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Student:
NGO Xuan Thuy-GE5S
Professor:
Mr.Eddie SMIGIEL
Tutor:
Mr. Ruthard MINKNER
Analysis, Classification Partial
Discharge with wavelet transform and
artificial neural network
Electrical Engineering: promotion 2011 September 2011
Purpose of my internship
Improve the measurement circuit of partial discharge created by Trench company
Capture and save the partial discharge signals into computer
Realize the analysis the signals with wavelet transform and chose the appropriate
wavelet for the analysis
Create an artificial neural network to classify and recognize the defaults of these
partial discharge signals.
Test the performance of the algorithm chosen and conclude
Résumé: Décharge partielle est un phénomène très connu dans les appareils à haute tension.
Elle s‘est produite à cause des erreurs de production et aussi des défauts présentés dans les
matières d‘isolation utilisées dans ces appareils. Une fois que des décharges partielles
apparaissent, elles peuvent endommager le système d‘isolation de l‘appareil et donc mettre
hors-service ou pire détruire l‘appareil à partir d‘une certaine valeur de décharge. Dans la
chaine de production de l‘entreprise Trench, qui produit des transformateurs de mesure à
haute tension, il y a plus de 20% de produits qui sont défaillants à cause de ce phénomène. Le
but de mon stage est d‘étudier les décharges partielles présenté dans ces transformateurs pour
déterminer les causes (les défauts) de ces phénomènes afin de pouvoir récupérer les produits
défaillants. Le stage est divisé en trois phases principales : améliorer le schéma de mesure des
décharges partielles, l‘analyse les signaux des décharges partielles avec la transformée en
ondelettes (l‘outil de traitement signal) et classifier des différentes types des décharges avec le
réseau de neurone artificiel.
Abstract: Partial discharge is a well-known phenomenon in High Voltage (HV) apparatus. It
occurs because of production‘s errors and also the defaults which are introduced in the
isolating system used in these apparatus. Ones the partial discharge occurs, it can damage the
isolating system of apparatus and so can disable or destroy the apparatus from certain value of
discharge. In the production line of Trench Company, which produces transformers in High-
Voltage, there are more than 20% of products that are defective because of this phenomenon.
The purpose of my internship is to study the partial discharges occurred in these transformers
to determine the cause (defects) of these phenomena in order to recover the faulty products.
My internship is divided into three main phases: improving the measurement circuit of partial
discharge, analysis of partial discharge signals with the wavelet transform (the signal
processing tool) and classify different types of partial discharges with an artificial neural
network.
Table of Contents 1 Introduction ............................................................................................................ 1 2 Presentation of the company ................................................................................ 2
2.1 The Trench Group ....................................................................................................2 2.2 The company Trench Switzerland AG ......................................................................3 2.3 Research and Development department (R&D) .......................................................4
3 Partial discharge introduction ............................................................................... 5 3.1 Partial discharge.......................................................................................................5 3.2. Measurement of Partial discharges signals ..............................................................7
4 Final measurement circuit of our project ............................................................. 9 Fig. 4.2: PD test circuit elements ...................................................................................... 10
4.1 Some important parts in the measurement circuit ...................................................10 Coaxial shunt (100 ohm) see the fig 4.1..................................................................................10 4.2 Some problem with the measurement circuit ..........................................................11
5 Some result with the measurement circuit created ........................................... 12 5.1 With cylindrical capacitors ......................................................................................12 Test 2 .................................................................................................................................13 5.2 LOPOs ...................................................................................................................14
6 Wavelet Transform analysis ................................................................................ 16 6.1 Introduction ............................................................................................................16 6.2 Fourier transform and Wavelet transform ...............................................................17
6.2.1 Fourier transform .............................................................................................17 6.3 Wavelet Analysis ....................................................................................................19
6.3.1 What is wavelet analysis .................................................................................19 6.3.2 The continuous wavelet transform ...................................................................19 6.3.3 The discrete wavelet transform .......................................................................24
6.4 Application wavelet analysis with partial discharge signal .......................................27 6.4.1 Wavelet analysis signals with MATLAB software. ............................................29 6.4.2 Use command lines for the wavelet analysis. ..................................................30 6.4.3 Using Graphic User Interface of wavelet toolbox .............................................36
7 Artificial Neural Network (ANN) ........................................................................... 40 7.1 Introduction of artificial neural network ...................................................................41 7.2 Perceptron neural network .....................................................................................43 7.3 The back-propagation algorithm .............................................................................46 7.4 Artificial neural network created for partial discharge classification .........................48
8 Graphic User Interface (GUI) ............................................................................... 62 9 Conclusion ............................................................................................................ 75
This Semesterwork bases on a written contract between the Company Trench/Siemens CH, the School INSA Strasbourg and the two students Goeffrey BERTIN and Xuan Thuy NGO.
The report is literary property of the Students Mr. BERTIN and Mr. NGO and the R&D department of the company Trench SA/FR and Siemens AG/CH. The companies Trench SA/FR and Siemens AG/CH own all rights of the Semesterwork.
