Representation of process trends-Part II. The problem of scale and qualitative scaling

The formal representation of process trends introduced in Part I of this series is completed in this paper through the formal definition and representation of time scales, which allow: (a) the systematic and unambiguous description of trends at any time scale of interest; and (b) the discovery of descriptions at dominant time scales. The representation is based on the concept of "scaling episodes," which are constructed from the "triangular episodes" introduced in Part I, to describe the distinct events characterizing the time scales of process trends. The "qualitative spectrum of scales" can then be synthesized to reveal the distribution of the underlying physicochemical events occurring at various time scales. Specific procedures are proposed to carry out local or global scaling as well as the transformation of information between different time scales, leading to the construction of the "qualitative structure of scale," which provides simultaneous descriptions of a trend at all scales. In contrast to the Fourier notion of scale, the time-domain approach proposed in this paper allows interpretations of time scales on the basis of the occurring physicochemical phenomena.