MODELING PROCESSES FROM TIMED OBSERVATIONS

Marc Le Goc

, Emilie Masse

1,2

LSIS, Laboratory for Systems and Information Sciences, UMR CNRS 6168

Aix-Marseille University, Marseilles, France

Corinne Curt

Cemagref, Unit´e Ouvrages Hydrauliques et Hydrologie, Aix en Provence, France

Keywords:

Multi modeling, diagnosis reasoning, dynamic system.

Abstract:

This paper presents a modelling approach of dynamic process for diagnosis that is compatible with the Stochas-

tic Approach framework for discovering temporal knowledge from the timed observations contained in a

database. The motivation is to deﬁne a multi-model formalism that is able to represent both the knowledge

of these two sources. The aim is to model the process at the same level of abstraction that an expert uses to

diagnose the process. The underlying idea is that at this level of abstraction, the model is simple enough to

allow an efﬁcient diagnosis. The proposed formalism represents the knowledge in four models: a structural

model deﬁning the components and the connection relations of the process, a behavioural model deﬁning the

states and the transitions states of the process, a functional model containing the logical relations between the

values of the process’s variables, which are deﬁned in the perception model. The models are linked with the

process’s variables. This point facilitates the analysis of the consistency of the four models and is the basis of

the corresponding knowledge modelling methodology. The formalism and the methodology is illustrated with

the model of a hydraulic dam of Cublize (France).

1 INTRODUCTION

The design of knowledge based systems to supervise,

diagnose and control industrial processes pose the dif-

ﬁcult problem of the acquisition and the representa-

tion of temporal knowledge which is the core of the

solving problem method of dynamic system diagnosis

(Basseville and Cordier, 1996).

The aim of the MultiModel Based Diagnosis

(MMBD) is to solve this problem. One of the major

difﬁculties is the deﬁnition of the right level of ab-

straction at which the models have to be constructed

to have an efﬁcient diagnosis. This investigation be-

ing still an open problem, most of the proposed mod-

eling approaches use the abstraction level of the avail-

able models, typically the design model(s). But the

abstraction level required to the design of a process re-

quires the deﬁnition of a lot of components. Using the

design model(s) leads then to diagnosis models con-

taining a large number of components. Such models

entails strong computational difﬁculties for the usual

diagnosis algorithms.

Our works consist then in developing a modeling

method, called TOM4D (Timed Observations Mod-

eling for Diagnosis) with the aim of using the same

level of abstraction that the Experts use to diagnose a

process: deﬁned at this level of abstraction, the mod-

els lead up to a minimal set of components allowing

an efﬁcient and sure diagnosis reasoning. This notion

of minimality is intuitive: only the components that

are concerned with a diagnosis have to be identiﬁed in

the models. Consequently, when using such models,

the computational difﬁculties of the usual diagnosis

algorithms will decrease. The TOM4D methodology

is based on the idea that the Experts use implicit mod-

els to formulate their knowledge about the process

and the way to diagnose about it. The methodology

aims then to explicit these models when combining

a CommonKads-like conceptual approach (Schreiber

et al., 2000) with a multimodeling approach (Chittaro

et al., 1993) and the Stochastic Approach framework

for discovering temporal knowledge from timed ob-

servations (Le Goc et al., 2005), (Le Goc, 2006). The

modeling methodology is directed by the timed obser-

vations provided either with a set of scenarios describ-

ing a concrete deterioration of a process or with the a

priori knowledge about the main events that plays a

role in the different diagnosis. The next section of

249

Le Goc M., Masse E. and Curt C. (2008).

MODELING PROCESSES FROM TIMED OBSERVATIONS.

In Proceedings of the Third International Conference on Software and Data Technologies - PL/DPS/KE, pages 249-256

DOI: 10.5220/0001884502490256

 SciTePress

the paper (Section 2) provides a brief overview of the

main modeling approaches. Section 3 presents the

formalisms of the four models of the TOM4D mod-

eling methodology, and section 4 describes the corre-

sponding modeling process through a real world ap-

plication to the Cublize dam (France). Finally, section

5 states our conclusions and proposes some perspec-

tives to our works.

2 MODELING APPROACHES

FOR DIAGNOSIS

The limitations and the problems of the heuristic ap-

proach (Clancey, 1987) have motivated the deﬁnition

of the Model Based Diagnosis (MBD) approach (Re-

iter, 1987). Reiter’s algorithm of diagnosis uses a

logical model of the system. This model represents

both the structure of the system (components and in-

terconnections) and the correct behaviors of the com-

ponents through a set of relations between input and

output values of the components. The MBD, either

in a component (De Kleer and Brown, 1984), in a

process (Forbus et al., 1984) or in a constraint (Lee

and Kuipers, 1988) based approach, applies the well

known “no function in structure” principle. This pro-

vides a clear and general framework for diagnosis.