It is forbidden to publish this report in the next five years and only Mr. SMIGIEL and another Person of the School INSA Strasbourg are allowed to read this report.
During the presentation of this Semester-work the content can be explained, drawn, etc, or can be shown with a beamer. No printed explanations, drawings, etc are allowed to be distributed. Basel, 21. July 2011 Dr. Ing. Ruthard MINKNER Trench SA/FR and Trench AG/Siemens/CH
We wish to thanks Mr. MINKNER and Mr. SCHMID to allow us to carry out this project. We
also want to thank Mr. MINKNER for all his interest about this internship and for bringing
his knowledge to help us during this period. . Also a special thank you to our tutor professor Mr.
SMIGIEL for his support. Finally we would like to say many thanks to all the people who made
our work placement such a pleasant stay and particularly to the department R&D of Trench
Switzerland AG.
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Analysis, Classification of partial discharge with
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NGO Xuan Thuy-GE5S
1 Introduction
For my final internship (―Projet de Fin d‘Etude‖ in French), I decided to join the
Trench Group company in Basel, Switzerland, during a 6 months period from the 1st of
February to the 29th of July 2011.
During the first semester, from October to February, I already had the opportunity to
work with this company for a project named: ―Partial Discharges analysis with wavelet
method‖. This work experience is the continuity of this project and consists in an
improvement of the wavelet method and inserts the delicate part of Partial Discharge
measurement that we didn‘t deal with in the previous work.
The problematic is the following. Trench group product several kinds of instrument
transformers. In these devices, partial discharges phenomena can occur (developed in chapter
3). A partial discharge limit has been fixed by IEC standard for instrument transformers.
Exceeding this limit, the device is considered like faulty and can‘t be sold by the company. As
all transformers can‘t be operational at the production line output, faulty devices have to be
checked and reintroduced somewhere in the production line. The problem is that sometimes, it
is difficult to determine the internal defect of the device and therefore, it can cost time for the
company and then losing money.
Therefore, partial discharge detection is important for the evaluation construction and
to recognize defects in these designs. The trend towards the automation of this process to test
bushings, instrument transformers and other insulated devices is evident. As the conventional
method of oscillographic observation provides only a limited recognition of defects, a better
method has to be developed. This method can be performed by measuring the current impulse
of partial discharges between the test object and earth. Then, these impulses can be analyzed
with a wavelet method which can help to classify the defects thanks to an artificial neural
network.
Task of the Semesterwork:
Description and frequency response measurement with one or two suitable sensors to
recognize partial discharge impulses and register the information in a laptop memory.
Development of an analysis method with the wavelet theory
Classification the partial discharges with an artificial neural network
Create an graphic user interface in Matlab for user who haven‘t knowledge about
wavelet and artificial neural network.
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2 Presentation of the company
2.1 The Trench Group
The Trench Group is a worldwide reputable company in the area of high voltage
technology developments. Till the year 1990 it was especially active in North America, where
grew by means of some fusions with other companies of the high voltage sector. Through
them it became a worldwide firm that nowadays possesses production installations in almost
every continent. Since 2004, the Trench Group has become a hundred percent subsidiary firm
to the multinational Siemens Group company.
Fig. 2.1.1: Extension of the Trench Group over the world at present
As it is seen, it has installations in several different countries, those which dedicate
themselves to the development of widely different technologies and the devices used for
them.
In this sense, we can focus on the kind of technology developed in each country:
In Austria, air cire by type reactors, iron core oil filled reactors and earth fault location
systems are produced.
In Brazil, the factory of Contagem manufactures air core reactors from 600 V to 345 kV,
50 kVA to 60 MVA and line traps from 72 kV to 800 kV, from 0.1 to 2 mH.
In Canada, there are four different installations belonging to the Trench Group. The main
products developed there are bushings for reactors or transformers of oil-to-air and oil
Linz, AUSTRIA
Bamberg, GERMANY
St. Louis, FRANCE
Basel, SWITZERLAND
Cairo Montenotte (SV), ITALY
Hebburn, ENGLAND
Shanghai, CHINA
Shenyang, CHINA
Contagem, BRAZIL
Ajax/Scarborough,
CANADA
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Image II.2. Installations of Trench Switzerland AG (red) and Haefely Test AG in Lehenmattstraβe, Basel. Image II.2. Installations of Trench Switzerland AG (red) and Haefely Test AG in Lehenmattstraβe, Basel
impregnated paper types, different kinds of current, voltage and combined transformers in
ranges that can go from 72.5 KV to 245, 550 or even 800 KV depending on the kind of
equipment, air core dry type reactors and some others devices to be used in relation to PLC(1)
technology.
In China, in Shanghai installations, SF6-insulated instrument transformer, coil products –
such as line traps, smoothers or filters – and low power instrument transformers are produced,
as well as HV AC and DC bushings – both oil impregnated paper and epoxy resin
impregnated paper – up to 1000 kV, in Shenyang.
In France, the installations of St. Louis work in the field of oil insulated instrument
transformers and bushings, sharing the branches of Engineering, R&D, Sales and Marketing,
Purchasing and Production with Trench Switzerland AG.
