=Paper=
{{Paper
|id=Vol-2416/paper33
|storemode=property
|title=Hybridization of fuzzy time series and fuzzy ontologies in the diagnosis of complex technical systems
|pdfUrl=https://ceur-ws.org/Vol-2416/paper33.pdf
|volume=Vol-2416
|authors=Nadezhda Yarushkina,Vadim Moshkin,Ilya Andreev,Gelya Ishmuratova
}}
==Hybridization of fuzzy time series and fuzzy ontologies in the diagnosis of complex technical systems ==
https://ceur-ws.org/Vol-2416/paper33.pdf
Hybridization of fuzzy time series and fuzzy ontologies in the
diagnosis of complex technical systems
N G Yarushkina1, V S Moshkin1, I A Andreev1 and G I Ishmuratova1
1
Ulyanovsk State Technical University, Severny Venetz street, 32, Ulyanovsk, Russia, 432027
e-mail: PostForVadim@yandex.ru
Abstract. The article provides a formal description of fuzzy ontologies and features of the
representation of elements of fuzzy axioms in FuzzyOWL notation. An ontological model for
assessing the state of helicopter units has been developed. According to the proposed approach,
the summarizing of the state of a complex technical system is carried out by means of an
inference based on a fuzzy ontology. As part of this work, experiments were conducted to
search for anomalous situations and search for possible faulty helicopter units using the
developed approach to the integration of fuzzy time series and fuzzy ontology. The proposed
approach of hybridization of fuzzy time series and fuzzy ontologies made it possible to reliably
recognize anomalous situations with a certain degree of truth, and to find possible faulty
aggregates corresponding to each anomalous situation.
1. Introduction
The uncertainty of data and information incompleteness is an inalienable part of any complex
technical system, in which the functioning quality of processes depends on a person. In the analysis,
modeling, and design of such systems, a large distribution was obtained by expert systems that use
experience and knowledge of the expert.
Expert assessments represent the qualitative aspect of the system element being evaluated and are
presented in linguistic form.
Currently, the inference methodology of expert assessments based on the subject ontologies that
play the role of a knowledge base in decision support systems (DSS) is used in various subject areas,
including in the field of situational control in the energy sector [1], designing complex diagnostic
systems [2], etc. Also, ontologies have been used as a knowledge base of intelligent risk prevention
systems in the context of heterogeneous information for the complex technical systems critical
infrastructure design phase [3].
Despite the application breadth, the classical languages of ontology and semantic networks, which
are usually used to summarize and characterize the features of a subject domain, cannot be used to
solve uncertainties and inaccuracies in the knowledge inherent in most real world applications in this
area.
Fuzzy set theory, as well as fuzzy logic, is formalism suitable for processing incomplete
knowledge, therefore ontologies based on such logic are adequate means of formalization.
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One of the most effective solutions for representing a knowledge base in the context of accounting
for fuzziness and uncertainty in human reasoning and evaluations in the DSS is a representation in the
form of fuzzy ontologies. For example, fuzzy ontologies are used in such systems as disease diagnosis
systems [4-6], fuzzy search engines [7, 8], knowledge systems based on group decision making about
the importance of data [9], etc. In most cases, such systems operate with facts objects or terms that are
described in natural language and contain the features of the considered domain [10, 11].
Fuzzy time series (FTS) is a way to obtain expert assessments that satisfy the conditions for
completeness, consistency, and adequacy [12].
One of the main areas of application for FTS is process diagnostics. Diagnosis is the process by
which a search for problems in the system occurs: defects, anomalies, faults, or lack thereof. When
solving problems of diagnostics of complex technical systems, the state of which is determined by the
data set in the form of FTS, it is advisable to apply methods for comparing the dynamics of processes
with the expected or required dynamics.
Therefore an urgent task requiring a systemic solution is the interpretation of the results of the
analysis in the form of expert assessments. To summarize the results obtained in the analysis of FTS, a
system of rules is usually applied, which are stored in the knowledge base of the expert system. The
knowledge base for solving this problem is ontologies and similar graph forms of knowledge
representation and storage, which allow to take into account the semantic features of the object of the
specified subject area, and not only their inference [13, 14].
Interpretation of the extracted comparisons in the form of expert assessments, the values of which
are presented in the form of semantic units that correspond to certain classes of fuzzy ontology, taking
into account the deviations between the current and the required FTS, can be obtained by solving the
problem of integrating FTS and fuzzy ontology. Thus, the purpose of this work is the development of
algorithms and models for the integration of fuzzy ontologies and FTS in the tasks of diagnosing
complex technical systems.
2. Fuzzy time series and fuzzy ontology model
The models and algorithms for analyzing and forecasting the FTS are described in detail in [15, 16].