Nevertheless, these approaches present two ma-

jor drawbacks. First, the number of potential di-

agnosis is exponential with the number of compo-

nents. This leads to several difﬁculties with real

world systems where the number of components is

large. Second, even when the system contains few

components, the consistency based theory of diagno-

sis provides no means to eliminate diagnosis which

are logically acceptable but physically meaningless

(Struss and Dressler, 1989). A lot of extensions have

then been proposed to avoid these difﬁculties (Dague,

2001): using different levels of aggregation (Davis,

1984) corresponding to different approximations, us-

ing ontologies that represent the variable values at

multiple resolutions level (Hayes, 1989), using differ-

ent behavioral models either qualitative or quantita-

tive models (Murthy, 1988), and using multiple types

of knowledge (Abu-Hanna et al., 1991). Neverthe-

less, there is not a general solution to these problems.

Moreover, none of these approaches really explains

how to export partial results obtained with a model

into other models during the problem solving task.

This has led researchers to give up the “no func-

tion in structure” principle with the aim of using some

teleological and functional knowledge. This provides

information for driving the diagnosis reasoning about

the structure and the behavior of the system. For ex-

ample, the compositional modeling of (Falkeihainer

and Forbus, 1988), (Falkeihainer and Forbus, 1991),

uses the ideas of the Qualitative Physics theory. An

explicit abstract representation of the process is then

given where a model is made of fragments from a

general-purpose domain theory. Similarly, the Func-

tion Behavior Structure approach (FBS) of (Franke,

1991) and the multimodeling approach of (Chittaro

et al., 1993) consider the reasoning task as a cooper-

ative activity between diverse models. Each model

represents a speciﬁc type of knowledge and uses a

speciﬁc representation formalism. Both approaches

separate on one hand the structural and the behavioral

knowledge about the physical system and on the other

hand the knowledge about the functions and the pur-

poses of the system. But only the multimodeling ap-

proach proposes a physical basis for the relations be-

tween the different models.

The multimodeling approach of (Chittaro et al.,

1993) separates the available knowledge about a dy-

namic system in three main categories: the funda-

mental, the interpretative and the empirical knowl-

edge. The fundamental knowledge is the basic knowl-

edge (structural and behavioral models) used to rea-

son about a system using the objective and neutral lan-

guage of natural sciences (Chittaro et al., 1993). The

interpretative knowledge is provided by a subjective

interpretation of the fundamental knowledge. This in-

terpretation is made in terms of functions (functional

model) and goals (teleological model) of the system

components assigned by the designer(s). The empir-

ical knowledge is an explicit statement of the proper-

ties of the system and may refer to the two other cate-

gories. These three sets of knowledge are based on an

ontology which deﬁnes the type of entities the system

is made with. The functional model links the behav-

ioral model and the teleological model. The role of

a function is to describe how the behavior of the in-

dividual components contributes to the achievement

of a goal assigned to the system. The links between

the models allow a good continuity for modeling and

reasoning.

The behavioral model is the key point of the mul-

timodeling approach, notably because the diagnosis

reasoning process is based on this model. Behavioral

models are build according to physical equations of

the system studied. This set of equations is difﬁcult

to determine because there is an important number of

physical laws to respect. So the bond-graph concept

has been used to facilitate the determination of these

equations and the modeling of the behavior of compo-

nents and the generation of functional roles (Zouaoui

et al., 1997). These functional roles are identiﬁed

by the interpretation of the behavior of a system or

ICSOFT 2008 - International Conference on Software and Data Technologies

250

more precisely of its physical equations. The bond

graph approach (Rosenberg and Karnopp, 1983) ex-

presses system dynamics in terms of energy trans-

fer between constituent elements and more precisely

based on power echanges. This approach is based

on the tetrahedron of state which represents the rela-

tions between effort and power variables. It allows the

construction of dynamic system models. Neverthe-

less, the behavioral model and the functional model

are closed to the set of components (Thetiot, 1999)

because in most cases the “a priori” knowledge is

mainly provided by the design model of the system.

Thereby, the diagnosis process is still concerned with

computational problems. There is then a crucial need

to deﬁne the right level of abstraction for modeling

with a level of aggregation that allows an efﬁcient di-

agnosis process.

So, in this paper, we propose to use the same level

of abstraction the Experts use to diagnose a dynamic

system. This level of abstraction corresponds to a

level of aggregation that minimizes the set of compo-

nents and thereby improves the computational prob-

lem. This corresponds to associate the abstraction

level with the diagnostic task and not with the design

task.

3 TOM4D MODELING METHOD

TOM4D (”Timed Observations Multimodeling for

Diagnosis”) is a timed observations centered model-

ing method for dynamic systems or processes. The

aim of this method is to produce a model from a set

of sequences of timed observations and the a pri-

ori expert’s knowledge, the so produced model be-

ing used to diagnose a dynamic process. The main

constraints to deﬁne the TOM4D method is that the

modeling formalisms must be compatible with (i) the

Stochastic Approach Framework for discovering tem-

poral knowledge from timed data of (Le Goc, 2006),

(Le Goc and B´enayadi, 2008), (ii) the conceptual mul-

timodeling framework of (Zanni et al., 2005) and (iii)

the diagnosis algorithm of (Reiter, 1987).

