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Proceedings AAAI{90,pp. 373{379. MIT Press, 1990.
4. Gallanti, M., Gilardoni, L., Guida, G., and Stefanini, A. `Exploiting physical and design knowledge in the diagnosis of complex industrial systems'. Ineds.Du Boulay, B.,Hogg, D., and Steels,L.,Advances in Arti cial Intelligence { II,pp. 481{495. ElsevierScience PublishersB. V., 1987.
5. Knoblo ck, C.A. `Atheoryof abstractionforhierarchical planning'. In ed. Benjamin,P. D., Change of representation and inductive bias, pp. 81{104. Kluwer,1990.
6. Kuip ers, B. `Qualitative simulation'. Arti cial Intelligence, vol. 29, pp. 289{388, 1986.
7. Lakshmanan, R. and Stephanop oulos, G. `Synthesis of op erating pro-ceduresforcompletechemicalplants{1.hierarchical,structured mo d-elling for nonlinear planning'. Computing in Chemical Engineering, vol.12, #9/10, pp. 985{1002, 1988.
8. Lakshmanan, R. and Stephanop oulos, G. `Synthesis of op erating pro-ceduresforcompletechemicalplants{2.anonlinearplanningmetho d-ology'. Computing in Chemical Engineering, vol.12, #9/10,pp. 1003{ 1021, 1988.
9. Meystel, A. `Intelligent control: A sketch of the theory'. Journal of Intellinge nt and Robotic Systems, vol.2, pp. 97{107, 1989.
10. Sykes, D. J. and Co chran, J. K. `Development of diagnostic exp ert systems using qualitative simulation'. In AI and Simulation 1988, pp. 32{38. The So ciety for ComputerSimulation,1988.
11. Venkatasubramanian, V.and Rich,S.H. `Anobject{oriented two{tier architectureforintegratingcompiledanddeep{levelknowledgefor pro-cess diagnosis'. Computing in Chemical Engineering, vol. 12, #9/10, pp. 903{921, 1988.
12. Wylie, R. and Kamel, M. `Mo del based knowledge organization: A frameworkforconstructinghighlevelcontrolsystems'. Expert Systems With Applications, vol.4, #3, 1992. Acceptedfor publication.
13. Yang, Q. Abtweak user's manual. University of Waterlo o, Waterlo o, Ontario, Canada N2L 3G1, 1990.
14. Zeigler, B. P. Multifacetted modelling and discrete event simulation. Academic Press, 1984.
The pap er presents our e orts to date on de ning a domain indep endent languageandsetofop erators forrepresentingandmanipulatingmo delsand b ehaviour. We have shown that a certain domain indep endent op erator (BPP) can b e used to automatically identify appropriately sized mo dels for analysis of sensor data, for diagnosis, and for planning op erating mo de changes. We have also shown how the domain indep endent representation supp orts reasoning from multiple mo dels. Two typ es of interaction are shown: sharing of knowledge ab out the system (planning and QP mo del interactingtosolveop eratingmo de changeproblem);andpassingofcontrol (diagnosis task spawnedby sensor data analysis task).
A critical issue in this research isthe derivation and interpretation of dep endency information from domain sp eci c mo dels. This issue is rea-sonably well understo o d inhierarchicaland non{linear planning where the strips assumption severely restricts the manner in which variables can in-teract.
Thesamecannotb esaidforQPanddiscreteeventsimulation. Inthese domains there seems to b e a complex interaction b etween causal relation-shipsinthesystemb eing mo delled,knowledgeab outsystemstateprovided in the question, the sp eci c reasoning strategy used, and the overall goals ofthe reasoningtasks. Inthe workpresentedhere,dep endencyinformation was restrictedto knowledge ab out system state derived from the question and causal argumentsderivedfromthe system.
One imp ortant fo cus of this research in the immediate future will b e to extend and formalizethe derivation of dep endency knowledge.
A second immediate task to b e undertaken is to extend the example to includemonitoringofplanexecution,and todemonstratethe metho don more complex interpretation,diagnosis and planning problems.
Athird taskisto reimplementthe MBPrepresentationfacilityandto extenditsfunctionalitybyadding aninterfacetoadiscreteeventsimulation to ol.
Finally, the longer term research plan is to de ne and test other b e-haviour preserving transformation op erators which simplify mo dels by ag-gregation rather than pruning, and to consider op erators of b oth typ es (pruning and aggregation) which aren't strictly b ehaviour preserving but for whichthe divergencein b ehaviourmust b e estimatedempirically.
