A Theory of Mapping from Structure to FunctionApplied to Engineering Thermodynamics

Qualitative Reasoning Group at The Institute for the Learning SciencesNorthwestern University 1890 Maple Avenue Evanston, IL 60201 USA

phone 708-491-4790 fax 708-491-5258email : everett@ils .nvu .edu

Abstract : This paper presents a theoretical frame-work for mapping from structure to function inengineering domains . We argue that a generativeapproach grounded in Qualitative Process Theoryproduces useful functional explanations . Usefulexplanations are articulate, in that they enable theuser to explore their theoretical justifications andthey support counterfactual reasoning . These ex-planations stem from a teleological representationbased on goals, plans, roles, and views. We alsoshow that an ontology based on aggregated proc-esses provides a powerful means for recognizingrecurring thermodynamic structures . We describean implementation of this theory, a system calledCARNOT, that currently explains steady-flow ther-modynamic cycles ranging in complexity fromfour to twenty-four components .

1 . IntroductionThermodynamic cycles (e.g ., power plants, refrig-erators) form an important class of artifacts . De-vices based on them are typically complex andoften costly to operate, which provides severalmotivations for reasoning about them . Engineersand students need to verify that their designs willbehave as desired, and plant operators need togenerate and test hypotheses concerning systemfunctions from schematics .

Each of these cases calls for reasoning aboutfunction given a structural description . This pa-per describes a theory of structure-to-functionmapping that supports these tasks in the domainof thermodynamic cycles . We have implementedthis theory in a system called CARNOT that takes asinput a schematic depicting the structural configu-ration of a system such as a refrigerator and pro-duces a description of the system's function .

de Kleer (1984) was the first to investigate themapping from structure to function . He pro-posed, for the domain of electronic circuits, amethodology using qualitative physics to mapfrom structure (what the artifact is) to behavior(what the artifact does) and a separate, teleologicalreasoning process to map from behavior to func-

John O. Everett

tion (what the artifact is for) .

Thus the behaviorsof a working turbine include expansion of theworking fluid, cooling of the fluid and creation ofshaft work. Its function, however, may be eitherto produce work or to cool the working fluid, anddepends on the context in which it is embedded .

We observe that the causality of electronic circuitsis particularly ill-defined, especially when com-pared with other engineering domains, such asthermodynamics . For example, thermodynamiccycles have a readily-established direction of flow,and their constituent components typically havefew or no degrees of freedom in their potentialbehaviors. We initially believed that a simpler ap-proach than de Kleer's would suffice for mappingfrom structure to function in domains other thanelectronics.

This turns out not to be the case ; we encounteredsignificant ambiguities in mapping from thestructure of thermodynamic cycles to their func-tion . This paper describes how our theory re-solves these ambiguities to produce a single func-tional description of a schematic . Section 2 pres-ents an overview of the domain, Section 3 dis-cusses our theory, Section 4 describes our repre-sentations, Section 5 outlines the algorithm, andSection 6 presents in detail one example andsummarizes some of the more interesting resultsfrom other cycles CARNOT currently solves. Weconclude with a discussion of related and futurework.

2 . Domain OverviewArtifacts incorporating thermodynamic cycles arepervasive . Virtually all electrical power generatedtoday relies on a thermodynamic cycle in whichmassive boilers generate steam to turn turbinesthat drive generators . Refrigerators rely on thesame cycle, albeit running in reverse and suppliedwith a different working fluid that enables opera-tion at safer pressures . Automobile and jet en-gines operate in a so-called "open" cycle thattakes in air from, and expels exhaust gases to theenvironment. Industry relies on thermodynamic

cycles for power, for liquefying gases (e.g ., natu-ral gas), and for process steam.

A Simple Heat Engine The defining characteris-tic of a thermodynamic cycle is that it operatesbetween two reservoirs of different temperatures,typically by passing a working fluid through asystem of pipes and components . Figure 1 depictsa simple heat engine .

