7.4 Qualitative signal analysis: ALCMEN

ALCMEN (Automaticians Language for Causal Modelisation for Expert kNowledge) was conceived by as a language for representing and dealing with imprecision and uncertainty in algebraic and differential equations. The ultimate aim of the language is to facilitate communication between process engineers (domain experts) and control engineers. In ALCMEN, algebraic and differential equations have a representation for qualitative values. Because of the basic features in knowledge representation and capabilities for dealing with simple qualitative relations, ALCMEN has been chosen to be implemented in MATLAB/Simulink as a block based ToolBox for dealing with qualitative data. The objective is to implement this ToolBox with capabilities of dealing with qualitative data, embedded into object-variables by means of simple connections between blocks. The goal is to use abstraction tools as interface numeric to qualitative and ALCMEN to represent simple qualitative dependencies between variables when analytical relations are not known at all. ALCMEN has been tested as a tool for developing qualitative observers as is explained in .

Fundamentals of ALCMEN.

The principal idea of ALCMEN consists in graphical knowledge representation with blocks having the capability of representing a relationship among variables with imprecision. Basic operations in ALCMEN are thought to provide a simple qualitative operator between variables. Therefore, numeric to qualitative interfaces are needed. For this purpose abstraction tools can be useful to give the adequate representation for each design. Despite some simple algebraic operations available in ALCMEN, it is not defined as a qualitative algebra but only as a mechanism for knowledge representation and intuitive relation of qualitative variables.

In ALCMEN variables are thought to be structured as objects, encapsulating attributes and methods. These attributes are type (numerical, qualitative or mixed), range (set of possible values), subsets of values (desired or usual values, landmarks, and other useful information). The methods are basically conceived to perform operations or relationships between these variables and to obtain qualitative representations from numeric values. Blocks are used to graphically represent causal graphs where the input of blocks are variables, representing causes and the output are the effect variables.

ALCMEN variables allow both numerical and qualitative values in the same representation according to the following descriptions :

• Numerical variable: Values are given by a real number (Notation: x).
• Lexical domain, S_is: A set of ordered labels, describing symbolic (or qualitative) values, indexed by correlative integer indices. Each label is associated to one of these indices from the lowest, i, to the highest, s :

• Lexical variable, X : It is a qualitative variable. The set of possible values is defined in the lexical domain, S_is. Thus, a lexical variable in ALCMEN is represented by a pair formed by a label, <x>, and the corresponding integer index, n_x : (Notation : X=(<x>,n_x)).


Qualitative representation of magnitudes in ALCMEN is given by indexed labels or lexical variables (in the ALCMEN nomenclature). Labels are ordered using correlated (or corresponding) integer indices. The mechanism used as numerical to qualitative interface is called filtering, according to ALCMEN nomenclature. It basically consists in splitting the amplitude space of a numerical variable into crisp zones, see Fig.1. The indexed set of labels associated to these zones is called the lexical domain. Then, the filtering operation associates a numerical variable, with a lexical variable from its lexical domain at any time. Thus, given a lexical domain, S_is, formed by a set of qualitative labels and its associated indices, k, ordered from the lowest, i, to the highest, s, the filtering operator of numerical variable, x, is described by the operator F(x/i,s), (indices i and s, separated by a slash from the numerical variable, x , are the inferior, i, and superior, s , indices in the lexical domain used).

Given the lexical domain S_is :