Process trends representation

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. 

What is the appropriate representational model for describing the true process trends, and how is it generated from the process data ... 

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

Once a smooth signal has been constructed, how is the trend represented Most of the available techniques do not provide a framework for the representation (and thus, interpretation) of trends, because their representations (in the frequency or time domains) do not include primitives that capture the salient features of a trend, such as continuity, discontinuity, linearity, extremity, singularity, and locality. In other words, most of the approaches used to represent process signals are in fact data compaction techniques, rather than trend representation approaches. Furthermore, whether an approach employs a frequency or a time-domain representation, it must make several major decisions before the data are compacted. For frequency-domain representations, assumptions about the... 

It is clear from the preceding discussion that the deficiencies of the existing frequency- and time-domain representations of process trends stem from their procedural character (Cheung and Stephanopoulos, 1990), i.e. they represent trends as the outputs of a computational process, which quite often bears no relationships to the process physics and chemistry. What is needed is a declarative representation, which can capture explicitly all the desirable characteristics of process trends. 

Fig. 14. Esxtracting distinguishing features from noise pulse signal. Wavelet coefficients in shaded regions represent stable extrema, (a) Wavelet decomposition of noisy pulse signal (b) wavelet decomposition of pulse signal. (Reprinted from Bakshi and Stephanopoulos, Representation of process trends. Part III. Computers and Chemical Engineering, 18(4), p. 267, Copyright (1994), with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.)...

Once the stable reconstruction of a signal has been accomplished, its subsequent representation can be made at any level of detail, i.e. qualitative, semi-quantitative, or fully real-valued quantitative. The triangular episodes (described in Section I, A) can be constructed to offer an explicit, declarative description 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... 

Bakshi, B. R., and Stephanopoulos, G., Representation of process trends. Part III. Multi-scale extraction of trends from process data. Comput. Chem. Eng. 18, 267 (1994a). 

Cheung, J. T.-Y., Representation and extraction of trends from process data. Sc.D. Thesis, Massachusetts Institute of Technology, Dept. Chem. Eng., Cambridge, MA (1992). Cheung, J. T.-Y., and Stephanopoulos, G., Representation of process trends. Part I. A formal representation framework. Comput. Chem. Eng. 14, 495-510 (1990). 

The analysis of process signals may be facilitated if the time series data can be cast into a symbolic form. The relevant trends and generic data features can then be extracted and monitored using this qualitative representation. Such a transformation is often carried out by defining a set of primitives (alphabet) that define a visual characteristic of the signal [78, 142, 247]. Here, the methodology proposed by Stephanopoulos and coworkers is discussed [9, 34, 35]. They treated the problem of trend representation graphically... 

JTY Cheung and G. Stephanopoulos. Representation of process trends, Part I. A formal representation framework. Comp. Chem. Engg., 14 495-510, 1990. 

JC Wong, KA McDonald, and A Palazoglu. Classification of process trends based on fuzzified symbolic representation and hidden Markov models. J. Process Control, 8 395-408, 1998. 

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