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A method of qualitative reasoning for model-based problem solving and its application to a nuclear plant
Expert Systems With Applications, Vol. 10, No. 3/4, pp. 441-448, 1996 Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0957-4174/96 $15.00+0.00
Pergamon
S0957-4174(96)00023-1
A Method of Qualitative Reasoning for Model-Based Problem Solving and its Application to a Nuclear Plant YOSHINOBU KITAMURA, MUNEHIKO SASAJIMA, MITSURU IKEDA AND RIICHIRO MIZOGUCHI I.S.I.R., Osaka University, 8-1 Mihogaoka, Ibaraki 567, Japan
SHINJI YOSHIKAWA AND AKIRA ENDOU Power Reactorand NuclearFuel DevelopmentCorporation,Japan
0SAMU KAKUSHO Faculty of Economicsand InformationScience, HyogoUniversity,Japan
Abstract--Model-based expert systems are expected to contribute to overcoming the difficulties of conventional rule-based systems. This paper describes the modeling of mechanical systems and a method of qualitative reasoning based on causal specifications. The causal specifications represent a component's local causal properties, following the principles for reusability and composability. It contributes to providing intuitive causal ordering of complex behavior originated in the combination of components, including inter-component negative feedback. A model of a system is represented by combining a set of local component models and global knowledge derived from general properties of the physical entity. This allows for reusable knowledge which is easy to describe. Furthermore, the method has been successfully applied to a nuclear power plant. Reasoning results were unambiguous and matched those obtained by domain experts. Copyright © 1996 Elsevier Science Ltd
1. I N T R O D U C T I O N
mathematical qualitative equations. However, ordinary mathematical equations are not enough for generating causal relations, because polynomial equations 2 do not represent time or causality. For example, consider the inlet and outlet temperature of a pipe. Assuming that no thermal energy is lost, the polynomial equation inlet_ temp=outlet_temp holds. A change in the inlet temperature causes the outlet temperature to change, but not vice versa. In spite of this asymmetry, the polynomial equation represents the causal relation as if it is symmetric. According to conventional qualitative reasoning methods (e.g. Kuipers, 1986), using only mathematical equations, values of parameters constrained by simultaneous polynomial equations are simultaneously determined, that is, no causal relation among them is identified. Humans, however, can recognize causal
LOT of research has been carried out on model-based expert systems (ESs). Much attention has been paid to qualitative reasoning as a fundamental inference technique. Conventional ESs based on associative rules (known as shallow knowledge) have many difficulties. Model-based (known as deep knowledge) ESs are expected to contribute to overcoming these difficulties. The long-term goal of this research is to develop a model-based diagnostic shell (called KCIIP) applicable to real world systems. One of the main issues here is to provide intuitive explanations of why the symptoms are 'caused' by the fault in terms of causality. That is, the system should show causal ordering of the behavior of the target systems with the fault. An approach to qualitative reasoning is based on RECENTLY, A
'III is a versionnumber.The authors have developeda diagnostic shell called KCII-DST(Hirai & Mizoguchi, 1991).
2That is, the equations only involve addition, negation and multiplication, but no integration. 441
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relations according to the system's topology and/or its physical features, even if the mathematical model does not represent temporal order among them. Conversely, in cases where time is explicitly represented, conventional qualitative reasoning methods generate the ordering among the changes predicted. Humans, however, do not always pay attention to the ordering of events. Therefore, conventional qualitative reasoning based on mathematical equations cannot always explain the behavior of the system appropriately. Another important requirement is that knowledge should be reusable and easy to describe. A model of the whole system should be easily built by composing appropriate context-independent pieces of knowledge. In cases where pieces of knowledge represent components, the principles for reusability and composability are described by the No Function In Structure (NFIS) principle and the locality principle (de Kleer & Brown, 1984). Because locality is an important characteristic of causality (Motoda, 1991), causal ordering generated by the system should preserve the locality of the knowledge. Notable work towards satisfying the requirements mentioned above have been conducted by de Kleer and Brown (1984). In their theory, by introducing mythical causality, causal relations among the changes caused by polynomial equations are derived. When polynomial equations are simultaneous, assumptions are introduced according to three heuristic rules, since these equations cannot be solved by ordinary propagations. However, reasoning with the heuristics does not always achieve results consistent with the causality recognized by humans. This is because the heuristics cannot always specify to which parameters the assumptions are to be introduced in order to identify the appropriate causality. Moreover, applications of de Kleer and Brown's theory to systems with a complex topology or negative feedback loop may generate ambiguous results (Schryver, 1992). Iwasaki and Simon criticize de Kleer and Brown's approach from the viewpoint of causality. They propose their own approach to causal ordering (Iwasaki & Simon, 1986, 1994). In their research, the importance has been pointed out of specifying exogenous parameters explicitly against the assumptions introduced by the heuristics in de Kleer's theory. The causal ordering theory, however, does not try to derive causal relations among changes caused by simultaneous polynomial equations. 3 Furthermore, the locality principle of both domain knowledge and the reasoning mechanism are not considered in any way. The authors have been involved in research on modelbased diagnostic systems for many years, aiming at the development of a method satisfying the requirements s In terms of (Iwasaki & Simon, 1986) changes in a minimal complete subset. They claim parameters in a minimal complete subset do not stand in any unique causal ordering.
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mentioned above. In this paper, a method of qualitative reasoning based on causal specification is proposed. Our approach is to take a positive attitude towards incorporating knowledge which cannot be represented locally into mathematical equations. The basic idea is that, although causal relations in the whole system depend on context (i.e structures of the system), part of a component's causality is context-independent (i.e. local). Causal ordering in the whole system is derived from local causal properties and topology of connections among the components. In the example mentioned above, causality of the pipe, whereby the outlet temperature does not affect the inlet temperature, is independent of context. In the case where the pipe is integrated into a loop structure, however, a change in the inlet temperature caused by a change in the outlet temperature is derived by propagating the effects along the loop topology of connections among the components. The causal specifications represent such local causal properties of components, following both the NFIS and the locality principles. Introducing causal specifications, the method proposed in this paper can generate intuitive causal ordering of behavior caused by inter-component negative feedback. The model of a target system is represented by a combination of local component models and global knowledge derived from the general properties of the physical entity. Thus, knowledge is reusable and easy to describe. The next section describes model building and reasoning methods. In Section 2.1, the method of diagnosis is briefly mentioned, since the reasoning method reported in this paper is designed for diagnosis, which is one of the most typical problem solving. In Section 3, application to a nuclear power plant is presented. A model of the heat transportation system of the plant and the simulation results are described. Related work is discussed in Section 4.
