snapshot fault changes state-based location and duration of manifestation is irrelevant

Transcription

1 On he dimensions of emporal model-based diagnosis Luca Console, Daniele Theseider Dupre Diparimeno di Informaica, Universia di Torino Corso Svizzera 185, Torino, Ialy Absrac The goal of his paper is o analyse he dieren dimensions in emporal model-based diagnosis and he dieren choices, as regards boh modeling and reasoning, in he design of a emporal diagnosic sysem. We relae he modeling choices and he absracions ha can be made o simplify a emporal diagnosic sysem o he dimensions of he problem, discussing when each ype of model is adequae, i.e., when some absracions can be made safely. Finally, we provide a knowledge-level classicaion of he approaches o emporal model-based diagnosis in he lieraure and some guidelines o choose he mos adequae approach, given an applicaion o be considered. Inroducion One of he challenging problems for researchers working on model-based diagnosis (MBD) is he emporal dimension of he diagnosic ask. Mos of he devices o be diagnosed have a ime dependen behavior and diagnosis is performed over ime and is usually inegraed wih oher aciviies spanning over ime, such as monioring or reconguraion or repair. However, dealing wih he emporal dimension is problemaic (see (Hamscher & Davis 1984) and (Hamscher, Console, & de Kleer 1992), chapers 5 and 6) and indeed several of he successful approaches o MBD absrac, a leas parially, from ime. There are several dimensions in emporal MBD, concerning a leas hree relaed aspecs: The diagnosic ask as a whole and is dynamics. This corresponds o how and when diagnosis is performed and which are he goals of he diagnosic process: issues such as \is diagnosis performed online, while monioring a sysem, or pos-morem?", \When are he soluions needed?", \When and how is repair or reconguraion performed?". The naure of he device o be diagnosed. Dieren devices, in fac, may have very dieren forms of ime-dependen behavior. The ype of daa (and emporal daa) ha can be available during he diagnosic process. These dimensions inuence boh modeling (i.e., choosing he appropriae model for a device) and reasoning (i.e., he deniion of he diagnosic process). Indeed, each one of he approaches in he lieraure focuses on some of hese dimensions. The goal of his paper is o analyse hese dieren dimensions, providing a knowledge-level accoun of emporal MBD. In paricular, we also analyse under which condiions some of he aspecs concerning ime can be absraced for simplifying he diagnosic process. Finally we overview some of he approaches in he lieraure comparing hem according o he dimensions of emporal diagnosis. In his way he paper also provides some guidelines for choosing which of he dimensions are relevan, given a diagnosic applicaion. An exended discussion, considering furher dimensions and providing a logical framework for emporal MBD can be found in (Brusoni e al. 1998). Dimensions in emporal MBD In his secion we analyse he various dimensions concerning emporal diagnosis. We disinguish beween he aspecs concerning he diagnosic ask and hose concerning he naure of he device o be diagnosed. The diagnosic ask Diagnosis is a process ha spans over ime and ha includes several dieren aciviies, such as gahering informaion from he device o be diagnosed, generaing candidae explanaions for he observaions, suggesing ess/probes for discriminaing beween he candidaes. However, he diagnosic process is no he same in all cases and several disincions can be made. Some of hese disincions are fundamenal when sudying he dynamics of he process. An imporan disincion is he one beween on-line and o-line diagnosis.