In Germany, it is placed the technological centre for gas-insulated equipment of the
Trench Group.
In Italy, it has the center for the design and manufacturing of high voltage instrument
transformers, having the European production of capacitor voltage transformers and grading
capacitors for the whole group concentrated in this installation, with a significant
manufacturing of SF6 instrument transformers.
In England, the one known as "The Bushing Company" is located, pioneer in the design
and manufacture of bushings for transformers and switchgear since 1929.
And finally, Trench Switzerland AG, that will be described as follows because of being in
which this work has been developed.
2.2 The company Trench Switzerland AG
Trench Switzerland draws from over 95 years of experience in the field of oil
insulated instrument transformers and bushings.
Its history comes from the foundation by Emil Haefely in 1904 of his own firm. At the
beginning it was based on a patented design for manufacturing of resin-impregnated paper
insulators – this material, known as haefelite, will be mentioned in section 4.2.6.1 –, growing
quickly and being expanded into testing in 1922. Over the years, this company evolved to
become a specialist in the fabrication of electrical devices such as bushings, capacitors and in
insulation technology and high-voltage testing equipment. It meant that there were two big
areas of development into the company, one dedicated to transmission technology and other
one dedicated to high-voltage testing. Nowadays, the first of these mentioned branches
belongs to the Trench Group, being now Trench Switzerland AG, while the second one –
Haefely Test AG – belongs to the Special Technologies Platform of Hubbell Inc. Because of
this, both companies have today their installations in the same area, the one showed in this
picture.
(1) System for carrying data on a conductor also used for electric power transmission PLC (Power Line Carrier):
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(2) LOPO: Acronym of LOW POWER, referred to the low power transducers technology.
Fig. 2.1.2: Installations of Trench Switzerland AG (red) and Haefely Test AG in
Lehenmattstraβe, Basel
Focusing on Trench Switzerland AG, as it has been said before, today it shares
Engineering, R&D, Sales and Marketing, Purchasing and Production with Trench France SA.
Its main area is focused on measurement transformers (current transformers, inductive and
capacitive voltage transformers, RC voltage dividers) and bushings, having with them more
than a hundred years of experience.
Since July, 1st 2011, the company became officially Siemens Switzerland AG.
2.3 Research and Development department (R&D)
This Masterwork has been mainly carried out in close collaboration with the engineers
of the department R&D, what makes particularly required the following clarification of the
kind of work developed there.
This department is part of the Engineering branch, and is mainly dedicated to the next
tasks:
- Research of new materials and developments.
- Organization of the interchange of technology between the different locations.
- Standardization of Trench Group/Siemens products.
- Production optimization for the whole Group.
- Development and presentation of the new products.
- Promotion of the LOPO(2) technology.
As a result of these functions, some parts of the installations of the company, such as
the testing rooms and the workshops are exclusively used by this department, what also means
that every new student is working here for the development of his work.
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3 Partial discharge introduction
3.1 Partial discharge
Referring to [1], partial discharges (PD) are localized electrical discharges within an
insulation system, restricted to only a part of a dielectric material, and thus only partially
bridging the electrodes. The insulation may consist of solid, liquid or gaseous materials, or of
any combination. The term ―partial discharge‖ is relatively new, as it includes a wide group of
discharge phenomena. The type of discharge is often divided into 3 groups due to their
different origin.
Corona discharges: i.e. discharges in gases or liquids caused by a locally enhanced
field from sharp points on the electrodes. Corona is often harmless, but by-products
like ozone and nitric acids may chemically deteriorate closely lying materials.
Internal discharges:
o Cavity discharges: i.e. discharges from gas-filled voids, delaminations,
cracks, etc. within solid insulation. A refined classification could be made to
cavities that are on one side bounded by the metallic electrode, and to cavities
that are completely surrounded by the insulating material. Voids may have its
origin from
o cast insulation like epoxy spacers in SF6 bus bars, from dried out regions in
oil-impregnated paper-cables, from gas-bubbles in plastic insulation, etc.
Delaminations occur in laminated insulation like the stator-bar insulation of
large electrical machines that often is composed of mica based types with
binding enamel like epoxy. Cracks could for example occur in mechanically
stressed insulation, e.g. in loose stator bars that are vibrating.
o Treeing discharges: i.e. current pulses within an electrical tree. The electrical
tree may start from a protrusion on the electrode or from imperfections like
contaminating particles embedded in solid insulation.
Surface discharges: i.e. discharges on the surface of an electrical insulation where the
tangential field is high, e.g. the porcelain or polymeric housing of high-voltage
devices. Other common sources of surface discharges are terminations of cables or the
end-windings of stator windings.
Fig. 3.1.1: Some types of partial discharge (a) Corona discharge, (b) Surface discharge, and
(c) Cavity discharge.
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The significance of partial discharges on the life of insulation has long been
recognized. Every discharge event causes a deterioration of the material by the energy impact
of high energy electrons or accelerated ions, causing chemical transformations of many types.