2. MODEL AND REASONING 2.1. A Qualitative Reasoning for Diagnosis KCIII is designed to diagnose mechanical systems by reasoning about the qualitative behavior of the systems. Given a model of a target system and a symptom, KCIII generates faults explaining the symptom. A symptom is represented by an abnormal value of an observable parameter, that is, the value can be obtained from sensors and/or testers. There are two types of faults, a parameterfault and a mode-fault. By a parameter-fault we mean one represented by an abnormal value of a parameter which is not caused by any other parameter of the model. That is, the values representing parameter-faults are caused by factors external to the system under consideration. Such parameters are called the exogenous parameters of the system (Iwasaki & Simon, 1986). In
Qualitative Reasoning for Model-Based Problem Solving
our method, exogenous parameters of a system are explicitly specified.4 By a mode-fault, on the other hand, we mean one in which an equation characterizing the behavior of a component changes. Such a fault is represented by a fault mode of a component. KCIII diagnoses a system according to the two steps, retrospective reasoning and prospective reasoning. The retrospective reasoning method generates plausible faulthypotheses covering a given symptom. Given a fault-hypothesis generated by the retrospective reasoning, on the other hand, the prospective reasoning method generates all possible symptoms that could be caused by it on the basis of a single fault assumption. The prospective reasoning engine reported in this paper reasons how a fault affects other parameters (i.e. the behavior of the system with the fault), and then generates all symptoms and explanations why the symptoms are caused by the fault. In addition to fault-hypotheses generation and faulthypotheses verification, complete diagnostic task includes evaluation of the symptoms according to how well they can distinguish between the hypotheses and check predicted values against actual values of the symptoms. Much research has been carried out on frameworks of model-based diagnosis (Hamscher et al., 1992; Puma & Yamaguchi, 1993; Yamaguchi & Mizoguchi, 1992). In this paper, we concentrate on prospective reasoning, since it plays a crucial role in KCIII. Retrospective reasoning and the evaluation step of symptoms are not discussed in this paper.
2.2. Local Knowledge The overall structure of the system is represented by a combination of component models and connections. The model of a component contains local knowledge described independently of the global structure of the system. It consists of (1) a set of parameters, (2) constraints over parameters, (3) connections to neighboring components and (4) causal specifications representing causality in the component. A parameter takes one of the three qualitative values related to the deviation from a normal value. [+] ([ - ]) represents a quantity greater(less) than the normal value. [0] represents a quantity equal to the normal value. The normal value of a parameter is defined as a permitted range of the parameter when the overall system is in a normal equilibrium state without any fault. In the normal equilibrium state, one can assume all derivatives of parameters with respect to time equal to zero. The assumption is based on the fact that the intended continuous behavior of the mechanical artifacts can be represented by the equilibrim state model by selecting 4The definitionof exogenousparametersis describedin Section2 . 2 .
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appropriate parameters. 5 Constraints are described in terms of qualitative operators and parameters. D(para) represents a derivative of para. It takes one of the three qualitative values [+], [ - ] , [0] which correspond to the sign of the derivatives. The following equation regarding the qualitative parameters holds: para ~,÷~)=paras,) + D(para)t,)
Constraints marked "[In equilibrium state]" hold only in the equilibrium states. Constraints marked "D(para)=O [In equilibrium state]" mean that the parameter converges to the equilibrium state. Observing the behavior of physical systems, humans can intuitionally recognize asymmetric causal relations. But ordinary mathematical equations cannot express it. A causal specification is an attribute of a parameter which expresses asymmetric causal relations within a component. A causal specification is denoted by the following two flags representing causal conditions. Cause: C Changes in the value of the parameter can cause those of values of other parameters in the component. Effect : E Changes in the value of the parameter can be caused by those of values of other parameters in the component.
A causal specification takes one of three values, CI~, ~E and CE, where "^" is a negation symbol. CI~, for example, represents a causal property of a parameter that a change in its value will never be caused by changes in values of other parameters in the component and that the change may cause the values of other parameters in the component to change. Parameters with a constant value, for example, a resistance R in an electric circuit, have CI~ as causal specification. Note that it does not violate the NFIS or locality principle to describe causal specifications in each component model. Causal specifications represent only the possible causes and effects from the viewpoint of the component's mechanism independently of context. According to the causal specifications, exogenous parameters of the whole system can be defined. A kind of fault can be represented by abnormal values of the exogenous parameters as mentioned in Section 2.1. Exogeneous parameters have CI~ as causal specification and are not connected to other components. That is, values of exogenous parameters are changed by factors external to the system only, i.e. the faults. 5For example,stable oscillationis representedby the equilibriumstate modeledin terms of the frequencyand amplitude parameters.
444 2.3. R e a s o n i n g
In the initial state of reasoning, an abnormal value 6 representing the fault must be specified. Other parameters have normal values. The reasoning engine has two processes, that is, intra-component reasoning and intercomponent reasoning. In the intra-component reasoning process, an abnormal value is propagated from cause parameters to effect parameters according to constraints and causal specifications. In the inter-component reasoning process, on the other hand, an abnormal value is propagated to parameters of neighboring components according to connections between ports. The reasoning engine has two time counters, that is, a fine-grained time counter and a coarse-grained time counter. The fine-grained time counter counts time for polymonial equations which only involve addition, negation and multiplication, but no integration. The counter increases when the effects derived from the polynomial equations of a component are propagated to the neighboring components. The coarse-grained time counter increases when equations involving integration are used. Time in conventional qualitative reasoning corresponds to coarse-grained time. In the case where parameters within the same component are constrained by a polynomial equation, neither fine-grained nor coarse-grained time counters increase. This means that the reasoning system considers that the changes of parameters within a component which are caused by polynomial equations occur at the same time. Thus, any causal ordering among such changes is not derived. We adopt a simple generate-andtest mechanism to solve simultaneous polynomial equations. One of the equations generates the possible states and then prunes the states violating the others. This generate-and-test cycle is repeated until all values are determined. On the other hand, when the values of parameters in a component are propagated to neighboring components, fine-grained time increases by one. Since the time cannot be modeled in the polynomial equations in any way, we should view fine-grained time as virtual. Inter-components simultaneous polynomial equations cannot be resolved by ordinary local propagation. Introducing assumptions according to causal specifications, the reasoning engine provides causal relations in the finegrained time. It assumes that parameters marked with CI~ as causal specifications are [0], and then propagates them to other parameters. A value of a parameter marked with C]~ cannot be affected by other parameters in the same component, so it can be assumed to remain as [0] in the initial equilibrium state. In the case where a loop exists in the propagation path, the value of the parameter assumed may cause a 6Parameters having an abnormal value should be exogenous parameters.
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change to the parameter itself. Such a process is a kind of feedback. 7 Assumed values ([0]), if any, are dismissed. Intra-component reasoning resumes propagating the effects of the new value. Since the feedback time interval is fine-grained, the original values are not changed even if different values are calculated based on the value determined by the feedback. This is based on the heuristic for negative feedback: if a negative feedback exists in a set of polynomial equations among components then the effect of the feedback will not instantaneously override the original values. For example, consider that the power supply to a pump driving fluid decreases. In the pump component, the equation p = f * a holds, where p is the power supply to the pump, f is the flow rate of the fluid and a is the total pressure drop of the fluid. According to its characteristics, the pump changes flow rate reacting to changes of power supply and total pressure drop. Parameters f and a are marked ~ E and CI~, respectively. When p takes [ - ], the reasoning engine derives f = [ - ] by introducing the assumption that a is [0]. Because the pressure drop is proportional to the flow rate in the line (e.g. piping), the value of a changes to [ - ].8 When a = [ - ] is propagated to the pump component, the value o f f is ambiguous derived from p = [ - ] and a = [ - - ] . 9 According to the heuristics, however, the system obtains f = [ - ] which matches reality. This example shows the plausibility of the above heuristics. A set of constraints representing feedback sometimes includes integral equations. In such a case, because the time interval of feedback is coarse-grained time, the old values are dismissed. If a parameter is marked with "converges to equilibrium state", then the reasoning engine derives the value of the parameter in the equilibrium state by ignoring the states during transition among the successive equilibriums. This is justified from the viewpoint of diagnosis. 2.4. Global K n o w l e d g e
A reasoning engine based on local knowledge may only generate ambiguous reasoning results and inappropriate causal ordering of parameters among different components. Therefore, we employ global knowledge derived from the general properties of the physical entity, such as heat and fluid, according to the topology of the connections among the components. According to the 7We use the term feedbackto representthe phenomenonthat the effect of a change propagates itself via other parameters. This definition is similar to that of Iwasaki and Simon (1986) but not to de Kleer and Brown (1984) or Williams (1984).
gIn the actual model,the line consistsof some components.Thus, using global knowledge mentioned in the paragraph below, a = [ - I is derived. 9Differentfrom other qualitative calculus, multiplicationhas the same effectas addition. Becausethe qualitative values representnot sign but deviation from a normal value.