2 In he former case diagnosis is performed on a device while he device is operaing (possibly in a fauly way). Diagnosis is hus performed across ime and mus be inegraed wih monioring and wih planning and acing for reconguraion and/or repair. Moreover, in many cases diagnosis mus cope wih he fac ha he device has a conrol sysem ha reacs o he presence of anomalous condiions, independenly of he diagnosic process iself. The overall diagnosic process should rack he device and is behavior diagnosis (in is resriced sense, i.e., candidae generaion and discriminaion) can be performed a dieren imes: as soon as here is a deviaion from expeced behavior or as soon as here is an alarm or when he sysem canno recover auomaically (wihin a deadline). Wha is imporan is ha here mus be a emporal window for diagnosis and ha such a window overlaps wih he emporal evoluion of he device. This overlap is paricularly signican in hose cases where diagnosis (and hen reconguraion or repair) mus be performed wihin a given ime in order o mach wih he emporal evoluion of he device, avoiding some unaccepable degradaion of is behavior. In he o-line case diagnosis is performed on a posmorem dump of he sympoms of he device. Such a dump can be a snapsho or a se of snapshos or a se of hisorical daa (if he occurrence of he sympoms across ime is aken ino accoun). Noice ha in boh cases diagnosis can be performed a several imes. In he o-line case his means ha diagnosis is performed on dieren ses of daa (snapshos). In he on-line case, diagnosis can be performed eiher on snapshos (aken periodically) or coninuously (i.e., inerpreing a coninuous ow of daa). The device o be diagnosed In his secion we analyse he emporal dimensions concerning he device o be diagnosed. Two dieren ypes of ime-dependen behavior can be disinguished: (1) Temporal/dynamic behavior (2) Time varying behavior Temporal behavior occurs when he consequences of he fac ha he device is in a specic (normal or fauly) mode manifes hemselves afer some ime and for some ime. In his case a diagnosis should accoun for boh he observaions and heir emporal locaion. A emporal behavior is usually dynamic, depending on he inernal sae (memory) of he sysem, as in sequenial circuis in some cases he emporal behavior can be convenienly absraced o avoid a dynamic (i.e., sae dependen) model. A ypical model of a dynamic device includes (i) a descripion of how he sae changes (over ime), given he inpu and he mode of he device and (ii) a descripion of how he oupu depends on inpu, sae and mode. A dynamic behavior involves a sae change. A disincion which is imporan and has a serious impac on modeling issues is he one beween discree and coninuous change. The former case includes hose sysems in which he inernal sae can assume a nie number of dieren (possibly non-ordered) values (as, e.g., in sequenial digial circuis) and a sae change corresponds oachange beween such discree values he laer includes hose sysems in which one may have coninuous changes (as, e.g., in analog sysems). The behavior of a device is ime-varying when he device may have dieren fauls across ime. As a special case, he behavior may be inermien in case he device can alernae normal and fauly behavior. A second problem concerning he device o be diagnosed is he dynamics of he manifesaions of fauls, which, in general, manifes hemselves across ime. This means ha here may ormay no be a delay beween a faul and is sympoms and ha he sympoms may be visible for some ime. Moreover, i may behe case ha also he sympoms are inermien. Similarly, here may be some dynamics for repair/reconguraion, in he sense ha a device (or, beer, is uses) may impose some emporal consrains on he acions for repair and/or conguraion. Moreover, such acions may require ime o be execued and heir eecs may manifes only afer some ime. Modeling choices for emporal diagnosis The previous secion discussed some of he dimensions ha should be aken ino accoun when designing a diagnosic sysem ha can deal wih ime. Taking ino accoun all (or many) of such dimensions makes diagnosis a very complex ask. More specically, in some cases he ask may resul an unsolvable or very underconsrained one (see, e.g., (Hamscher & Davis 1984) for he diagnosis of sequenial circuis). Indeed, mos of he approaches o modeling and diagnosis in he lieraure concenraed on a specic diagnosic ask and modeled only some aspecs of he ime dependen behavior of a device, absracing oher aspecs. In some cases major absracions are adoped in he exreme case one may limi o saic models and perform diagnosis on a se of daa corresponding o a snapsho or o muliple snapshos. In oher cases, he absracions are more limied for example, some approaches focus only on emporal behavior avoiding he dynamic or ime-varying one while oher approaches focus on ime-varying behavior only. In his secion we analyse when some of he forms of ime-dependen behavior discussed in he previous

