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A Strategy for Qualitative Model Based Diagnosis
Copyright © 1996 IFAC 13th Triennial World Congress, San Francisco, USA
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A STRATEGY FOR QUALITATIVE MODEL BASED DIAGNOSIS
Andrew Steele and Roy Leitch
Intelligent Systems Laboratory Dept. of Computing and Electrical Engineering Heriot- Watt University Edinburgh EHI4 4AS, United Kingdom. {ads, leitch} @cee.hw.ac.uk Tel. +441314513328 Fax. +441314513327
Abstract: A novel approach to time-constrained model based fault diagnosis of ill-defined dynamic systems is presented. Fuzzy qualitative simulation techniques are utilised to generate qualitative predictions of the dynamic behaviour of the faulty plant. These are then compared to the observed behaviour to identify the correct qualitative parameter values. The precision of the diagnosis is determined by the precision of the fuzzy model. This allows the precision of the solution to be part of the problem specification and, hence, traded-off against time-constraints; less precise models take less computation time. Experimental results for a simplified 3rd order dynamic system are presented. Keywords: Artificial Intelligence, Fault Diagnosis, Fuzzy models, Parameter Identification, Qualitative simulation, Real-time AI.
1. INTRODUCTION
Automated fault diagnosis of engineering systems is an active research area in both the control systems engineering (Patton et al., 89) and the artificial intelligence (Hamscher et al., 92) research communities. Naturally, these two communities have taken very different approaches to solving the common problem. Our approach to this problem combines aspects of both the AI and control engineering approaches: a tool is developed which uses qualitative modelling and simulation techniques from the AI domain to represent and reason about ill-defined dynamic physical systems, and use these techniques to form a novel approach to parameter identification of dynamic systems. Further, an overall strategy for diagnosis which can trade-off quality of the solution for computation time is developed, to facilitate time-constrained diagnosis. This is achieved by using qualitative models of varying precision (Leitch and Shen 94). Model identification forms an important part of a process supervisory system, with the identified model of a faulty plant often being used by as the basis of further actions by control, fault diagnosis and fault explanation agents. This
paper concentrates on the task of model identification. Motivations for the use of qualitative model representation and reasoning are given in Section 2. The architecture used for qualitative parameter identification is outlined in Section 3. Section 4 describes how varying the precision of the qualitative model representation facilitates timeconstrained reasoning. Experimental results from a third order flow system are given in Section 5. Finally, Section 6 gives conclusions on this approach to model identification.
2. PARAMETER IDENTIFICATION USING QUALITATIVE MODELS
This paper presents a novel approach to parameter identification for dynamic systems, based on the use of qualitative modelling and simulation techniques. There are two principle motivations for developing this approach: • Using qualitative models eases the modelling process when the plant is ill-defined. • The finite value domains of the qualitative models lead to a novel search-based procedure for parameter identification.
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Both of these motivations will be developed further, but first it is important to introduce the approach to modelling and simulation adopted as the basis of this research. This work on qualitative parameter identification builds on the work on fuzzy qualitative simulation in (Shen and Leitch, 93). The FuSim simulation algorithm extends the original QSIM (Kuipers, 86) approach through the use of arbitrarily defined quantity spaces consisting of fuzzy sets defined over the real number line (fuzzy numbers), as shown in figure 1.
from the Cartesian product of the value domains, D, of the n parameters of a model i.e. p" DJ xD2x ... xDn
Figure 2 presents two exemplary Parameter Spaces generated from the three parameters (n=3) of a quantitative and a qualitative model respectively:
Q
membership(Temperature)
lCx->C\, o
10
20
30
R,
Q.
low med high
Temperature
Q.
Figure 1 A Fuzzy Quantity Space Using such a representation for the qualitative values enables the modeller to explicitly encode their imprecision and uncertainty about the values of model parameters and variables. The fuzzy qualitative models used by FuSim consist of two distinct parts: 1. Constraints (or qualitative equations); the relationships between model variables and parameters expressed in terms of differential and algebraic operators (e.g. 1,*,+,,sqrt etc.; all defined for fuzzy sets). 2. Quantity Spaces; finite sets of qualitative values (fuzzy numbers) from which the model's variables and parameters take their values. It has long been argued that the fuzzy set representation fits closer to the form of subjective human knowledge, by allowing our imprecision and uncertainty about our knowledge to be explicitly encoded. The principle motivation for developing the fuzzy qualitative model representation was to ease knowledge acquisition from domain experts, particularly in the case of ill-defined dynamic systems where knowledge may indeed be imprecise and uncertain. By providing the additional degree of freedom (over quantitative models) of arbitrarily defining the value domains of the qualitative model, we eliminate the requirement for a modeller to have to 'guestimate' the values of process parameters to real valued precision. Thus, qualitative models can provide a more appropriate, or more 'honest', representation of our imprecise and uncertain process knowledge.
