Exploiting Ontology to Build Bayesian Network

Ahmed Mabrouk, Sarra Ben Abbes, Lynda Temal, Ledia Isaj and Philippe Calvez

LAB CSAI ENGIE, 4 Rue Jos

ephine Baker, 93240 Stains, France

Keywords:

Bayesian Network Structure, Ontology, Expert Knowledge, Learning, Dependencies, Renewable Energies.

Abstract:

Exploiting experts’ domain knowledge represented in the ontology can signiﬁcantly enhance the quality of

the Bayesian network (BN) structure learning. However, in practice, using such information is not a trivial

task. In fact, knowledge encompassed in ontologies doesn’t share the same semantics as those represented in

a BN. To tackle this issue, a large effort has been devoted to create a bridge between both models. But, as far

as we know, most state-of-the-art approaches require a Bayesian network-speciﬁc ontology for which the BN

structure could be easily derived. In this paper, we propose a generic method that allows deriving knowledge

from ontology to enhance the learning process of BN. We provide several steps to infer dependencies as well

as orientations of some edges between variables. The proposition is implemented and applied to the wind

energy domain.

1 INTRODUCTION

Over the last three decades, probabilistic graphical

models (PGMs) such as Bayesian networks (Pearl,

1988) are considered as one of the most successful

tools for reasoning about beliefs in many real-world

applications (cancer diagnosis, robotics, machine di-

agnosis, etc). Unlike many state-of-the-art predictive

models such as random forests, support vector ma-

chine (SVM), BN provides a prominent model that

enables to represent complex systems using graphi-

cal and probabilistic formalisms (easy for humans to

understand). The graphical structure encodes a set of

dependencies among random variables. The proba-

bilistic part is composed of a set of conditional prob-

ability tables to represent uncertainties. Both compo-

nents are jointly used to perform automated reasoning

under uncertainty by enabling to answer efﬁciently a

very wide range of diagnosis queries (Pearl, 2014).

Ontology, also represented by a graphical model,

is well known to be the best way to represent knowl-

edge in a domain of discourse according to different

points of view and purposes. It allows representing

explicitly and formally existing entities in an appli-

cation domain. Ontology formalization can use De-

scription Logic (DL) language, which is based on

First-order logic to describe concepts, relationships,

and constraints. It then enables us to make inferences.

Both models appear to be useful to perform rea-

soning and domain knowledge explanation using dif-

ferent paradigms. Intuitively, we believe that com-

bining BNs and ontologies gives rise to provide high

expressiveness and more reliable reasoning under un-

certainty. In this sense, several approaches have been

proposed to create a bridge between both models.

Basically, they can be divided into three categories:

(i) introducing additional notations to represent prob-

abilistic values in the ontology (Yang and Calmet,

2005; Zhang et al., 2009; Carvalho et al., 2010;

Mohammed et al., 2016), (ii) exploiting the seman-

tic richness of the ontology to guide the BN learn-

ing (Fenz, 2012; Jeon and Ko, 2007; Ishak et al.,

2011a; Messaoud et al., 2013), and (iii) using BN

results to enrich the ontology (Ishak et al., 2011b;

Wang, 2007). In this paper, we are interested in ex-

ploiting the knowledge in the ontology within the BN

structure learning. Unlike classical methods which,

naively rely on ontological relationships to identify

dependencies between variables, our approach ex-

ploits in an intelligent way existing knowledge to de-

duce more efﬁcient dependencies in the BN. To do

so, we propose a generic method that allows deriving

key knowledge from ontology. This method is based

on a set of rules allowing to infer dependencies and

edges orientation in an original way. The rest of this

paper is organized as follows. In section 2 we give the

main deﬁnitions of BN and ontology models. In sec-

tion 3, we discuss the most common state-of-the-art

approaches dedicated to exploit ontologies during the

BN learning phase. Then, in section 4, we describe

our new approach and justify its correctness within

the wind turbine domain. Its efﬁciency is highlighted

through experiments in section 5. Finally, a conclu-

sion and some future works are given in section 6.

578

Mabrouk, A., Ben Abbes, S., Temal, L., Isaj, L. and Calvez, P.

Exploiting Ontology to Build Bayesian Network.

