Process trends multiscale representation

The engineering context of the need for multiscale representation of process trends can be best seen within the framework of the hierarchical... 

The extraction, though, of the so-called pivotal features from operating data, encounters the same impediments that we discussed earlier on the subject of process trends representation (1) localization in time of operating features and (2) the multiscale content of operating trends. It is clear, therefore, that any systematic and sound methodology for the identification of patterns between process data and operating conditions can be built only on formal and sound descriptions of process trends. 

These disadvantages are overcome by the methodology we will describe in the subsequent paragraph developed by Bakshi and Stephanopoulos. Effects of the curse of dimensionality may be decreased by using the hierarchical representation of process data, described in Section III. Such a multiscale representation of process data permits hierarchical development of the empirical model, by increasing the amount of input information in a stepwise and controlled manner. An explicit model between the features in the process trends, and the process conditions may be learned... 

BR Bakshi and G Stephanopoulos. Representation of process trends, part iii. Multiscale extraction of trends from process data. Comput. Chem. Engg., 18 267-302, 1994. 

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