3 secion can be absraced safely. The analysis is a knowledge-level one a concree and sysemaic analysis of he approaches in he lieraure will be presened in he las secion of he paper. Approaches o emporal MBD In he following we consider ve dieren approaches o emporal diagnosis. The rs four of hem correspond o common absracions: (a) Aemporal diagnosis. In his case all ypes of emporal informaion are disregarded. Two cases can be disinguished: (a.1) Single-snapsho diagnosis. Diagnosis is performed on he sympoms observed by aking a single snapsho of he behavior of he device. A soluion is a se of fauls explaining hese sympoms. (a.2) Sympom-collecion diagnosis. The se of sympoms ha arise in a emporal window are colleced (wihou keeping rack of heir emporal locaions and exens) and hen diagnosis is performed on such a se of sympoms. More specically, a diagnosis is a se of fauls explaining all he sympoms. (b) Sae-based (or muliple-snapsho) diagnosis. In his case diagnosis is performed by considering several snapshos aken during a emporal window. Each snapsho is solved independenly of he ohers and a diagnosis is a se of fauls ha is a soluion for each snapsho. The emporal dimension is disregarded in he sense ha he ordering and emporal locaion of he snapshos is no aken ino accoun. (c) Time-varying diagnosis. These approaches exploi models of he ime-varying behavior of a device, i.e., models ha specify which ransiions beween fauls are possible (and may provide emporal consrains on such ransiions) and absrac emporal/dynamic behavior, i.e., hey adop saic models of he consequences of each faul. Solving a diagnosic problem corresponds o reconsrucing he hisory of he fauls of he device (or of is componens) a differen imepoins. In oher words, we cancharacerize a soluion as a se assigning a faul o he device (or o is componens) for each ime poin awhich diagnosis is performed and such ha: 1. The faul assignmen a each poin explains he sympoms observed a ha ime poin 2. The hisory of faul assignmens is consisen wih he model of ime-varying behavior of he device. Noice ha, dierenly from he sae based approach, he emporal locaion (or ordering) of he snapshos is aken ino accoun and a model of ime-varying behavior is adoped. (d) Temporal diagnosis. In his case he emporal/dynamic behavior of a device is modeled bu he ime-varying one is disregarded. In oher words, he assumpion is ha some faul(s) occurred in he sysem bu ha fauls canno change over he emporal window for diagnosis. A diagnosis is a (se of) faul(s) ha allows o reconsruc he emporal/dynamic behavior of he device, i.e., ha accouns for he observed sympoms and for heir emporal occurrence. (e) General emporal diagnosis. In his case boh he emporal/dynamic and ime-varying behavior of a device are modeled and aken ino accoun in he diagnosic process. We hus have a merge of iems (c) and (d): a diagnosis is an assignmen of fauls over ime ha explains boh he dynamic and he imevarying behavior of he device as i is observed during a emporal window. The dieren approaches require dieren models of a device. The rs wo of hem ((a) and (b)) can deal wih a model describing in a saic way he behavior of a device (or of is componens). The model simply liss he consequences of he fac ha he device (componen) is in a given correc or fauly mode. In he oher hree cases he emporal evoluion of he device mus be modeled (he emporal/dynamic or he ime-varying behavior or boh). An imporan choice a his poin isheonology of ime o be adoped in he model and during he diagnosic process. Several dieren onologies can be considered: Meric (quaniaive) ime. In his case he model provides quaniaive emporal consrains on he evoluion of a device. For example, i may specify he expeced delay beween a faul and is eecs or he expeced duraion of a sympom (in he case of emporal behavior) or he expeced delay associaed wih a ransiion beween wo fauls (in he case of ime-varying behavior). During he diagnosic process, he locaion (duraion) of he sympoms mus be aken ino accoun and he proposed diagnosis mus accoun for hese aspecs. Noice ha one may adop a discree or coninuos model of ime for meric informaion. Qualiaive ime. This is a weaker case in which he model species only qualiaive consrains (as, e.g., in (Allen 1983)) on he evoluion of a device. For example, he model may specify he expeced ordering or conainmen relaions beween sympoms or beween fauls in faul ransiions. As a consequence, only qualiaive consrains beween he sympoms can be aken ino accoun in he diagnosic process and wo cases where he sympoms have dieren locaions (duraions) corresponding o he same qualiaive consrains canno be discriminaed. Time as a sequence ofsaes. This is an even weaker model where ime is simply regarded as a sequence