Simple Vapor-Cycle Heat Engine

Figure 1

This basic cycle (with modifications to increaseefficiency) is commonly used to generate elec-tricity. Heat energy from combustion or nuclearreaction converts the working fluid into vapor inthe boiler . This fluid leaves the boiler at highpressure and expands in the turbine, converting itspressure into velocity . The kinetic energy of thesteam striking the turbine blades forces the tur-bine shaft to rotate, producing work. The con-denser returns the working fluid to its originalstate by ejecting heat to the environment. Thepump ensures that the boiler gets a steady supplyof working fluid at a pressure high enough tomaintain the system's direction of flow .

The constituent devices of this and other thermo-dynamic systems are complex artifacts designedto accomplish specific functions, which led us tobelieve that teleological recognition in this do-main would be less ambiguous than de Kleerfound the electronics domain. However there aresignificant ambiguities in mapping from behaviorto function in this domain.

For example, a tur-bine may function as either a work-producer or acooler, and in cryogenic cycles the latter is thedesired function . Reaching human-like conclu-sions with little information despite such ambigu-ity has been the primary motivation for the devel-opment of our theory .

3. Teleological TheoryThe goal of this research is to automate the proc-ess of making functional inferences from struc-

tural information. To gauge our success, we needcriteria for what constitutes a good functional ex-planation . However, a system that produces"good" explanations will be useful only insofaras it scales up to solve real-world problems in areasonable amount of time .

We define a good functional explanation to beone that :"

Provides a single, internally-consistent expla-nation for the system

"

Takes into account all available information"

Relates each device to at least one design goal"

Provides an indication of the certainty of eachinferenceEnables counterfactual reasoning about thefunction of the system

"

Provides a chain of inference that grounds ina qualitative theory of behavior

The value of functional explanations lies not inthe explanations per se but in the inferences theysanction . A simple pattern-matching approachcould produce canned descriptions in great detail .However, such explanations would be unrespon-sive to user queries. A student might not under-stand a particular statement, and should thereforebe able to backtrack through that statement's in-ferential chain all the way to domain theory giv-ens. An engineer might want to know how a de-sign modification would affect the system's func-tioning.

A generative approach based on qualitative phys-ics is necessary to address these issues . To achievegenerativity, we minimize the size of knowledgefragments and rely on inference to assemble a setof fragments into an explanation. This minimizesthe redundant encoding of information (whichwould occur in a template-matching system) andenables the explanation of novel cycles . Modu-larizing the representation also facilitates the taskof maintaining a knowledge-base large enough tosupport a practical teleological reasoner . Our rep-resentation is consistent with Qualitative ProcessTheory (Forbus, 1984), and therefore producesexplanations grounded in 'qualitative behavioralinferences . However, it also enables the use ofquantitative information for making more precisefunctional inferences .

Finally, to prevent explosive inferencing, CARNOTadopts what de Kleer (1984) calls the teleologicalperspective, in that we assume by default that eachdevice contributes to the function of the system .This enables us to avoid extensive qualitativeand/or quantitative simulation because we assume

that components operate within their normalparametric ranges . Because this rational-designerpremise is assumed explicitly, retracting it enablesus to consider alternative situations, such as tem-peratures exceeding component tolerances .

4 . Knowledge RepresentationsPerusal of thermodynamic texts and referencematerials reveals no universal standards for sche-matics, although informal conventions do exist(e.g., turbines are generally represented as trape-zoids with vertical parallels) . We use the sche-matic representation we designed for CyclePad(Forbus & Whalley, 1994), a system that enablesstudents to design and experiment with thermo-dynamic cycles .

This representation, reflects the pedagogical con-siderations underlying CyclePad . To encouragestudents to consider modeling issues, only basicdevices are explicitly represented. For example,there is no jet-ejector (a pump utilizing a high-velocity jet) because a mixer can function in thiscapacity . Likewise, mixers may also function asopen heat-exchangers (heating via mixing) andsplitters may function as flash-chambers (devicesthat cause the working fluid to rapidly evaporatedue to a pressure drop).

CARNOT's functional descriptions are composedof plans and roles .