REFERENCES
1. Aho,A.V.,Hop croft,J.E.,andUllman,J.D. Thedesign andanalysis of algorithms. Addison{Wesley,1976.
hasinlet(p4)
hasinlet(p6)
hasinlet(p2)
hasinlet(p1)
on(pump1)
hasinlet(p8)
hasoutlet(p2)
hasoutlet(p6)
hasoutlet(p7)
hasinlet(p9)
hasoutlet(p8)
open(v3)
open(v6)
open(v5)
open(v1) open(v4)
hasinlet(p3)
open(v2)
hasinlet(p5)
hasoutlet(p4)
Figure5: Dep endency Graphand Decomp osition for Planning Mo del
suchagraphwouldb eunmanageablylarge. Forthis reasoninthe planning literature, only that p ortion of the graph required for a given question is constructed (seeKnoblo ck [5]).
In the decomp osed planning mo del, as in the decomp osed QP mo del, onlythosestronglyconnectedcomp onentswhichcontainliteralsmentioned in theproblemor whichare \upstream" of sucha comp onentneed b e con-sidered. As well,the reducedplanningtask can b epro tablysolved hierar-chically,starting withthemost dep endentsubmo delandworking upstream (for adetailed discussion of this please seeKnoblo ck [5]).
Inthecurrentproblem,pruningallows usto eliminateallreferencesto valve{2,pip e{1,pip e{4,pip e{5,andpump{1. Solvingthe reducedplanning problemresults inasetof four ordinalconstraintsb etweenthreeop erators and the initial and goal states:
Initial{stateb efore close{valve(valve1)
close-valve(valve1)b efore op en{valve(valve4)
op en-valve(valve4) b efore op en-valve(valve5)
op en-valve(valve5) b eforegoal{state
Both this reduced problem and the full problem were solved using a non{ linearplannercalledAbtweak(Yang[13]). Thesamesolution waspro duced inb othcaseswhilep erformanceimprovedby31%to40%(inb othnumb erof no des expandedand inpro cessing time). Whiletheseresultsmustb etaken as preliminary, they do supp ort the argument that Behaviour Preserving Pruning of the problemprior to solution isworthwhile.
In this simple problem,the resultingnon{linear plan admits only one ordering of the op erators. This will not generally b e the case, and we may exploitother systemmo dels to provide further ordering constraints and to
name op en{ valve(v, src,snk)
valve(v), pip e(src), pip e(snk), b e-tween(v,src,snk),
:has-outlet(src), :has-inlet(snk), has-inlet(src),:op en(v)
op en(v), has-outlet(src), has-inlet(snk) close{ valve(v, src,snk)
valve(v), pip e(src), pip e(snk), b e-tween(v,src,snk),op en(v)
:op en(v), :has-outlet(src), :has-inlet(snk) start{
pump(p, src,snk)
pump(p), pip e(src),
pip e(snk), b etween(v,src,snk), :on(p), has{inlet(src)
on(p)
stop{ pump(p)
pump(p), on(p) :on(p)
Table 5: Planning Op erator De nitions
The drain{and{isolate problem's goal state may b e expressed as an incompleteb ehaviourin the QPdomain
amount{A=((0;0);std)
outlow{B=((0;fmax);std)
CompletionoftheresultingMBPyields owratesthroughthe various pip es in the extended mo del. These ow rates in turn determine valve settingsconsistentwith the goal:
:op en (valve{1)
op en (valve{3, valve{4, valve{5)
on(pump{1 )
Notethat the goal state do es not stipulatethe stateof valves 2and 6 since their status isirrelevant to satisfaction of the goals.
UsingBPP in Planning Tosolvethe planning problem,the Behaviour Pre-serving Pruningop erator may once again b e applied. As with QP mo dels, thedomainindep endentdep endencygraphstructureisdeterminedby com-p onentinterconnections. In Figure5thefullgraphisshown. For space rea-sons,nameshaveb eenreducedsothatpireferstopip e{i,vjreferstovalve-j, and typ e relations(ie. valve(?x),pip e(?x), pump(?x)) are not shown. The edges in this graph are oriented from preconditions to e ects, and all the e ectsof a singleop erator are forced into asingle strongly connected com-p onent by linkingthem with bi{directionaledges.
phases: 1) de ne initial, goal and p ossibly intermediate (planning island) statesusingadetailedmo del ofthepro cess; 2)plana(non{linear)sequence of valve and pump op erations to solve each subproblem identi ed ab ove and, 3) derive additional temp oral constraints for these subproblems from detailed mo dels of the pro cess (and p ossibly from heuristics, prede ned op erating pro cedures etc.) Such hybrid approaches to planning are often required b ecause of the representation language used in classical planning oftento o restrictive(Chapman [2]).
pump-1
valve-6
valve-5
valve-3
valve-2
valve-1
valve-4
pipe-9
pipe-8
pipe-7
pipe-6
pipe-4
pipe-3
pipe-2
pipe-1
tankA
tankB
pipe-5
Figure 4: Extended TwoTankSystem
In this presentation, the two tank system discussed ab ove will b e ex-tended by addition of pumps, valves and by{pass piping. The resulting augmented system isshown inFigure4.