4 of saes (poins) and he only relaion is he one induced by he ordering of he saes. The model may only specify weak ordering consrains beween sympoms or beween faul ransiions. Ad-hoc absracions. Special onologies can be de- ned by aking ino accoun some of he aspecs of he hree cases above. Some examples will be given in he las secion of he paper. When modeling dynamics, a furher imporan disincion is he one beween discree and coninuous change. Noice ha his disincion is orhogonal o he one concerning qualiaive and quaniaive models. For example, one may have qualiaive models wih coninuous change (based on qualiaive derivaives) or quaniaive models wih discree saes and discree change. These consideraions inroduce furher possibiliies for building absracions. The behavior of a coninuously changing dynamic device can be described using a quaniaive or a (more absrac) qualiaive model in boh cases one mayadopamodel of coninuous change (using quaniaive or qualiaivederivaives, respecively) or a more absrac model based on discree change. Dealing wih models wih discree change is in fac generally simpler han dealingwihmodelsinvolving (quaniaive or qualiaive) derivaives. Noice, nally, ha he adopion of a model based on discree change is relaed o he adopion of a discree onology for ime. On he adequacy of absracions As we noiced above, making some absracions leads o a simplicaion of he diagnosic process, bu i may lead o approximaion in he se of soluions ha are compued. In paricular, some correc soluions may be los and some spurious ones may be produced. However, here may be cases (i.e., diagnosic asks and ypes of devices) where he absracions can be made safely. In he following we give, for each one of he absrac approaches o emporal diagnosis discussed above, a knowledge-level characerizaion of he cases where he absracions can be made safely. Figure 1 summarizes graphically he resuls of he analysis. In he gure we represen on a ime scale he dynamics of (i) faul changes, (ii) manifesaion of fauls and (iii) he diagnosic process. The las can be regarded as a window, i.e., as he ime inerval during which diagnosis is performed. We inend ha a diagnosis is correc if i is a possible diagnosis for he sysem during he considered window. In he rs wo cases (aemporal approach, boh sub-cases (a.1) and (a.2), and sae-based approach, case (b)) he device mus be non-ime-varying: he approaches produce reasonable soluions jus in case fauls do no change during he diagnosic window. In he aemporal single-snapsho approach (gure 1.(a.1)) he dynamics of he diagnosic process is no considered. Since diagnosis is performed on one snapsho (aken a some ime afer he faul(s) occurred), we have ha he approach produces accurae soluions jus in case he same sympoms can be observed a any ime during he diagnosic window. This is a srong condiion a weaker one is ha, alhough he locaion and exens of he sympoms may vary during he diagnosic window, i is possible o express some condiions on he sympoms ha are sucien for discriminaing beween fauls and ha hold a any poin in he emporal window for diagnosis. These condiions consiue he aemporal model of he behavior of he device. This is he approach usually aken in heurisic diagnosis, where he model can be regarded as a descripion of he sympoms ha are usually observable in he diagnosic window (in a snapsho). The aemporal sympom-collecion approach (gure 1.(a.2)) and he sae-based approach (gure 1.(b)) can be analysed ogeher. The approaches are dieren in he sense ha in he former he sympoms are colleced during he window (wihou keeping rack of heir emporal exen) and diagnosis is performed a he end of he window in he laer, several snapshos are aken during he window (wihou keeping rack of he emporal locaion or ordering of he snapshos) and one looks for a diagnosis ha is common o all snapshos. Thus, in boh cases he sympoms may change over ime bu no ordering (and emporal locaion) of he sympoms is aken ino accoun. This means ha he approaches produce accurae soluions when he emporal exens of he sympoms is no relevan for performing diagnosis and for discriminaing beween fauls. More precisely, his means ha here canno be wo fauls ha have he same se of sympoms bu wih dieren emporal consrains on he sympoms. In case here exis wo (or more) fauls for which such aspecs are relevan, hen hese fauls canno be discriminaed by hewoapproaches ha canno produce accurae soluions. The fac ha he aemporal sympom-collecion and he sae-based approach are similar as regard he emporal condiions on which hey provide accurae soluions is no surprising since in boh cases wha is relevan is he se of sympoms ha occur a some ime during he emporal window. Noice ha in he sae-based approach he accuracy of diagnosis may also depend on he fac ha he snapshos are aken a signican imes. This means ha he frequency of he snapshos mus be in accordance wih he emporal granulariy of he manifesaions.