At present, the basic notation of the fuzzy ontology representation is the FuzzyOWL standard [17-20].
Formally FuzzyOWL-ontology is:
I = (If , Cf , Pf , Af , Df , Qf , Lf , Modf ),
where If is an Individual that simply represents an individual of the vocabulary; Cf is a Concept that
represents a fuzzy concept of the vocabulary:
C f = {C fA , C Cf } ,
A C
where C f are Abstract Concepts, C f - Concrete Concepts; Pf is Property that represents a fuzzy
role:
Pf = {PfA , PfC } ,
A C
where Pf are Object Properties, Pf are Datatype Properties; Df is Axiom that represents the
axioms:
D f = { A fABox , ATBox
f , A RBox
f },
ABox
where A f is the Abox that contains role assertions between individuals and membership
TBox
assertions, A f is the Tbox that contains assertions about concepts such as subsumption and
RBox
equivalence, A f is the RBox that contains assertions about roles and role hierarchies. Some of the
axioms are subclasses of FuzzyAxiom, which indicates that the axiom is not either true or false, but
that it is true to some extent.
Of is Degree that represents a degree which can be added to an instance of FuzzyAxiom:
Of ={LDf , MDf, NDf , Varf },
where LDf are Linguistic Degrees, MDf are Modifier Degrees, NDf are Numeric Degrees, Varf are
Variables.
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Lf is Fuzzy Logic represents different families of fuzzy operators that can be used to give different
semantics to the logic.
L f = {LLuk
f , LZad
f , LGoed
f , LPrf od } ,
Luk Zad
where L f is the fuzzy operators logic of Lukasiewicz, L f is the fuzzy operators logic of Zadeh,
LGoed
f
Pr od
is the fuzzy operators logic of Goedel, L f is the fuzzy operators of produc logic.
Modf is Fuzzy Modifier that represents a fuzzy modifier, which can be used to modify the
membership function of a fuzzy concept or a fuzzy role. Current subclasses are Linear Fuzzy Modifier
and Triangular Fuzzy Modifier.
Table 1 shows the elements of fuzzy axioms FuzzyOWL, as well as their possible representation.
Table 1. Elements of Fuzzy Axioms in FuzzyOWL.
№ Element Possible values Representation in FuzzyOWL
#HighLoad
fuzzyOwl2
Degrees average», «low»
fuzzyType="datatype";
Datatype type="rightshoulder"; a="15.0";
b="30.0";/fuzzyOwl2
MDf – Modifier
2 «very», «not very» type="modified" modifier="very"
Degrees
NDf – Numeric
3 0≤ND≤1 Degree Value=0,6
Degrees
4 Varf – Variables a, b,c, k1, k2 b="30.0";
Zadeh, Lukasiewicz
5 Lf – Fuzzy Logic hasSemantics="Zadeh"
Goedel and Product
Modf – Fuzzy
3. Subject Area
Consider the use of the integration approach of FTS and fuzzy ontologies in solving the problem of
diagnosing the state of a helicopter. Diagnostics of a helicopter consists in checking its units in order
to establish their exploitation and the possibility of using the helicopter.
The result of the diagnosis will be assessment values of physical quantities key indicators. The
main goal is to assess the danger of values. To solve this problem, it is necessary to construct models
of the behavior of the selected nodes and make conclusions about the health of the nodes by using the
models. Models are built at expert base of assessment about the conduct of a particular component.
Table 2 show the parameters of the membership functions used for construct the FTS (Table 2).
Thus 5 fuzzy labels are defined for each physical quantity. The task of analyzing technical time
series is reduced to the task of searching for anomalous situations in TS of main gearbox and engine
propulsion system physical quantities indicators [21, 22]. The analysis is a sequence of the following
steps:
1. Formation of FTS on the basis of the received information on the values of key physical
quantities after the end of helicopter flight.
2. Search known abnormal situations in the resulting FTS.
3. Determination of the correct operation of the nodes. Work is incorrect if at least one abnormal
situation.
The fuzzy ontology was developed for experiments. The developed FuzzyOWL ontology has a
hierarchical structure and includes 55 classes, eight object properties, 40 data types.
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Table 2. Parameters of the membership function.