A simple axiomatization of the pump{and{valve domain will b e used whichconsistsoffourop erators: op en{valve(),close{valve(),start{pump(), and stop{pump(). System state is represented by eight relations: op en(), on(), has-outlet(),has-inlet(),b etween(),valve(),pip e(),and pump()). T a-ble5 shows the op erators.
To continue with the sensor failure problem. We consider here the problemof planninga sequenceofvalveand pumpop erations whichdrains tank A while maintaining owto tank B.This is the rst stage of a repair pro cedure which involves isolating and draining the tank with the failed sensor, replacing the sensor and then bringing the tankback on{line.
De ning initial and goal states The initial state for the planning problem is:
:op en (valve{4,valve{5, valve{6)
op en (valve{1,valve{2, valve{3)
Diagnosingsensorfailures,equipmentfailuresandpro cessupsetsareclosely relatedproblems. In allcases, the sensor data interpretationtask willhave encountered an inconsistencyb etweenthe observed b ehaviour and the b e-haviourpredictedby the no{faultsystemmo dels. When the diagnosis task starts,thefaulthasalreadyb eenisolatedto thesubmo delexhibitingthe in-consistencyand thosesubmo delsup on whichitdep ends. In the caseof our level sensor failure, submo del{1 from Table 3 (corresp onding to Tank{A) contains the fault.
Themoststraightforwardapproachto mo delbaseddiagnosis involves search through the space of p ossible fault hyp otheses for the one which most plausibly explains the observed b ehaviour. Sensor fault hyp otheses may b e testedby disregardingindividual sensorsto determinewhether the remaining sensors are consistent. In the case of equipment diagnosis, the fault hyp otheses require libraries of comp onent mo dels corresp onding to the known failure mo des for the comp onents. Heuristics based on fault frequency mayb e usedto guide the search.
Inthisproblem,assumethat sensorfailuresareequallylikelyandthat theyare morecommon than equipmentfaults. Thusthe searchof the fault spaceb egins withasetofquestionsintendedto test sensorfailurehyp othe-ses. The partial b ehaviour in eachof these questions disregards data from onesensorbutcontainsveri edb ehaviouraldatafromadjacent(consistent) submo dels. InTable4aretheresultsofcompletingtheseb ehaviours. Test{ 1disregards tanklevelsensordata while test{2 disregards inlet owsensor data. Becausethe mo del isconsistentwith theinlet owdatabut not with the tank leveldata, the levelsensor isidenti ed as b eing at fault.
Time interval1 interval2 interval 3
Test Variable amt dir amt dir amt dir
test- Flow-in-A fnorm std fnorm std fnorm std
1 Flow-A-B (0,fmax) + (0,fmax) + (0,fmax) +
Net ow-A (0,nmax) + (0,nmax) + (0,nmax) +
Pressure-A (0,pmax) + (0,pmax) + (0,pmax) +
test- Level-A (0,lmax) + (0,lmax) std 0 std
2 Flow-A-B (0,fmax) + (0,fmax) std (0,fmax) ?
Net ow-A (0,nmax) ? 0 ? inconsistent
Pressure-A (0,pmax) + (0,pmax) std inconsistent
Table 4: Results of DiagnosticTests
Werethesensorstohavepassedthesetests,searchofequipmentfailure mo des would follow.
Planning
mo dels. When inconsistencies are encountered in the completion of one of the MBPs the problem is known to b e either in that MBP or in one of the MBP'spreviously completed. Thusthe resultingdiagnosis taskmay b e directlystated as a question comp osedof only these MBPs.
Time interval1 interval 2 interval3
Variable amt dir amt dir amt dir
Flow-in-A fnorm std fnorm std fnorm std
Level-A (0,lmax) + (0,lmax) std 0 std
Level-B (0,lmax) + (0,lmax) + (0,lmax) +
Flow-out-B (o,fmax) + (0,fmax) + (0,fmax) +
Table 2: Sensor Data Set
Time Interval interval1 interval2 interval3
mo del Variable amt dir amt dir amt dir
sub- Net ow-A (0,nmax) + (0,nmax) std inconsistent
mo del Pressure-A (0,pmax) + (0,pmax) std inconsistent
1 Flow-A-B (0,fmax) + (0,fmax) std inconsistent
sub- Net ow-B (0,nmax) ? (0,nmax) ? (0,nmax) ?
Mo del Pressure-B (0,pmax) + (0,pmax) + (0,pmax) +
2 Flow-A-B (0,fmax) + (0,fmax) ? (0,fmax) ?
full Flow-A-B (0,fmax) + (0,fmax) std inconsistent
Table 3: Results of MBP completions
To make this more clear, consider once again the two tank system of Figure3. InTable 2isprepro cessedsensor datainQPform(amt,dir). The dep endency graph and resulting decomp osition of the QP mo del based on this sensor set isjust that shown in Figure3.