DOI: 10.5220/0010840400003122

In Proceedings of the 11th International Conference on Pattern Recognition Applications and Methods (ICPRAM 2022), pages 578-585

ISBN: 978-989-758-549-4; ISSN: 2184-4313

2 BACKGROUND

In this section, we present the main deﬁnitions and

semantics of BN and ontology models.

2.1 Bayesian Network

Deﬁnition 1 (Bayesian network). A BN is a pair

(G, Θ) where G = (V, E

) is a directed acyclic graph

(DAG), V represents a set of random variables

, E

a set of arcs, and Θ = {θ

|Pa(V

)

}

∈V

is the set of con-

ditional probability tables (CPTs) of the nodes / ran-

dom variables V

in G given their parents Pa(V

), i.e.

|Pa(V

)

= P(V

|Pa(V

)). The BN encodes the joint

probability over V as:

P(V) =

∏

∈V

P(V

|Pa(V

)) (1)

Eq.1 is also called the chain rule or the general

product rule. BN provides a mechanism for exploit-

ing structure in high-dimensional joint distributions

to describe them compactly, and in a way that al-

lows them to be constructed and utilized effectively.

By their graphical structure, BNs encode an indepen-

dence model, i.e., a set of conditional independences

between random variables, characterized by the d-

separation property:

Deﬁnition 2 (d-separation). Two nodes V

and V

are

said to be d-separated in G by a set of nodes Z ⊆ V \

}, which is denoted by V

⊥

|Z, if, for every

trail (directed path) linking V

and V

in G, there exists

a node S on the trail such that one of the following

conditions holds:

1. S has converging arrows on the trail and neither

S nor any of its descendants are in Z;

2. S does not have converging arrows on the trail

and S ∈ Z.

In other words, any independence reported by d-

separation is satisﬁed by the underlying distribution.

When two variables V

and V

are not d-separated by

Z ⊂ V, they are said to be d-connected. With these

deﬁnitions, relationships encoded in a BN can be seen

as a ﬂow in the graph. The d-separation tells us when

inﬂuence from V

can “ﬂow” through Z to affect our

beliefs about V

2.2 Ontology

Ontologies are complex artifacts (composed of con-

cepts, hierarchical relations, and roles) that are built

By abuse of notation, we use interchangeably V

∈ V to

denote a node in the BN or the voltage of bus i

according to different points of view and purposes.

The most widely cited deﬁnition of an ontology is a

formal, explicit speciﬁcation of a shared conceptual-

ization, used to help humans and machines to share

common knowledge (Gruber, 1993; Guarino, 1995).

This deﬁnition highlights the following characteris-

tics of an ontology:

• Conceptualization: deﬁnes the objects, con-

cepts, and other entities that are assumed to ex-

ist in some area of interest and the relationships

that hold among them (Genesereth and Nilsson,

1987). A conceptualization is an abstract, simpli-

ﬁed view of the world that we wish to represent

for some purpose (Gruber, 1993) .

• Explicit: corresponds to the precise deﬁnition of

the concepts and the constraints of their use.

• Formal: refers to the fact that the expressions

must be machine-readable.

• Shared: refers to a common understanding of do-

main knowledge among people or agents.

An ontology is formally deﬁned by

O = (C, 6

, R, 6

, A)

• C and R are two disjoint sets whose elements are

respectively called Concepts (e.g. Room, Build-

ing) and Relations (e.g.part-of, sub-Zone-of ).

• 6

is a partial order over C, called concept hier-

archy or taxonomy (is-a)

• 6

is a partial order over R, called a hierarchy of

relations (e.g.sub-Zone-Of 6

part-Of )

• A a set of axioms and inferences rules (e.g. Phys-

ical Entity part-of Only Physical Entity)

3 RELATED WORK

In our paper, we shall focus our discussion on the use

of ontology to construct a BN structure. In this con-

text, several approaches have been developed for as-

sisting in eliciting knowledge from ontology and then

derive a BN (Bucci et al., 2011; Helsper and Van

Der Gaag, 2002). In (Devitt et al., 2006), authors

expose a direct correspondence between BN formal-

ism and the original domain ontology: (i) concepts

→ nodes, (ii) concepts attributes → CPTs, and (iii)

inheritance relations → arcs. The main drawback of

this approach is that it requires BN-speciﬁc ontology

extensions. (Fenz, 2012) proposed a semi-automatic

approach composed of the following steps: (i) selec-

tion of relevant classes, individuals, and properties (ii)

