Wavelet-PLS regression models for both exploratory data analysis and process monitoring
Two novel approaches an presented which take into account the collinearity among variables and the different phenomena occurring at different scales. This is achieved by combining partial least squares (PLS) and multiresolution analysis (MRA). In this work the two novel approaches are interconnected. First, a standard exploratory PLS model is scrutinized with MRA. In this way, different events at different scales and latent variables are recognized. In this case, especially periodic seasonal fluctuations and long-term drifting introduce problems. These low-frequency variations mask and interfere with the detection of small and moderate-level transient phenomena. As a result, the confidence limits become too wide. This relatively common problem caused by autocorrelated measurements can be avoided by detrending. In practice, this is realized by using fixed-size moving windows and by detrending these windows Based on the MRA of the standard model, the second PLS model for process monitoring is constructed based on the filtered measurements. This filtering is done by removing the low-frequency scales representing low-frequency components, such as seasonal fluctuations and other long-term variations, prior to standard PLS modeling. For these particular data the results are shown to be superior compared to a conventional PLS model based on the non-filtered measurements. Often, model updating is necessary owing to non-stationary characteristics of the process and variables. As a big advantage, this new approach seems to remove any further need for model updating, at least in this particular case. This is because the presented approach removes low-frequency fluctuations and results in a more stationary filtered data set that is more suitable for monitoring. Copyright (C) 2000 John Wiley & Sons, Ltd.
exploratory data analysis process monitoring partial least squares multiresolution analysis paper and pulp industry activated sludge wastewater treatment plant chemometrics wavelets