Qualitative model based methods

In these techniques the knowledge is obtained from the structure and the behaviour of the process as a set of relations that describe the interactions between various process variables. The goal is to dispose of a rough model to be used as a model-based

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approach. Contrary to the analytical model, the qualitative models can be incomplete or contain uncertainties.

In this section, some causal model-based methods will be briefly discussed. Cause- effect arguments are a basic component of human reasoning about system behaviour, and a causal model reflects the causal relationships between process variables.

Signed Directed Graph (SDG)

The most widely used form of causal knowledge is the Signed Directed Graph (SDG). The process variables are represented as graph nodes and causal relations by directed arcs. Nodes have qualitative states, then, the state of the system is described qualitatively by a pattern. The cause-effect graph is a subgraph of the signed digraph consisting of valid nodes (any variable which is first affected by the root cause) and consistent branches (a consistent path for the propagation of the influence of its initial node to its terminal node).

A problem with the SDG process models is that they only describe local, direct causalities between variables. To overcome this problem, Oyeleye, 1989 introduces the Extended SDG, which analyzes the loops in the SDG and insert additional non-physical arcs into the graphs.

In Wilcox and Himmelblau, 1994 the Possible Cause-Effect Graph (PCEG) was presented as a generalization of the SDG. There are two concepts involved in representing the process state relative to the PCEG: the representation of the complete state using a pattern, and the representation of incomplete knowledge of the process state using a constraint.

Li and Wang, 2001 presents a methodology for qualitative modelling and simulation of the temporal behaviour using a fuzzy clustered digraph. The qualitative information is represented by several classes, obtained as clusters using PCA to categorically characterize dynamic trends of individual variables. The quantitative information is introduced by the utilization of fuzzy c-means clustering approach for automatic fuzzy grouping of the data points in the PCx plots. The study is focused on simulation, rather than on fault diagnosis, and as a data based method it needs extensive training.

Recent works considered the use of wavelets as signal preprocessors in order to perform SDG in processes with load-fluctuations (Tsuge et al., 2000).

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Fault Tree Analysis (FTA)

FTA is an analysis technique for safety and reliability aspects that uses a graphical representation to model causal chains leading to failures. The fault tree is a logic tree that begins with the top event (incident) and continues by deductive reasoning through all the intermediate events to primary events and initiating events. The tree usually has layers of nodes. They provide a computational means for combining logic to analyze systems faults. At each node different logic operations like AND and OR are performed for propagation. The main difference between a SDG and a fault tree representation is in the primary unit that makes them. In a fault tree, the primary unit is an event, while in a SDG, the primary unit is a process variable.

The fault tree is constructed by asking questions such as what could cause a top level event. In answering this question, one generates other events connected by logic nodes. The tree is expanded in this manner till one encounters events (primary events) which need not be developed further (Lapp and Powers, 1977). Once the fault tree is constructed, the next step in the analysis is the evaluation of the fault tree. Fault trees are usually generated manually. Considerable knowledge, system insight and overview are necessary to consider various failure modes and their consequences at a time. Because of this, the effort can be diminished by the automation of Fault Tree generation (Liggesmeyer and Rothfelder, 1998; Mäckel and Rothfelder, 2001).

Qualitative physics

Qualitative physics is an area of AI concerned with modeling a physical system in order to simulate it or solve particular problems regarding the system (Ramil and Smith, 2002). Three examples of qualitative models without using graphical representation but focused on representing the dynamics of systems using equations are:

The Qualitative Simulation (QSIM) method by Kuipers, 1986 which represents qualitative behavior using qualitative differential equations. Qualitative modeling involves specifying a constraint model of the physical process in terms of qualitative versions of mathematical relationships such as addition, multiplication and differentiation. QSIM representation and simulation algorithm allows to reason mathematically about the description of the process.

Qualitative Process Theory (QPT) construes physical systems as consisting of entities whose changes are caused by physical processes (Forbus, 1996). The domain is described by a collection of objects and each of these objects

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completely defines a qualitative state. The qualitative state is defined by a set of parameters which take on values in a quantity of space.

Compositional modelling is a strategy for organising and reasoning about models of physical phenomenon. It uses explicit modelling assumptions to decompose domain knowledge and semi-independent model fragments, each describing various aspects of objects and processes (Falkenhainer and Forbus, 1991).