creation of the BN structure (iii) construction of the

CPTs, and (iv) incorporation of existing knowledge

Exploiting Ontology to Build Bayesian Network

579

facts. In this work, the BN is built from a security

ontology describing threat, vulnerability, and control

dependencies. The author extends the basic idea of

(Devitt et al., 2006) to a more generalized framework

by introducing the following analogies: (i) axioms

→ BN nodes scales and weights, and (ii) instances

→ ﬁndings. To generate a BN, (Fenz, 2012) devel-

oped a Prot

e plug-in called Bayesian Network Tab

(BNTab)

. A key issue in the proposed approach is

that it works only with boolean (or binary) variables,

so the application scope is limited to restricted real-

world domains. Moreover, this approach doesn’t take

into account the meaning of the ontology relations to

identify the more signiﬁcant ones that ﬁt better with

the dependency semantic in the BN. In (Jeon and Ko,

2007), a semi-automatic approach of BN construc-

tion for diagnosing diseases in the e-health domain

is proposed. This method starts by generating nodes

in a BN based on a set of selected concepts from the

e-health ontology. Then, developers identiﬁed valid

links among nodes in the BN based on a meta-model

that represents cause-and-effect relationships among

ontologies. This approach demonstrates several is-

sues. First, it requires the presence of causal rela-

tionships between ontologies which are not always

tractable in practice. Second, the links generating step

ends up with a complex BN structure in the form of

a hierarchical graph. Such topology is not suitable

for all applications. In (Messaoud et al., 2013), au-

thors present SemCaDo (Semantical Causal Discov-

ery) algorithm for integrating ontological knowledge

for learning causal BNs. The SemCaDo algorithm

takes an observational dataset and a corresponding

ontology as inputs. In the ﬁrst phase, causal relations

are extracted from the ontology and then integrated

in the form of constraints (white lists) during BN

structure learning. Then, the second phase optimizes

the orientation of the remaining undirected edges in

the complete partially directed graph (CPDAG) using

a semantic distance calculus provided by the ontol-

ogy. Finally, the algorithm re-iterates over the sec-

ond phase if there are still some non-directed edges

in the graph. All discovered causal links will be

introduced as semantic causal relations between the

corresponding ontology concepts. BN and OWL In-

tegration Framework (ByNowLife) (Setiawan et al.,

2019) is a framework proposed to integrate BN with

OWL by providing an interface for probabilistic rea-

soning information through SPARQL queries. This

approach consists of transforming logical information

contained in an ontology into a BN and vice-versa.

This framework is composed of three main parts:

https://protegewiki.stanford.edu/wiki/Bayesian

Network Tab (BNTab) 1.1.3

(1) application, which allows querying the Knowl-

edge Base in SPARQL format for logical reasoning

and hasProbValueOf special property for probabilis-

tic reasoning, (2) reasoner, which involves two com-

ponents; logical reasoner and probabilistic reasoner,

and (3) knowledge base, contains the domain ontol-

ogy and BN knowledge. The main drawback of the

two last approaches is that causal relations in the on-

tology are not always available. In addition, semantic

characteristics of ontological relations are not taken

into consideration during BN construction.

4 PROPOSED APPROACH

In this section, we describe a new approach that ex-

ploits in an efﬁcient way the knowledge capitalized in

ontologies to enhance BN structure learning results.

We justify the correctness of our approach based on

the wind turbine example.

4.1 Problem Formalization

Although BNs are seldom constructed entirely by ex-

perts, the knowledge given by these latter can still

prove to be a useful source of information that should

be exploited by BN learning algorithms. In this con-

text, the ontology can be particularly helpful since

it represents explicit knowledge. While the com-

plementarity between ontology and BN mights seem

trivial in general, it turns out that the joint use of both

models can be subject to many issues. In fact, rela-

tions between concepts do not necessarily encode a

dependence/independence between concepts. There-

fore, generate automatically a BN graphical struc-

ture from a given ontology, appears completely in-

tractable. To tackle this issue, we propose a semi-

automatic solution to facilitate knowledge elicitation

from ontology and knowledge-guided BN structure

learning. The general pipeline of the proposed ap-

proach is summarized as follows:

1. identify a set of relations that encapsulate a de-

pendence property between concepts,

2. compute dependence scores between concepts

based on selected relationships,

3. build an initial BN skeleton

based on the com-

puted scores,

4. orient some edges in the skeleton using the seman-

tic of selected relationships in the ontology,

a skeleton of the BN is the DAG where arcs are substi-

tuted by (undirected) edges.