Physical parameter Range Very little Little Good Big Very big
boundaries
Exhaust gases 0-1000 a<100 a=100 a=350 a=600 a=720
temperature, °C b=200 b=275 b=560 b=700 b=800
c=200.5 c=350.5 c=600.5 c=720.5 c>1000
Engine oil 0-150 a<0 a=10 a=20 a=80 a=120
temperature, °C b=5 b=15 b=30 b=100 b=135
c=10.5 c=20.5 c=60.5 c=120.5 c>150
Engine oil pressure, 0-20 a<0 a=2.0 a=5.00 a=10 a=15.2
kgf/cm2 b=1 b=3.5 b=8 b=12 b=17.5
c=2.05 c=5.05 c=10.5 c=15.5 c>20
Main gearbox oil 0-100 a<0 a=10 a=20 a=50 a=80
temperature, °C b=5 b=15 b=35 b=70 b=90
c=10.5 c=20.5 c=50.5 c=80.5 c>100
Main gearbox oil 0-8 a<0 a=2.0 a=3.45 a=4.50 a=7.5
pressure, kgf/cm2 b=1 b=2.5 b=4 b=5 b=7.8
c=2.05 c=3.5 c=4.55 c=7.55 c>8
Table 3 contains objects properties of the used in the work (OP - oil pressure, EGT - exhaust gas
temperature, OT - oil temperature, PP - power plant).
Table 3. Property of objects.
Property Domain Range
has OP main gearbox main gearbox OP main gearbox
has OP left engine PP gearbox OP PP gearbox
has OP right engine PP gearbox OP PP gearbox
has EGT left engine x PP gearbox EGT PP gearbox
has EGT right engine PP gearbox EGT PP gearbox
has OT main gearbox main gearbox OT main gearbox
has OT left engine PP gearbox OT PP gearbox
has OT right engine PP gearbox OT PP gearbox
Property declaration example for «hasOPMainGearbox»
In addition, 40 data types were allocated: 5 fuzzy labels for 8 variants of relationships. The data
type parameters correspond to the parameters of the membership function. The type of membership
function in all data types was chosen triangular. Example of declaring a data type in FuzzyOWL
notation:
#BigOPMainGearbox
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As an object of experiments, time series for the diagnostics of helicopter units and the fuzzy
ontology of the helicopter units design were investigated. In the course of these experiments, the fuzzy
time series and fuzzy ontologies integration algorithms were used.
4. FTS and Fuzzy ontology integration system
A software system was developed to solve the problems of forming the inference of the
recommendation based on the integration of fuzzy time series and fuzzy ontologies. The software
system is written in C # on the .NET 4.5 platform. The system development was carried out in the
Microsoft Visual Studio 2015 environment. SQLite was used as the DBMS. The exchange protocol is
a function call to the SQLite library. This method simplifies the program and shortens the response
time. To store the database (definitions, tables, indexes, and the data itself), a single standard file is
used on the computer on which the program runs.
The expert develops a fuzzy ontology of the domain with the help of the ontology editor Protégé.
To check the adequacy and consistency of the ontology, the built-in Reasoner HermiT or FACT ++ is
used. The scheme of the used software package is presented in Figure 1.
Figure 1. FTS and Fuzzy-ontology integration system.
The user has the opportunity to conduct research using the developed integration system. A
prerequisite for obtaining an inference is to combine a time series with annotation properties. The
result of the study is the resulting list of abnormal situations and possible faulty helicopter units.
5. Experiments
Diagnostics of a helicopter consists in checking its units in order to establish their serviceability and
the possibility of operating the whole helicopter. The result of the diagnosis will be an assessment of
the values of key physical quantities. The main goal is to assess the danger of values. To check the
adequacy of the algorithm for integrating fuzzy time series and fuzzy ontology based on FuzzyOWL,
as well as the correctness of the software that implements this algorithm, a series of experiments were
conducted in which possible problem situations were performed. As part of the experiment, the
following actions were carried out:
1. The expert has developed a fuzzy ontology according to the FuzzyOWL standard. To build a
fuzzy ontology, the Protégé [23] editor with the connected FuzzyOWL Plugin [24] was used.
2. FuzzyOWL fuzzy ontology data types contain parameters of membership functions.
3. FuzzyOWL fuzzy ontology data types contain a binding to a specific class of ontology (Table 4).
The task of the experiments is to search for possible faulty helicopter units. The analysis represents
the sequence of the following steps:
1. the formation of TS on the basis of the obtained information on the values of key physical
quantities after running the machine;
2. search for defective helicopter units in the received TS;
3. determination of defective helicopter units.
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Table 4. Data Type Descriptions.
Datatype Type of Specific a b c
membership class
function
VeryLittleEGTLeftEngine triangular PP engine 100 200 200.5
Little EGTLeftEngine triangular PP engine 200 275 350.5
GoodEGTLeftEngine triangular PP engine 350 560 600.5
Big EGTLeftEngine triangular PP engine 600 700 720.5
VeryBigEGTLeftEngine triangular PP engine 720 800 1000
VeryLittleOPMainGearbox triangular main 0 1 2.05
gearbox
LittleOPMainGearbox triangular main 2.0 2.5 3.5
gearbox
GoodOPMainGearbox triangular main 3.45 4 4.55
gearbox
BigOPMainGearbox triangular main 4.5 5 7.55
gearbox
VeryBigOPMainGearbox triangular main 7.5 7.8 8
gearbox
A helicopter unit will be considered faulty if at least one abnormal situation is detected for a
physical quantity associated with a specific ontology class corresponding to the faulty unit.
