6.9 Data abstraction tools

In the previous subsection, the use of OOP in the definition of variables has been introduced in order to give a multi-aspect representation to the process variables. Object-variables have been presented for encapsulating data and methods used to obtain these multiple representations. But, what kind of information is needed from process variables and which methods can be used with this purpose?. These topics are discussed below and several algorithms are proposed. Thus, abstraction tools, also called abstractors, refer to such algorithms that can be encapsulated into object-variables to supply qualitative representation of process variables.

Significant information from process variables.

Process variables, coming from real data (sensors and controllers) or simulation (analytical models) are mainly thought to be numerical data. This is the kind of information used for control loops, monitoring, alarm generation and fault detection in model-based systems. On the other hand, knowledge-based systems (used in fault detection, diagnosis and supervision) use inference methods for reasoning about both numerical (fuzzy reasoning) and qualitative information (qualitative reasoning). This qualitative data can be abstracted from the process, provided by engineers or supplied from a qualitative simulator or knowledge-based system.

The particular form of abstract data obtained from process variables depends on the process and on the application to be developed. Therefore, different techniques for obtaining significant information (numerical, qualitative, symbolic and logical) from process variables could be used. Moreover, they could be used by qualitative reasoning tools as numerical to qualitative interfaces. See for example Fig. 5.8. The significant information which can be obtained from signals analysis, is :

• Numerical information (additional) :
• Derivatives.
• Trends.
• Deviations.
• Distances with respect to some predefined shapes.
• Relative extreme.
• Landmarks (significant points and alarms).
• Indices and associated parameters (damping factor, areas, overshoot, ...)
• Frequency contents.
• Integrals.
• Certain mean values.
• Qualitative or symbolic description of signals (numerical to qualitative interface) :
• Labels.
• Episodes.
• Qualitative level of signal.
• Qualitative Trends.
• Qualitative deviations, and so on.


These descriptions and additional information, such performance indices or ratios, may be obtained on line with data acquisition. Moreover, their combination could be applied in event generation or for obtaining trends of certain parameters, for example. A wider enumeration and description can be found in [Rakoto-Ravalontsalama N., 1993]. Several qualitative representations of signals can be obtained with different methods as is depicted in Fig. 5.7 and Fig. 5.8. The choice of one or the other depends on the tool that must use this information.

Fig. .7 A simple division in zones of the amplitude space can
give several qualitative representations of a signal.

Fig. .8 Qualification of filtered signals in crisp zones could be used
to provide with qualitative tendency and qualitative deviation.

Further, elaborated numerical information is obtained using some classical signal processing methods:

• Derivatives permit to know instantaneous changes in dynamics of variables.
• Polynomial regression could be useful for obtaining an analytical description of variables before performing some additional calculation.
• Filtering is applied not only for smoothing signals, but also for dynamics isolation.
• Fourier transform for frequency analysis of dynamics of variables can help in tuning and selecting parameters.
• Wavelet transform gives a representation of signals at different scales, in both frequency and time.
• Statistical signal processing methods are used to capture statistical features, such as mean value, variance and standard deviation, correlation analysis, and so on.


Other, non-classical methods can be used to obtain a qualitative description of signals. As a result of such application, a label (linguistic description) or a set of labels of signals is obtained. Thus, a label is used to describe in a symbolic way signal behaviour during a certain time period. Some characteristic labels cover particular general changes of the signal level, which are distinguished by the description of selected episodes. A more complex signal characterisation can also be formed in this way.
 

• Triangular episodes is another representation of signals that allows time representation at several degrees of resolution.
• Amplitude splitting, is used to associate qualitative labels to representative zones of the operative range of a variable.
• histogrames are used with the same purpose, but with low pass filtering capabilities.
• Pattern matching gives a distance related to expected shapes of trajectory behaviour.


These methods could be combined to obtain a more elaborated description of the process behaviour according to the process variables. Fig. 5.9 shows a more extended classification of numerical methods to be used for obtaining qualitative representation from numerical data. The main division is given between frequency based and temporal methods according to the kind of features to extract. Note that the majority of methods taken into account are based on not only in a single sample but the history of signal. For example, frequency based methods, such as FFT or Wavelet based need a representative number of samples, while filtering methods could be implemented with less samples. Signal history is also needed in window-based (histogrames, regression, pattern matching, ...) temporal methods or triangular representations.

Fig. .9 Classification of abstraction methods.

A taxonomy/selection of abstraction tools.

Since the currently applied sensors provide only numerical data, some tools must be supplied to infer qualitative appreciation of the process behaviour from these measures. Then, the necessity of tools designed to provide external components with significant information is clear. These tools are called abstractors (abstraction tools).

Abstractors are useful in process supervision in three different ways: The first one is to perform the numeric to qualitative conversion in order to provide expert systems or reasoning tools with handily significative information and to reduce the information overload. The second, from the analysis point of view, to avoid meaningless information from measured signals and other variables, giving visual representation of the process dynamics through abstractors like trends, deviations, tendencies, and so on. Third, they are used to form the symbolic information, constituting the input for knowledge-based inference tools, such as ES and qualitative reasoning tools as is explained in following subsection.

Moreover, it is clear that sensors provide only dated samples of a process variable. Thus, interpretation of acquired values according to process behaviour must be done by taking into account all additional information that can be supplied to obtain the necessary knowledge of interest about process behaviour.

Kinds of abstractors.

As pointed in [Aguilar-Martin, 1993] supervision and diagnosis tasks must include expert knowledge and reasoning about qualitative information. Therefore, several methods have been proposed to obtain qualitative representation of situations using process variables to generate qualitative information for these tools for supervision, detection and diagnostic tasks [Dorf R.C., 1993] and [Ganz, Kolb and Rickli, 1993].