ICPRAM 2022 - 11th International Conference on Pattern Recognition Applications and Methods

580

Figure 1: Selected Relations used in the Wind Turbine On-

tology.

5. reﬁne the resulted BN through the use of observa-

tional data and a score-based approach.

In the following, we discuss in greater detail each of

the previous steps. To facilitate understanding, we ap-

ply our approach on the wind turbine domain.

4.2 Identiﬁcation of Key Relationships

As discussed previously, the BN model allows repre-

senting conditional independencies as a DAG. In fact,

conditional independencies could be directly inferred

from the BN graph via the d-separation criterion. In

this context, we need to extract relevant relations from

the ontology that provide novel insights about vari-

able interactions (dependence, causality, etc.). To

identify these relations called R

dep

⊆ R, it is quite

natural to ask questions to one or multiple experts,

following this format: Given a relation R

∈ O, is our

belief about the state of the concept C

(resp. C

)

is inﬂuenced when we have an observation regard-

ing the concept C

(resp. C

)? The binary decision

(yes/no) returned by the expert for this question in-

dicates whether the relationship should be considered

to capture dependencies between variables. After the

accumulation of all of these binary answers, we end

up the ﬁrst step of our approach with the selected

relations shown in ﬁgure1. As can be easily seen,

the selected relationships focus mainly on the loca-

tion (s4bldg:contains (resp. s4bldg:isContainedIn))

as well as the set of connections between the different

components (seas:connectedTo, seas:subSystemOf

(resp. seas:hasSubSystem))

. According to the ex-

pert, the lower the semantic distance between two

components (or concepts in the ontology) in the sys-

tem, the greater dependent they are. For example,

since the concept Main Bearing is connected to the

concept Hub in the ontology, it is likely that, if the

temperature of the Main Bearing is high, the temper-

ature of the Hub will get higher as well, or vice-versa.

The same idea applies to the other selected relations.

Note that subSystemOf of can inferred from hasSub-

System if it is not explicitly mentioned in O Same thing for

the relation contains according to iscontainedIn

In this step, SPARQL queries were used to extract

concepts linked by the selected relationships from O

as described in the algorithm1.

Algorithm 1: Dependency triples extraction.

1: Input: Ontology O, Selected relations R

dep

2: Output: Set T of extracted triples

3: for R

in R

dep

4: Perform SPARQL query:

5: SELECT ??C

WHERE {

rdfs:subClassOf ?S .

?S a owl:Restriction; owl:onProperty R

;

owl:someValuesFrom k owl:allValuesFrom ?C

}

6: Add < C

, R

> to T

7: end for

8: return T

4.3 Dependence Scores Calculation and

BN Skeleton Building

In this section, we explain how the extracted infor-

mation from O can be exploited during the different

BN construction steps. Given the extracted triples

T, we merely generate a graph G, where edges are

weighted by the strength of dependency w

that ev-

ery relation R

represents, i.e., an undirected edge in

G is inserted between nodes V

(corresponds to C

)

and V

(corresponds to C

)

if < C

, R

>∈ T or

< C

, R

>∈ T. In the example of wind turbine,

the selected relations were ranked by the experts ac-

cording to the dependency semantic, as follows: the

relation contains

(resp. isContainedIn) transcribes

a stronger dependency between concepts, as certain

components are contained in another one, followed

by subSystemOf (resp. hasSubSystem), and ﬁnally

connectedTo. For these relations, the assigned de-

pendency weights are: w

contains

(resp. w

isContainedIn

)

← 1, w

subSystemO f

(resp. w

hasSubSystem

) ← 1.2, and

connectedTo

← 1.4. Figure 2 depicts an example of

a weighted graph resulting from the ontology shown

in ﬁgure3. Based on the resulted graph, we compute

the dependence between any two nodes V

and V

G (denoted by dep(V

)) as:

dep(V

) =

shortPath

)

(2)

The shortest path between nodes V

and V

(shortPath

)) is calculated using the weighted

We use V

to denote nodes in the weighted graph rather

than C

in order to be consistent with BN notations

For simplicity, in the rest of the paper, we remove the

preﬁx part from all concepts and relationships.