As will be shown later, the number of discharge events during a chosen time interval is
strongly dependent on the kind of voltage applied and will be largest for a.c. voltages. It is
also obvious that the actual deterioration is dependent upon the material used. Corona
discharges in air will have no influence on the life expectancy of an overhead line; but PDs
within a thermoplastic dielectric, e.g. PE, may cause breakdown within a few days. It is still
the aim of many investigations to relate partial discharge to the lifetime of specified materials.
Such a quantitatively defined relationship is, however, difficult to ensure. PD measurements
have nevertheless gained great importance during the last four decades and a large number of
publications are concerned either with the measuring techniques involved or with the
deterioration effects of the insulation. The detection and measurement of discharges is based
on the exchange of energy taking place during the discharge. These exchanges are manifested
as: (i) electrical pulse currents (with some exceptions, i.e. some types of glow discharges); (ii)
dielectric losses; (iii) e.m. radiation (light); (iv) sound (noise); (v) increased gas pressure; (vi)
chemical reactions. Therefore, discharge detection and measuring techniques may be based on
the observation of any of the above phenomena. The oldest and simplest method relies on
listening of the acoustic noise from the discharge, the ‗hissing test‘. The sensitivity is,
however, often low and difficulties arise in distinguishing between discharges and extraneous
noise sources, particularly when tests are carried out on factory premises. It is also well
known that the energy released by PD will increase the dissipation factor; a measurement of
tan υ in dependency of voltage applied displays an ‗ionization knee‘, a bending of the
otherwise straight dependency. This knee, however, is blurred and not pronounced, even with
an appreciable amount of PD, as the additional losses generated in much localized sections
can be very small in comparison to the volume losses resulting from polarization processes.
The use of optical techniques is limited to discharges within transparent media and thus not
applicable in most cases. Only modern acoustical detection methods utilizing ultrasonic
transducers can successfully be used to localize the discharges. These very specialized
methods are not treated here. The most frequently used and successful detection methods are
the electrical ones, to which the new IEC 60270 Standard [19] is also related. These methods
aim to separate the impulse currents linked with partial discharges from any other phenomena.
The adequate application of different PD detectors which became now quite well defined and
standardized, presupposes a fundamental knowledge about the electrical phenomena within
the test samples and the test circuits.
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3.2. Measurement of Partial discharges signals
The partial discharge phenomena are produced in an object which has two electrodes and one
isolation material between these two electrodes. This system can be considered like one
capacitor (figure 3.2.1).
Fig. 3.2.1: Simulation of a PD test object. (a) Scheme of an insulation system comprising a
cavity. (b) Equivalent circuit.
In the figure 3.2.1, we have an object which has 2 electrodes (A and B). The isolation system
between these two electrodes has one default (one cavity). This object is placed on high
voltage (the electrode A is connected to high voltage and the electrode B connected to earth).
From one certain value of voltage we will obtain the partial discharges signals. The reason is
from certain value of voltage, the electrical field created by this voltage is bigger than
dielectric rigidity of cavity within the isolation system. So some electrons will go to electrode
B to electrode A to decrease this electrical field and also produce the partial discharge
phenomena. Theses partial discharges are very quick (some nanosecond) and also very
difficult to measure. For the measurement of theses discharges, we use a capacitor which is
connected in parallel to object (figure 3.2.2). This capacitor is called ‗coupling capacitor‘.
Fig. 3.2.2: the PD test object Ct within a PD test circuit with coupling capacitor Ck
When the system in figure 3.2.2 is supplied on high voltage, the test object and coupling
capacitor is charged with certain charge amount according to their value. When a partial
discharge occurs, we found a dropping of voltage (dropping of Vs) between two electrodes of
test object and the charge amount of test object will be decreased. Now the report between the
charge amount of test object and the one of coupling capacitor is not respected (this is due to
their capacitor value). So some charge will immediately be sent from coupling capacitor to
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test object in order to respect the charge amount report between these two. This phenomenon
creates a current i(t) which characterize the number of charges exchanged within the test
object during the partial discharge phenomena. Now we must just measure this current (i(t)) to
obtain all information about partial discharge signal. We can consult [2] to get more
information about the theory of partial discharge measurement.
In the literature we can found 3 standard measurement process used to obtain partial signal
information (figure 3.2.3) [3].
Fig. 3.2.3: Standard PD test circuits recommended in IEC 60270
So the first circuit is the measurement of current in the side of test object. The second is the
measurement of current in the side of coupling capacitor and the last one is using a bridge
between these two capacitors (coupling capacitor and object). For our project, we use the
circuit which measures the current in the side of test object.
