TIMED OBSERVATIONS MODELLING

FOR DIAGNOSIS METHODOLOGY

A Case Study

Laura Pomponio and Marc Le Goc

LSIS, Laboratoire des Sciences de l’Information et des Syst

emes, UMR CNRS 6168

Aix-Marseille III University, Marseilles, France

Keywords:

Model based diagnosis, Multi-modelling, Knowledge.

Abstract:

The TOM4D methodology is based on constructing models at the same level of abstraction that experts use to

diagnose a process; thus, the resultant models are more simple and abstract allowing a more efﬁcient diagnosis.

For this purpose, the framework CommonKADS to interpret and organize the available knowledge of experts is

combined with a multi-modelling approach in order to describe the knowledge. This paper complements works

accomplished previously about TOM4D, introducing the combined use of Formal Logic and the Tetrahedron

of States in order to build models more suitable for the diagnosis task. Formal Logic provides a logical

interpretation of expert’s reasoning. The Tetrahedron of States provides a physical interpretation of the process

variables and allows to exclude of the logical model those states physically impossible.

1 INTRODUCTION

Knowledge-based diagnosis of systems deals with the

difﬁculty of knowledge acquisition and representa-

tion. The main problem is to determinate the right

level of abstraction in which the models have to be

constructed to obtain an efﬁcient diagnosis. Most

modelling approaches use the abstraction level of the

available models, generally design models. How-

ever the abstraction level of the design task requires

the deﬁnition of a lot of components, some of which

might be meaningless in the diagnosis task. This re-

sults in a hight computational cost since the number

of possible diagnosis increases exponentially with the

number of components.

TOM4D (Timed Observations Modelling For Di-

agnosis) (Goc and Masse, 2007; Goc et al., 2008) is

a modelling methodology based on the idea that ex-

perts use implicit models to formulate their knowl-

edge about a process and the way of diagnosing it.

Such models only consider components that are con-

cerned with a diagnosis and thus, the number of com-

ponents is minimal allowing a more efﬁcient diagno-

sis.

This paper completes the TOM4D modelling pro-

cess presented in (Goc et al., 2008) to propose the

construction of two models that complement each

other: a logical model that provides a reasoning

model consistent with the Reiter’s theory (Reiter,

1987) and a physical model that provides a physi-

cal dimension to the process variables and so, deﬁnes

its physical structure. This latter allows to identify

those states that, although they are valid in the logical

model, are physically impossible.

The next section provides a brief overview of the

main modelling approaches and the major difﬁculties

that they present. Section 3 presents a case study on

the use of Formal Logic and the Tetrahedron of States

(ToS) (Chittaro et al., 1993) to deﬁne a logical model

and a physical model which complement each other

and are presumably close to those models that experts

build to carry out a diagnosis. Finally, section 4 states

our conclusions and perspectives.

2 MODELLING APPROACHES

FOR DIAGNOSIS

The diagnosis of malfunctioning of devices or sys-

tems is a research area of Artiﬁcial Intelligence since

the decade of the seventies. Different approaches

(Zanni, 2004), such as heuristic reasoning (Clancey,

1985), Model-Based Diagnosis (MBD) (Reiter, 1987;

Dagues, 2001) and Multi Model Based Diagnosis

504

Pomponio L. and Le Goc M. (2010).

TIMED OBSERVATIONS MODELLING FOR DIAGNOSIS METHODOLOGY - A Case Study.

In Proceedings of the 5th International Conference on Software and Data Technologies, pages 504-507

DOI: 10.5220/0003005805040507

 SciTePress

(MMBD) (Chittaro et al., 1993), have arisen from that

time to the present. However, diagnostic reasoning

approaches present, in general, two major drawbacks

(Goc and Masse, 2007; Goc et al., 2008). First, the

large number of components of the resulting model

leads to computing difﬁculties in the diagnosis task.

That is to say, the number of possible diagnoses grows

exponentially with the number of components. This

problem is directly connected to the level of abstrac-

tion used. These models generally come from the de-

sign model which has nothing to do with knowledge

model to diagnosis. Second, even when the system

has few components, the consistency based theory of

diagnosis provides no means to eliminate diagnoses

which are logically acceptable but meaningless.