5 aemporal single snapsho approach aemporal sympom-collecion approach snapsho (a.1) (a.2) Legenda faul changes sae-based approach Time varying behavior only locaion and duraion of manifesaion is irrelevan (b) (c) emporal exen of manifesaions of fauls Temporal behavior only (d) window for he diagnosic ask Temporal and ime varying behavior (e) Figure 1: A graphical represenaion of he condiions for making absracions in emporal MBD. Le us consider now he oher hree cases, where some form of emporal informaion is aken ino accoun. The speed or frequency of: (1) faul change, (2) faul manifesaion, (3) he diagnosic ask mus be compared for a given domain. A general consrain is ha (3) canno be faser han (2) since a faul canno be diagnosed unil i manifess iself. Focusing on ime-varying behavior only is reasonable when (2) is very fas wr (1) while (3) is no faser han (1). In his case diagnosis should hypohesize he presence of fauls and heir changes, while he manifesaions of fauls can be regarded as insananeous wr faul changes (see gure 1.(c)). In oher words, he emporal/dynamic behavior is no relevan wr he diagnosic ask o be performed, while reconsrucing how faulschange over ime is relevan. Focusing on emporal/dynamic behavior only is reasonable when (2) is sill fas wr (1), bu (3) can be done (and has o be done) a a similar speed wr (2), and faser han (1). In his case diagnosis mus inerpre he emporal manifesaions of he fauly saes of he sysem, while hey are arising fauls change slowly and hus hese changes have noo be aken ino accoun in he diagnosic process (see gure 1.(d)). In oher words, his approach produces accurae soluions in hose cases where he device can be regarded as nonime-varying during he emporal window of diagnosis. Noice ha i is also possible o focus on emporal behavior, absracing he dynamic one. We remarked ha a emporal/dynamic device can be characerized by (i) a descripion of how he sae of he device changes, given is inpu and mode and (ii) a descripion of he observable consequences (e.g., inpu/oupu behavior) of he device being in a given sae and mode. Modeling he former corresponds o modeling he dynamic behavior of he device. Limiing o he laer corresponds o focusing on emporal behavior absracing he dynamic one. Acually, any emporal behavior has an underlying dynamic behavior: a delay beween a cause and an eec involves a sae change in (par of) he sysem similarly, duraion of sympoms is relaed o an underlying sae change ha makes he sympom disappear (eiher worsening, or improving due o some regulaory or conrol mechanism) afer some ime such a dynamics can also be absraced making assumpions on he correc behavior of he res of he sysem. Absracing only par of he dynamics may make sense if some of he dynamics is fas and some is (relaively) slow. In ha case he \slow" dynamics can be ignored if i is also slow wih respec o he diagnosic ask, concenraing on he emporal behavior (absracing he faser dynamics), similarly o he case of \slow" ime-varying behavior. Boh emporal/dynamic and ime-varying behavior musbeaken ino accoun when (1), (2) and (3) have he same ime granulariy (gure 1.(e)). This is he mos general case for emporal diagnosis and he goal

6 is o inerpre he manifesaions of fauls while he fauls are changing and heir manifesaions are arising. Similarly, boh ypes of behavior should be aken ino accoun when (1) is faser han (2) and (3) is, as usual, no faser han (2) bu his is he case where he manifesaions of a faul (and hen he possibiliy of diagnosing i) only arise when he faul has already disappeared or changed, and herefore diagnosis, if ever possible, is almos useless, since any acion o remove he faul is presumably oo lae. In he las hree cases dieren onologies for ime can be adoped. Choosing he righ one depends on wo main aspecs: he dynamics of faul manifesaions, i.e., which kinds of emporal informaion are relevan for recognizing he sympoms of a faul (or for discriminaing beween dieren fauls) observabiliy. If meric informaion is relevan in he dynamics of faul manifesaion, hen he approaches focusing on qualiaive (or sequence of saes) models of ime may be inaccurae, loosing he abiliy o recognize (or discriminae) dieren cases. However, if no precise informaion abou he locaion and duraion of sympoms can be gahered during diagnosis, hen using quaniaive informaion in he models may be useless. Noice ha here are cases where a oo absrac model of ime can lead o he same level of (in)accuracy ha can be achieved adoping a simpler approach o diagnosis. For example, suppose ha wo fauls f1 and f2 have he same manifesaions, wih he same ordering bu wih dieren delays beween fauls and manifesaions. Focusing on emporal behavior is adequae for such a case bu, if one adops a qualiaive model for ime, hen he fauls would no be disinguishable and his may lead o wrong diagnoses. In his case he same resuls could be probably obained wih a more limied eor using a sae-based approach. This is o say ha one can dene a sor of coninuum beween he sae-based approach and he approach focusing on emporal/dynamic behavior only and ha such a coninuum depends on he onology of ime been adoped. A emporal approach wih a weak onology of ime ends o be closer o a sae-based approach. These consideraions are similar o hose raised recenly by Sruss in a paper showing ha under some condiions one can adop he sae-based approach (which leads o signican compuaional advanages) wihou loosing diagnosic capabiliies (Sruss 1997). Noice, in conclusion, ha he discussion above isolaes he cases where absrac approaches produce accurae soluions. These condiions can be regarded as exreme cases in he sense ha one may adop an absrac approach even if he condiions are no mached compleely or in all he cases. In such a way, one may have anapproachhaworks well in mos of he cases (or in he mos frequen cases, or in almos all he cases, depending on when he condiions are no mached). Using a less absrac approach would probably produce in hese cases more accurae soluions bu a a higher cos boh from a concepual poin of view, in erms of design of he model and of he diagnosic sraegy, and from a compuaional poin of view. Approaches in he lieraure In his secion we briey analyse some of he approaches o emporal model-based diagnosis in he lieraure, comparing hem according o he dimensions isolaed in he previous secions. Table 1 summarizes he main resuls of he analysis. The able winesses he fac ha here is awidevariey ofapproaches in he lieraure and provides a knowledge-level comparison of he various approaches. Some brief commens on he approaches lised in able 1 are worhwhile. A more deailed discussion can be found in (Brusoni e al. 1998). Firs of all, noice ha focusing on emporal behavior only (absracing dynamics) is a common assumpion in many causal approaches o diagnosis (e.g., (Console & Torasso 1991 Long 1983)) however a similar approach hasbeen adoped also in (Porcheron e al. 1994) for he diagnosis of power plans. In case of dynamic behavior, some approaches concenrae on he diagnosis of sequenial circuis (e.g., (Hamscher & Davis 1984 Guckenbiehl & Schafer- Richer 1990 Hamscher 1991)) and model change in a discree way. These approaches dier as regards he model of ime: ime is a sequence of ordered saes in (Hamscher & Davis 1984) while meric informaion is aken ino accoun in (Guckenbiehl & Schafer-Richer 1990) and ad-hoc absracions in (Hamscher 1991). Oher approaches model change using (qualiaive) derivaives. For example, boh (Ng 1991) and (Dvorak & Kuipers 1989) use qsim (Kuipers 1986) for simulaing he dynamic behavior of a sysem. dami (DeCose 1991) has similar goals bu i assumes ha a oal envisionmen isavailable and exends Forbus' heory of measuremen inerpreaion (Forbus 1986) by considering measuremens across a sequence of saes (wih limied meric informaion). The work by Dague e al. focuses on he diagnosis of analog (dynamic) sysems, especially elecronic circuis (see (Dague e al ). Thus, hey deal wih dynamic sysems and coninuous change, using meric ime. The approach in (Moserman & Biswas 1997) can deal wih emporal and dynamic be-

7 Reference Type of phenomena Onology of ime Temp Dynamic Time meric quali sae ad-hoc con. discr. var seq. abs (Brusoni e al. 1997) X X X (Console & Torasso 1991) X X (Console e al. 1994) X X (Dague e al. 1991) X X X (DeCose 1991) X X X X (Downing 1992) X X X X X (Dvorak & Kuipers 1989) X X X (Friedrich & Lackinger 1991) X X X X (Guckenbiehl & Schafer-Richer 1990) X X X (Hamscher 1991) X X X X X (Hamscher&Davis 1984) X X X (Long 1983) X X (Moserman & Biswas 1997) X X X (Nejdl & Gamper 1994) X X X (Ng 1991) X X X (Pan 1984) X X X X X (Sruss 1997) X (Williams & Nayak 1996) X X Table 1: A classicaion of approaches in he lieraure as regards he phenomena being considered (Temporal, Dynamic wih a disincion beween coninuous and discree change, Time varying) he onology of ime being considered meric or qualiaive informaion, ime as a sae sequence, ad-hoc absracions. havior wih coninuos change. Models are expressed as causal/emporal graphs derived auomaically from bond graphs. As regards ime-varying behavior, boh (Console e al. 1994) and (Williams & Nayak 1996) use models describing he possible ransiions beween modes of behavior of a device and hey perform diagnosis on a sequence of saes across ime rying o reconsruc he evoluion of he mode of behavior of a device (of is componens). Similar models are used also in (Nejdl & Gamper 1994). (Friedrich & Lackinger 1991) deals wih emporal and ime-varying behavior and presens an ineresing disincion beween permanen and ransien failures. (Nejdl & Gamper 1994) deals wih emporal (nondynamic) and ime-varying behavior. The former is described by a se of consrains relaing fauls o heir consequences (he emporal consrains are qualiaive ones based on Allen's inerval algebra (Allen 1983)). As noed above, ime-varying behavior is represened using mode-ransiion graphs. The approach in (Sruss 1997) suppors he adopion of a sae-based approach odiagnosis. Sruss claims ha a sae-based approach can solve many diagnosic problems wih a limied eor (i.e., re-using he same machinery used for saic diagnosis). Conclusions The paper presened a knowledge-level analysis of he dimensions in emporal MBD. A formal characerizaion of he framework, inroducing furher dimensions concerning he deniion of diagnosis can be found in (Brusoni e al. 1998). We presened he modeling choices ha can be made in emporal MBD, discussing some common absracions ha can be made for simplying he ask of emporal MBD. We analysed when such absracion can be made safely, i.e., when hey do no lead o inaccurae diagnoses. Finally, we classied some of he approaches in he lieraure according o he dimensions we isolaed. The paper can be also seen as a guideline for choosing he appropriae approach, given an applicaion domain. Such a choice should be based on a knowledge-level analysis of he problem o be solved, considering he dimensions isolaed in his paper, considering, in paricular, he following iems: (1) Analyze he diagnosic ask and is goals, wih specic aenion o he emporal condiions: on-line vs. o-line diagnosis granulariy of diagnosis, i.e., emporal window for diagnosis (when is a diagnosis needed, e.g., aking ino accoun ime consrains for repair and/or reconguraion).

