Multivariate Wavelet De-noising Strategy for Process Data
Industrial chemical process data are highly exposed to noises. The noises have to be suppressed before the process data can be utilised for process computations. Wavelets have been widely accepted as a powerful technique for signal de-nosing. In a typical wavelet de-noising approach, an appropriate threshold is applied on the de-composition coefficients and the de-noising process is performed on individual signal. In contrast, chemical process data are multivariate in nature. Applying wavelet de-noising on individual signal basis in multivariate environment requires extensive analysis and computation, which could result a cumbersome activity. As multi-level decompositions are applied recursively, more information is being transferred from approximation function to detail function. If the signal is overly decomposed, it will eventually smoothing out the underlying features in the approximation function in one or more of the signals. Therefore, if a single wavelet and a single decomposition level to be applied on all process variables, multivariate optimal wavelet decomposition level must be identified to avoid over smoothing condition in any variable involved.
In this paper, an approach of using principal component analysis concept is proposed to determine the multivariate optimal wavelet decomposition level. Principal components analysis has been widely known as one of the important techniques to deal with correlated data which is normally occurred in chemical process. In this proposed approach, a multivariate optimal wavelet decomposition level will be identified based on a property of explained variance of approximation function in each decomposition level. It will be shown that once the optimal wavelet decomposition is identified, it is adequate to use approximation reconstruction only to represent the underlying features of the process variables. As a result, a less-computational wavelet de-noising analysis is achieved in multivariate environment.