Exploiting Ontology to Build Bayesian Network

581

Dijkstra’s algorithm(Dijkstra et al., 1959). From the

given results, we deduce dependency strengths be-

tween all pairs of nodes in G. For instance, the depen-

dence strength between Main Bearing and Generator-

Bearing (dep(MB, GBe)) is equal to 0.29 (see Fig.2).

The obtained results were approved by the wind tur-

bine experts. Using dependency scores, we can there-

fore build an initial skeleton of the BN. Remind that

edges in the BN represent probabilistic dependencies

(or correlations) between nodes. In this case, an edge

is inserted in the BN if and only if dep(V

)

is greater than some deﬁned threshold k:



Accept if dep(V

) ≥ k

Re ject else.

With all these rules, our approach ends up this ﬁrst

step by constructing an initial skeleton of the BN us-

ing dependencies information derived from the ontol-

ogy. In this phase, the expert domain can check and

then correct the automatically detected edges between

variables if needed.

H B

GBeG

LSS

1.2

1.4

1.2 1.2

1.2

1.4

Figure 2: Extracted weighted graph from ontology using

the selected relations where H: Hub, B: Blade, WT: Wind

Turbine, N: Nacelle, R: Rotor, GBe: Generator bearing, G:

Generator, MB: Main Bearing, LSS: Low Speed Shaft, and

GB: GearBox.

In the next section, we will describe how we can de-

termine the orientations of some edges and how we

exploit such information to make the BN learning,

more reliable.

4.4 Knowledge-guided BN Structure

Learning

We start by explaining how certain edges in the skele-

ton are oriented based on the semantic of relationships

in O. Then, we use a score-based algorithm to reﬁne

the BN. For example, if we consider the dependency

semantic encapsulated in subSystemOf and contains

relations, an ordering ≺ over the associated variables

(corresponding to concepts), can be inferred. The

relation subSystemOf is used to represent the com-

position of different systems. These systems can be

Figure 3: Extract of Wind Turbine ontology.

divided into two categories: mechanical and electri-

cal sub-systems. According to the wind turbine on-

tology, the mechanical component has the following

sub-systems: wind turbine blade, the rotor, the na-

celle, etc. Regarding the electrical component, it is

composed of the generator and the power electronic

converter, etc.. Both sub-systems are also composed

of a set of smaller sub-systems. Thus, the subSys-

temOf can be considered as a relationship linking a

component to smaller ones, which makes it usable per

se as a prior about corresponding variables (or con-

cepts) ordering. To illustrate this idea, let us consider

an extract of the wind turbine ontology as shown in

ﬁgure3. Based on the subSystemOf property, the fol-

lowing ordering can be deduced:

Nacelle ≺ Generator ≺ Generator-bearing ≺ ...

Intuitively, the ordering ≺ over variables is very use-

ful to deﬁne the list of parents for some variables in

the constructed skeleton. For this purpose, a node V

is set as a parent of node V

(i.e., V

→ V

) only when

≺ V

and they are connected in the skeleton. It

should be emphasized that the variables ordering de-

duced from the relation subSystemOf is acyclic since

a variable V

cannot be at the same time a subSystemOf

and hasSubSystem with the same variable V

. Accord-

ing to the expert, this approach is quite reasonable

in practice since the impact is generally more impor-

tant from the global component to the more speciﬁc

one. For instance, a high temperature of the nacelle

implies that the temperature of all its subsystems are

also high. The opposite scenario does not necessarily

hold in practice. The relation contains depicts the set

of mechanical/electronic elements that a component

may contain. Thus, an ordering over variables that

satisﬁes the position of each component w.r.t. the oth-

ers can be deduced. Note that both relations subSys-

temOf and contains (resp. hasSubSystem and isCon-

tainedIn) may be linked to the same concepts. Impor-

tantly, these ordering results do not contradict each

other, because their semantics are very close. If two

ICPRAM 2022 - 11th International Conference on Pattern Recognition Applications and Methods

582

concepts C

and C

are linked by contains and subSys-

temOf, the following properties are satisﬁed:

< C

, subSystemO f ,C

>→ @ < C

, contains,C

(3)

< C

, contains,C

>→ @ < C

, subSystemO f ,C

(4)

With all these properties, our approach converts the

skeleton G into a partially directed graph (PDAG) us-

ing Algorithm2. For the remaining undirected edges,

we select arbitrarily orientations. At this point, our

algorithm has constructed an initial DAG of the BN.