3.1 The Stochastic Approach

Framework

The Stochastic Approach Framework of (Le Goc,

2006), (Le Goc and B´enayadi, 2008) for discover-

ing temporal knowledge from timed data provides a

general framework for modeling dynamic processes.

This framework considers that the timed messages

of a series are written in a database by a program,

called a monitoring cognitive agent MCA, that mon-

itors, diagnoses or controls a production process Pr.

A timed message is represented with an occurrence

o(t

) ≡ (δ

, k) of a discrete event class C

= {(x

, δ

)}

that is an arbitrary set of discrete event e

≡ (x

, δ

where δ

is one of the discrete value of the variable

. A discrete event class is often a singleton because

in that case, two discrete event classes C

= {(x

, δ

)}

and C

= {(x

, δ

)} are only linked with the variables

and x

when the constants δ

and δ

are independent

(Le Goc, 2006). This condition is only concerned

with the programs the MCA is made with. This means

that a relation between the occurrences of two classes

and C

subsumes a relation between the corre-

sponding two functions x

(t) and x

(t). A sequence of

discrete event class occurrences is then considered as

the observable manifestation of a series of state transi-

tions in a timed stochastic automaton representing the

couple (Pr, MCA). The BJT4G algorithm represents

a set of sequences of discrete event class occurrences

with a Markov chain and apply an abductive reason-

ing on this representation to identify the set M =

, [τ

−

, τ

])} of the most probable timed se-

quential binary relations R

, [τ

−

, τ

]) between

discrete event classes leading to a given class. A

timed sequential binary relation R

, [τ

−

, τ

])

is an oriented relation between two discrete event

classes C

and C

that is timed constrained with the

interval [τ

−

, τ

]. [τ

−

i, j

, τ

i, j

] is the time interval for ob-

serving an occurrence of the C

class after an occur-

rence of the C

class. The set M of timed sequential

binary relation is an abstract chronicle model that is

graphically represented with the ELP language (Event

Language for Process) where the nodes are discrete

event classes and the links are timed sequential binary

relations.

3.2 TOM4D Model Formalisms

The conceptual multimodeling framework of (Zanni

et al., 2005) organizes the available knowledge about

a process according to three models: a Structural

Model describing the relations between the compo-

nents of the process, a Functional Model providing

the relations between the values of the process vari-

ables (i.e. a set of mathematical functions) and a Be-

havioral Model deﬁning the states of the process and

the discrete events ﬁring the state transitions.

The TOM4D method extends this framework to

add a complementary model, called the Perception

Model (PM) of the process. This model speciﬁes

the process P(t) = R(x

(t), . . . , x

(t)) as a

relation between n variables x

of a set X = {x

}

and a set {Q

, δ

)} of constraints about the val-

MODELING PROCESSES FROM TIMED OBSERVATIONS

251

ues of the process variables. The Structural, Func-

tional and Behavioral models must be deduced from

Given PM. Consequently,with the TOM4D method, a

model M(P(t)) of a process is a quadrupletM(P(t)) =

hPM, SM(P(t)), FM(P(t)), BM(P(t))i.

The Perception Model PM = hΨ, X, R

i deﬁnes

the process P(t) and its operating modes:

• Ψ = {ψ

} is a set of constants ψ

typically corre-

sponding to thresholds;

• X(t) = {x

(t)} ⊆ V(t) is a sub set of all the mea-

sured variables V(t) of the process;

• R

= {

∏

(t), ψ

)} is a set of binary predicate

conjunctions Q(x

, ψ

) linking a variable x

∈ X

and a constant ψ

∈ Ψ. These predicates formu-

late some constraints about the values of the pro-

cess variables x

. R

is partitioned in three parts

∪C

(i.e. C

∩C

= {φ}):

– C

contains the sub set of R

describing the pro-

cess operating goals;

– C

contains the sub set of R

describing the nor-

mal operating modes of the process;

– C

contains the sub set of R

describing the ab-

normal operating modes of the process;

The Structural Model SM(P(t)) =

hCOMPS, R

, R

i of a process P(t) describes re-

lations between components of the system and the

relations between the components and the variable

X(t) of P(t):

• COMPS = {c

} is a set of components

≡ {{e

)}, {s

)}} where {e

)} (resp.

)}) is the set of input (reps. output) ports of

the component c

;

• R

= {= (s

), e

))} is a set of assignment of

the binary predicate ’Equal’ linking an output of

a component c

with an input of the component c

(i.e. the interconnection relations);

• R

= {= (x

(t), s

))} is a set of assignment of

the binary predicate ’Equal’ linking each variable

(t) ∈ X(t) with an output s

of a component c

∈

COMPS.