TOM4D (Goc and Masse, 2007; Goc et al., 2008)

is a modelling methodology for dynamic systems

based on the hypothesis that an expert uses a set of

models at a level of abstraction that allows efﬁcient

diagnostic reasoning, and this level is directly linked

with the diagnosis task, not with the design task. This

methodology proposes to combine the modelling of

the experts’ cognitive process, using CommonKADS

(Breuker and de Velde, 1994; Schreiber et al., 2000),

with a multi-modelling approach for dynamic systems

(Chittaro et al., 1993; Chittaro and Ranon, 1999), in

order to try to get around the aforesaid problems.

3 TOM4D: INTERPRETATION

MODELS

The TOM4D modelling process (Goc et al., 2008),

shown in Figure 1, aims to produce a generic model

of system, from the available knowledge and data, in

order to obtain a suitable model for the diagnosis task.

This modelling process consists of three fundamental

phases: knowledge interpretation, whose objective

is organizing and interpreting the available knowl-

edge; process deﬁnition where the boundary of the

process that governs the system, operating goals and

normal and abnormal operating modes are deﬁned;

and generic modelling, in which the aim is to deﬁne

a more general and more abstract model. This mod-

elling process is generally cyclical and each stage can

require to return to previous phases with the objective

of revising expert’s knowledge, results, ideas, mod-

elling decisions, etc. We shall focus our attention on

how, in the second and the third phases, Logic Formal

and the ToS can be used as interpretation paradigms in

order to carry out a logical interpretation and a physi-

cal interpretation of the process.

Figure 2 depicts the domain concerning the di-

agnosis of problems with a car that the authors of

Knowledge Source

CommonKADS

Template

Interpretation

Model

Scenario Model

Perception Model

Generic Model

knowledge

interpretation

process

definition

generic

modelling

T.o.S.

Formal

Logic

Scenario

Ω={ω

, ω

,..., ω

}

Figure 1: TOM4D modelling process.

(Schreiber et al., 2000) introduce in their book. The

ﬁgure presents nine rules of knowledge, noted as

,..,R

, whose meaning is, for example: R

indi-

cates that if the fuse is blown then the result of the

fuse inspection is broken.

fuse

blown

fuse

inspection

broken

battery dial

zero

gas dial

zero

gas in engine

false

battery

low

fuel tank

empty

power

off

engine behaviour

does not start

engine behaviour

stops

Figure 2: Knowledge pieces in the car-diagnosis domain.

We shall suppose that the components associated

with concepts fuse inspection, battery dial and gas

dial work properly. Therefore, the variables and com-

ponents considered in the modelling process are listed

below and rewritten as x

, x

and c

, c

, respectively.

≡ fuse.status c

≡ fuse

≡ battery.status c

≡ battery

≡fuel-tank.status c

≡ fuel-tank

≡ power.status c

≡ electric supply

≡ gas-in- c

≡ gas supply

engine.status

≡ engine- c

≡ engine

behaviour.status

The rules R

and R

establish fuzzy knowl-

edge since the value of x

is indeterminate; that

is, if x

= f alse, then x

= does

not start ∧ x

stops. In order to eliminate this ambiguity, we

TIMED OBSERVATIONS MODELLING FOR DIAGNOSIS METHODOLOGY - A Case Study

505

shall interpret and rewrite the values does not start

and stops as ¬works; that is to say, if x

f alse then x

= ¬works. Therefore, the val-

ues that the variables can assume are the follow-

ing ones: x

∈ {blown, ¬blown}, x

∈ {low, ¬low},

∈ {empty,¬empty}, x

∈ {o f f ,¬o f f }, x

∈

{ f alse,¬ f alse}, x

∈ {works,¬works}.

From the modelling process and analysis on this

example presented in (Goc and Masse, 2007), a rep-

resentation by means of logical gates of the process is

possible, as Figure 3 shows.

Figure 3: Logical model of the process.

The process variables x

are then

interpreted as binary variables x

re-

spectively, which take values 1 (true) or 0 ( f alse).

