Consistency-based diagnosis of dynamic systems using quantitative models and off-line dependency-recording

For more than ten years different techniques have been proposed to perform model-based diagnosis of dynamic systems from the Artificial Intelligence community. Nevertheless, there is no general framework yet. Main part of the research effort has been devoted to modeling issues. Most approaches have relied upon qualitative models due to the lack of accuracy, certainty and precision in quantitative models. Hence, one question arises, is still possible to use quantitative models in the Artificial Intelligence approach to model-based diagnosis? Despite of mentioned drawbacks, quantitative models offer some advantages. If combined with pre-compiled dependency-recording, these systems avoid one of the traditional problems in the qualitative modeling approach, the feedback loop problem. These are the bases of MORDRED, a model-based diagnosis system that combines quantitative models and the possible conflict concept. This work presents results obtained in MORDRED verification and validation phases. Moreover, it analyses drawbacks found during the whole design and implementation cycle, and proposed solutions. Introduction Model-based diagnosis seems to be a quite ambiguous diagnosis category, since two different communities have made two different approaches. On the one hand, the FDI community has mainly used quantitative models and Control Theory techniques. State observers (Frank 1987), parameter estimation (Isermann 1987), and analytical redundancy (Gertler 1991) seem to be the most successful approaches. Usually, these methods have a residual generation phase followed by a residual analysis phase based on heuristic criteria (Isermann 1993; Gertler 1998). (Patton, Frank, & Clark 2000) and (R. Isermann et al 1997) provide recent reviews on such techniques. On the other hand, the AI community approaches are based on reasoning from structure and behaviour (Davis & Hamscher 1988). These methods usually obtain global behaviour based on local models of components and structural information. Consistency-based (Reiter 1987; de Kleer & Williams 1987) and abduction-based (Poole 1988) methods are the main approaches from a theoretical point of view, although there is no general classification. This paper fits within the consistency-based approach. Copyright c 2001, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. In 1988, Davis and Hamscher (Davis & Hamscher 1988) pointed out that the extension of model-based diagnosis techniques to dynamic systems would be a major step to validate the approach in real systems. Four years later, Hamscher et al. (Hamscher, Console, & de Kleer(Eds.) 1992) mentioned that main advances had been devoted to modeling issues, however no general paradigm had been stablished. In 1996, Dressler and Struss (Dressler & Struss 1996) considered again this issue as an open research field. Nowadays, a lot of research effort is still devoted to this area (Chantler, Daus, & Coghill 1996; Mosterman, Manders, & Biswas 2000), because dynamic systems have some features which increase the complexity of the diagnosis process: it is necessary to model dynamics and, usually, to simulate dynamic behaviour over time, uncertainty in model parameters together with model simulation over time might cause wrong fault detection, if the state of the system is not completely observed, there could be a feedback loop problem, in order to fulfill condition monitoring requirements, diagnosis needs to be an on-line incremental process. Initial proposals to tackle these problems, such as XDE (Hamscher 1990), CATS (Dague et al. 1991), or SIDIA (Guckenbiehl & Schaefer-Richter 1990), tried to extend the GDE paradigm (de Kleer & Williams 1987) to deal with temporal information. In the last decade, new kinds of models and distinct diagnosis techniques were proposed. On the one hand, initially most of them relied upon qualitative models. For instance, Magellan (Dressler & Struss 1994) introduced qualitative constraints in the GDE framework, MIMIC (Dvorak & Kuipers 1992) performed continuous monitoring based on QSIM (Kuipers 1986) models, CAEN (Bousson & Trave-Massuyes 1992) generalized causal graphs to diagnose dynamic systems, or Mosterman and Biswas (Mosterman 1997) used temporal causal graphs derived from bond-graph models. Afterwards, there have been a considerable evolution towards semi-qualitative modelling (Kuipers 2000; Trave-Massuyes, Escobet, & Quevedo 2000). Recently, Dressler (Dressler 1996) and Struss (Struss 1997) have proposed state-based diagnosis as an alternative to simulation-based diagnosis. On the other hand, there is a small number of references to quantitative approaches to model-based diagnosis (Chantler, Daus, & Coghill 1996) from the AI community. When