Table 3 shows the results of completing the MBPs in order of their dep endency(so that Submo del{1refersto theSCCs asso ciated withTank{ A and Submo del{2 refers to the SCCs asso ciated with Tank{B). In the rst two intervals,no inconsistencies are encountered and the sensor data interpretation task succeeds. In the third interval, an inconsistency is en-countered inthe rst submo del.
Anticipating the next section, assume that a diagnostic task has de-termined that it is the level sensor in tank A has failed. This fact forces a rede nition of the sensor diagnosis task. The question de ning this new taskuses thesame mo del but the incompleteb ehaviourwillno longer con-tain information ab out the level of tank A. The new MBP is decomp osed to yielda new hierarchy of mo dels and sensor dataanalysis continues.
Many issuesof sensor data analysis haveb eendisregarded inthis pre-sentation. For adiscussionoftheseissuesinthecontextofQPseeDeCoste
The nal concept to formalize is that of a collectionof mo dels. We de ne a mo del base to b e a triple:
MB =<fM i g;R v ;R c > where: M i are mo dels, R v is a binary relation f< v i;k ;v j;l >g each tuple of which relates a pair of variables from di erent mo dels, R c is a binary relation f< c i;k ;c j;l >g each tuple of which relates a pair of comp onents from di erent mo dels
Wheremo delsfromdi erentdomainsoverlapwithresp ecttothe physi-calsystemb eingrepresentedtheywillcontaincommoncomp onents. Where mo dels fromthe same domainoverlap,they must corresp ond b oth with re-sp ectto comp onentsand with resp ect to variables.
EXAMPLES OF REASONING
This section continues from the tank example used ab ove to describ e the BPP op erator. While simple, this example is adequate for showing the use of the language and op erators in a range of reasoning tasks and for showing how these reasoning tasks can share knowledge and interact. The sp eci c reasoning tasks which will b e considered are: interpreting sensor data;diagnosingequipmentandsensorfaults;andplanningop eratingmo de changes.
Sensor data interpretation
Sensor data interpretation can b e de nedas completion of MBPsin which partial b ehaviours contain only sensor data. Sensor data interpretation stops short of diagnosing equipment and sensor failures. When it cannot reconcilethesensordatawithitsmo delofthepro cess,itpassestheproblem on to another task dedicated to diagnosis.
Theb ehaviourpreservingpruningop erationmayb eusedto automati-callydecomp osealargemo delintoappropriatesubmo delsforinterpretation ofsensordata. Whenchangeso ccurtoeitherthepro cessmo delorthe avail-able sensordata (eg. dueto sensoror equipmentfailures), thesesubmo dels may b e automatically redecomp osed.
Given a sensor suite, the BPP op erator identi es a dep endency hier-archy of submo dels. Sensor data interpretation involves completion of an MBP for each of these sub{mo dels in the order of their dep endency. The completed b ehaviours fromthe submo delscontain the desiredsystemstate information. This approach reduces computational costs by reducing the
acharacteristicof the reasoning metho dsin aparticular mo dellingdomain (Kuip ersQSIM [6]). However,eveninsuch domains, certainedges,suchas thoseasso ciated withirreversiblepro cessescanb egivenaunique direction. Themeaningofthesedirectededgesisthatknowingthevalueofthevariable at the origin of the edge can change the value of the variable at the edge's destination. Knowledge of the value of the destination variable can only restrictthe value of the origin variable.
NowconsideraquestionQ=fM;B Q
;g. Say i
=61for every vari-able exceptpressure-A.Following the de nition of questions,this indicates that for this reasoning task only the pressure in tank A is of interest. Say also that the partialb ehaviour B
Q
provides values for four variables: ows into tank{A and out of tank{B, and uid levels in b oth tanks. Hence all edges incident on the no de representing tank level will p oint away. The resultingproblemsp eci c dep endencydiagram is shown in Figure3.
+
M+
d/dt
M+
inflowA
netflowA
amountA
pressureA
outflowA
outflowB
pressureB
amountB
netflowB
inflowB
M+
M+
d/dt
+
M+
outflowA
pressureA
amountA
netflowA
inflowA
M+
M+
d/dt
M+
+
+
d/dt
M+
M+
inflowB
netflowB
amountB
pressureB
outflowB
outflowB
pressureB
amountB
netflowB
inflowB
outflowA
pressureA
amountA
netflowA
inflowA
Figure 3: Dep endencygraph and decomp osition of QPmo del
From this dep endency graph it should b e clear that the b ehaviour of the down{streamtankisirrelevantto thequestion athand. OurBehaviour Preserving Pruning (BPP) op erator identi es this fact by partitioning the variables into sets (called strongly connected comp onents or SCCs) where any pair of variables in the same SCC are mutually dep endent and any pairof variablesselectedfromdi erentSCCsare eitherunidirectionally de-p endentor are mutually indep endent. This partitioningof the dep endency graph is shown by the dotted lines in Figure 3. The submo dels resulting fromthis decomp ositionare also shown inFigure 3(note that the uninter-esting SCCs asso ciated with singlevariables have b eencollapsed).