The effectiveness of the diagnostic algorithm of technical systems can be evaluated when solving
the problem of modeling the behavior of helicopter units. The system should correctly identify
possible faulty helicopter units. To confirm the efficiency, it is necessary to analyze the data
characterizing the machines, both without defects and with possible defects, and then analyze the
information about the faulty units obtained by the system and received from an expert.
For the experiment, data were obtained on the run of the three machines, and data was generated
that simulates certain abnormal situations. Description of the time series is given in table 5.
Table 5. Description of time series.
Series Airplane Period TVG1 TVG2 Pm1 Рm2 Pmp Tm1 Tm2 Tmp
numbe number
1 210111 15.09.205 739.59 258.85 2.3 0.8 0 58.1 59.2 29.3
2 210111 16.09.205 757.29 256.93 2.4 0.8 0 57.1 59 29.3
3 210111 30.09.205 503 227.78 7.4 0.8 1.8 47.5 51.3 29
4 210111 12.04.205 536.85 520.93 7.6 6.6 4 53.9 56.5 35
5 240111 11.09.205 176.43 178 0.8 0.8 0 42.5 46 31.3
6 240111 12.09.205 176.57 178 0.8 0.8 0 42.5 46 31.3
7 240111 13.11.204 483 448.85 6.4 5.6 3.4 49.5 51.9 23.5
8 240111 11.08.204 479.13 0 6.4 5.4 3.3 51.6 55.1 29
9 250111 22.01.204 189.72 206.22 0.8 1 1.6 52.5 55.5 24.5
10 250111 23.01.204 193.3 209.22 0.8 1 1.6 52.5 55.5 24.5
The following designations are used: TVG1- left engine exhaust temperature, TVG2- right engine
exhaust temperature, Pm1 - left engine oil pressure, Pm2 - right engine oil pressure, Tm1 - left engine
oil temperature, Tm2 - right oil temperature engine, Pmp - oil pressure of the main gearbox, Tmp - oil
temperature of the main gearbox.
Experiments were conducted with ten-time series. The results of experiments are shown in Table 6.
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Table 6. Experiment results.
Period TVG1 TVG2 Pm1 Рm2 Pmp Tm1 Tm2 Tmp Faulty part
#EnginePowerPlan
15.09.2050 739.59 258.85 2.3 0.8 0 58.1 59.2 29.3
t
16.09.2050 757.29 256.93 2.4 0.8 0 57.1 59 29.3 #EnginePowerPlan
30.09.2050 503 227.78 7.4 0.8 1.8 47.5 51.3 29 #EnginePowerPlan
12.04.2052 536.85 520.93 7.6 6.6 4 53.9 56.5 35 No broken parts
11.09.2054 176.43 178 0.8 0.8 0 42.5 46 31.3 #MainGearbox
12.09.2054 176.57 178 0.8 0.8 0 42.5 46 31.3 #MainGearbox
13.11.2046 483 448.85 6.4 5.6 3.4 49.5 51.9 23.5 No broken parts
11.08.2047 479.13 0 6.4 5.4 3.3 51.6 55.1 29 #MainGearbox
22.01.2046 189.72 206.22 0.8 1 1.6 52.5 55.5 24.5 #EnginePowerPlan
23.01.2046 193.3 209.22 0.8 1 1.6 52.5 55.5 24.5 #MainGearbox
The result of the experiment is the construction of a fuzzy time series fuzzy ontology allowed us to
conclude that the helicopter unit was malfunctioning when analyzing the precise values of the
aggregates.
6. Conclusion
In this paper a technique for constructing fuzzy ontologies was investigated and an ontological model
of the state of helicopter units was developed. In the process of integrating fuzzy time series and fuzzy
ontology, the method integrating TS and ontology was implemented, and a software product was
developed that ensures the implementation of this method.
Also, experiments were conducted to search for anomalous situations and search for possible faulty
units using the developed approach to the integration of fuzzy time series and fuzzy ontology.
Thus, the proposed approach of hybridization of FTS and fuzzy ontologies allows one to reliably
recognize anomalous situations with some degree of truth. The algorithm also finds possible faulty
units corresponding to each abnormal situation.
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Acknowledgments
The study was supported by: The Ministry of Education and Science of the Russian Federation in the
framework of the projects No. 2.1182.2017/4.6 and 2.1182.2017 and The Russian Foundation for
Basic Research (Grants No. 19-07-00999 and 18-37-00450, 18-47-732007).
V International Conference on "Information Technology and Nanotechnology" (ITNT-2019) 259