Plans summarize common

Goal: Achieve state .change in environment

CARNOT's Representations

Figure 2

structural configurations that have particularfunctional import. Roles specify which behaviorof a particular component is its intended function .Intermediate view and process constructs enablethe instantiation of the proper plans and roles.Views describe possible behaviors of particulardevices, while processes ground explanations in aqualitative model of thermodynamics and providea useful definition of locality . Figure 2 providesan overview of these representations. Arrows in-dicate constraining relationships . For example,the topology of the schematic determines whichprocesses, roles, and views are instantiated . Wedescribe these constructs in more detail in the bal-ance of this section.

Goals The rational-designer premise allows us torestrict the number of goals we impute to a sys-tem. From this point of view, thermodynamic cy-cles have three possible design goals, (1) achiev-ing a change of state in the environment, (2) do-ing so with a minimal input of energy, and (3)preserving the integrity of the system . In the caseof a heat engine, the first goal is to convert heatenergy into shaft-work, whereas for a refrigeratorit is to move heat from one location to another.The second goal, of maximizing efficiency, fol-lows from the teleological perspective; each deviceis assumed to contribute to the function of thewhole because the designer faces tight economicconstraints. Finally, because configurations that

Goat: Achieve maximumchange per unit of input

Goal : Preserve(stem integrity

1Available system data (e.g .,

parameter values, fluid phases)

FUNCTION

BEHAVIOR

STRUCTUREQ

achieve the first two goals also create potentiallydamaging conditions, some devices may be pres-ent solely to prevent the occurrence of such states .For example, most pumps cannot handle fluidscomposed of a mixture of liquid and gas, so anupstream pump may ensure that preheating of theworking fluid does not cause it to flash into vapor.

Views Views are device-specific behavioral de-scriptions . For example, a pump's views includedefault, coasting, cavitating, and losing . By de-fault, CARNOT considers pumps to compress liq-uids (compressors compress gasses), so a defaultpump view sanctions inferences that both inputand output stuffs are liquid and that the inputstuff pressure is less than that of the output .

Views are biconditionals of the form "if and onlyif this particular conjunct of facts is found to betrue, then this view is active ." For example, theconjunct of facts for a liquid-heater view includes(1) flow is positive, (2) phase of stuff in is liquid,(3) phase of stuff out is liquid and (4) tempera-ture of stuff in is less than temperature of stuffout. Views propagate phase information, whichcan resolve ambiguities and prevent devicesknown to be behaving abnormally from partici-pating in process and plan inferences .

Roles Roles are the functional counterpart ofviews. For example, the potential roles of a pumpinclude (1) flow-producer and (2) flash-preventer .The behavior of a default-view pump is to com-press liquid ; its function is to produce a flow . Thedifference is a presumption that this flow is essen-tial achieving one or more of the three designgoals. A view is insufficient to support this pre-sumption, because it is possible that the actualfunction is to act as a work-sink rather than tocreate a flow .

Although roles are device-specific, they generallyrequire consideration of the structural context fora device, and hence more reasoning. Unlikeviews, roles are not always mutually exclusive; in-deed, achieving multiple functions via a singledevice is often desirable from a design standpoint,for potential cost-savings and/or efficiency im-provements . For example, a pump may act asboth a flash-preventer and a flow-producer. Inthe flash-preventer role a pump functions to pre-vent the fluid downstream from suddenly vapor-izing .

Processes Although the fixed flow direction andcomponent-oriented schematics for thermody-namic cycles would appear to make them suited to

a device-centered ontology, we have found aprocess-oriented ontology more useful . Processesare central to thermodynamics ; the components ofa particular cycle exist solely to create and controlthem . Moreover, processes often span several de-vices, which may or may not be immediately adja-cent . Reifying such processes provides CARNOTwith a powerful definition of locality .

CARNOT distinguishes three types of process: (1)local, (2) boundary, and (3) aggregate. Devicescreate one or more local processes across theirfluid-paths . For example, a pump creates a localfluid-flow process from its inlet to its outlet.