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4 Final measurement circuit of our project
The final whole circuit solution we kept is the following:
Ck
1nF
Coaxial Rshunt
100 Ohm
Rfilter 47 Ohm
Lfilter
39µH
Coaxial cable
10m 50 Ohm
Oscilloscope
AC Signal
50 Hz
V
Test object
AKV
Isolation transformer
PD measuring system
1 2 3 4
12
13
5
6
7
8
9
11
10 50 Ohm
Fig. 4.1: PD test circuit diagram
1- Variac used to change the supply voltage
2- Transformer
3- Coupling capacitor
4- Test object
5- Coaxial shunt (100 ohm)
6- Epcos 90 08 0 used for overvoltage security
7- Filter resistor
8- Filter inductance 39µH
9- Oscilloscope Tektronix TDS 3024B
10- Internal resistor of the oscilloscope (50 Ohm)
11- Isolation transformer to ensure earth connection
12- AKV used to measure impedance and peak detection
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Here we can see the different parts of this circuit:
Fig. 4.2: PD test circuit elements
4.1 Some important parts in the measurement circuit
Coaxial shunt (100 ohm) see the fig 4.1
The coaxial shunt is a special resistor which is placed between the test object and earth. This
one is used to pick up the signal of current created by partial discharge phenomena. The
principal is to pick up the voltage between two terminals of coaxial shunt. This voltage is the
image of current come through object. The specialty of this Shunt is that it is purely
resistance. It‘s created with the resistances which have no inductance or capacitance value so
we can observe the partial discharge signals with a maximum performance. The figure below
shows the coaxial shunt created for the project.
Fig. 4.1.1: 100 Ω coaxial shunt
More information about coaxial shunt can be found in the final year report of Mr. Jeoffey
BERTIN
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Filter (filter resistor and filter inductance)
These two components are used to create a high pass filter. This filter is used to eliminate the
50Hz signal which is the signal created directly from High voltage (The frequency of high
voltage is 50 Hz). The filter band is preciously calculated in order to keep the waveform of
partial discharge signals (the band pass of this filter is 250 kHz).
Isolation transformer
This transformer is used to ensure that there is only one earth connection. It‘s very important
to eliminate noises which can be come from other voltage source and also other earth
connection.
AKV used to measure impedance and peak detection
This is a standard device used to measure the amplitude of partial discharges. It‘s very
important to know if the partial discharge limit is exceeded or not. So this device is always
allowed before the measurement to avoid the destruction of measurement system.
4.2 Some problem with the measurement circuit
During the project, there are two main problems occurred in the measurement of partial
discharge signals:
Reflexion phenomenon
Loop inductance effect
Reflexion phenomenon
This is a known problem of the signal‘s transmission in high frequency. This phenomenon is
come from the difference of impedance of each part of circuit used for the transmission of
signal. The principal of this reflexion phenomenon is the same than reflexion phenomenon in
optical field. During the transmission of electrical signal, if the signals see a change of
impedance in his way, a part of signal will continue his way and another part will come back
to the point that gave birth. And this phenomenon will completely modify the waveform of
partial discharges signals. To correct this problem, some impedance adaptations are used to
eliminate the reflexion phenomena. More information about this phenomenon are given in [4]
and also in the final years report of Mr. Jeoffrey BERTIN (GE5E).
Loop inductance effect
In electrical circuit, all the loops created by cables, copper, etc… are equivalent to
inductances. This inductance can modify the waveform of partial discharge signals. It is
important to notice that the waveform change with the impedances of the circuit. Hence, the PD
waveforms can be different from one place to another with the same test object. For an accurate classification of the PD waveforms, we have to be sure they come from the same test circuit.
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5 Some result with the measurement circuit created
5.1 With cylindrical capacitors
Fig. 5.1.1: Capacitor diagram
They are composed of two cylindrical metallic parts separated by several layers of
polypropylene film.
The thickness of a layer δf is always the same: δf = 36 µm.
The distance between the two metallic part δis is given by N*δf where N is the number
of layers.
The capacitance can be calculated with the following equation:
C = 2π.εr.ε0.l/ln(r2/r1)
(9.1.1.1)
l is the shared distance between the two metallic cylinder.
r2 is the radius of the external cylinder.
r1 is the radius of the internal cylinder.
εr is the relative permittivity of the insulation between the two cylinder (εr ≈ 2.2 for
polypropylene).
Test 1
o Test object reference: MSIL 1-2
o Number of layers: 2
o Voltage: 463 V
o PD level: 100pC
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Fig. 5.1.2: MSIL 1-2 PD waveform – 400 ns/div
Test 2
o Test object reference: MSIL 3-2
o Number of layers: 2
o Voltage: 692 V
o PD level: 200pC
Fig. 5.1.3: MSIL 3-2 PD waveform – 400 ns/div
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5.2 LOPOs
LOPO is an acronym of LOW POWER, referred to the low power transducer
technology. They are 3 kind of LOPO designed by Trench group:
The type VT which include a Voltage Transducer
The type CT which include a Current Transducer
The type VCT which include a Voltage Transducer and a Current Transducer
For our work, we only tested VT or CT transducers but the VCT is just a combination
of these ones.
The next drawing shows an internal view of a VCT transducer where we can see all
the elements which compose it.
Fig. 5.2.1: VCT internal view
The current transducer is composed of a typical current transformer and a shunt
connected to the secondary. Thus, a relation between the primary current and the output
voltage allows to get the current value.
The voltage transducer is composed by a compensated R-divider.