For the particular task of parameter identification, there is also a strong motivation to exploit the finite value domain descriptions of qualitative models to provide a novel, state-space search based solution procedure. Firstly, we define the Parameter Space, P, as that space generated
Figure 2 Quantitative and Qualitative Parameter Spaces Importantly, the value domains of the parameters of qualitative models are finite domains, and thus they generate a finite sized Parameter Space. A state-space search approach to parameter identification can now be implemented (detailed in next section) to search amongst the finite number of variations in the parameter values of a qualitative model for those values which best represent the current plant condition. In contrast, each value domain, Rx, underlying the parameters of the quantitative model is an infinitely dense domain, thus the Parameter Space generated from these domains is an infinitely dense space. That is, there exists an infinite number of possible parameter assignments for a given quantitative model, which necessitates the use of an analytic parameter identification procedure (Isermann, 84). In turn, these analytic procedures generally restrict the class of possible models to linearised process models only. By adopting a novel state-space search procedure to select from the finite possibilities of the parameterised qualitative model, we eliminate the need for any such restriction on the form of the process model.
3. QPID: AN ARCIDTECTURE FOR TIMECONSTRAINED MODEL-BASED DIAGNOSIS The QPID (Qualitative Parameter Identification for Diagnosis) system performs parameter identification of fuzzy qualitative models of dynamic systems from batches of plant data. The system is designed to operate under a variety of user requirements. In particular, QPID is required to provide a solution within a prescribed timeconstraint. Figure 3 shows the architecture of QPID, an instantiation of the generic model-based diagnosis architecture developed for ARTIST (Leitch et aI., 92).
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7f-04 1
A STRATEGY FOR QUALITATIVE MODEL BASED DIAGNOSIS
Andrew Steele and Roy Leitch
Intelligent Systems Laboratory Dept. of Computing and Electrical Engineering Heriot- Watt University Edinburgh EHI4 4AS, United Kingdom. {ads, leitch} @cee.hw.ac.uk Tel. +441314513328 Fax. +441314513327
Abstract: A novel approach to time-constrained model based fault diagnosis of ill-defined dynamic systems is presented. Fuzzy qualitative simulation techniques are utilised to generate qualitative predictions of the dynamic behaviour of the faulty plant. These are then compared to the observed behaviour to identify the correct qualitative parameter values. The precision of the diagnosis is determined by the precision of the fuzzy model. This allows the precision of the solution to be part of the problem specification and, hence, traded-off against time-constraints; less precise models take less computation time. Experimental results for a simplified 3rd order dynamic system are presented. Keywords: Artificial Intelligence, Fault Diagnosis, Fuzzy models, Parameter Identification, Qualitative simulation, Real-time AI.
1. INTRODUCTION
Automated fault diagnosis of engineering systems is an active research area in both the control systems engineering (Patton et al., 89) and the artificial intelligence (Hamscher et al., 92) research communities. Naturally, these two communities have taken very different approaches to solving the common problem. Our approach to this problem combines aspects of both the AI and control engineering approaches: a tool is developed which uses qualitative modelling and simulation techniques from the AI domain to represent and reason about ill-defined dynamic physical systems, and use these techniques to form a novel approach to parameter identification of dynamic systems. Further, an overall strategy for diagnosis which can trade-off quality of the solution for computation time is developed, to facilitate time-constrained diagnosis. This is achieved by using qualitative models of varying precision (Leitch and Shen 94). Model identification forms an important part of a process supervisory system, with the identified model of a faulty plant often being used by as the basis of further actions by control, fault diagnosis and fault explanation agents. This
paper concentrates on the task of model identification. Motivations for the use of qualitative model representation and reasoning are given in Section 2. The architecture used for qualitative parameter identification is outlined in Section 3. Section 4 describes how varying the precision of the qualitative model representation facilitates timeconstrained reasoning. Experimental results from a third order flow system are given in Section 5. Finally, Section 6 gives conclusions on this approach to model identification.