The obtained DAG is then reﬁned through a score-

based search algorithm. In our wind turbine case, we

used a SCADA data to learn the ﬁnal BN. During the

search phase, we pick the resulted DAG from the on-

tology as a starting point and we compute its score.

After that, we consider all the neighbor graphs of G

in the search space — all of the legal (without cy-

cle) networks obtained by applying a single operator

(edge deletion, edge addition, or edge reversal) to G

— and compute the score for each of them given the

dataset. We then consider the change that leads to

the best improvement. We continue this process until

no modiﬁcation improves the score. During this re-

ﬁnement process, there are two ways to consider the

knowledge derived from the ontology:

• scenario 1: enable the learning algorithm to mod-

ify the initial DAG deduced from O.

• scenario 2: consider the ontology-based oriented

edges as constraints that we want to enforce, i.e.,

the algorithm is not allowed to modify these arcs.

Algorithm 2: Construct an initial PDAG-BN.

1: Input: BN skeleton G, Ontology O

2: Output: PDAG-BN G

3: ≺

= order(O, subSystemOf)

4: ≺

= order(O, contains)

5: ≺= {≺

∪ ≺

}

6: for each E

in E

7: if V

≺ V

then

8: E

← (V

→ V

)

9: end if

10: if V

≺ V

then

11: E

← (V

→ V

)

12: end if

13: end for

14: return G

5 EXPERIMENTAL RESULTS

This section is dedicated to present the use-case and

highlight the impact of ontology’s knowledge in the

BN learning process.

5.1 Wind Turbine Use Case

In this paper, we evaluate our approach using the

data from supervisory control and data acquisition

(SCADA) of wind turbines. This data represents a

cost-effective way to monitor wind turbine compo-

nents for early failures and performance issues. In our

experiment, we used the SCADA data coming from

La Haute Borne wind farm between 2013 and 2016.

This data is composed by a massive amounts of time-

series that are stored, manipulated, and ﬁltered via

the DARWIN Platform of ENGIE

. Overall, 210095

records have been generated during this period. In

this section, we focus our attention on the study of

the main components of the wind turbine such as na-

celle, generator, gearbox, etc

. To build the BN, we

also used the wind turbine ontology (see an extract in

Fig.3), designed within H2020 European project. For

each concerned concept (nacelle, generator, gearbox,

etc.), we extract all the concepts that are related to

it with the selected relations as described in our ap-

proach (subSystemOf (resp. hasSubSystem), contains

(resp. isContainedIn), and connectedTo).

In the following, both knowledge resources (SCADA

data and ontology) are exploited to derive a BN model

representing wind turbine system.

5.2 Evaluation of the Approach

We evaluate the performance of our approach w.r.t.

the quality of the detected relationships for a set of

selected temperature variables (gearbox and nacelle).

For each record in the data, we predict the value of the

temperature classes given the observations about the

explanatory variables in the BN. The evaluation of the

BN’s classiﬁcation task is been carried out using the

10-fold cross-validation procedure and the expected

loss estimation. We studied the impact of the ontol-

ogy knowledge integration on the predictions qual-

ity and the computation time. To make the compar-

ison evaluation more thorough, in our experiments,

we vary the following parameters:

• the size of the dataset,

• the dependence threshold k,

https://digital.engie.com/solutions/darwin

By abuse of notation, we use the word Gear and Gen to

denote respectively gearbox and generator.

Exploiting Ontology to Build Bayesian Network

583

• the scenario of the score-based setting (see the end

of section 4.4).

All experiments are performed on a 1.9GHz Intel

Core i7 computer with 16GB of memory running

Windows 10. Our approach has been implemented

using the bnlearn R package (Scutari, 2009) and

Prot

e tool

. We start by building the initial BN

DAG using the information in the ontology. Note that

we have done the matching between SCADA tem-

perature variables and the ontological entities (con-

cepts/relations). For example: the generator temper-

ature, which is a variable in SCADA, is represented

in the ontology by this triple <Generator, hasTem-

perature, Temperature>. Table 1 mentions an extract

of detected dependencies between SCADA variables

using the ontology. In these results, we observe a

strong dependency between temperatures of nacelle

and gearbox oil sump (equal to 1). A high depen-

dency is also observed between rotor bearing and na-

celle temperatures.