Qualitative Reasoning for Model-Based Problem Solving
heat conservation law, for example, the reasoning engine can reason about the change of temperature caused by a heat balance of the global loop structure. Fine-grained time passes during propagation of the effects among components. Some physical phenomena, however, change globally at the same time. For example, on the assumption that fluid is incompressible, the flow rate of such a fluid at each component changes at the same time. Deriving an ordering of the changes does not make sense for humans and may cause ambiguity. Therefore, using global knowledge, the reasoning engine propagates such effects simultaneously.
445 Ports: symbol
in out up
This section describes the application of our qualitative reasoning method to a nuclear power plant. To concentrate on the behavior of the flow of thermal energy and the fluid, we built the model of the heat transportation system of the nuclear power plant. Figure 1 overviews the heat transportation system. The reactor vessel (RX) generates thermal energy which flows into the hotleg pipings of the primary loop (LOOP1). Next the thermal energy flows into the hotleg pipings of the secondary loop (LOOP2) through the intermediate heat exchanger (IHX). Lastly, the thermal energy is transported into open air through the air dump heat exchanger (AC). 3.1. C o n s t r u c t i o n o f the Model
The model of the heat transportation system consists of three local components (RX, IHX and AC) and two global components (LOOP1 and LOOP2). The models of RX and LOOP1 are shown in Figs 2 and 3, respectively. Eight parameters represent the state of RX. The value of Tlcold, one of the parameters which represents the temperature of the coolant at the inlet port of RX, affects the values of the other parameters of RX (for example, Tlhot which represents the temperature of the coolant at the outlet port of RX), while any other parameter of RX does not affect the value of Tlcold. Thus the causal specification of Tlcold is CI~. The qualitative constraints Iry Hotleg Reactor Vessel
2ry Hotlegpipings
piPlingsIntermediate
Air Dump
Heat Exchanger
Heat Exchanger
I
Tlcold
Coolant inlet Temp. Coolant outlet Temp. Avg. Temp of Core Heat generated by core (per second) Heat transported to coolant (per second) Time for coolant to go through RX
Tlhot
Trx Qt0 Qt01
Flovl
Flow rate of coolant
Qlin
Total amount of heat transported to coolant
causal specification
port
C'E -CE "CE C~E,XO
in,up out,up
CE CE C~E CE
Constraints:
up up
(t) (2) (3) (4) (s)
Q l i n ffi Qt01*T1
I]lin = Tlhot - Tlcold I]tO1 ffi T r x - ( T l h o t + T l c o l d ) D ( T r x ) = q t 0 - Qt01
In equilibrium state, D(Trx) = 0 T1 = 1 / Flowl
(6)
FIGURE 2. The qualitative model of RX
are derived from physical principles. Equation (2), for example, is derived by applying the heat conservation law to the coolant in RX. Expressions (7) and (8) of LOOP1 indicate that the total amount of variation in temperature of the hotleg and coldleg in LOOP1 is equal to the difference between the thermal energy inflow and outflow. Consider the thermal energy of a molecule of fluid circulating in a loop. After the molecule has been around the loop once, the total amount of variation of thermal energy of the molecule equals the difference between the amount of energy the molecule receives and releases. If the thermal energy of a molecule in a loop, in which the same fluid circulates, is changed, the temperature in each location of the loop changes in the same direction as the molecule. Applying this knowledge to LOOP1, the following is derived: the Port: symbol
in out
connected component
connected port
RX IHX
up upl
Parameters: symbol parameter
Qlin Qlout Tlhot TlcoXd Flowl LOOP2
connected port
outl inl in
Parameters: symbol parameter
T1 3. A P P L I C A T I O N OF T H E M E T H O D TO A NUCLEAR POWER PLANT
connected component
IHX IHX LOOP1
Heat transported from RX Heat transported to IHX Coolant Temp.(hotleg) Coolant Temp.(coldleg) Flowrate of primary loop
causal specification
port
C'E C'E "CE "CE CE
ill out
in,out in,out in,out
Constraints:
lry Coldlegpipings
2ry Coldlegpipings
FIGURE 1. Outline of the heat transportation system
D ( T l h o t ) ffi Qlin - I ] l o u t D ( T l c o l d ) ffi Q l i n - Q l o u t
(7) (8)
In equilibrium In equilibrium
(9) (10)
state, state,
D(Tlhot) = 0 D ( T l c o l d ) ffi 0
FIGURE 3. The qualitative model of LOOP1
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variation in temperature of the hotleg and coldleg in LOOP1 is determined by the difference between the thermal energy inflow from RX (Qlin) and outflow to IHX (Qlout). We thus obtain expressions (7) and (8). Expressions (9) and (10) indicate that the temperature of the fluid in LOOP1 is stable when the heat inflow and outflow of LOOP1 are balanced. Long after the occurrence of this anomaly, the heat transportation system achieves the equilibrium state and, hence, the temperature of the fluid is stable. 3.2. Result of the Reasoning Table 1 shows the simulation results of the proposed method applied to the heat transportation system of the nuclear power plant. An anomaly is represented by an exogenous parameter taking an abnormal value. Given one of the anomalous observations, the reasoning engine determines which value the other parameters take when the system achieves the heat balanced state. Items of the horizontal axis in Table 1 show candidate anomalies. The vertical axis lists the names of the other parameters. All results in the table correspond to those of the domain experts, without any ambiguity. Although our model itself represents part of the whole function of the heat transportation system, the result of the qualitative simulation of our model of a real plant is very satisfactory. 3.3. Discussions and Implementation of the System The application described above suggests that the method reported in this paper satisfies the requirements mentioned in Section 1. Let us consider the first requirement, that is, "intuitive explanation based on
TABLE 1 Results of Qualitative Simulation of our Model
Trx Qt01 T1 T1 hot T1 cold Hihx Qt12 T2 T2hot T2cold Qt23 Hair T3 T3hot T3cold
RX fission power (high)
IHX heat trans. resist, (high)
LOOP1 flow rate (low)
LOOP2 flow rate (low)
AC heat trans. resist. (high)
+ + 0 + + 0 + 0 + +
+ 0 0 + + 0 0 0 0 0
0 0 + + 0 0 0 0 0
0 0 0 0 0 0 0 + + -
+ + 0 + + 0 0 0 + +
+
0
0
0
0
0 0 + 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0
causality" along the application mentioned above. Temperatures of fluid at the inlet and outlet of each component are constrained by simultaneous polynomial equations. Introducing fine-grained time, the reasoning engine provides causal relations among the changes in temperature. When the heat transfer resistance of IHX decreases, for example, the reasoning engine derives the changes in the outlet temperatures of IHX. Because the outlet of IHX connects with the inlet of RX, the change in IHX's outlet temperature is propagated by RX's inlet temperature. Then in RX, the change in the inlet temperature causes a change in the outlet temperature. This example shows that the method provides causal ordering for intuitive explanation according to the topology of the system. In order to solve simultaneous polynomial equations, the reasoning engine introduces an assumption according to the causal specifications. In the same example mentioned above, the reasoning engine assumes that the inlet temperatures of IHX remain [0] while propagating the effect of the first disturbance on the heat transfer resistance of IHX. This assumption is based on a mechanism of IHX, that is, the fluid flows through pipes from the inlet to the outlet. Assumptions justified by the properties of the components contribute to providing intuitive causal ordering. The model of the system is represented by combining local component models and global knowledge derived from the general properties of the physical entity. The knowledge is thus reusable and easy to describe (the second requirement). According to the heat conservation law, for example, the reasoning engine can reason about the change in temperature caused by the heat balance of the global loop structure. This system is currently under implementation in Common ESP, an object oriented Prolog, on a UNIX workstation. The intra- and inter-component reasoning modules and part of the reasoning about global phenomena have been implemented. 4. RELATED WORK The method reported in this paper is similar to the one proposed by de Kleer and Brown (1984). Fine-grained time corresponds to de Kleer's mythical time. One of the differentiating features of our approach is the causal specifications which explicitly represent causal properties. Causal specifications contribute to reducing the arbitrariness of the decision on which parameters should be assumed. In de Kleer's teleogical analysis (de Kleer, 1984), local causal patterns of a component (known as configurations) are described. Our causal specifications are not so specific as configurations, and they do not represent teleogical or functional but mechanical properties. Functional knowledge is mentioned in the next section. In de Kleer's research, constraints from the topology