The Functional Model FM(P(t)) = h∆, F, R

i of a

process P(t) describes the relations between the val-

ues δ

of the variables x

∈ X with mathematical func-

tions:

• ∆ = {

∆

}

{φ} is the union of the sets ∆

{δ

} of constants associated with each variable

of X. The sets ∆

= {δ

} is deduced from

the set Ψ = {ψ

} of the Perception Model PM

when applying the ”Spatial Discretization Prin-

ciple” of the Stochastic Approach Framework (Le

Goc et al., 2005). The constant φ is added to as-

sign an unknown value to a variable.

• F = { f

(t), x

(t), ..., x

(t))} is a set of func-

tion f

(t), x

(t), ..., x

(t)) linking each value of

the variables x

(t), x

(t), ..., x

(t) with the out-

put value of the function f

(t), x

(t), ..., x

(t)).

Typically, these functions are deﬁned with tables

of values.

• R

= {= (x

(t), f

(t), x

(t), ..., x

(t)))} is a set

of assignments of the binary predicate ”Equal”

linking the value of a variable x

with the output

values of a function f

(t), x

(t), ..., x

(t))).

The Functional Model FM(P(t)) speciﬁes the rela-

tions between the variables x

of the process P(t) but

any mention about the normal and the abnormal val-

ues is contained in FM(P(t)). These properties are

deduced from the Behavioral Model of P(t).

The Behavioral Model BM(P(t)) = hS,C, R

i of a

process P(t) describes its operating modes (accord-

ing to (Chittaro et al., 1993)) with a set of states and

discrete event classes ﬁring the state transitions:

• S = {s

} is a set of distinguishable states. Each

state s

is identiﬁed with a unique value X

≡

{(x

= δ

)} of X(t) so that:

– X(t) = X

⇔ ∀x

(t) ∈ X(t), ∃δ

∈ ∆, x

(t) = δ

– ∀s

, s

∈ S, s

= s

⇔ X

= X

• C = {C

} ∪C

is a set of classes C

= {e

} of dis-

crete event e

= (x

, δ

). C

= {e

} is a techni-

cal class containing the event e

= (φ, φ) which

matches with the observation of a date. In this

modeling context, each class C

= { e

} is a sin-

gleton (i.e. C

= {e

} = {(x

, δ

)}).

• R

= { = (s

, γ

, s

)} is a set of assignment of

the binary predicate ”Equal” linking a state s

a state s

conditioned with the observation of an

occurrence of the class C

Given a sequence ω = {o(k)} of discrete event

class occurrences o(k) ≡ (δ

), a transition from the

state s

to the state s

is ﬁred when:

• there is an occurrence o(k) ≡ (δ

) of the class

= {e

}, e

= (x

, δ

), in ω;

• the currentstate s(t) of the ﬁnite state machine im-

plementing BM(P(t)) is in the state s

(i.e. s(t) =

);

• there exist an assignment = (s

, γ

, s

)) in R

In that case, the new value of the current state s(t)

is provided with the σ function deﬁned on S × ω ×

→ S of a ﬁnite state machine such as s(t

) =

σ(s(t),o(k), R

• ∀t

≥ t, ∀o(k) ∈ ω, ∀s

∈ S, ∀ = (s

, γ

, s

)) ∈ R

s(t) = s

∧ o(k) ≡ (δ

) ∧C

= {(x

, δ

)},

⇒ σ(s(t), o(k), R

) = γ

, s

)

ICSOFT 2008 - International Conference on Software and Data Technologies

252

According to the set R

of constraints in the Per-

ception Model PM of the process P(t), the set S of

states BM(P(t)) can be partitioned in three categories

∪ S

(i.e. S

∩ S

= φ):

• A set S

containing the states satisfying the pro-

cess operating goals of P(t):

∀s

∈ S

, ∃

∏

(Q(x

, δ

)) ∈ C

s(t) = s

⇒ X(t) = X

X(t) = X

⇒

∏

(Q(x

, δ

))

• A set S

⊆ S containing the states corresponding

to the normal operating modes of P(t):

∀s

∈ S

, ∃

∏

(Q(x

, δ

)) ∈ C

s(t) = s

⇒ X(t) = X

X(t) = X

⇒

∏

(Q(x

, δ

))

• A set S

⊆ S containing the states corresponding

to the abnormal operating modes of P(t):

∀s

∈ S

, ∃

∏

(Q(x

, δ

)) ∈ C

s(t) = s

⇒ X(t) = X

X(t) = X

⇒

∏

(Q(x

, δ

))

Consequently, the S

set of states deﬁnes the ab-

normal values X(t) = X

of the variables x

of P(t). So

the qualiﬁcation ”normal value” or ”abnormal value”

depends on the states:

