This chapter introduces the formal framework for the definition and description of process trends at all levels of detail: qualitative, order-of magnitude, and analytic. A detour through the basic concepts of scale-space filtering is necessary in order to see the connection between the concept of process trends and the classical material on signal analysis. It introduces the theory of the multiresolution analysis of signals using wavelet decomposition that is used to provide the scalespace image of a function with correct local characteristics. This localized description of a signal's features allows the correct extraction of distinguished attributes from a signal, a task that forms the basis for the inductive generation of pattern-based logical relationships among input and output variables, or the efficient compaction of process data. Of particular value is the construction of “translationally invariant” wavelet decompositions that allow the correct formation of temporal patterns in process variables. The use of wavelet decomposition as the most appropriate framework for the extraction and representation of trends of process operating data has been discussed. The chapter presents development of an efficient methodology for the compression of process data. Of particular importance is the conceptual foundation of the data compression algorithm; instead of seeking noninterpretable, numerical compaction of data, it strives for an explicit retention of distinguished features in a signal. It is shown that this approach is both numerically efficient and amenable to explicit interpretations of historical process trends. It also discusses how the temporal distinguished features of many input and output signals can be correlated in propositional forms to provide logical rules for the diagnosis and control of processes that are difficult to model. The chapter provides illustrations on the use of the various techniques, using real-world case studies.
ASJC Scopus subject areas
- Chemical Engineering(all)