Algorithms for decomp osing directed graphs into strongly connected comp onents can b e found in any go o d algorithms text (eg. Aho Hop croft and Ullman[1]).
While the example given involves decomp osing a QP mo del, BPP is equally applicableto any other domainwhere dep endency relationscan b e identi edb etweenvariables. Examplesincludeplanning(Knoblo ck[5])and
are giventhe second. A question,Q, is de nedas the 3-tuple:
Q=< M;B;>
where: M is the (p ossibly incomplete) mo del B is the (p ossibly incomplete) b ehaviour
isavectorof errorterms,one p eroutput variable
Behaviourpreservingop erations on MBPs
The most obvious b ehaviour preserving mo del transformations (BPT) are the domain dep endent op erators. Examples of these op erators are simula-torsandplanners whichtakewellformeddomainsp eci cmo delsandderive b ehaviourfromthem. Byde nition,iftheseop eratorsareimplemented cor-rectly,then theyare b ehaviour preserving.
Less obvious are BPTs applicable to many di erent typ es of mo dels. Such op erators trade o predictive p ower for generality. They are of use in sp ecializing mo dels to particular questions and in decomp osing large problems into computationallytractable subproblems.
Domain indep endent BPTs may b e characterized by the typ e of op-erations they apply to mo dels, and the typ es of guarantees of b ehavioural delity theyprovide. In this pap er wediscuss only BPTs which use delete op erations (the other major class uses aggregate op erations). Also, weare concerned with op erations which provide formal guaranteesof b ehavioural equivalence (insteadof empiricalguarantees).
Behaviour Preserving Pruning The BehaviourPreserving Pruning(BPP) op erator isimplementedin twoparts. The rst part sp ecializes the dep en-dency graph of the mo del to the particular question b eing addressed, and thesecondpartdecomp osesthisgraphintostronglyconnectedcomp onents.
outflowB
pressureB
amountB
netflowB
inflowB
M+
M+
d/dt
+
+
M+
d/dt
M+
M+
inflowA
netflowA
amountA
pressureA
outflowA
pressureB
pressureA
outflowB
outflowA
inflowA
tankB
tankA
inflowA
netflowA
amountA
pressureA
outflowA
inflowB
netflowB
amountB
pressureB
outflowB
Figure2: Two Tank System
pro duces a single b ehaviouroverthe state space de nedby adjoin (V ;V ) (where adjoin(fa;b;cg;fd;b;eg)=fa;b;c;d;eg. Each pair of tuples(b
1 i ;b 2 j ) which agree on all shared variables (V
1 \V
2
) including time, pro duces a tupleinB
3
. Thisop eratorallowsustoexpressb othsimpleconcatenationof b ehavioursequences(wherethetimep ointshavenooverlapandthevariable sets areidentical)as wellas thereconstruction ofpartialb ehaviours(where the timesets do overlap and the variable sets are distinct).
The variable{domain transformation operator If V 1
is the variable set in B 1 withvariable{domainsD 1 andV 2
isthevariablesetinB 2 withvariable{ domains D 2 , and a mapping f D :D 1 !D 2 exists fromD 1 to D 2 , then B 2 =Dom(f D ;B 1 )
willyield b ehaviourin the new state space.
Other op erators on b ehaviour such as aggregation op erators which serveto collapsesets ofvariablesto single variables(eg. spatial averaging) or to collapse sequences to single quantities(eg. time averaging) may also b e de ned.
Mo del{BehaviourPairs
Behaviouralandmo dellingknowledgeare linkedthrough theircommon ref-erences to variables. This relationshipis madeexplicitby grouping mo dels and b ehaviours into pairs (Mo del{b ehaviourpairs or MBPs).
MBP =<M;B >
where: M is amo del ofsome system
B is b ehavioursyntacticallyconsistent with M
Minimally, these pairs must corresp ond with resp ect to numb er and typ e of variables. However since M is a weakened representation of some domain sp eci c mo del, B must also b e consistent with this more restric-tive mo delling knowledge. One of the central ideas in this research is that domain indep endent mo del transformations can b e de ned which do not disturb this deep er relationship.
The notion that many typ es of reasoning can b e expressed as op er-ations on MBPs was presented brie y in the section on reasoning with mo dels. In this view,a problemor question issimply an incompleteMBP, and problem solving involves using b ehaviour and mo del transformations to completeit.