• ∀t ∈ ℜ, ∀s

∈ S

s(t) = s

⇒ X(t) = X

∧ AB(s(t))

• ∀t ∈ ℜ, ∀s

∈ S

∪ S

s(t) = s

⇒ X(t) = X

∧ ¬AB(s(t))

The Perception Model PM = hΨ, X, R

i, the

Structural Model SM(P(t)) = hCOMPS, R

, R

i, the

Functional Model FM(P(t)) = h∆, F, R

i and the Be-

havioral Model BM(P(t)) = hS,C, R

i degining a pro-

cess P(t) are linked together with the variable set

X = {x

• each component c

∈ COMPS is linked with at

least one variable x

∈ X through a relation

= (x

(t), s

)) in R

;

• each function f

(t), x

(t), ..., x

(t)) ∈ F is

linked with at least one variable x

∈ X through a

relation = (x

(t), f

(t), x

(t), ..., x

(t))) in R

;

• each state transition = (s

, γ

, s

) ∈ R

is linked

with at least one variable x

∈ X through a discrete

event class C

= {(x

, δ

)} in C.

4 TOM4D MODELING PROCESS

The TOM4D method is made with three steps (cf.

Figure 1) aiming at producing a model M(P(t)) =

hPM, SM(P(t)), FM(P(t)), BM(P(t))i from the avail-

able knowledge and data. The Knowledge Inter-

pretation step uses a CommonKADS-like template

1. Knowledge interpretation Template CommonKADS

Knowledge gives by

experts

Generic

Model

Knowledge

Source

3. Generic modeling T.O.S.

Perception

Model

2. Process definition

Scenario

Model

Figure 1: TOM4D Modeling Process.

(Schreiber et al., 2000) to interpret and organize the

available knowledge about a process (i.e. the knowl-

edge conceptual model of Sachem (Le Goc, 2004) in

the example of this paper). This knowledge is pro-

vided by a knowledge source (an expert, a set of doc-

uments, etc) and at least one scenario ω = {x

) =

, . . . , x

) = δ

, . . .} describing a typical evolution

of the process with a series of timed measures x

) =

. This ﬁrst step produces then the scenario model

M(ω) = hSM(ω), FM(ω), BM(ω)i of the process that

is coherent with the scenario ω = {o

) ≡ (δ

, k)}

when formulated with a series of occurrences o

)

of discrete event classes C

= {(x

, δ

)}. The Process

Deﬁnition step aims at deﬁning the Perception Model

(PM) of the process from the available knowledge

and the scenario model M(ω). Finally, the Generic

Modeling step uses the tetrahedron of states (TOS,

(Rosenberg and Karnopp, 1983)) to provide a ”physi-

cal” dimension to each variable x

of the process P(t)

and an interpretation of the relations linking the vari-

ables between them. The analysis of the properties of

the perception model PM with this interpretation pro-

duces some knowledge about the process that is dis-

tributed in the different parts of the model M(P(t)).

This model is called the ”Generic Model” of the pro-

cess because it is independent of the concrete instru-

mentation. This section explains the steps 2 and 3 of

the TOM4D modeling process trough its application

with a real world process, the Cublize dam (France)

that has been diagnosed wy the Expert’s of the Cema-

gref, the French governmental organization that as-

sumes the security of French hydraulic civil engineer-

ing structures. The step 1, the Knowledge Interpreta-

tion step), produces the scenario model M(ω) that is

presented in (Masse and Le Goc, 2007).

This scenario model leads to deﬁne the process

P(t) as a relation P(t) = R(V(t), Qs(t), Qf(t)) be-

tween three variables: a volume V(t) and two out-

ﬂows, a ”normal” outﬂow Qs(t) and a water leak out-

MODELING PROCESSES FROM TIMED OBSERVATIONS

253

ﬂow Qf(t). The following constraints have been de-

duced from M(ω):

• The goal of the process operations is to avoid any

water leak outﬂow:

– ∀t, Qf(t) = Qfmin

• Two normal process operations have been iden-

tiﬁed, one before the ﬁrst dam’s ﬁlling and one

after:

– ∃t

, ∀t < t

,V(t) = Vmin ∧ Qs(t) = Qsmin ∧

Qf(t) = Qfmin

– ∃t

, ∀t ≥ t

,Vmax > V(t) > Vmin ∧ Qsmax >

Qs(t) > Qsmin ∧ Qf(t) = Qfmin

• Three abnormal process operations have been

identiﬁed:

– ∃t

> t

, ∀t ≥ t

, Qs(t) ≤ Qsmin

– ∃t

> t

, ∀t ≥ t

, Qs(t) ≥ Qsmax

– ∃t > t

, Qf(t) > Qfmin

Consequently, the set X of the process variable is

then:

• X(t) = {V(t),Qs(t), Qf(t)};

the set of threshold constants is:

• Ψ = {Vmax,Vmin, Qfmax, Qfmin, Qsmax, Qsmin};

and the set of constraints is

• R

= { (Qf(t) = Qfmin), (Vmax > V(t) >

Vmin) ∧ (Qsmax > Qs(t) > Qsmin) ∧ (Qf(t) =

Qfmin), (Qs(t) ≤ Qsmin), (Qs(t) ≥ Qsmax),

(Qf(t) > Qfmin)}.