For example, x

= blown is logically interpreted and

represented as x

= 0, x

= ¬blown is represented

as x

= 1, and so on for each variable. Consequently,

each component c

, i = 1,2,3,7,8,9 is interpreted as a log-

ical gate c

i = 1,2,3,7,8,9 in Figure 3. For example,

allow to write x

= 0 ∨ x

= 0 ⇒ x

= 0 and

to deﬁne x

= and(x

), which is the functional

model of the component c

This logical interpretation leads to build a logical

model according to the consistency-based diagnosis

theory of (Reiter, 1987) as a set of ﬁrst order predicate

formula. The problem with Reiter’s theory is that it

subsumes that logically consistent states corresponds

to normal (desired) behaviours and the inconsistent

states to abnormal (undesired) behaviour denoting a

problem with at least one component. But this cor-

respondence does not resist with a physical interpre-

tation of the states. For example, the consistent state

= 0,x

= 1,x

= 0,x

= 1,x

= 0 describes

a normal behaviour that is not desirable: the fuse is

blown and the engine does not work. The inconsistent

state x

= 0, x

= 1, x

= 0, x

= 0 is

abnormal (the tank has fuel (x

= 1) but there is not

gas in engine (x

= 0)) and corresponds to a problem

with the gas supply (component c

). In contrast, the

inconsistent state x

= 0,x

1,x

= 0 (the fuel tank is empty and there is gas in

the engine) can not be associated with a problem of

a component: it is a transient state that is a normal

behaviour.

These examples shows that the logical interpreta-

tion of the variables that is required by Reiter’s the-

ory must be completed with a physical interpretation.

For this purpose, (Chittaro et al., 1993) proposes to

use ToS: in our example, the Hydraulic ToS and the

Electric ToS will be used (Figure 4). So, with the

TOM4D methodology, each variable x

of the pro-

cess is mapped both with a logical variable x

and a

physical variable x

of the corresponding ToS. For ex-

ample, using the Hydraulic ToS, the variable x

(fuel

tank status) is associated with the gas volume V (t)

in the tank so that x

= 0 is interpreted as V (t) = 0

= empty) and x

= 0 is interpreted as V (t) 6= 0

= ¬empty ). The variable x

(gas supply status) is

associated with the gas ﬂow Qv(t) in the gas supply

so that x

= 0 is interpreted as Qv(t) = 0 (x

= f alse)

and x

= 1 is interpreted as Qv(t) 6= 0 (x

= ¬ f alse).

Similarly, the Electric ToS allows the following asso-

ciations: x

(battery status) corresponds to the elec-

tric charge Q(t) in the battery, x

(fuse status) with

the system resistance R(t), x

(electric supply status)

with the voltage U (t). In this interpretation phase, the

functions of time F(t) corresponding to a variable x

are deﬁned over ℜ. Now to interpret the process be-

haviour and the correspond states, we assume that the

current I(t), the voltage U(t) and the resistance R(t)

are piecewise constant over time: I(t) = i

or I(t) = 0

(no current), U(t) = u

or U(t) = 0 (no voltage) and

R(t) = r

or R(t) = ∞ (the fuse is blown). Thus,

= blown (x

= 0) means R(t) = ∞ and R(t) = r

otherwise, and x

= o f f (x

= 0) means U(t) = 0 and

U(t) = u

6= 0 otherwise. Since I(t) =

dQ(t)

, when

I(t) is zero, the electric charge of the battery is a con-

stant: x

= low (x

= 0) means Q(t) = q and other-

wise Q(t) evolves over time.

engine

I t =

dQ t 

R  t 

charge

resistance

battery

fuse

Q t

current

U t =R t. It 

voltage

fuel tank

Qv t =

dV t 

V  t 

flow

volume

Figure 4: Physical model of the process.

The physical interpretation with through the ToS

allows to provide a semantic to each states and to

identiﬁes those that are useful for diagnosis. For ex-

ample, because Qv(t) = dV (t)/dt, all the states where

= 0 and x

= 1 corresponds to a transitory situ-

ICSOFT 2010 - 5th International Conference on Software and Data Technologies

506

ation: the fuel tank is empty (V (t) = 0) but there is

still a fuel ﬂow in the engine (Qv(t) 6= 0). We can

then assume that ∃t

∈ ℜ so that: ∀t ≥ t

,V (t) = 0 ⇒

Qv(t) = 0. This interpretation allows to consider that

= empty ⇒ x

= f alse and hence, x

= 0 ⇒ x

0. Consequently, each states containing x

= 0 and

= 1 can be removed from the logical model.