We adopt the thermodynamic convention of es-tablishing control volumes around systems andsubsystems of interest . Control volumes requirean accounting of all mass and energy crossingtheir boundaries . CARNOT explicitly labels allboundary-crossing processes. For example, theheat-flow to a boiler must cross the systemboundary, so all heaters give rise to boundaryheat-flow processes.

Aggregate processes provide a flexible means formatching canonical plans to cycles, because theycapture critical aspects of a system without beingoverly sensitive to its particular topology . Forexample, inserting a pump and a heater immedi-ately after the cooler in Figure 1 would improvethe cycle's efficiency yet not alter its function norits identity as a Rankine cycle. The example pre-sented in Figure 9 is, despite its complexity, still aRankine cycle.

Plans Certain thermodynamic configurations re-cur so often that their idealized abstractions havebeen reified . For example, most electrical powergenerating systems use the Rankine cycle, aroundwhich a working fluid is vaporized and con-densed . We refer to such named configurations asplans because they are in effect strategies for therealization of design goals.

Figure 3 shows ourrepresentation of the Rankine cycle plan.

Othercommon plans include the Carrot cycle, a theo-

Rankine Cycle PlanVaporize working fluid at constant pressureCreate a constant-entropy resisted expansionto produce shaft workFully condense working fluid at constantpressurePump liquid working-fluid at constant en-tropy to maintain flow direction

Figure 3

retical ideal, and the Brayton cycle, used for jetengines.

Idealization simplifies analyses by assuming cer-tain state parameters remain constant across theplan's processes. In the ideal, the Rankine cycleis comprised of constant-pressure (isobaric) heat-ing and cooling processes and constant-entropy(isentropic) expansion and compression proc-esses.

CARNOT distinguishes truly ideal from stepwise-ideal processes . The latter occur when the crea-tion of two processes is interleaved. For example,pumps and heaters may be interleaved, obviouslypreventing the aggregate heating process fromoccurring at constant pressure. However, if eachconstituent local process is ideal, then CARNOT la-bels the aggregate as stepwise-ideal . This distinc-tion enables CARNOT to differentiate practical fromideal cycles . An ideal cycle maximizes efficiencyeven at the cost of destroying system integrity.Such cycles are useful for pedagogical reasonsand as benchmarks for assessing the efficiency ofpractical cycles .

CARNOT'S plans vary in generality .

The mostgeneral are the heat-engine and refrigerator plans,which have no ideal-process requirements . Themore information CARNOT is given, the more spe-cific the plans instantiated . For possible plans,CARNOT backchains on their antecedents and in-cludes them in the final description with a caveatthat the antecedents must be true . In addition tocycle plans, CARNOT recognizes inter-cycle plans,such as CASCADE-CYCLES and USE-wORK-NTERNALLY. In cascaded systems one cycle usesthe heat ejected by the other, while in systems thatcombine heat-engine and refrigerator cycles, theheat-engine's work drives the refrigerator .

CARNOT'S most specific plans arise from particu-lar device roles. For example, a mixer serving as ajet-ejector (a type of pump in which a high-velocity jet entrains the working-fluid beingpumped) will cause the instantiation of a plan topreserve system integrity by reducing complexity,because jet-ejectors replace turbine-compressorcombinations .

$ . CARNOT's AlgorithmCARNOT uses a logic-based truth maintenancesystem (Forbus & de Kleer, 1993) coupled to apattern-directed rule engine . CARNOT's knowl-edge base is encoded as a set of rules. The un-derlying TMS caches the resulting chains of in-

ference, enabling CARNOT to perform counterfac-tual reasoning and to construct causal explana-tions on demand. Figure 4 shows the steps of thealgorithm.

Instantiating Domain Knowledge CARNOT firstinstantiates a set of device models that describe thestructure of the input system and result in the in-stantiation of views. In some cases there isn'tenough initial information for a particular deviceto have an active view . For these devices CARNOTinstantiates the most specific view consistent withthe known information.

For example, the default view for a heater makesno commitment about the phase of the stuff atinlet or outlet . However, if CARNOT detects thatthere are only compressors (which can only com-press gasses) present, it will assume a Gas Heaterview, which implies that the phase of the stuffs atinlet and outlet is gas .