The electrical insulation of those devices is an epoxy resin with a dielectric strength
between 18 and 22 kV/mm.
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Test 1
o Test object reference: CT16
o Voltage: 2.3 kV
o PD level: 250pC
Fig. 5.2.2: CT16 PD waveform – positive alternation
Test 2
o Test object reference: VT9
o Voltage: 9.2 kV
o PD level: 30pC
Fig. 5.2.3: VT9 PD waveform – positive alternation
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6 Wavelet Transform analysis
6.1 Introduction
The data is obtained via Tektronix Oscilloscope TD3004. This data give the waveform
of the current created by the partial discharge phenomena.
Ck
1nF
Coaxial Rshunt
100 Ohm
Rfilter 47 Ohm
Lfilter
39µH
Coaxial cable
10m 50 Ohm
Oscilloscope
AC Signal
50 Hz
V
Test object
AKV
Isolation transformer
PD measuring system
1 2 3 4
12
13
5
6
7
8
9
11
10 50 Ohm
Fig. 6.1.1: PD measuring circuit and one type of PD obtained
The figure 6.1.1 above show the PD measuring circuit and also the signal come from
Tektronix Oscilloscope. Now we use the signal processing tool to pick up all characters of
signal used for the classification and recognition of partial discharge. For this analysis, we
choose the wavelet transform to pick up the feature vector used for the neural network (The
notion of feature vector and neural network analysis will be shown in the next chapter).
Wavelet analysis is a processing tool which is more suitable for the non stationary
signal with fast change (rise time) like partial discharge signals than Fourier analysis. Another
advantage of wavelet analysis is that this one has also frequency resolution and time
resolution contrary to Fourier analysis which has only frequency resolution. In this chapter,
we will talk about Fourier transform and also wavelet transforms to see the differences
between them.
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6.2 Fourier transform and Wavelet transform
6.2.1 Fourier transform
Signal analysts already have at their disposal an impressive arsenal of tools. Perhaps
the most well-known of these is Fourier analysis, which breaks down a signal into constituent
sinusoids of different frequencies. Another way to think of Fourier analysis is as a
mathematical technique for transforming our view of the signal from a time-based one to a
frequency-based one [5].
Fig. 6.2.1.1: Fourier transforms analysis
Fourier analysis has a serious drawback. In transforming to the frequency domain, time
information is lost. When looking at a Fourier transform of a signal, it is impossible to tell
when a particular event took place.
If a signal doesn‘t change much over time — that is, if it is what is called a stationary signal
[5] — this drawback isn‘t very important. However, most interesting signals contain
numerous non-stationary or transitory characteristics: drift, trends, abrupt changes, and
beginnings and ends of events. These characteristics are often the most important part of the
signal, and Fourier analysis is not suited to detecting them. To correct this, Dennis Gabor
(1946) invented a new technique called the Short-Time Fourier Transform (STFT), maps a
signal into a two-dimensional function of time and frequency (Figure 6.2.1.2).
Fig. 6.2.1.2: principal of Short Time Fourier Transform
The STFT represents a sort of compromise between the time- and frequency-based
views of a signal. It provides some information about both when and at what frequencies a
signal event occurs. However, we can only obtain this information with limited precision, and
that precision is determined by the size of the window (See Annex 4).
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Wavelet analysis represents the next logical step: a windowing technique with
variable-sized regions. Wavelet analysis allows the use of long time intervals where we want
more precise low frequency information, and shorter regions where we want high frequency
information.
Here‘s what this looks like in contrast with the time-based, frequency-based, and
STFT views of a signal:
Fig. 6.2.1.3: The differences views of signal via FT, STFT and Wavelet analysis
Our study case is partial discharge phenomena. These types of signal are extremely
quick (rise time is some ns) and with enormous of variation. These aren‘t stationary signal
and we need both frequency and time information. It isn‘t suitable analyze these signals with
Fourier analysis so that why we want use Wavelet transform for the signal processing
analysis.
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6.3 Wavelet Analysis
6.3.1 What is wavelet analysis
A wavelet is a waveform of effectively limited duration that has an average value of
zero.
Compare wavelets with sine waves, which are the basis of Fourier analysis. Sinusoids
do not have limited duration — they extend from minus to plus infinity. And where sinusoids
are smooth and predictable, wavelets tend to be irregular and asymmetric.
Fig. 6.3.1.1: Sine wave and wavelet (db10)
This figure shows the differences between sine wave and wavelet. Sine wave is
periodic but wavelet isn‘t.
Fourier analysis consists of breaking up a signal into sine waves of various
frequencies. Similarly, wavelet analysis is the breaking up of a signal into shifted and scaled
versions of the original (or mother) wavelet.
Just looking at pictures of wavelets and sine waves, we can see intuitively that signals
with sharp changes might be better analyzed with an irregular wavelet than with a smooth
sinusoid, just as some foods are better handled with a fork than a spoon.
It also makes sense that local features can be described better with wavelets, which have
local extent.
6.3.2 The continuous wavelet transform
Mathematically, the process of Fourier analysis is represented by the Fourier transform:
Which is the sum over all time of the signal f (t) multiplied by a complex exponential.