Similarly, the logical states x

= 0 (battery is low)

and x

= 1 (electric supply is on) can be removed:

∃t

∈ ℜ, ∀t ∈ ℜ,t ≥ t

, Q(t) = q ⇒ I(t) = 0. Be-

cause U(t) = R(t).I(t), this rule can be rewritten:

Q(t) = 0 ⇒ U(t) = 0. Then, all states where Q(t) = 0

and U(t) 6= 0 are not usefull for diagnosis, and all

states where x

= 0 and x

= 1 can be eliminate of

the logical model. The same reasoning can be done

with the resistance (R(t) = ∞ ⇒ U(t) = 0) so that all

states where x

= 0 and x

= 1 can be eliminated of

the logical model. In our example, the physical inter-

pretation of the variables allows to reduce the 2

= 64

states of the logical model to 16 interesting states for

diagnosis.

As a consequence, the TOM4D methodology con-

siders that to build a generic model of a process, the

expert’s knowledge must be interpreted both in logi-

cal and physical terms. The logical model (Figure 3)

describes the structure of the expert’s diagnosis rea-

soning and the physical model (Figure 4) provides the

diagnosis knowledge required for this reasoning. So

both logical and physical models are necessary and

complement each other. These models are, ultimately,

those ”constructed” by experts to do the diagnosis

tasks. In practice, the combination of these two mod-

els simplify the diagnosis task.

4 CONCLUSIONS

The present paper complements the works presented

in (Goc and Masse, 2007; Goc et al., 2008) about

TOM4D, introducing a case study that veriﬁes the

main hypothesis of TOM4D: experts use implicit

models to formulate their knowledge about a process

and the way of diagnosing it, these models belong to

a level of abstraction linked with the diagnosis task

but not with the design task. The combination be-

tween Formal Logic and the ToS allows to build mod-

els close to those constructed by experts. The former

provides a logic reasoning mechanism, the latter al-

lows to discriminate the states having a meaning ac-

cording to the diagnosis task and thus, to reduce the

state space to only those concerned with the diagno-

sis.

Our current work focus on relating TOM4D with

a method to discover experts’ knowledge from se-

quence of discrete event occurrences registered by a

machine. Linking this two approaches would allow

to deﬁne a modelling process which takes experts’

knowledge and data recorded by a machine and pro-

duces models useful to diagnosis.

This work is ﬁnanced by the CSTB, Centre Scien-

tiﬁque et Technique du B

atiment, Sophia-Antipolis,

France, under the contract number 1256/2008.

REFERENCES

Breuker, J. and de Velde, W. V. (1994). CommonKADS Li-

brary For Expertise Modelling. IOS Press.

Chittaro, L., Guida, G., Tasso, C., and Toppano, E. (1993).

Functional and teleological knowledge in the multi-

modeling approach for reasoning about physical sys-

tems: A case study in diagnosis. IEEE Transactions

on Systems, Man and Cybernetics, 23(6):1718–1751.

Chittaro, L. and Ranon, R. (1999). Diagnosis of multiple

faults with ﬂow-based functional models: the func-

tional diagnosis with efforts and ﬂows approach. Re-

liability Engineering and System Safety, 64(2):137–

150.

Clancey, W. J. (1985). Heuristic classiﬁcation. Report No.

STAN-CS-85 1066. Also numbered KSL-85-5. Depart-

ment of Computer Science. Stanford University.

Dagues, P. (2001). Th

eorie logique du diagnostic

a base

de mod

eles. In Diagnostic, Intelligence Artiﬁcielle, et

Reconnaissance des Formes. Hermes Science Publi-

cations, 17-105.

Goc, M. L. and Masse, E. (2007). Towards a Multimodel-

ing Approach of Dynamic Systems for Diagnosis. In

Proceedings of the 2nd International Conference on

Software and Data Technologies (ICSoft’07).

Goc, M. L., Masse, E., and Curt, C. (2008). Modeling Pro-

cess From Timed Observations. In Proceedings of the

3rd International Conference on Software and Data

Technologies (ICSoft’08).

Reiter, R. (1987). A theory of diagnosis from ﬁrst princi-

ples. Artif. Intell., 32(1):57–95.

Schreiber, G., Akkermans, H., Anjewierden, A., de Hoog,

R., Shadbolt, N., de Velde, W. V., and Wielinga, B.

(2000). Knowledge Engineering and Management:

The CommonKADS Methodology. MIT Press.

Zanni, C. (2004). Proposition of a Conceptual Frame-

work for the Analysis, Classiﬁcation and Choice of

Knowledge Based Diagnosis Systems. These pour

obtenir le grade de Docteur de l’Universit de Droit,

d’Econocmie et des Sciences d’Aix-Marseille. Nro.

d’dentiﬁcation 04AIX30010.

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