Identifying Topological Structures CARNOT nextparses the cycle topologically into Poops (shortfor "fluid loops") . These are directed cycles inwhich neither arcs nor vertices are duplicated .'CARNOT breaks floops immediately upstream ofthe first compressing device to be found after thelast expansion device . This is the most "natural"point at which to break a cycle, because theworking fluid is closest to ambient conditionshere . For example, the automobile engine, whichoperates in a so-called "open" cycle, breaks thecycle at this point, because it takes in its workingfluid (i .e ., air) immediately prior to compressingit, and exhausts it immediately after the powerstroke .

Floops do not necessarily correspond to meaning-ful substructures in the input cycle, but merelyrepresent routes that a piece of working fluidcould traverse . Therefore CARNOT next generatesa hypothesis concerning the function of eachfloop. Each floop is potentially a heat-engine, arefrigerator, or a topological artifact. Initially wethought it would be possible to identify floops bythe order of device occurrence because the ca-nonical heat-engine has a pump, heater, turbine,and cooler in that order while the canonical re-frigerator swaps the heater and cooler, but thisturns out not to be the case, because splitters andmixers have several possible functions .

t To avoid terminological confusion, we reserve the term"cycle" for thermodynamically meaningful closed paths .

Algorithm Ste

A mixer can act as either a simple route-joiner, aheat-exchanger (if its two inputs are of differenttemperature) or a pump (if its two inputs are ofdifferent pressure). A splitter may either act as aroute-divider or a flash-chamber, in which theworking fluid evaporates, the gas leaving by oneexit and the remaining liquid by the other. Wefirst confronted this issue in breaking floops thathad no apparent compressor . In such situations,CARNOT considers mixers to be compressors, theonly remaining thermodynamic possibility if thefloop is in reality a subcycle .

This functional ambiguity means that valid subcy-cles may lack apparent pumps, expansion devices,heaters or coolers. To identify such floops,CARNOT uses the constraints shown in Figure 5 toconduct a dependency-directed search for a con-sistent set of views of each floop's devices. Theseconstraints follow from the rational-designerpremise; there is no thermodynamically soundreason to heat and immediately cool or compressand immediately expand a working fluid. For thissearch, CARNOT generates sets of potential roles foreach mixer and splitter, ordered such that any so-

Functional Labeling ConstraintsProcesses are considered neighbors if they areconsecutive on a particular route or if they areconnected by one or more splitting and/ormixing processes .Heating and cooling processes cannot beneighbors .Expansion and compression processes cannotbe neighbors.

-

Figure 5

Figure 4

Example of Result

lutions that allow the default mixing and splittingroles of those devices will be found first, so thatsimpler solutions are preferred .

On completion of the search, CARNOT generates arefrigerator, heat-engine, or topological-artifacthypothesis based on either the order of devices inthe floop or the presence of devices which couldaccomplish the essential compression, heating,expansion, and cooling processes . Device order,although more persuasive evidence than merepresence, is not a certain indicator of floop type .CARNOT therefore asserts hypothesis statementsthat contain the inferred floop type, the justifica-tion for the inference (ORDERED or ALL-PRESENT)and the set of role assumptions required for thatfloop type to pertain. CARNOT postpones commit-ting to a hypothesis, however, because that re-quires non-local reasoning and can be made withgreater certainty later in the processing .

Resolving Roles via Qualitative Inference Rolesdepend on the context in which the device is em-bedded . For the jet-ejector and open heat-exchanger roles, this context is limited to the stateof the mixer's inputs ; a temperature differenceacross the inputs indicates an open heat-exchanger, while a pressure difference implies ajet-ejector . When CARNOT instantiates its knowl-edge of mixers, it also expresses interest in findinginequalities in either pressure or temperatureacross the mixer's inputs, in order to avoid aim-less transitivity calculations .

