Wavelets for scrutinizing multivariate exploratory models? interpreting models through multiresolution analysis

Data are inherently multivariate in nature, and in many industrial processes the number of underlying correlation structures is very often much smaller than the number of measured variables. In other words, variables have redundancy, i.e. they carry the same kind of information, which often leads to a non-parsimonious and unstable model. To obtain parsimony, a principal component-based modeling philosophy can be applied; in this way, redundant information can even be used to stabilize the model. In this work a partial least squares (PLS) model is built to take advantage of the underlying correlation structures. However, the underlying events occur at different scales, and some of the events may easily stay undetected because of the masking effect of other events. Therefore wavelets and multiresolution analysis (MRA) are used to suppress this effect. In this work, first the PLS model is built and briefly interpreted. Then latent variable (LV) scores are studied at different scales. It is shown how process trends, faults and disturbances can be scrutinized by studying biplots at different scales and by computing variable contributions. Finally the conventional PLS model is briefly compared to another very different kind of PLS model called multiscale PLS.