Wemust extend thede nition of aMBPinorder to capturethe ideas that questions are incompleteMBPs and that some of the variables might b e uninteresting in the context of a sp eci c question. The extension takes the form of a MBP augmented with a vector of error b ounds. The error b ounds sp ecifythe tolerance to which we wish to know each variable. For
Variable amt dir amt dir amt dir
In ow fnorm std fnorm std 0 std
Net ow (0,nmax) + (0,nmax) std (nmin,0) +
Out ow (0,omax) + (0,omax) std (0,omax)
-Amount (0,lmax) + (0,lmax) std (0,lmax)
-Pressure (0,pmax) + (0,pmax) std (0,pmax)
-Table 1: Behaviour fora Single Tank
Asan exampleofb ehaviouralinformationTable 1containsthreestate vectors for the single tank example presented in Figure 1. In the table, eachtuplecorresp onds to apairof columnswhere\amt" de nesan interval representing quantity, and dir is direction or time derivative represented using the sign algebra (f0;std;+;?g). The b oundaries of the intervals (0, lmax, fmax, pmax...) are drawn from sets of \landmark" values which de nethevariable{domainsofthevariablesinQPmo dels(whereanamount isrepresentedbyasinglelandmarkitsvalueisconsideredtob eexactlyequal tothatlandmark,sofnor m =(fnor m;fnor m)). Thethreeintervalsshown corresp ond to lling, steady state (in ow matches out ow) and draining (where the xed owrate source has b een turnedo ).
Op erations on BehavioursThebasicdomainindep endentop erationsonmo d-els consist of the relational op erators join, project and select along with a mapping op erator to convertb ehaviour conforming to one mo dels schema into b ehaviourconforming to another mo dels schema.
The Project Operator IfV 1
isthe variable setof the source b ehaviour B 1
and V 2
V
1
is the variable set of the destination b ehaviour, then the op eration B 2 =Proj(V 2 ;B 1 )
will drop those variables not in V 2
and will collapse adjacent states when they are identicalto pro duce the destination b ehaviourB
2
The Select Operator IfO (V 1
)is afunctionwhichmaps statevectors from V
1
to ftr ue;fal segthen the select op erator
B 2
=Sel(O ;B 1
)
willselect only those tuplesfrom B 1
for whichO istrue.
The Join Operator Finally, we may de ne a \join" op erator to construct asingleb ehaviourfromtwob ehaviours. IfB
1
andB 2
areb ehaviours which share the same timeset then
is a characteristic of the particular domain (the qualitative physics (QP) of Kuip ers [6]): as with arithmetic equations, there is no directionality implied by a QP constraint. More sp eci c dep endency information arises fromcausality argumentsand from problemsp eci c knowledge.
Op erations on Mo dels The basic op erations on mo dels involveadding and deleting mo del elements. Elements may b e variables or constraints. By comp osingthemintheobviousway,comp onentsmayb eaddedorremoved.
The Cut Operator IfM 1 =(C 1 ;R 1 ) is amo del and c i 2C 1 then M 2 =(C 2 ;R 2 )=cut(M 1 ;c i )
yieldsamo delidenticaltoM 1
butwith comp onentc i
removedfromC 2
and allvariable bindings inR
1
referringto the variablesinc i
removedfrom R 2
.
The Add Operator If M 1
=(C 1
;R 1
) is amo del then a comp onent c may b e added to it by sp ecifying a relation of variable bindings R
0 = f(v i ;v j )g such that eachtuple in R
0
contains at least one variable fromc
M 2 = add(M 1 ;c;R 0 ) = (C 1 [c;R 1 [R 0 )
Note that not allvariablesof c need to b ementioned in R 0
since they may b e internal to c or may b e input or output variables not connected to any other comp onent.
Behaviour
Unlikemo dels,thedomainindep endentrepresentationofb ehavioural knowl-edge is quite complete. This results from the fundamental role of b e-havioural information in reasoning ab out dynamic systems. We have to b e able to at least compare b ehaviours at the domain indep endent level if we wish to select appropriate mo dels, control reasoning or express goals with resp ect to system state. Fortunately, we can de ne quite general op-erators for editing, transforming and comparing b ehavioural knowledge so this need to representb ehaviour completelyis not to o onerous.
We adopt a relational representation for b ehaviour in which each 2-tuple contains a timestamp (key) and a vector of values drawn from the variable{domains of the variables in the mo del to which the b ehaviour is attached. Thatis the b ehaviour Bis represented as:
B =f<S;t>g
where: S is a vector of values drawn from the variable{ domains of the variables v
i
in V (alternatively, a tokendrawn fromthe state set X),
the 3-tuple:
M 0
=< T;V;E >
where: T is the time set,
V is the setofunique variablesfv i
0gone for eachset of equivalentvariables found in R,
E is a binary relation f< v i
0;v j
0 >g representing all the unique dep endencies b etweenvariables ex-pressed in the comp onents' edge sets S
i
r3
r2
r1
s31
s24
s25
s23
s22
s21
v32
v31
v25
v24
v23
v22
v21
v11
Component C1
Component C3
Component C2
Dependencies
Components
Schematic
Flow
Pressure
Amount
Netflow
Inflow
Outflow
Outlet
Convection
Natural
Tank
Forced
Convection
inlet
d/dt
M+
+
M+
Pressure
Flow
Figure 1: Single tankwith twop orts
InFigure1isa3comp onentmo del ofasimple hydraulicsystem. The schematic depiction of this mo del shows the three comp onents: a pump which provides a constant inlet ow rate; a tank; and an outlet whos ow rate dep ends up on pressure.