Once CARNOT has identified the system's floops,whatever information necessary to find these ine-

1 . Assert propositions describing sys- (device turbine tur-1 s10 s20)tem (tur-1 HAS-INLET s10)

2. Run rules to instantiate immediate (tur-1 HAS-VIEWS (default eroding stalling) )consequences of description

3. Identify fluid loops in cycle (FLOOP fl-1 (pmp-1 htr-1 tur-1 clr-1)(s10 s20 s30 s40))

4. Create a consistent view structure for (VIEW default HEATER htr-1)system

5 . Do dependency-directed search for (ROLE mxr-1 JET-EJECTOR)roles

6. Identify routes in system (SUBCYCLE subc-1 (pmp-1 htr-1 tur-1 clr-1)(s10 s20 s30 s40))

7 . Refine view structure in light of new (VIEW EVAPORATING HEATER htr-1)informationAggregate local processes (PROCESS AGGR EXPANSION

(tur-1 tur-2 tur-3 tur-4 tur-5))9. Run rules to identify plans (PLAN RANKINE-CYCLE subc-1)

Identifying an Open Heat-Exchanger via Inequalities

Splitter-1

Splitter-2

Mixer

qualities, should it exist at all, will be present in thedatabase . At this point, CARNOT attempts to assertan inequality statement for the identified stuff pa-rameters via transitive reasoning . For example, inthe cycle fragment of Figure 6 the mixer can beidentified as an open heat-exchanger, givenCARNOT's domain knowledge. The transitivityreasoning proceeds as follows :

l .

No temperature drop across a default-viewsplitter gives T(A) = T(B) = T(X).

2 . Temperature drop across a default-viewturbine gives T(B) > T(C.

3 .

No temperature drop across a default-viewsplitter gives T(C) = T(D).

4 .

T(D) >_ T(Y) because, at best, perfect heattransfer in the default-view heat-exchanger would make T(D) = T(Y) .

5 .

By transitivity, T(Y) 5 T(C) and thereforeT(Y) < T(B) .

6.

Because T(X) = T(B), we can deduce thatT(Y) < T(X), thus satisfying the conditionsfor an open heat-exchanger .

Identifying Subcycles and Paths CARNOT now at-tempts to re-parse the input system into a set ofmutually exclusive and collectively exhaustivesubcycles and paths, the latter originating at split-ters and terminating at mixers . The only case inwhich CARNOT relaxes the "no-gaps/no-overlaps"constraint is when a hypothesized heat-engineshares structure with a hypothesized refrigerator,because such shared structure can improve effi-ciency and reliability.

CARNoT identifies subcycles by applying the fol-lowing heuristics :

1 . Should a floop exactly subsume two ormore floops, consider only the subsumedfloops .

2 . Floops that have no structure in commonwith other floops are considered subcy-cles, as are lone heat-engine and refrig-

Figure 6

HX-Heater

erator floops .3 . Of a set of floops sharing structure,

choose the putative heat engine with thegreatest number of worksources, orchoose the putative refrigerator with thegreatest number of fluid heaters (i.e ., re-frigerator coils) .

CARNOT now accepts or rejects the type hypothesisfor each identified subcycle . If all the views re-quired for the hypothesis to hold are true, thenCARNOT simply records the relevant type state-ment, while if a single view is false, CARNOT assertsthe implication that the subcycle is not of pur-ported type . When one or more view statementsare unknown, CARNOT assumes in turn that eachunknown is true and looks for any resulting con-tradictions in its knowledge of the system. Forexample, CARNOT may know that the temperatureacross a mixer is constant, so assuming that themixer is an open heat-exchanger would cause acontradiction. Should such a contradiction occur,CARNOT retracts the view and asserts that both theview and the hypothesized type cannot mutuallypertain. Otherwise, CARNOT assumes the views arevalid and accepts the hypothesized floop type .

Aggregating Processes and Inferring Plans Theset of active views determines what processes areconsidered to be active . For example, a boilingprocess is only active if its associated heater isviewed as a Boiling-Heater .