This mean that the Perception Model PM = hΨ, X, R

is only concerned with a ﬁlled dam.

The hydraulic TOS of Figure 2 (b) provides a

physical dimension to the variables of X(t) leading to

deﬁne the structural model SM(P(t)) of P(t) as a pipe

(a glass, Figure 2a) with a constant capacity C that

contains a variable volume V(t) of water and that is

closed with a permeable stopper (a porous cork). The

resistivity to water of the stopper evolve as a not mea-

sured variable denoted R(t). The relation between the

volume V(t) and the outﬂow Qs(t) is made through

the pressure Pr(t) on the top of the stopper, which is

not measured. So the complete set of variable is:

• {V(t), Qs(t), Qf(t), Pr(t), R(t)},

but the generic process is instrumented with only

three abstract sensors measuring the outﬂow Qs(t)

through the stopper, the outﬂow over the pipe Q f(t)

and the volume V(t) of the column of water in the

pipe.

The Structural Model SM(P(t)) =

hCOMPS, R

, R

i of P(t) is then made with three

components:

Qs(t)

V(t)

Qf(t)

Qs(t)

V(t)V(t)

Qf(t)Qf(t)

V(t) Pr(t)

Qv(t)

V(t) = C.Pr(t)

Pr(t) = R(t).Qs(t)

Qv(t)=dV(t)/dt

Qs(t)

(a) (b)

Figure 2: (a) Structural Model and (b) TOS Relations.

• COMPS = { pipe, stopper, waterColumn},

pipe ≡ {e

(pipe), s

(pipe)}, stopper ≡

(stopper), s

(stopper)},

waterColumn ≡ {s

(waterColumn)}};

• R

= { s

(waterColumn) = e

(pipe), s

(pipe) =

(stopper))} (i.e. there is two interconnection

relations);

• R

= { V(t) = s

(waterColumn), Qf(t) =

(pipe), Pr(t) = s

(pipe), Qs(t) = s

(stopper),

R(t) = s

(stopper)}.

The set Ψ of PM allows to deﬁne a set of 8

ranges for each variables of X(t) and consequently (i)

the set ∆ of 8 constants δ

of the Functional Model

FM(P(t)) (column ”range values” in the Figure 3)

and (ii) the corresponding set C of 8 discrete event

classes C

= {e

} (column ”Events” in the Figure 3).

These constants deﬁne also the set X

of the 17 possi-

ble values for X(t). The Structural Model SM(P(t))

and the TOS allows to eliminates 7 of these values that

are note physically possible for X(t): for example, a

value X

so thatV(t) = 0 and Qf = 1 is physically im-

possible. The resulting set X

of the 10 possible val-

ues of X(t) deﬁnes then the 10 distinguishable states

S = {s

} of the Behavioral Model BM(P(t)).

Variables

Constants

Range

Range Values

Events

V(t)<Vmin

e1:V(t)<Vmin

e2:V(t)>Vmin

e3:V(t)<Vmax

V(t)>Vmax

e4:V(t)>Vmax

Qs(t)<Qsmin

e5:Qs(t)<Qsmin

e6:Qs(t)>Qsmin

e7:Qs(t)<Qsmax

Qs(t)>Qsmax

e8:Qs(t)>Qsmax

Qf(t)<Qfmin

e9:Qf(t)<Qfmin

Qf(t)>Qfmin

e10:Qf(t)>Qfmin

V(t) Vmax, Vmin

Qf(t) Qfmin

Vmin<V(t)<Vmax

Qs(t) Qsmax, Qsmin Qsmin<Qs(t)<Qsmax

Figure 3: Constraint table.

Given the sets {X

} of 10 values and C, three ma-

trix are ﬁlled in to identify the physically possible

temporal successions:

• an event-to-event matrix E = [e

] deﬁned on E ×

E at value on {0, 1} so that e

= 1 when the an

occurrence o(k) of the C

class can be followed

by an occurrence o(k + 1) of the C

class (i.e.

(o(k), o(k + 1)) is physically observable on P(t)).

• a value-to-value matrix X = [x

] deﬁned on X ×

X at value on {0, 1} so that x

= 1 when a X(t)

ICSOFT 2008 - International Conference on Software and Data Technologies

254

can physically move from the value X

at time t

(i.e. X(t

) = X

) to the value X

at the next time

k+1

in one occurrence of a discrete event class

(i.e. X(t

k+1

= X

• a value-to-event matrix T = [t

] deﬁned on X × X

at value on C so that t

= {C

} is a set of discrete

event class that is not empty when there exist at

leat an occurrence of a class C

making the value

of X(t) moving from X

to X

in P(t).

