSTR) system. A major contribution of the paper is to extend fault isolation methods based on contribution plots to multiscale approaches. In particular, once a fault is detected, the contributions of the variations at each scale to the fault are computed. These scale contributions can be very helpful in isolating faults that occur mainly at a single scale. For those scales having large contributions to the fault, one can further compute the variable contributions to those scales, thereby making fault diagnosis much easier. A comparison study is done through Monte Carlo simulation. The proposed method can enhance fault detection and isolation (FDI) performance when the frequency content of a fault effect is confined to a narrow‐frequency band. However, when the fault frequency content is not localized, the multiscale approaches perform very comparably to the standard single‐scale approaches, and offer no real advantage. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2891–2903, 2004