8 (2) Analyze he naure of he device o be diagnosed, in paricular as regards he emporal granulariy of: fauls and faul change manifesaion of fauls sae change (3) Choose he ypes of phenomena o be aken ino accoun, based on he resuls of he analysis of (1) and (2). If dynamic behavior is relevan, informaion abou sae change should sugges wheher discree or coninuous change is more adequae. (4) Analyze he ype of informaion ha can be available on observaions, wih specic aenion o he emporal granulariy of such pieces of informaion. Moreover, analyze which ypes of emporal informaion on he observaions (and on he relaions beween fauls and observaions) is relevan (needed) for discriminaing beween fauls. (5) Choose which onology of ime o adop, based on he resuls of (2) and (4). References Allen, J Mainaining knowledge abou emporal inervals. Comm. of he ACM 26:832{843. Brusoni, V. Console, L. Terenziani, P. and Theseider Dupre, D An ecien algorihm for emporal abducion. In Lecure Noes in Compuer Science 1321, 195{206. Springer-Verlag. Also in Proc. DX 95. Brusoni, V. Console, L. Terenziani, P. and Theseider Dupre, D A specrum of deniions for emporal model-based diagnosis. Aricial Inelligence (o appear). Console, L., and Torasso, P On he cooperaion beween abducive and emporal reasoning in medical diagnosis. Aricial Inelligence in Medicine 3(6):291{311. Console, L. Porinale, L. Theseider Dupre, D. and Torasso, P Diagnosing ime-varying misbehavior: an approach based on model decomposiion. Annals of Mahemaics and Aricial Inelligence 11(1-4):381{398. Dague, P. Deves, P. Luciani, P. and Tailliber, P Analog sysems diagnosis. In Proc. 9h ECAI, 173{178. Dague, P. Jehl, O. Deves, P. Luciani, P. and Tailliber, P When oscillaors sop oscillaing. In Proc. 12h IJCAI, 1109{1115. DeCose, D Dynamic across-ime measuremen inerpreaion. Aricial Inelligence 51(1-3):273{341. Downing, K Consisency-based diagnosis in physiological domains. In Proc. AAAI-92, 558{563. Dvorak, D., and Kuipers, B Model-based monioring of dynamic sysems. In Proc. 11h IJCAI, 1238{1243. Forbus, K. D Inerpreing measuremens of physical sysems. In Proc. AAAI 86, 113{117. Friedrich, G., and Lackinger, F Diagnosing emporal misbehaviour. In Proc. 12h IJCAI, 1116{ Guckenbiehl, T., and Schafer-Richer, G SIDIA: Exending predicion based diagnosis o dynamic models. In Golob, G., and Nejdl, W., eds., Proc. In. Workshop on Exper Sysems in Engineering. Springer Verlag LNCS {68. Hamscher, W., and Davis, R Diagnosing circui wih sae: an inherenly underconsrained problem. In Proc. AAAI 84, 142{147. Hamscher, W. Console, L. and de Kleer, J., eds Readings in Model-Based Diagnosis. Morgan Kaufmann. Hamscher, W Modeling digial circuis for roubleshooing. Aricial Inelligence 51(1-3):223{ 271. Kuipers, B Qualiaive simulaion. Aricial Inelligence 29(3):289{338. Long, W Reasoning abou sae from causaion and ime in a medical domain. In Proc AAAI 83, 251{ 254. Moserman, P., and Biswas, G Monioring, predicion and faul isolaion in dynamic physical sysems. In Proc. AAAI 97, 100{105. Nejdl, W., and Gamper, J Harnessing he power of emporal absracions in model-based diagnosis of dynamic sysems. In Proc. 11h ECAI, 667{ 671. Ng, H Model-based, muliple faul diagnosis of dynamic, coninuous physical devices. IEEE Exper 6(6):38{43. Pan, J Qualiaive reasoning wih deep-level mechanism models for diagnoses of mechanisms failures. In Proc. 1s IEEE CAIA, 295{301. Porcheron, M. Ricard, B. Busque, J. and Paren, P DIAPO: a case sudy in applying advanced AI echniques o he diagnosis of a complex sysem. In Proc. 11h ECAI, 43{47. Sruss, P Fundamenals of model-based diagnosis of dynamic sysems. In Proc. IJCAI 97. Williams, B., and Nayak, P A model-based approach o reacive self-conguring sysems. In Proc. AAAI 96, 971{978.