Table 1: An extract of dependency computed scores.

Var1 name Var2 name Score

Nacelle temp Gear oil temp 1

Gear inlet temp Gear oil temp 1

Rotor bear temp Nacelle temp 1

Converter torque Torque 0.83

Gear bear 1 temp Gear oil temp 0.83

Gear bear 2 temp Gear oil temp 0.83

Hub temp Rotor bear temp 0.71

Gear inlet temp Nacelle temp 0.5

Rotor bear temp Gear oil temp 0.5

Gear inlet temp Gear bear 1 temp 0.45

Gear inlet temp Gear bear 2 temp 0.45

Nacelle temp Gear bear 1 temp 0.45

Nacelle temp Gear bear 2 temp 0.45

Gen stator temp Gen bear 1 temp 0.42

Gen stator temp Gen bear 2 temp 0.42

Gen stator temp Nacelle temp 0.42

Gen bear 1 temp Nacelle temp 0.42

Figure 4 displays the expected loss for the gear-

box inlet temperature prediction using models learned

with the hill-climbing algorithm (HC) alone, and our

approach without and with constraints, respectively

denoted by sc=1 and sc=2. We ﬁxed the threshold

k = 0.2. As can be observed, our approach always

outperforms the simple HC method, whatever the size

of the dataset. For a dataset size equal to 10000, the

expected loss of our approach with scenarios 1 and 2

is actually lower than that of the HC by ∼ 6% and ∼

5%. These results can be explained by the fact that our

https://protege.stanford.edu/

approach rules enable us to detect key dependencies

with gearbox inlet temperature variable, hence obtain-

ing better predictions.

0 2 4

·10

0.1

0.2

0.3

0.4

0.5

Sample size

Expected Loss

HC, sc=1, k=0.2

HC, sc=2, k=0.2

Figure 4: Gearbox inlet temperature prediction errors.

Figure 5 shows results for nacelle temperature pre-

dictions. As can be seen, our approach using con-

straints got better results than the simple use of HC

algorithm. Our approach with scenario 1 (sc=1) is al-

ways outperformed by the simple use of HC, in this

case. These results happened because we enable the

reﬁnement score-based algorithm to modify our ini-

tial DAG (derived mostly from the ontology), which

may lead to loose some key relationships.

0 2 4

·10

0.2

0.4

Sample size

Expected Loss

HC, sc=1, k=0.2

HC, sc=2, k=0.2

Figure 5: Nacelle temperature prediction errors.

Figure 6 depicts runtimes associated with each al-

gorithm according to the data size parameter. As ex-

pected, except for the case where the data size is equal

to 10000, our approach (sc=1 and sc=2) is mostly

faster than HC. This is explained by the use of ini-

tial knowledge derived from the ontology which op-

timizes the DAG search space. For data size equal

to 80000, our approach with scenarios 1 and 2 are

ICPRAM 2022 - 11th International Conference on Pattern Recognition Applications and Methods

584

respectively about ∼19% and ∼16% faster than the

only use of HC.

0 2 4

·10

Sample size

Expected Loss

HC, sc=1, k=0.2

HC, sc=2, k=0.2

Figure 6: Runtime w.r.t. the data size.

6 CONCLUSION AND FUTURE

WORKS

In this paper, we proposed a new generic method for

the BN learning structure by exploiting the knowl-

edge in the ontology. Our method is divided into sev-

eral steps: (i) constructing a weighted graph from the

ontology (ii) deriving dependencies and constructing

the BN skeleton (iii) orienting edges using the seman-

tic of relations in the ontology (iv) reﬁning the BN via

a scored based algorithm. By integrating knowledge

from the ontology, our approach leads to a signiﬁcant

improvement in terms of runtime computations and

expected loss results. The proposed approach can be

easily applied to other domains. As future works, our

current approach can be extended by integrating addi-

tional knowledge from ontologies and also by reﬁning

these latter through the use of BN results (adding re-

lationships, uncertainty, etc.). Additional experimen-

tations on more complex real-world datasets will be

also explored.

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