Qualitative Reasoning for Model-Based Problem Solving
of the system are represented as local conditions only. We think the approach is not expensive enough for modeling the complex systems. In our method, a variety of constraints which arise from global structures of systems can be represented as global knowledge. The global knowledge regarding heat mentioned in Section 2.4, for example, corresponds to an energy constraint for QSIM (Fouch6 & Kuipers, 1992). Moreover, propagation time among components can be represented as global knowledge. According to global knowledge concerning the flow rate of a fluid, for example, the reasoning engine propagates effects simultaneously. Schryver has proposed an extended version of the qualitative calculus of de Kleer and Brown in order to apply it to complex systems (Schryver, 1992). Invisible connections for flow compatibility and iterative propagation were among the new features provided for deriving causal ordering in complex systems. They are the result of enforcement of the locality. Schryver, however, suggests that non-local assumptions are probably unavoidable in accounting for the behavior of complex systems (Schryver, 1992, p. 540). TQ analysis (Williams, 1984) provides heuristics to determine the effect and feedback terms of feedback ~°for limited kinds of feedback involving integration. The causal specifications can identify the effect terms of feedback consisting only of polynomial equations. However, they do not distinguish between feedback terms and cause terms. Moreover, TQ analysis uses two heuristics to disambiguate the value of the effect term in a negative feedback loop. Our method generates the same results by reasoning about time and using heuristics for negative feedback consisting only of polynomial equations. Top and Akkermans has proposed a method to generate causal order using the bond-graph [16]. Bondgraphs are based on a small set of generic physical mechanisms: storage processes, sources and sinks etc. Bond-graphs assign causality within all types of feedback, but in the case of feedback consisting only of polynomial equations, the direction is arbitrary. We believe that there is no way to assign a unique direction of such feedback using only mathematical and/or generic knowledge. According to Lee and Compton (1994) and Skorstad (1992), causal relations in the whole system depend on context. However, there are components which have context-independent causal relations specific to them. We describe such causality within components in terms of the causal specification. The reasoning engine provides causal ordering over the whole system by reasoning about the complex effects originated in the combination of components using local causality in each ~°In Williams (1984), the general form of feedback is A+B=C, B=f(C). Then A is an independent cause term, in which B is a feedback term and C is an effect term.
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component. The computed causal ordering preserves locality based on components, including changes caused by simultaneous polynomial equations in different components. In Forbus (1984) and Washio (1990), causal properties of physical processes and/or laws are described, while we describe causal properties within components, adopting device-centered modeling. 5. SUMMARY A new qualitative reasoning method has been proposed. Structural and causal properties of components are described explicitly, following the principles for reusability and composability. It contributes to providing intuitive causal ordering and disambiguation of reasoning results. Following the qualitative modeling method we proposed, we built a model of the heat transportation system of a nuclear power plant. The reasoning results correspond exactly to those of domain experts, though the model itself represents a portion of the whole function of the system running in a real world. The single fault assumption (mentioned in Section 2.1), the normal equilibrium state (Section 2.2) and heuristics for negative feedback (Section 2.3) contribute to the efficiency of the reasoning process. The application to a nuclear power plant, concentrating on the behavior of the flow of thermal energy and the fluid, suggests the plausibility of these assumptions. Understanding the limitation of the method remains future work. In the application mentioned in Section 3, global knowledge is directly described as constraints in global components. We think that global knowledge can be derived from the general properties of the physical entity such as heat and fluid according to the topology of the connections among the components. Currently, investigation on mechanisms which automatically generate global knowledge is in progress. Causal specificiations do not represent constituents of functions. In order to provide sophisticated explanations, currently an investigation to establish an ontology for representing function is also progress (Sasajima et al., 1994).
Acknowledgement--The authors
would like to thank Dr Johan Vanwelkenhuysen for his valuable comments.
REFERENCES Forbus, K. D. (1984). Qualitative process theory. Artificial Intelligence, 24, 85-168. Fouch~, P. & Kuipers, B. J. (1992). Reasoning about energy in qualitative simulation. IEEE Trans. on Systems, Man, and Cybernetics, 22-1, 47-63. Hamscher, W. et al. (Eds) (1992). Readings in model-based diagnosis.
448 San Mateo, CA: Kaufmann. Hirai, K. & Mizoguchi, R. (1991). The organization of the domain knowledge oriented to sharability--Domain-specific tool based on the deep knowledge (KCII-DST). Proc. of the 5th Annual Conference of JSAL 1,325-328 (in Japanese). Iwasaki, Y. & Simon, H. A. (1986). Causality in device behavior. Artificial Intelligence, 29, 3-32. Iwasaki, Y. & Simon, H. A. (1994). Causality and model abstraction. Artificial Intelligence, 67, 143-194. de Kleer, J. & Brown, J. S. (1984). A qualitative physics based on confluences. Artificial Intelligence, 24, 7-83. de Kleer, J. (1984). How circuits work. Artificial Intelligence, 24, 205-280. Kuipers, B. (1986). Causal simulation. Artificial Intelligence, 26, 289-338. Lee, M. & Compton, P. (1994). Context-dependent causal explanations. In Proc. of the Eighth International Workshop on Qualitative Reasoning about Physical Systems, pp. 176-186. Motoda, H. (1991). Causal understanding. In Cognitive science handbook, pp. 119-127 (in Japanese). Puma, Y. W. & Yamaguchi, T. (1993). Exploiting useful sorts of knowledge and strategies for fault diagnosis: A framework for
Y Kitamura et aL hypothesis generation in model-based diagnosis. In Proc. of the 7th Annual Conferrence of JSAl, pp. 619-622. Sasajima, M., Kitamura Y., Mizoghuchi, R. et al. (1994). An investigation to domain ontology to represent functional models. In Proc. of the Eighth International Workshop on Qualitative Reasoning about Physical Systems, pp. 224-233. Schryver, J. C. (1992). Object-oriented qualitative simulation of human mental models of complex systems. IEEE Trans. on Systems, Man, and Cybernetics 22-3, 526-541. Skorstad, G. (1992). Finding stable causal interpretations of equations. In Recent advances in qualitative physics, Faltings & Struss (Eds), pp. 399-413. Cambridge, MA: MIT Press. Top, J. & Akkermans, H. (1991). Computational and physical causality. In Proc. of the IJCAI '91, pp. 1171-1176. Washio, T. (1990). Derivation of exogenously-driven causality based on physical laws. Journal of Japanese Society for Artificial Intelligence, 5..4, 94-103 (in Japenese). Williams, B. C. (1984) Qualitative analysis of MOS circuits. Artificial Intelligence, 24, 281-346. Yamaguchi, T. & Mizoguchi, R. (1992). Knowledge compiler II based on domain model and failure model. Journal of Japanese Society for Artificial Intelligence, 7-4, 663-674 (in Japanese).