Fig. .10 Different qualitative representations for the same process
variable using qualitative labels, event generation and episodes.

Qualitative description of signals is inherent to the method applied to signals. Thus, different methods applied to the same signal can supply distinct qualitative information. Moreover, these qualitative representations of signals can be supplied using several temporal references (synchronous or asynchronous references). According to the time sequence, this text considers qualitative information obtained from signals is divided into three categories (Fig. 5.10):

• Qualitative labels are labels associated to the level of signals and actualised at every sampling time or every selected time period.
• Event generation. It is the description of specific situations. These are asynchronous results related to process variable evolution used to identify that a landmark is reached or to fire simple alarms when applied directly to that task.
• Episodes, or historic description of signals as sets of labels, used to define a specific behaviour during an interval or period of time. An episode is defined by a starting and an ending time point and a event. Thus, the same label can be applied to episodes of different duration.


Different techniques for obtaining qualitative information from process variables are described in the following paragraphs. Some of the most representative include the following ones :
 

• Qualification of filtered signals : Signal filtering is a straightforward way of isolating process dynamics from variables. Filtering, and its later qualification, allows to obtain global trends as for example, the description based on qualitative representation of tendency and a deviation from this tendency. This was employed in [Melendez et al. 1995] to provide an expert system with qualitative information. In this case qualitative labels have been used. This representation is reproduced in Fig. 5.11.

Fig. .11 Qualification of filtered signals in crisp zones could be used to
obtain a representation of signals in terms of qualitative tendency and
qualitative deviation degree.

• Histogrames.  Histogrames [Rakoto-Ravalontsalama N., 1993] perform a segmentation of the amplitude spaces of measured signals during a period of time (temporary window). [Sarrate R. et al., 1995] uses histograms to evaluate the signals in their evolution in a sliding time window. Several histogram indices could be used in supervisory applications. For instance, dominant mode is a simple way for obtaining a qualitative label corresponding to the principal zone used in the time interval corresponding to the chosen time window. Other indices, such as dominance degree or entropy, offer numerical information to be added to qualitative labels. Histogrammes have some characteristics of low pass filter, which frequency cut corresponds to the length (or memory) of the time window, reducing noise effects. In consequence, a time delay is expected in the response. This technique can be directly applied to signals before or after filtering. Fig. 5.12 shows the use of a dominant mode to represent qualitative states of a noisy signal.

• Triangular representation. [Bakshi B.R. et al., 1994], [Ayrolles, 1996] and [Cheung and G. Stephanopoulos, 1990]: Triangular representation is a qualitative description of measured signals behaviour. Using singular points of the signals (maxima, minima and inflexion points) and time intervals between these points, triangular episodes can be represented. These episodes give information about the tendency and curvature of signals. If triangles are grouped in trapezes, then the representation at different temporal scales is obtained (See "Fig. 5.13"). This kind of representation is used in the multi-scale qualitative description of trends. [Colomer et al. 1997] add numerical information to this episodes for describing areas, lines, slopes and so on.

• Wavelet transform [Bakshi B.R. et al., 1994]: Wavelet transform is a signal decomposition technique in temporal and frequency domains with various resolutions. In this way, several temporary and frequency scales of representation can be achieved. This allows a description of measured signals to contain quite different dynamics. These signals decomposition could be very useful for supervisory processes to study the most distinguished signal features and dispose others without interest, as suggested in [Bakshi and Stephanopoulos, 1994].

Fig. .14 Pattern matching

• Pattern matching, could be used to detect special situations (for instance in fault detection) comparing signal evolution with patterns extracted from the previous faulty situations. A distance is used to define the degree of coincidence ("Fig. 5.14"). Also correlation methods can be applied with this goal. As a result, events are fired when a threshold in the distance or correlation is surpassed.
• Linear (or polynomial) regression, of signals in a period of time allows to represent tendencies and classify signals behaviour according to polynomial parameters and properties.


Despite of the utility of such tools for obtaining qualitative representations of process variables, the main drawback resides in the election of the adequate method. Moreover, in the majority of such algorithms, it is necessary to tune some parameters as crisp limits for qualitative zones, sampling time, orders, number of samples (history length) and so on. For an adequate election of these abstraction tools, sometimes it is necessary to know how the algorithm works or the adequacy for obtaining specific information. Next table treats to resume some dependencies among algorithm characteristics, process and abstracted information.

For example, when using pattern matching techniques it is necessary to have a register of signals stored in a previous failure. Or the use of filtering techniques is associated to the presence of variations in the evolution of signals. The richer the signal, in terms of frequency, the better results are reached. On the other hand, all the algorithms that operate with signals history are submitted to a delay in the response time, but their fiability increases.

"Table 5-3", extracted from [Melendez et al. 1996a] , resumes the main features of these abstractors according to the facility in configuration, the dependency with process dynamics and the information provided from numerical signals. These features are obtained from the experience and the use of these algorithms with different types of signals with the purpose of obtaining qualitative representations of them.

Abstraction tools and object-variables.

Abstractors are the proposed tools or algorithms to interface purely numerical process variables and components based on more abstract expert knowledge, providing reasoning tools for the generation of qualitative representation of variables. This interface is different depending on the supervisory strategy to be developed and the expert knowledge base. Taking benefit of the object-oriented approach presented in the previous subsection for describing process variables as object-variables, abstraction methods are proposed to be encapsulated in the object structure as internal methods to obtain significant information for the qualitative representation of process variables. Graphical representation of object-variables as individual blocks are used to identify each process variable and the abstracted information supplied by the embedded algorithms. Then, a set of blocks representing object-variables with the same internal structure, can be associated to different abstraction methods. The only difference resides in the method or methods implemented and the information obtained and stored in them.