2. PARAMETER IDENTIFICATION USING QUALITATIVE MODELS
This paper presents a novel approach to parameter identification for dynamic systems, based on the use of qualitative modelling and simulation techniques. There are two principle motivations for developing this approach: • Using qualitative models eases the modelling process when the plant is ill-defined. • The finite value domains of the qualitative models lead to a novel search-based procedure for parameter identification.
6429
Both of these motivations will be developed further, but first it is important to introduce the approach to modelling and simulation adopted as the basis of this research. This work on qualitative parameter identification builds on the work on fuzzy qualitative simulation in (Shen and Leitch, 93). The FuSim simulation algorithm extends the original QSIM (Kuipers, 86) approach through the use of arbitrarily defined quantity spaces consisting of fuzzy sets defined over the real number line (fuzzy numbers), as shown in figure 1.
from the Cartesian product of the value domains, D, of the n parameters of a model i.e. p" DJ xD2x ... xDn
Figure 2 presents two exemplary Parameter Spaces generated from the three parameters (n=3) of a quantitative and a qualitative model respectively:
Q
membership(Temperature)
lCx->C\, o
10
20
30
R,
Q.
low med high
Temperature
Q.
Figure 1 A Fuzzy Quantity Space Using such a representation for the qualitative values enables the modeller to explicitly encode their imprecision and uncertainty about the values of model parameters and variables. The fuzzy qualitative models used by FuSim consist of two distinct parts: 1. Constraints (or qualitative equations); the relationships between model variables and parameters expressed in terms of differential and algebraic operators (e.g. 1,*,+,,sqrt etc.; all defined for fuzzy sets). 2. Quantity Spaces; finite sets of qualitative values (fuzzy numbers) from which the model's variables and parameters take their values. It has long been argued that the fuzzy set representation fits closer to the form of subjective human knowledge, by allowing our imprecision and uncertainty about our knowledge to be explicitly encoded. The principle motivation for developing the fuzzy qualitative model representation was to ease knowledge acquisition from domain experts, particularly in the case of ill-defined dynamic systems where knowledge may indeed be imprecise and uncertain. By providing the additional degree of freedom (over quantitative models) of arbitrarily defining the value domains of the qualitative model, we eliminate the requirement for a modeller to have to 'guestimate' the values of process parameters to real valued precision. Thus, qualitative models can provide a more appropriate, or more 'honest', representation of our imprecise and uncertain process knowledge.
For the particular task of parameter identification, there is also a strong motivation to exploit the finite value domain descriptions of qualitative models to provide a novel, state-space search based solution procedure. Firstly, we define the Parameter Space, P, as that space generated
Figure 2 Quantitative and Qualitative Parameter Spaces Importantly, the value domains of the parameters of qualitative models are finite domains, and thus they generate a finite sized Parameter Space. A state-space search approach to parameter identification can now be implemented (detailed in next section) to search amongst the finite number of variations in the parameter values of a qualitative model for those values which best represent the current plant condition. In contrast, each value domain, Rx, underlying the parameters of the quantitative model is an infinitely dense domain, thus the Parameter Space generated from these domains is an infinitely dense space. That is, there exists an infinite number of possible parameter assignments for a given quantitative model, which necessitates the use of an analytic parameter identification procedure (Isermann, 84). In turn, these analytic procedures generally restrict the class of possible models to linearised process models only. By adopting a novel state-space search procedure to select from the finite possibilities of the parameterised qualitative model, we eliminate the need for any such restriction on the form of the process model.
3. QPID: AN ARCIDTECTURE FOR TIMECONSTRAINED MODEL-BASED DIAGNOSIS The QPID (Qualitative Parameter Identification for Diagnosis) system performs parameter identification of fuzzy qualitative models of dynamic systems from batches of plant data. The system is designed to operate under a variety of user requirements. In particular, QPID is required to provide a solution within a prescribed timeconstraint. Figure 3 shows the architecture of QPID, an instantiation of the generic model-based diagnosis architecture developed for ARTIST (Leitch et aI., 92).
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