Pergamon
S0957-4174(96)00023-1
A Method of Qualitative Reasoning for Model-Based Problem Solving and its Application to a Nuclear Plant YOSHINOBU KITAMURA, MUNEHIKO SASAJIMA, MITSURU IKEDA AND RIICHIRO MIZOGUCHI I.S.I.R., Osaka University, 8-1 Mihogaoka, Ibaraki 567, Japan
SHINJI YOSHIKAWA AND AKIRA ENDOU Power Reactorand NuclearFuel DevelopmentCorporation,Japan
0SAMU KAKUSHO Faculty of Economicsand InformationScience, HyogoUniversity,Japan
Abstract--Model-based expert systems are expected to contribute to overcoming the difficulties of conventional rule-based systems. This paper describes the modeling of mechanical systems and a method of qualitative reasoning based on causal specifications. The causal specifications represent a component's local causal properties, following the principles for reusability and composability. It contributes to providing intuitive causal ordering of complex behavior originated in the combination of components, including inter-component negative feedback. A model of a system is represented by combining a set of local component models and global knowledge derived from general properties of the physical entity. This allows for reusable knowledge which is easy to describe. Furthermore, the method has been successfully applied to a nuclear power plant. Reasoning results were unambiguous and matched those obtained by domain experts. Copyright © 1996 Elsevier Science Ltd
1. I N T R O D U C T I O N
mathematical qualitative equations. However, ordinary mathematical equations are not enough for generating causal relations, because polynomial equations 2 do not represent time or causality. For example, consider the inlet and outlet temperature of a pipe. Assuming that no thermal energy is lost, the polynomial equation inlet_ temp=outlet_temp holds. A change in the inlet temperature causes the outlet temperature to change, but not vice versa. In spite of this asymmetry, the polynomial equation represents the causal relation as if it is symmetric. According to conventional qualitative reasoning methods (e.g. Kuipers, 1986), using only mathematical equations, values of parameters constrained by simultaneous polynomial equations are simultaneously determined, that is, no causal relation among them is identified. Humans, however, can recognize causal
LOT of research has been carried out on model-based expert systems (ESs). Much attention has been paid to qualitative reasoning as a fundamental inference technique. Conventional ESs based on associative rules (known as shallow knowledge) have many difficulties. Model-based (known as deep knowledge) ESs are expected to contribute to overcoming these difficulties. The long-term goal of this research is to develop a model-based diagnostic shell (called KCIIP) applicable to real world systems. One of the main issues here is to provide intuitive explanations of why the symptoms are 'caused' by the fault in terms of causality. That is, the system should show causal ordering of the behavior of the target systems with the fault. An approach to qualitative reasoning is based on RECENTLY, A
'III is a versionnumber.The authors have developeda diagnostic shell called KCII-DST(Hirai & Mizoguchi, 1991).
2That is, the equations only involve addition, negation and multiplication, but no integration. 441
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relations according to the system's topology and/or its physical features, even if the mathematical model does not represent temporal order among them. Conversely, in cases where time is explicitly represented, conventional qualitative reasoning methods generate the ordering among the changes predicted. Humans, however, do not always pay attention to the ordering of events. Therefore, conventional qualitative reasoning based on mathematical equations cannot always explain the behavior of the system appropriately. Another important requirement is that knowledge should be reusable and easy to describe. A model of the whole system should be easily built by composing appropriate context-independent pieces of knowledge. In cases where pieces of knowledge represent components, the principles for reusability and composability are described by the No Function In Structure (NFIS) principle and the locality principle (de Kleer & Brown, 1984). Because locality is an important characteristic of causality (Motoda, 1991), causal ordering generated by the system should preserve the locality of the knowledge. Notable work towards satisfying the requirements mentioned above have been conducted by de Kleer and Brown (1984). In their theory, by introducing mythical causality, causal relations among the changes caused by polynomial equations are derived. When polynomial equations are simultaneous, assumptions are introduced according to three heuristic rules, since these equations cannot be solved by ordinary propagations. However, reasoning with the heuristics does not always achieve results consistent with the causality recognized by humans. This is because the heuristics cannot always specify to which parameters the assumptions are to be introduced in order to identify the appropriate causality. Moreover, applications of de Kleer and Brown's theory to systems with a complex topology or negative feedback loop may generate ambiguous results (Schryver, 1992). Iwasaki and Simon criticize de Kleer and Brown's approach from the viewpoint of causality. They propose their own approach to causal ordering (Iwasaki & Simon, 1986, 1994). In their research, the importance has been pointed out of specifying exogenous parameters explicitly against the assumptions introduced by the heuristics in de Kleer's theory. The causal ordering theory, however, does not try to derive causal relations among changes caused by simultaneous polynomial equations. 3 Furthermore, the locality principle of both domain knowledge and the reasoning mechanism are not considered in any way. The authors have been involved in research on modelbased diagnostic systems for many years, aiming at the development of a method satisfying the requirements s In terms of (Iwasaki & Simon, 1986) changes in a minimal complete subset. They claim parameters in a minimal complete subset do not stand in any unique causal ordering.
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mentioned above. In this paper, a method of qualitative reasoning based on causal specification is proposed. Our approach is to take a positive attitude towards incorporating knowledge which cannot be represented locally into mathematical equations. The basic idea is that, although causal relations in the whole system depend on context (i.e structures of the system), part of a component's causality is context-independent (i.e. local). Causal ordering in the whole system is derived from local causal properties and topology of connections among the components. In the example mentioned above, causality of the pipe, whereby the outlet temperature does not affect the inlet temperature, is independent of context. In the case where the pipe is integrated into a loop structure, however, a change in the inlet temperature caused by a change in the outlet temperature is derived by propagating the effects along the loop topology of connections among the components. The causal specifications represent such local causal properties of components, following both the NFIS and the locality principles. Introducing causal specifications, the method proposed in this paper can generate intuitive causal ordering of behavior caused by inter-component negative feedback. The model of a target system is represented by a combination of local component models and global knowledge derived from the general properties of the physical entity. Thus, knowledge is reusable and easy to describe. The next section describes model building and reasoning methods. In Section 2.1, the method of diagnosis is briefly mentioned, since the reasoning method reported in this paper is designed for diagnosis, which is one of the most typical problem solving. In Section 3, application to a nuclear power plant is presented. A model of the heat transportation system of the plant and the simulation results are described. Related work is discussed in Section 4.