Aggregate processes arise from two or more de-vices operating in conjunction to produce a singleeffect. CARNOT aggregates local processes ac-cording to the set of heuristics shown in Figure 7,which are based on the rational-designer premise;there is no physical law enforcing these con-straints, but violating them would serve no ther-modynamic purpose, and in fact be at odds withone or more of the three teleological goalsCARNOT imputes to an input system . Figure 9 il-

Rules For Composing Aggregate Processes"

Heating processes- May have an arbitrary number of interveningpumping, mixing, and splitting processes

- Last local heating process must be downstream oflast local pumping process

- No intervening cooling, expansion, or throttlingprocesses

"

Cooling processes- May have an arbitrary number of interveningmixing, splitting, and expansion processes

- No intervening heating processes"

Compression processes- May have an arbitrary number of interveningheating, mixing, and cooling processes

- First local compression process must be upstreamof the first heating process

- No intervening expansion processes"

Expansion processes- May have any number of intervening heating,cooling, splitting, and mixing processes

- Last local expansion process must be downstreamof last heating process

- No intervening throttling or compression processes

Figure 7

lustrates the aggregation resulting from an appli-cation of these rules to a cycle .

The assertion of plans is simply a local propaga-tion based on the current set of active aggregateprocesses and other information cached in thedatabase . Figure 8 shows the rules for instantiat-ing an ideal Rankine cycle plan .

6 . ExampleWe present here a cycle typical of those CARNOTcan explain . The cycle shown in Figure 9 is apractical Rankine cycle for electrical power gen-

(RULE

(RULE

Rules for Instantiating Rankine Cycle Plan

(( :true (PLAN HEAT-ENGINE ?name ?cmp ?htg:test (every #'liquid-pump? (cadr

(let ((pumps (make-pump-exprs ?cmp)))(assert! ( :implies ( :and ?pl pumps)

?exp ?clg) :var ?pl?cmp))))

?cmp ?htg ?exp ?clg))(PLAN RANKINE IDEAL ?name:ideal-Rankine-cycle-inference))

Figure 8

eration. Steam bleeds from the turbine(represented by the five turbines in series acrossthe top of the schematic) preheat the feedwater toincrease the efficiency of the cycle. CARNOT'Sexplanation of this system is, translated from thepredicate calculus :

"

The system is a heat engine . Given stepwiseisentropic expansion in the turbines andstepwise isobaric heating in the heaters, it isa practical Rankine cycle, because it is a va-por power cycle. It is a vapor power cyclebecause it condenses its working fluid.

" Turbines 1-5 create the resisted expansionprocess of the system. Heaters Hx-1, MIXER-2, Hx-2, Hx-3 and BomER create the heatingprocess. Pumps 1-3 create the compressionprocess. CoNDENsER creates the coolingprocess.

"

MIXER-2 is an open heat-exchanger becausethe fluid from splitter sPL-3 has a higher tem-perature than the fluid from Hx-1 . This isdone to achieve the design goal of mAiNTA N-sYsTEM-INTEGRITY, because an open heat-exchanger removes harmful impurities fromthe working fluid.

"

Pumps PUMP-2 and PUMP-3 may act to prevent the working fluid from flashing .

Thiswould achieve the design goal of mAiNTAIN-sYsTEM-r,rrEGRITY, because flashing wouldcause downstream pumps to cavitate, cavita-tion would cause the pump's fluid-flow-rateto decrease, and a decrease in fluid-flow tothe boiler would cause the boiler to melt .[This inference is uncertain because it is

(PLAN VAPOR-POWER:vapor-power-cycle-inference)))

?name ?cmp ?htg ?exp ?clg))

(( :true (PLAN HEAT-ENGINE ?name ?cmp ?htg ?exp ?clg) :var ?p1)( :true (PLAN VAPOR-POWER ?name ?cmp ?htg ?exp ?clg) :var ?p2)( :false (INTERLEAVED ?cmp ?htg) :var ?p3)( :false (INTERLEAVED ?htg ?exp) :var ?p4)( :false (INTERLEAVED ?exp ?clg) :var ?p5))

(assert! implies ( :and ?pl ?p2 ( :not ?p3) ( :not ?p4) ( :not ?p5))(ISOBARIC ?htg) (ISOBARIC ?clg) (ISENTROPIC ?exp))

based solely on the cycle's topology ; Pump-2and PUMP-3 have both heaters and pumpsdownstream of them, so it is possible that theremoval of either pump would enable adownstream heater to cause the fluid to flashinto vapor. Given numeric information,CARNOT can determine whether this wouldactually occur] .