quantitative models are used, it is obvious that there is neither easy nor straightforward application of classical modelbased diagnosis paradigm to dynamic systems, due to inherent complexity of dynamic behaviour modeling and simulation. One drawback is that imprecision and uncertainty make necessary to redefine what we mean by ”consistency” check. Another drawback when consistency-based diagnosis is applied to dynamic systems is on-line dependencyrecording. This can cause the so-called feedback loop problem (Williams 1990; Guckenbiehl & Schaefer-Richter 1990; Dressler & Struss 1994), which produces estimations dependent upon the majority of the constraints in the model in few integration steps (Chantler, Daus, & Coghill 1996). Few years ago, pre-compilation of dependencies has emerged as a suitable alternative to on-line dependency-recording. Several works had been proposed to use structural information to reduce computation effort while doing diagnosis (Nooteboom & Leemeijer 1993; Dague et al. 1991; Misra, Sztipanovits, & Carnes 1994). Pre-compilation goes a step further, and takes advantage of behavioural information, implicit in system description. These techniques identify, off-line, behavioural and/or functional dependencies among components or variables (Lunze & Schiller 1992; Loiez 1997; Froelich & Nejdl 1997; Pulido & Alonso 1999; Cordier et al. 2000). Furthermore, in the field of industrial continuous processes there are special features which can be used to introduce pre-compilation techniques. In those processes, the topology of the plant seldom changes and the number and location of available measurements are known and fixed beforehand. MORDRED, a diagnosis system relying upon offline dependency recording and quantitative models, takes advantage of these characteristics and organises the diagnosis process around the possible conflict concept (Pulido & Alonso 1999; 2000). This work analyses results obtained by MORDRED when it was used to diagnose a real laboratory plant. This paper is organised as follows. In the next section we review the possible conflict concept and its integration in the consistency-based diagnosis cycle. Afterwards we analyse problems found during the verification phase of the approach. Next section presents results obtained when the approach was validated on a real system. Last section is devoted to discussion. Consistency-based diagnosis of dynamic systems using possible conflicts The main idea behind the possible conflict concept (Pulido & Alonso 1999; 2000) is that the set of subsystems capable to generate a conflict can be identified off-line, disregarding observations, and with no model evaluation. Initially, MORDRED analyses an abstract representation of system description looking for minimal overconstrained sets of relations, which are essential for model-based diagnosis. These subsystems are called minimal evaluable chains. Afterwards, it introduces an abstraction of behavioural constraints to build a model for each minimal evaluable chain, if possible. These models, called minimal evaluable models, can predict the behaviour of parts of the system. If there is a discrepancy between predictions and observations, the set of constraints in the minimal evaluable model responsible for the prediction is confirmed as a conflict. Afterwards, diagnosis candidates are obtained from conflicts following Reiter’s theory (Reiter 1987). To diagnose dynamic systems MORDRED makes difference of two kinds of constraints: instantaneous, which estimate static or causal behaviour, and differential, which predict system evolution over time. The diagnosis system is able to detect and localize faults which can be modelled as abrupt changes in model parameters. Since differential constraints do not contain such kind of parameters, it is assumed that only instantaneous relations contain useful information for diagnosis purposes (Chantler, Daus, & Coghill 1996). Moreover, MORDRED should be classified as an integration method since differential constraints must be used only to estimate the value of a variable through the integration step: Summarizing, every possible conflict can be precomputed off-line because no observation is needed. Since conflicts will arise only when models are evaluated with available observations, the set of constraints in a minimal evaluable model is called a possible conflict, for short pc. Therefore, MORDRED does interpret classical consistency-based diagnosis in the following way: 1. the system must be analysed looking for any minimal evaluable chain; 2. those minimal evaluable chains with no evaluable model must be rejected, 3. exactly one minimal evaluable model associated to a minimal evaluable chain must be selected, 4. build the model of the possible conflict , , from the description of the minimal evaluable model,