2. MODEL AND REASONING 2.1. A Qualitative Reasoning for Diagnosis KCIII is designed to diagnose mechanical systems by reasoning about the qualitative behavior of the systems. Given a model of a target system and a symptom, KCIII generates faults explaining the symptom. A symptom is represented by an abnormal value of an observable parameter, that is, the value can be obtained from sensors and/or testers. There are two types of faults, a parameterfault and a mode-fault. By a parameter-fault we mean one represented by an abnormal value of a parameter which is not caused by any other parameter of the model. That is, the values representing parameter-faults are caused by factors external to the system under consideration. Such parameters are called the exogenous parameters of the system (Iwasaki & Simon, 1986). In
Qualitative Reasoning for Model-Based Problem Solving
our method, exogenous parameters of a system are explicitly specified.4 By a mode-fault, on the other hand, we mean one in which an equation characterizing the behavior of a component changes. Such a fault is represented by a fault mode of a component. KCIII diagnoses a system according to the two steps, retrospective reasoning and prospective reasoning. The retrospective reasoning method generates plausible faulthypotheses covering a given symptom. Given a fault-hypothesis generated by the retrospective reasoning, on the other hand, the prospective reasoning method generates all possible symptoms that could be caused by it on the basis of a single fault assumption. The prospective reasoning engine reported in this paper reasons how a fault affects other parameters (i.e. the behavior of the system with the fault), and then generates all symptoms and explanations why the symptoms are caused by the fault. In addition to fault-hypotheses generation and faulthypotheses verification, complete diagnostic task includes evaluation of the symptoms according to how well they can distinguish between the hypotheses and check predicted values against actual values of the symptoms. Much research has been carried out on frameworks of model-based diagnosis (Hamscher et al., 1992; Puma & Yamaguchi, 1993; Yamaguchi & Mizoguchi, 1992). In this paper, we concentrate on prospective reasoning, since it plays a crucial role in KCIII. Retrospective reasoning and the evaluation step of symptoms are not discussed in this paper.
2.2. Local Knowledge The overall structure of the system is represented by a combination of component models and connections. The model of a component contains local knowledge described independently of the global structure of the system. It consists of (1) a set of parameters, (2) constraints over parameters, (3) connections to neighboring components and (4) causal specifications representing causality in the component. A parameter takes one of the three qualitative values related to the deviation from a normal value. [+] ([ - ]) represents a quantity greater(less) than the normal value. [0] represents a quantity equal to the normal value. The normal value of a parameter is defined as a permitted range of the parameter when the overall system is in a normal equilibrium state without any fault. In the normal equilibrium state, one can assume all derivatives of parameters with respect to time equal to zero. The assumption is based on the fact that the intended continuous behavior of the mechanical artifacts can be represented by the equilibrim state model by selecting 4The definitionof exogenousparametersis describedin Section2 . 2 .
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appropriate parameters. 5 Constraints are described in terms of qualitative operators and parameters. D(para) represents a derivative of para. It takes one of the three qualitative values [+], [ - ] , [0] which correspond to the sign of the derivatives. The following equation regarding the qualitative parameters holds: para ~,÷~)=paras,) + D(para)t,)
Constraints marked "[In equilibrium state]" hold only in the equilibrium states. Constraints marked "D(para)=O [In equilibrium state]" mean that the parameter converges to the equilibrium state. Observing the behavior of physical systems, humans can intuitionally recognize asymmetric causal relations. But ordinary mathematical equations cannot express it. A causal specification is an attribute of a parameter which expresses asymmetric causal relations within a component. A causal specification is denoted by the following two flags representing causal conditions. Cause: C Changes in the value of the parameter can cause those of values of other parameters in the component. Effect : E Changes in the value of the parameter can be caused by those of values of other parameters in the component.
A causal specification takes one of three values, CI~, ~E and CE, where "^" is a negation symbol. CI~, for example, represents a causal property of a parameter that a change in its value will never be caused by changes in values of other parameters in the component and that the change may cause the values of other parameters in the component to change. Parameters with a constant value, for example, a resistance R in an electric circuit, have CI~ as causal specification. Note that it does not violate the NFIS or locality principle to describe causal specifications in each component model. Causal specifications represent only the possible causes and effects from the viewpoint of the component's mechanism independently of context. According to the causal specifications, exogenous parameters of the whole system can be defined. A kind of fault can be represented by abnormal values of the exogenous parameters as mentioned in Section 2.1. Exogeneous parameters have CI~ as causal specification and are not connected to other components. That is, values of exogenous parameters are changed by factors external to the system only, i.e. the faults. 5For example,stable oscillationis representedby the equilibriumstate modeledin terms of the frequencyand amplitude parameters.
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In the initial state of reasoning, an abnormal value 6 representing the fault must be specified. Other parameters have normal values. The reasoning engine has two processes, that is, intra-component reasoning and intercomponent reasoning. In the intra-component reasoning process, an abnormal value is propagated from cause parameters to effect parameters according to constraints and causal specifications. In the inter-component reasoning process, on the other hand, an abnormal value is propagated to parameters of neighboring components according to connections between ports. The reasoning engine has two time counters, that is, a fine-grained time counter and a coarse-grained time counter. The fine-grained time counter counts time for polymonial equations which only involve addition, negation and multiplication, but no integration. The counter increases when the effects derived from the polynomial equations of a component are propagated to the neighboring components. The coarse-grained time counter increases when equations involving integration are used. Time in conventional qualitative reasoning corresponds to coarse-grained time. In the case where parameters within the same component are constrained by a polynomial equation, neither fine-grained nor coarse-grained time counters increase. This means that the reasoning system considers that the changes of parameters within a component which are caused by polynomial equations occur at the same time. Thus, any causal ordering among such changes is not derived. We adopt a simple generate-andtest mechanism to solve simultaneous polynomial equations. One of the equations generates the possible states and then prunes the states violating the others. This generate-and-test cycle is repeated until all values are determined. On the other hand, when the values of parameters in a component are propagated to neighboring components, fine-grained time increases by one. Since the time cannot be modeled in the polynomial equations in any way, we should view fine-grained time as virtual. Inter-components simultaneous polynomial equations cannot be resolved by ordinary local propagation. Introducing assumptions according to causal specifications, the reasoning engine provides causal relations in the finegrained time. It assumes that parameters marked with CI~ as causal specifications are [0], and then propagates them to other parameters. A value of a parameter marked with C]~ cannot be affected by other parameters in the same component, so it can be assumed to remain as [0] in the initial equilibrium state. In the case where a loop exists in the propagation path, the value of the parameter assumed may cause a 6Parameters having an abnormal value should be exogenous parameters.