This latter transition matrix T is deduced from the

other two matrix E and X.

X0 X1

X5X4

X11

X14

X17

Normal states

Awry states

Figure 4: Behavioral model and Cublize dam story.

The state graph of the Figure 4 is a graphical

representation of the T transition matrix and repre-

sents the Behavioral Model BM(P(t)) of P(t). In this

graph, a nodeis a state s

and a relation R(s

, s

) be-

tween two states is labeled with a discrete event class

when C

∈ t

. This state graph is then transformed

in an discrete event graph where a node is a class C

and a link is binary relation between two classes C

and C

if and only if e

= 1. Next, the classes C

the nodes are replaced with the associated assignation

of the variables x

(t) = δ

according to the Stochastic

Approach framework. The resulting graph is made a

set of relations between two assignations R

(t) =

, x

(t) = δ

). Using the sets R

and the R

of the

Structural Model SM(P(t)), the set R= { R

} is made

with the relations R

(t) = δ

, x

(t) = δ

) that are

physically supported with an interconnection relation

= (s

), e

)) of R

. The set R is then transformed

in the set F of functions f

(t), x

(t), ..., x

(t))

of the Functional Model FM(P(t)) and their corre-

sponding table of values (cf. Figure 5), and the set R

is then constituted (i.e. R

= { Qs(t) = f

(V(t), R(t)),

Qf(t) = f

(V(t))}. The R(t) variable is an internal

variable of the component ”stopper” that explains the

different values Qs(t) can take when V(t) = 1. This

is the role of the diagnosis to determine that P(t) is in

an abnormal state like X

for example because of the

value of R(t).

The red paths of the Behavioral Model BM(P(t))

of Figure 4 illustrates the concrete story of Cublize’s

Qf(t)V(t)

Qs(t)V(t)

0,12

0,1,21

Qs(t)V(t)

0,12

0,1,21

V(t)

Qs(t)

Qf(t)f2

R(t)

(a) (b)

Figure 5: Table of values and the functional model associ-

ated.

dam, that is to say the Behavioral Model BM(ω) of

the scenario model M(ω) provided in (Masse and Le

Goc, 2007). It can be see that BM(ω) ⊂ BM(P(t)):

BM(P(t)) can be used to generate a large set of

scenarios that can be used to simulate the behav-

ior and to learn to diagnose a dam. Similarly, the

Figure 6) shows the relation between the Functional

Model FM(ω) of the scenario model and the Func-

tional Model FM(P(t)) of the process P(t). The

Generic Model M(P(t)) is then an abstract descrip-

tion of the relations between the concrete variables

of Cublize dam. The experts of the Cemagref hav-

ing validated this generic model, this shows that the

TOM4D method can be used to represent a real world

set of knowledge.

F2F1 F3

x7F5

F2F1 F3

x7F5

V(t) Qs(t) Qf(t)

Functional model of the Cublize dam translates with process variables

Functional model of the Cublize dam obtained at the first step of modeling

Functional Model of the process obtained at the third step of modeling

V(t)

Qs(t)

Qf(t)f2

R(t)

Figure 6: Comparison between the functional models.

5 CONCLUSIONS

This paper presents the principles of the TOM4D

methodology used to represent a process at the level

of abstraction that an Expert uses when diagnosing.

At such a level of abstraction, the number of compo-

nents is minimized so that the computational problem

of the usual diagnosis algorithm is decreased. The

TOM4D methodology represents the implicit model

of an Expert with four models: a perception, a struc-

tural, a behavioral and a functional model. These

models are linked together with the concept of vari-

able, which allows to deﬁne a way to analyze the con-

sistency between them. The methodology is directed

with the timed observations to be adequate with the

Stochastic Approach framework for discovering tem-

MODELING PROCESSES FROM TIMED OBSERVATIONS

255

poral knowledge from the timed observations con-

tained in a database. One of the main advantage of

the models of the TOM4D methodology is to be hu-

manly understandable.

The methodology is applied to a real world prob-

lem: the hydraulic dam of Cublize (France). The re-

sulting models have then been validated by the hy-

draulic dam Expert’s of the Cemagref, the French

governmental organization that assumes the security

of French hydraulic civil engineering structures. Our

current works are oriented towards the adaptation of

Reiter’s algorithm of diagnosis to timed observations

and the generalization of this modeling approach to

introduce a recursive principle of modeling.

REFERENCES

Abu-Hanna, A., Benjamins, R., and Jansweijer, W. (1991).

Device understanding and modeling for diagnosis.

IEEE Expert, 6(2):26–31.

Basseville, M. and Cordier, M.-O. (1996). Surveil-

lance et diagnostic de syst`emes dynamiques : ap-

proche compl´ementaire du traitement de signal et de

l’intelligence artiﬁcielle. Rapport.