"

Heaters Hx-1, MIXER-2, Hx-2 and Hx-3 preheatthe working fluid. This is done to achieve thedesign goal of MAxwuE-SYSTEM-EFFICIENCY,because a Rankine Cycle's efficiency is di-rectly related to the average temperature ofheat addition .

7. Related WorkChandrasekaran has developed a theory of Func-tional Reasoning that is consistent with the workpresented here . He has proposed that teleologicalknowledge be encoded in Causal Process Descrip-tions (CPDs) that are represented as directedgraphs whose arcs are causal links (e.g ., Chan-drasekaran, 1994). CARNOT's knowledge base isorganized along similar lines, although we prefernot to encode the causal links explicitly, and in-stead allow the inference engine to instantiatethem as they become relevant, via the view androle mechanisms .

Vescovi, Iwasaki, Fikes, and Chandrasekaran haveproposed a modeling language, CFRL, for inte-

Regenerative Rankine CycleAggregate Expansion Process

Figure 9grating qualitative and functional reasoning(Vescovi et al, 1994) . CFRL composes a qualita-tive model from model fragments and then at-tempts to fit a causal story (encoded in CPDs) to aparticular trajectory through the qualitative statespace. Because thermodynamic cycle analysis issteady-state, we have been able to avoid the com-plexities arising from such explicit temporal rea-soning .

Franke has proposed a rigorous language forteleological description (TeD) (Franke, 1993) thatmay in the future provide us with useful formal-isms as we extend CARNOT. He approaches theissue of teleology from the designer's point ofview, while CARNOT attempts to infer the intentionsof the designer after the fact, given only the arti-fact.

Narayanan, Suwa and Motoda have described asystem that predicts the operation of simple me-chanical devices from labeled schematic diagrams(Narayanan et al, 1994) . Their system producesexplanations similar to CARNOVS, via visual rea-soning, whereas CARNOT'S input is a set of propo-sitions describing devices in a particular structuralconfiguration.

8 . DiscussionWe have described a set of teleological represen-tations consisting of goals, plans, roles, and viewsthat enable the production of functional explana-

tions of complex thermodynamic cyclesgrounded in a qualitative domain theory . Wehave also shown that aggregating processes pro-vides a powerful heuristic for recognizing cyclesdespite structural variations .

We believe the generativity of our approach willenable it to scale up to explain any thermody-namically valid system . CARNOT now explains alleight of the steady-flow cycles contained in anintroductory text (Whalley, 1992), and twenty-four of the thirty-two cycles in a more compre-hensive text (Van Wylen & Sonntag, 1985) .

In the worst case, CARNOT could exhibit exponen-tial behavior due to the dependency-directedsearch it conducts to resolve device roles. How-ever, the structure of the domain is such that boththe number and size of choice sets for this searchremain small (typically five choice sets of size twoor three each). We anticipate that CARNOT willcontinue to exhibit the polynomial performancewe have seen to date .

CARNOT' S current limitations stem from gaps in itsknowledge base . For instance, the rules needed toinfer the presence of an air-standard refrigerationcycle have yet to be implemented. Our next goalis the explanation of non-steady-flow systems,such as the Otto and Diesel cycles used in automotive engines .

We believe that some improve-ments to the algorithm combined with roughly aone-third increase in CARNOT's current rulebase(which now contains about 140 rules) will enablethe explanation of all thirty-five cycles containedin Analysis of Engineering Cycles (Heywood,1980), considered to be the definitive text onthermodynamic cycles .2

As an initial test of its capabilities, we intend toincorporate CARNOT into the coaching module ofa thermodynamics tutoring system . We also in-tend to test the applicability of this theory to otherdomains, such as hydraulics or pneumatics .

AcknowledgmentsThis work has been supported by the ComputerScience Division of the Office of Naval Research.

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