Process trends

P/M processing of titanium aluminides results in more consistent product quaHty than the conventional casting process, and offers novel alloy/microstmcture possibiHties and improved ductiHty. Processing trends include use of high (1200—1350°C) temperature sintering to improve mechanical properties of steel and stainless steel parts. 

Reasoning in Time Modeling, Analysis, and Pattern Recognition of Temporal Process Trends... 

A. The Content of Process Trends Local in Time and Multiscale.488... 

REASONING IN TIME MODELING, ANALYSIS, AND PATTERN RECOGNITION OF TEMPORAL PROCESS TRENDS... 

Identify the causes of process trends, e.g., external load disturbances, equipment faults, operational degradation, operator-induced mishandling. 

Evaluate current process trends and anticipate future operational states. 

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

How does one generate relationships among process trends in order to provide the desired mental model of process operations ... 

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

The term, process trend, undoubtedly carries an intuitive meaning about how process behavior changes over time. However, the exact mean-... 

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. 

The correct interpretation of measured process data is essential for the satisfactory execution of many computer-aided, intelligent decision support systems that modern processing plants require. In supervisory control, detection and diagnosis of faults, adaptive control, product quality control, and recovery from large operational deviations, determining the mapping from process trends to operational conditions is the pivotal task. Plant operators skilled in the extraction of real-time patterns of process data and the identification of distinguishing features in process trends, can form a mental model on the operational status and its anticipated evolution in time. 

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. 

None of the practiced compression techniques satisfies all of these requirements. In addition, it should be remembered that compression of process data is not a task in isolation, but it is intimately related to the other two subjects of this chapter (1) description of process trends and (2) recognition of temporal patterns in process trends. Consequently, we need to develop a common theoretical framework, which will provide a uniformly consistent basis for all three needs. This is the aim of the present chapter. 

Section II introduces the formal framework for the definition anc description of process trends at all levels of detail qualitative, order-of magnitude, and analytic. A detour through the basic concepts of scale-spact filtering is necessary in order to see the connection between the concept o process trends and the classical material on signal analysis. Within th( framework of scale-space filtering we can then elucidate the notions o episode, scale, local filtering, structure of scale, distinguishec features, and others. 

The ideas presented in Section III are used to develop a concise and efficient methodology for the compression of process data, which is presented in Section IV. Of particular importance here 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. 

Although the term process trend emulates a certain intuitive understanding in the minds of the speaker and the listener, this understanding may not be the same. Certainly, we do not have a clear, sound, and unambiguous definition of the term trend, and this must be the first issue to be addressed. 

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. 

Fig. 15. Process trends of the signal in Fig. 1, extracted at various scales (a) original data (b) stable trend at m = 3 (see Fig. 13) (c) stable trend at m = 4 (d) stable trend at m = 5, neglecting small extrema.

Fig. 17. Generalization of process trends for three distinct records (a) raw data (b)-(gl scaled signals (h) stable trends.

For solving the pattern recognition problem encountered in the operation of chemical processes, the analysis of measured process data and extraction of process trends at multiple scales constitutes the feature extraction, whereas induction via decision trees is used for inductive... 

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