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

Functional and teological knowledge in the multimod-

eling approach for reasoning about physical systems:

A case study in diagnosis. IEEE Transactions on sys-

tems.

Clancey, W. (1987). Heuristic classiﬁcation. Artiﬁcial In-

telligence, 25(3):289–350.

Dague, P. (2001). Th´eorie logique du diagnostic `a base de

mod`eles. Diagnostic, Intelligence Artiﬁcielle et Re-

connaissance des Formes, pages 17–105.

Davis, R. (1984). Diagnostic reasoning based on structure

and behavior. Artiﬁcial Intelligence, 24:347–410.

De Kleer, J. and Brown, J. (1984). A Qualitative Physics

Conﬂuences. Artiﬁcial Intelligence, 24:7–83.

Falkeihainer, B. and Forbus, K. D. (1988). Seting up large

scale qualitative models. In Proceedings of the 7th

National Conference of Artiﬁcial Intelligence, pages

301–306, St. Paul, MN, USA.

Falkeihainer, B. and Forbus, K. D. (1991). Compositional

modeling: Finding the right model for the job. Artiﬁ-

cial Intelligence, 51:95–143.

Forbus, K. et al. (1984). Qualitative Process Theory. Artiﬁ-

cial Intelligence, 24(1-3):85–168.

Franke, D. W. (1991). Deriving and using descriptions of

purpose. IEEE Expert, 6(2):41–47.

Hayes, P. (1989). Naive physics I: ontology for liquids.

Morgan Kaufmann Publishers Inc. San Francisco, CA,

USA.

Le Goc, M. (2004). Sachem, a real time intelligent diagno-

sis system based on the discrete event paradigm. Sim-

ulation, The Society for Modeling and Simulation In-

ternational Ed., 80(11):591–617.

Le Goc, M. (2006). Notion d’Observation pour le Di-

agnostic des Processus Dynamiques: Application `a

Sachem et `a la d´ecouverte de Connaissances Tem-

porelles. Hdr, Facult´e des Sciences et Techniques de

Saint J´erˆome, Marseille, France.

Le Goc, M. and B´enayadi, N. (2008). Dicovering expert’s

knowledge from sequences of discrete event class oc-

currences. In To appear in the proceedings of the 10th

International Conference on Enterprise Information

Systems (ICEIS08), Barcelona, Spain, 12-16th of June

2008.

Le Goc, M., Bouch´e, P., and Giambiasi, N. (2005). Stochas-

tic modeling of continuous time discrete event se-

quence for diagnosis. 16th International Workshop on

Principles of Diagnosis (DX’05) Paciﬁc Grove, Cali-

fornia, USA.

Lee, W. and Kuipers, B. (1988). Non-Intersection of Trajec-

tories in Qualitative Phase Space: A Global Constraint

for Qualitative Simulation. Proceedings of the Seventh

National Conference on Artiﬁcial Intelligence, AAAI-

88, pages 286–291.

Masse, E. and Le Goc, M. (2007). Modeling dynamic

systems from their behavior for a multi model based

diagnosis. In Proceedings of the 18th International

Workshop on the Principles of Diagnosis (DX’07),

Nashville, TN, USA, May 29-31 2007.

Murthy, S. (1988). Qualitative reasoning at multiple reso-

lutions. Proceedings of the National Conference on

Artiﬁcial Intelligence, pages 296–300.

Reiter, R. (1987). A theory for diagnosis for ﬁrst principles.

Artiﬁcial Intelligence, 32:57–95.

Rosenberg, R. and Karnopp, D. (1983). Introduction to

Physical System Dynamics. McGraw-Hill, Inc. New

York, NY, USA.

Schreiber, A., Akkermans, J. M., Anjewierden, A. A.,

de Hogg, R., Shadbolt, N. R., Van de Velde, W., and

Wielinga, B. J. (2000). Knowledge Engineering and

Management, The CommonKADS Methodology. MIT

Press.

Struss, P. and Dressler, O. (1989). Physical negation –

integrating fault models into the general diagnostic

engine. In Proceedings of the 11th International

Joint Conference on Artiﬁcial Intelligence (IJCAI-89),

pages 1318–1323.

Thetiot, R. (1999). Utilisation de l’Approche Multi-

mod`eles pour l’Aide au Diagnostic d’Installations In-

dustrielles. Phd in sciences, Universit´e d’Evry Val

d’Essonne, France.

Zanni, C., Le Goc, M., and Frydman, C. (2005). A con-

ceptual framework for the analysis, classiﬁcation and

choice of knowledge-based diagnosis systems.

Zouaoui, F., Th´etiot, R., and Dumas, M. (1997). Multimod-

eling representation of pwr primary coolant loop. In

Proceedings Poster of International Joint Conference

on Artiﬁcial Intelligence (IJCAI-97), page 116.

ICSOFT 2008 - International Conference on Software and Data Technologies

256