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change to the parameter itself. Such a process is a kind of feedback. 7 Assumed values ([0]), if any, are dismissed. Intra-component reasoning resumes propagating the effects of the new value. Since the feedback time interval is fine-grained, the original values are not changed even if different values are calculated based on the value determined by the feedback. This is based on the heuristic for negative feedback: if a negative feedback exists in a set of polynomial equations among components then the effect of the feedback will not instantaneously override the original values. For example, consider that the power supply to a pump driving fluid decreases. In the pump component, the equation p = f * a holds, where p is the power supply to the pump, f is the flow rate of the fluid and a is the total pressure drop of the fluid. According to its characteristics, the pump changes flow rate reacting to changes of power supply and total pressure drop. Parameters f and a are marked ~ E and CI~, respectively. When p takes [ - ], the reasoning engine derives f = [ - ] by introducing the assumption that a is [0]. Because the pressure drop is proportional to the flow rate in the line (e.g. piping), the value of a changes to [ - ].8 When a = [ - ] is propagated to the pump component, the value o f f is ambiguous derived from p = [ - ] and a = [ - - ] . 9 According to the heuristics, however, the system obtains f = [ - ] which matches reality. This example shows the plausibility of the above heuristics. A set of constraints representing feedback sometimes includes integral equations. In such a case, because the time interval of feedback is coarse-grained time, the old values are dismissed. If a parameter is marked with "converges to equilibrium state", then the reasoning engine derives the value of the parameter in the equilibrium state by ignoring the states during transition among the successive equilibriums. This is justified from the viewpoint of diagnosis. 2.4. Global K n o w l e d g e
A reasoning engine based on local knowledge may only generate ambiguous reasoning results and inappropriate causal ordering of parameters among different components. Therefore, we employ global knowledge derived from the general properties of the physical entity, such as heat and fluid, according to the topology of the connections among the components. According to the 7We use the term feedbackto representthe phenomenonthat the effect of a change propagates itself via other parameters. This definition is similar to that of Iwasaki and Simon (1986) but not to de Kleer and Brown (1984) or Williams (1984).
gIn the actual model,the line consistsof some components.Thus, using global knowledge mentioned in the paragraph below, a = [ - I is derived. 9Differentfrom other qualitative calculus, multiplicationhas the same effectas addition. Becausethe qualitative values representnot sign but deviation from a normal value.
Qualitative Reasoning for Model-Based Problem Solving
heat conservation law, for example, the reasoning engine can reason about the change of temperature caused by a heat balance of the global loop structure. Fine-grained time passes during propagation of the effects among components. Some physical phenomena, however, change globally at the same time. For example, on the assumption that fluid is incompressible, the flow rate of such a fluid at each component changes at the same time. Deriving an ordering of the changes does not make sense for humans and may cause ambiguity. Therefore, using global knowledge, the reasoning engine propagates such effects simultaneously.
445 Ports: symbol
in out up
This section describes the application of our qualitative reasoning method to a nuclear power plant. To concentrate on the behavior of the flow of thermal energy and the fluid, we built the model of the heat transportation system of the nuclear power plant. Figure 1 overviews the heat transportation system. The reactor vessel (RX) generates thermal energy which flows into the hotleg pipings of the primary loop (LOOP1). Next the thermal energy flows into the hotleg pipings of the secondary loop (LOOP2) through the intermediate heat exchanger (IHX). Lastly, the thermal energy is transported into open air through the air dump heat exchanger (AC). 3.1. C o n s t r u c t i o n o f the Model
The model of the heat transportation system consists of three local components (RX, IHX and AC) and two global components (LOOP1 and LOOP2). The models of RX and LOOP1 are shown in Figs 2 and 3, respectively. Eight parameters represent the state of RX. The value of Tlcold, one of the parameters which represents the temperature of the coolant at the inlet port of RX, affects the values of the other parameters of RX (for example, Tlhot which represents the temperature of the coolant at the outlet port of RX), while any other parameter of RX does not affect the value of Tlcold. Thus the causal specification of Tlcold is CI~. The qualitative constraints Iry Hotleg Reactor Vessel
2ry Hotlegpipings
piPlingsIntermediate
Air Dump
Heat Exchanger
Heat Exchanger
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Tlcold
Coolant inlet Temp. Coolant outlet Temp. Avg. Temp of Core Heat generated by core (per second) Heat transported to coolant (per second) Time for coolant to go through RX
Tlhot
Trx Qt0 Qt01
Flovl
Flow rate of coolant
Qlin
Total amount of heat transported to coolant
causal specification
port
C'E -CE "CE C~E,XO
in,up out,up
CE CE C~E CE
Constraints:
up up
(t) (2) (3) (4) (s)
Q l i n ffi Qt01*T1
I]lin = Tlhot - Tlcold I]tO1 ffi T r x - ( T l h o t + T l c o l d ) D ( T r x ) = q t 0 - Qt01
In equilibrium state, D(Trx) = 0 T1 = 1 / Flowl
(6)
FIGURE 2. The qualitative model of RX
are derived from physical principles. Equation (2), for example, is derived by applying the heat conservation law to the coolant in RX. Expressions (7) and (8) of LOOP1 indicate that the total amount of variation in temperature of the hotleg and coldleg in LOOP1 is equal to the difference between the thermal energy inflow and outflow. Consider the thermal energy of a molecule of fluid circulating in a loop. After the molecule has been around the loop once, the total amount of variation of thermal energy of the molecule equals the difference between the amount of energy the molecule receives and releases. If the thermal energy of a molecule in a loop, in which the same fluid circulates, is changed, the temperature in each location of the loop changes in the same direction as the molecule. Applying this knowledge to LOOP1, the following is derived: the Port: symbol
in out
connected component
connected port
RX IHX
up upl
Parameters: symbol parameter
Qlin Qlout Tlhot TlcoXd Flowl LOOP2
connected port
outl inl in
Parameters: symbol parameter
T1 3. A P P L I C A T I O N OF T H E M E T H O D TO A NUCLEAR POWER PLANT
connected component
IHX IHX LOOP1
Heat transported from RX Heat transported to IHX Coolant Temp.(hotleg) Coolant Temp.(coldleg) Flowrate of primary loop
causal specification
port
C'E C'E "CE "CE CE
ill out
in,out in,out in,out
Constraints:
lry Coldlegpipings
2ry Coldlegpipings
FIGURE 1. Outline of the heat transportation system
D ( T l h o t ) ffi Qlin - I ] l o u t D ( T l c o l d ) ffi Q l i n - Q l o u t
(7) (8)
In equilibrium In equilibrium
(9) (10)
state, state,
D(Tlhot) = 0 D ( T l c o l d ) ffi 0
FIGURE 3. The qualitative model of LOOP1
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variation in temperature of the hotleg and coldleg in LOOP1 is determined by the difference between the thermal energy inflow from RX (Qlin) and outflow to IHX (Qlout). We thus obtain expressions (7) and (8). Expressions (9) and (10) indicate that the temperature of the fluid in LOOP1 is stable when the heat inflow and outflow of LOOP1 are balanced. Long after the occurrence of this anomaly, the heat transportation system achieves the equilibrium state and, hence, the temperature of the fluid is stable. 3.2. Result of the Reasoning Table 1 shows the simulation results of the proposed method applied to the heat transportation system of the nuclear power plant. An anomaly is represented by an exogenous parameter taking an abnormal value. Given one of the anomalous observations, the reasoning engine determines which value the other parameters take when the system achieves the heat balanced state. Items of the horizontal axis in Table 1 show candidate anomalies. The vertical axis lists the names of the other parameters. All results in the table correspond to those of the domain experts, without any ambiguity. Although our model itself represents part of the whole function of the heat transportation system, the result of the qualitative simulation of our model of a real plant is very satisfactory. 3.3. Discussions and Implementation of the System The application described above suggests that the method reported in this paper satisfies the requirements mentioned in Section 1. Let us consider the first requirement, that is, "intuitive explanation based on
TABLE 1 Results of Qualitative Simulation of our Model
Trx Qt01 T1 T1 hot T1 cold Hihx Qt12 T2 T2hot T2cold Qt23 Hair T3 T3hot T3cold
RX fission power (high)
IHX heat trans. resist, (high)
LOOP1 flow rate (low)
LOOP2 flow rate (low)
AC heat trans. resist. (high)
+ + 0 + + 0 + 0 + +