In the comp onent oriented depiction of the mo del the sp eci c vari-ablesandconstraintsasso ciatedwitheachcomp onentareshown: thepump is represented by a single variable with no dep endencies; the tank is repre-sentedbyamassbalanceconstraintb etweenthethree owrates,aderivative relationship b etween amount (level) and net ow, and a monotonic (M+) relationship b etween amount and pressureat the outlet; nally, the outlet comp onent isa monotonic relationship b etween owrateand pressure.
In the domain indep endent representation the constraints have b een replacedwith edges representing dep endenciesand the edges and variables haveb eenlab eledaccording tothe schemepresentedab ove. Thusv
i;j isthe j-th variablein comp onent i,r
i
is an equivalenceedge b etween variablesin di erentcomp onents, and s
i;j
isthe j-thdep endency incomp onent i. The variable oriented representation (not shown) would app ear very similar to the comp onentoriented dep endency graph. The onlydi erences would b e that those sets of variables connected by equivalence edges (r
i )
Domainindep endencetakestheformofaweakrepresentationofconstraints b etweenvariables. Where domain sp eci c mo del representation languages express sp ecializedconstraints b etweenvariables,our language can express onlydep endencyrelationsb etweenvariables. Asaresult,thislanguageisn't expressiveenough tosupp ortthederivationofb ehaviourfrommo dels. One must return to the domaindep endent representationto p erform taskssuch as simulationor planning. However, the dep endency based representation provesto b e quiteusefulin guidingmo del transformations.
Another imp ortant feature of the domain indep endent representation isthe abilityto representsubsystemsor comp onents. This isesp ecially im-p ortantinthecurrentcontextb ecauseweareinterestedintherelationships b etweenmultiplemo dels of asingle systemindi erent mo dellingdomains. Identi cation of common comp onents is often the most natural way to ex-press these relationships.
Athirdfeatureisrepresentationofvariablesand thevariable{domains from which values may b e taken. Together these features allow variables to de ned and interconnected by dep endency relationships which may in turn b eclusteredinto comp onents. This yieldstworelatedrepresentations: one emphasizing the comp onent structure and the other emphasizing the variable/dep endency structure.
For the comp onentoriented view,a mo del M is de nedas a3-tuple:
M =<T;C ;R >
where: T is the timeset,
C is the set of comp onents inthe mo del. Each com-p onent c i =< V i ;S i
> is a 2-tuple comp osed of a set of variables, V
i = fv
i;j
g and a set of directed edges b etweenthese variablesS
i =f<v i;j ;v i;k >g representingdep endencies.
Eachvariablehas atyp e whichdep ends up on the domain of the underlying mo del v
i;j
: D . A vari-able'svariable{domainmayb efurtherrestrictedif suchinformation is available,
R is a set, f< v i;j
;v k ;l
>g, of 2-tuples which cap-tures the manner in which comp onents are inter-connected. Each tuple in R is comp osed of a pair of variables drawn from the comp onents' variable sets and serves to equate them.
The variable oriented view may b e derived from the comp onent ori-entedview. Thevariablesinthenewrepresentationincludeallthevariables fromthe comp onentsinM but withthe equivalentvariables(de nedinR) represented only once. All dep endency edges are inherited,but
redundan-it follows that the development pro cess must involve mo del construction, mo di cation and veri cation.
In conclusion, implementation and maintenance of high level control systems can b ene t from organizing knowledge into mo dels. For each sp e-cialized mo del typ e, sp ecialized representation and reasoning to ols will b e required. In order to integratethese sp ecialized representations,weneed a domain indep endentframework for keeping track of relationships b etween mo dels, for selecting mo dels for sp eci c reasoning tasks, and for moving knowledge fromone mo del to another.
MODEL BASED KNOWLEDGEORGANIZATION
Mo del Based Knowledge Organization (MBKO) is an attempt to resolve certain problems surrounding the development and maintenanceof KBS's byco ercingknowledgeintoarepresentationalframeworkreminiscentofthat commonlyused indynamic, quantitativephysical systems mo delling.
AdetailedknowledgerepresentationschemebasedonMBKOhas b een develop edand presentedbythe authors elsewhere(Wylie and Kamel[12]). The current pap er avoids most of the detail of this representation and in-stead fo cuses on the role of a domain indep endent mo del representation language and transformation op erators to improve eciencyand exibility in mo del based problemsolving.