(Recall that a complex exponential can be broken down into real and imaginary sinusoidal
components.)
(6.3.1)
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The results of the transform are the Fourier coefficients F (w), which when multiplied by a
sinusoid of appropriate frequency w; yield the constituent sinusoidal components of the
original signal. Graphically, the process looks like:
Fig. 6.3.2.1: demonstration of Fourier Transform
Similarly, the continuous wavelet transform (CWT) is defined as the sum over all time
of the signal multiplied by scaled, shifted versions of the wavelet function ψ:
Where g(s,η) is coefficient of wavelet transform with wavelet scaled by s and shifted by η.
f(t) is the original signal.
The results of the CWT are many wavelet coefficients C, which are a function of scale
and position.
Multiplying each coefficient by the appropriately scaled and shifted wavelet yields the
constituent wavelets of the original signal:
Fig. 6.3.2.2: demonstration of wavelet transforms
Scaling a wavelet simply means stretching (or compressing) it (Figure 6.3.2.3) (See Annex 1).
(6.3.2)
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Fig. 6.3.2.3: The scaling of wavelet
Shifting a wavelet simply means delaying (or hastening) its onset. Mathematically,
delaying a function f(t) by k is represented by f(t-k):
Fig. 6.3.2.5: the shifting function
Regarding this figure, we found that the shifted wavelet function ψ (t-k) is just
translated to the right with respect to the function ψ (t).
Five easy steps to a Continuous Wavelet Transform
The continuous wavelet transform is the sum over all time of the signal multiplied by
scaled, shifted versions of the wavelet. This process produces wavelet coefficients that are a
function of scale and position.
It‘s really a very simple process. In fact, here are the five steps of an easy recipe for
creating a CWT:
Take a wavelet and compare it to a section at the start of the original signal.
Calculate a number, C, the represents how closely correlated the wavelet is with this
section of the signal. The higher C is, the more the similarity. Note that the results will
depend on the shape of the wavelet you choose.
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Shift the wavelet to the right and repeat steps 1 and 2 until you‘ve covered the whole
signal.
Scale (stretch) the wavelet and repeat steps 1 through 3.
Repeat steps 1 through 4 for all scales.
When the continuous wavelet transform is done, we‘ll have the coefficients produced
at different scales by different sections of the signal. The coefficients constitute the results of
a regression of the original signal performed on the wavelets.
How to make sense of all these coefficients? We could make a plot on which the x-
axis represents position along the signal (time), the y-axis represents scale, and the color at
each x-y point represents the magnitude of the wavelet coefficient C (Figure 6.3.2.6). These
are the coefficient plots generated by the graphical tools.
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Fig. 6.3.2.6: Wavelet transforms of sinus wave + noise with wavelet db2
Figure 6.3.2.6 show an example of magnitude of all coefficients of continuous wavelet
transform. Their magnitudes are presented by the color (large coefficients are light and small
coefficients are dark). In 3D view, we can see better the representation of coefficients like the
figure below.
Fig. 6.3.2.7: Coefficients of CWT in 3D plot
In this plot, we can see the differences of all coefficients. To realize wavelet analysis,
we can use differences families of wavelet. Some wavelets are shown in the Wavelet toolbox
tutorial (P53-P57).
Time Scale
Magnitude
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It is a different view of signal data than the time-frequency Fourier view, but it is not
unrelated because there is a relation between scale coefficient and frequency of signal that is
shown below.
Relation between scale coefficient and frequency of signal
The wavelet analysis will produce a time-scale view and not time-frequency view. But
there is a relation between scale and frequency
Low scale a => compressed wavelet => rapidly changing detail => High frequency w.
High scale a => stretched wavelet => slowly changing, coarse features => Low
frequency w.
It‘s important to understand that the fact that wavelet analysis does not produce a
time-frequency view of a signal is not a weakness but a strength of the technique.
Not only time-scale is a different way to view data, it is a very natural way to view data
deriving from a great number of natural phenomena (See Annex 2).
With the continuous wavelet transform, there are 3 properties that make it difficult to
use directly. The first is the redundancy of the CWT. In (6.3.2) the wavelet transform is
calculated by continuously shifting a continuously scalable function over a signal and
calculating the correlation between the two. Even without the redundancy of the CWT we still
have an infinite number of wavelets in the wavelet transform and we would like to see this
number reduced to a more manageable count. This is the second problem we have. The third
problem is that for most functions the wavelet transforms have no analytical solutions and
they can be calculated only numerically or by an optical analog computer. So to remedy these
problems, the discrete wavelet transform is used. The next chapter will talk about this
algorithm
6.3.3 The discrete wavelet transform
As we know, Calculating wavelet coefficients at every possible scale is a fair amount
of work, and it generates an awful lot of data. What if we choose only a subset of scales and
positions at which to make our calculations?
It turns out, rather remarkably, that if we choose scales and positions based on powers
of two — so-called dyadic scales and positions — then our analysis will be much more
efficient and just as accurate. We obtain just such an analysis from the discrete wavelet
transform (DWT) (See Annex 3).