+ 0 0 + + 0 0 0 0 0
0 0 + + 0 0 0 0 0
0 0 0 0 0 0 0 + + -
+ + 0 + + 0 0 0 + +
+
0
0
0
0
0 0 + 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0
causality" along the application mentioned above. Temperatures of fluid at the inlet and outlet of each component are constrained by simultaneous polynomial equations. Introducing fine-grained time, the reasoning engine provides causal relations among the changes in temperature. When the heat transfer resistance of IHX decreases, for example, the reasoning engine derives the changes in the outlet temperatures of IHX. Because the outlet of IHX connects with the inlet of RX, the change in IHX's outlet temperature is propagated by RX's inlet temperature. Then in RX, the change in the inlet temperature causes a change in the outlet temperature. This example shows that the method provides causal ordering for intuitive explanation according to the topology of the system. In order to solve simultaneous polynomial equations, the reasoning engine introduces an assumption according to the causal specifications. In the same example mentioned above, the reasoning engine assumes that the inlet temperatures of IHX remain [0] while propagating the effect of the first disturbance on the heat transfer resistance of IHX. This assumption is based on a mechanism of IHX, that is, the fluid flows through pipes from the inlet to the outlet. Assumptions justified by the properties of the components contribute to providing intuitive causal ordering. The model of the system is represented by combining local component models and global knowledge derived from the general properties of the physical entity. The knowledge is thus reusable and easy to describe (the second requirement). According to the heat conservation law, for example, the reasoning engine can reason about the change in temperature caused by the heat balance of the global loop structure. This system is currently under implementation in Common ESP, an object oriented Prolog, on a UNIX workstation. The intra- and inter-component reasoning modules and part of the reasoning about global phenomena have been implemented. 4. RELATED WORK The method reported in this paper is similar to the one proposed by de Kleer and Brown (1984). Fine-grained time corresponds to de Kleer's mythical time. One of the differentiating features of our approach is the causal specifications which explicitly represent causal properties. Causal specifications contribute to reducing the arbitrariness of the decision on which parameters should be assumed. In de Kleer's teleogical analysis (de Kleer, 1984), local causal patterns of a component (known as configurations) are described. Our causal specifications are not so specific as configurations, and they do not represent teleogical or functional but mechanical properties. Functional knowledge is mentioned in the next section. In de Kleer's research, constraints from the topology
Qualitative Reasoning for Model-Based Problem Solving
of the system are represented as local conditions only. We think the approach is not expensive enough for modeling the complex systems. In our method, a variety of constraints which arise from global structures of systems can be represented as global knowledge. The global knowledge regarding heat mentioned in Section 2.4, for example, corresponds to an energy constraint for QSIM (Fouch6 & Kuipers, 1992). Moreover, propagation time among components can be represented as global knowledge. According to global knowledge concerning the flow rate of a fluid, for example, the reasoning engine propagates effects simultaneously. Schryver has proposed an extended version of the qualitative calculus of de Kleer and Brown in order to apply it to complex systems (Schryver, 1992). Invisible connections for flow compatibility and iterative propagation were among the new features provided for deriving causal ordering in complex systems. They are the result of enforcement of the locality. Schryver, however, suggests that non-local assumptions are probably unavoidable in accounting for the behavior of complex systems (Schryver, 1992, p. 540). TQ analysis (Williams, 1984) provides heuristics to determine the effect and feedback terms of feedback ~°for limited kinds of feedback involving integration. The causal specifications can identify the effect terms of feedback consisting only of polynomial equations. However, they do not distinguish between feedback terms and cause terms. Moreover, TQ analysis uses two heuristics to disambiguate the value of the effect term in a negative feedback loop. Our method generates the same results by reasoning about time and using heuristics for negative feedback consisting only of polynomial equations. Top and Akkermans has proposed a method to generate causal order using the bond-graph [16]. Bondgraphs are based on a small set of generic physical mechanisms: storage processes, sources and sinks etc. Bond-graphs assign causality within all types of feedback, but in the case of feedback consisting only of polynomial equations, the direction is arbitrary. We believe that there is no way to assign a unique direction of such feedback using only mathematical and/or generic knowledge. According to Lee and Compton (1994) and Skorstad (1992), causal relations in the whole system depend on context. However, there are components which have context-independent causal relations specific to them. We describe such causality within components in terms of the causal specification. The reasoning engine provides causal ordering over the whole system by reasoning about the complex effects originated in the combination of components using local causality in each ~°In Williams (1984), the general form of feedback is A+B=C, B=f(C). Then A is an independent cause term, in which B is a feedback term and C is an effect term.
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component. The computed causal ordering preserves locality based on components, including changes caused by simultaneous polynomial equations in different components. In Forbus (1984) and Washio (1990), causal properties of physical processes and/or laws are described, while we describe causal properties within components, adopting device-centered modeling. 5. SUMMARY A new qualitative reasoning method has been proposed. Structural and causal properties of components are described explicitly, following the principles for reusability and composability. It contributes to providing intuitive causal ordering and disambiguation of reasoning results. Following the qualitative modeling method we proposed, we built a model of the heat transportation system of a nuclear power plant. The reasoning results correspond exactly to those of domain experts, though the model itself represents a portion of the whole function of the system running in a real world. The single fault assumption (mentioned in Section 2.1), the normal equilibrium state (Section 2.2) and heuristics for negative feedback (Section 2.3) contribute to the efficiency of the reasoning process. The application to a nuclear power plant, concentrating on the behavior of the flow of thermal energy and the fluid, suggests the plausibility of these assumptions. Understanding the limitation of the method remains future work. In the application mentioned in Section 3, global knowledge is directly described as constraints in global components. We think that global knowledge can be derived from the general properties of the physical entity such as heat and fluid according to the topology of the connections among the components. Currently, investigation on mechanisms which automatically generate global knowledge is in progress. Causal specificiations do not represent constituents of functions. In order to provide sophisticated explanations, currently an investigation to establish an ontology for representing function is also progress (Sasajima et al., 1994).
Acknowledgement--The authors
would like to thank Dr Johan Vanwelkenhuysen for his valuable comments.
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Y Kitamura et aL hypothesis generation in model-based diagnosis. In Proc. of the 7th Annual Conferrence of JSAl, pp. 619-622. Sasajima, M., Kitamura Y., Mizoghuchi, R. et al. (1994). An investigation to domain ontology to represent functional models. In Proc. of the Eighth International Workshop on Qualitative Reasoning about Physical Systems, pp. 224-233. Schryver, J. C. (1992). Object-oriented qualitative simulation of human mental models of complex systems. IEEE Trans. on Systems, Man, and Cybernetics 22-3, 526-541. Skorstad, G. (1992). Finding stable causal interpretations of equations. In Recent advances in qualitative physics, Faltings & Struss (Eds), pp. 399-413. Cambridge, MA: MIT Press. Top, J. & Akkermans, H. (1991). Computational and physical causality. In Proc. of the IJCAI '91, pp. 1171-1176. Washio, T. (1990). Derivation of exogenously-driven causality based on physical laws. Journal of Japanese Society for Artificial Intelligence, 5..4, 94-103 (in Japenese). Williams, B. C. (1984) Qualitative analysis of MOS circuits. Artificial Intelligence, 24, 281-346. Yamaguchi, T. & Mizoguchi, R. (1992). Knowledge compiler II based on domain model and failure model. Journal of Japanese Society for Artificial Intelligence, 7-4, 663-674 (in Japanese).