Reasoning with mo dels
In the context ofhigh levelcontrolmany reasoning tasksmay b eexpressed as eitheridenti cationofamo del whichexplains b ehaviouror derivationof b ehaviourimplied by a mo del. Examples of this are:
sensordatainterpretation. Givenamo delof thesystemandapartial b ehavioural description (from sensors),derivea completedescription of the system's state.
diagnosis. Givenamo delofsomesystemandb ehaviouralinformation whichdo esn'tcorresp ondtothemo del, ndthemostplausiblevariant of that mo del which do es explain the observations.
planning. Given an incomplete description of the b ehaviour of the system (ie current state and goal state) and a mo del for the system, completethe b ehaviour using onlyfeasiblecontrol actions.
LANGUAGE
d-formation op erators. A sp ecial typ e of op erator called a b ehaviour pre-serving pruning op erator (BPP) ispresented. It has the desirableprop erty of simplifying a mo del without compromising its predictive p ower in the contextof a sp eci c question.
The rest of the pap er is structured into 5 sections. The rst presents an overview of the problem domain: high level control of large industrial systems. The second discusses the b ene ts of adopting a mo del centered viewof knowledgeinthis (and other)applicationareas. Thethird presents the prop osed language and op erators. The fourth presents some examples of their use. The pap er is concluded by a discussion of the work to date and the direction inwhichthis researchwillcontinue.
HIGHLEVEL CONTROL
In the management and control of large industrial systems, there are a numb er of signi cant problems which are not amenable to solution by ei-therconventionalcontroltechniquesorMIS/DSS(ManagementInformation System/ Decision Supp ort System) software. Examples of these problems are: equipment and sensor diagnosis; pro cess tuning (optimization); and planning changes inmo de of op eration of the plant (eg. Wylie and Kamel [12], Meystel [9]). These tasks are usually left to op erators and plant engi-neers. Recently,an assortment ofsolutions to these typ es ofproblems have b eendemonstratedwhichexploitreasoning strategiesderivedfromresearch in Arti cial Intelligence (eg. Venkatasubramanian and Rich [11], Laksh-manan and Stephanop olous [7,8], Sykesand Co chran [10], Gallanti et. al. [4]). While these systems have achieved reasonable technical success, the cost, risk, and exp ertise requiredfor their developmentmake themnot yet commerciallyviable.
To reduce the cost, risk and exp ertise required to build and maintain such systems two related questions might b e asked: what organizing prin-ciples underliethe sort of KBS's which solve these problems; and how are these high levelcontrol systems to b ebuilt ecientlyand reliably.
The rst of these questions can b e partially answered by referring to the literaturefor examples. This willshow that realistic solutions to these problems usually entailreasoning from multiple representations of the sys-temb eingcontrolled. Examples ofthis includeplanners whichexploitb oth a STRIPS{op erator mo del and a detailed simulation mo del of the situ-ation (Lakshmanan and Stephanop olous [7, 8]). Other examples include diagnostic systems which exploit b oth mo del and classi cation based rep-resentations (Venkatasubramanian and Rich [11]). Not only do individual reasoning tasks oftenrequiremultiplemo dels of the situation, but b ecause ofthe integratedcharacterofthehighlevelcontrol,distincttasksmust also b e able to share mo delingknowledgeand pass control.
Rob Wylie y
and Mohamed Kamel
Pattern Analysis and Machine Intelligence Lab, Department
of Systems Design, University of Waterloo, Waterloo,
Ontario, Canada, N2L-3G1
y
On educational leave from the Knowledge Systems Lab,
Institute for Information Technology, National Research
Council of Canada, Ottawa, Canada, K1A-0R6
ABSTRACT
Reasoning ab out the b ehaviour of large industrial pro cesses is a dicult and complex computational task. To p erform it ecientlyrequires the use of numerous sp ecialized representations of the system. Any successful in-formation pro cessing system in such an environment must have e ective waysto managethese representations,the individualreasoning taskswhich use them, andthe owofinformation b etweenthem. This pap er addresses theseissuesbyprop osingamo delcenteredviewofknowledgeandpresentsa domainindep endentrepresentationlanguage alongwithop erators for man-aging multiple overlapping mo dels of dynamic physical systems. Examples are given of its use in sensor interpretation, diagnosis and planning in a simple pip e{and{tank network.
INTRODUCTION
This pap er presents a domain indep endent scheme for representing and manipulatingmo dels of dynamicphysical systems. Itis intendedfor appli-cationsinwhichonephysicalsystemisthefo cusofadiversesetofreasoning tasks. To b e useful in such an environment, the representation must sup-p ort dynamic mo del selection and construction as well as communication b etweentasksusing di erent typ es of mo dels.
Communication b etween tasks across mo delling domains is directly supp orted by auniform representationfor mo dels b ecauseit allows match-ing of comp onents and variables across domains. This in turn provides a foundation for communicating b ehavioural,structural andcontrol