An efficient way to implement this scheme using filters was developed in 1988 by
Mallat. The Mallat algorithm is in fact a classical scheme known in the signal processing
community as a two-channel sub-band coder (See Annex 3).
This very practical filtering algorithm yields a fast wavelet transform — a box into
which a signal passes, and out of which wavelet coefficients quickly emerge.
The principal of discrete wavelet transform is passing the signal in two additional
filters (low-pass filter and high-pass filter) to obtain the coefficients of discrete wavelet
transform. The coefficients of low-pass filter are created by the scaling function (See Annex
3) and the coefficients of high-pass filter are created by wavelet function (See Annex 3).
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In DWT, we talk about 2 terms approximation and detail. Approximation is all
coefficients obtained at the output of low pass filter (it contains the information of low
frequencies). The detail is all coefficients obtained at the output of high pass filter (it contains
the information of high frequencies).
Fig. 6.3.3.1: filtering process of the first level
In figure 6.3.3.1, the original signal, S, passes through two complementary filters
(scaling filter and wavelet filter) and emerges as two signals. A means approximations and D
means details. In this case, A and D are the approximation and detail of the first level of
decomposition.
Unfortunately, if we actually perform this operation on a real digital signal, we wind
up with twice as much data as we started with. Suppose, for instance, that the original signal S
consists of 1000 samples of data. Then the approximation and the detail will each have 1000
samples, for a total of 2000.
To correct this problem, we introduce the notion of down-sampling. This simply
means throwing away every second data point. While doing this introduces aliasing (a type of
error) [8] in the signal components, it turns out we can account for this later on in the process.
Fig. 6.3.3.2: Generate wavelet coefficient by filtering method
The process on the right, which includes down-sampling, produces DWT coefficients.
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Fig. 6.3.3.3: example of DWT of a sinusoidal signal with noise at the first level
The figure above shows the discrete wavelet transform at the first level using filtering
method. The signal ‗S‘ is pass through two complementary filters and down-sampling phase
to generate DWT coefficients. cA means coefficients of approximation and cD means
coefficients of detail.
The decomposition process can be iterated, with successive approximations being
decomposed in turn, so that one signal is broken down into many lower-resolution
components. This is called the wavelet decomposition tree.
Fig. 6.3.3.4: wavelet decomposition tree
Looking at Figure 6.3.3.4, a signal‘s wavelet decomposition tree can yield valuable
information.
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Fig. 6.3.3.5: An example of wavelet decomposition tree
The figure 6.3.3.5 shows the principal of wavelet decomposition tree. The bandwidth
of signal is divided by 2 for each level of decomposition (because there are two
complementary filters). For each level, we pass the approximations into 2 others
complementary filters and at the outputs of these 2 news filters we get news coefficients of
details and approximation. With this technical, we have information about differences
frequency band. cA3 contains information of low frequencies. cD1 contains information of
highest frequencies. cD2 and cD3 contain information of frequencies between cA3 and cD1.
Since the analysis process is iterative, in theory it can be continued indefinitely. In
reality, the decomposition can proceed only until the individual details consist of a single
sample or pixel. In practice, we‘ll select a suitable number of levels based on the nature of the
signal, or on a suitable criterion. For a signal of length N, the signal can be projected onto a
maximum of log2N scales. For most signals it is adequate to go up to a scale (log2N)-3 [9].
6.4 Application wavelet analysis with partial discharge signal
As mentioned before, partial discharge signals are captured by the oscilloscope
Tektronix TDS3024B. The oscilloscope samples the signals and sends this information to
computer via Ethernet cable. So each data has 10000 samples with this kind of oscilloscope.
These data are saved in isf files.
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Fig. 6.4.1: Capturing data process
Fig. 6.4.2: Data captured from oscilloscope
In the figure 6.4.2, we have an example of data sent to computer from oscilloscope
TDS3024D via Ethernet cable. This data has 10000 samples, each sample represent the
magnitude of current pass through coaxial shunt resistor. Effectively, the data send to
computer has 10004 values (10004 samples). The first four values contain the configuration
information of oscilloscope. The first one is the total number of samples of data (this one is
always equal to 10000 which is the number of sample of data, see figure 6.4.2). The second
one is the sampling time. And two others values which show some other configurations.
Before starting the wavelet analysis, we must exclude these four values from data. It‘s very
simple with computer.
Ethernet cable
Numeric data With 10000 Samples (isf format)
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6.4.1 Wavelet analysis signals with MATLAB software.
To perform the wavelet analysis of partial discharge signals, we decided to use
MATLAB software.
MATLAB is a high-performance language for technical computing. It integrates
computation, visualization, and programming in an easy-to-use environment where problems
and solutions are expressed in familiar mathematical notation. Typical uses include:
Math and computation
Algorithm development
Modeling, simulation, and prototyping
Data analysis, exploration, and visualization
Scientific and engineering graphics
Application development, including Graphical User Interface building
MATLAB features a family of application-specific solutions called toolboxes. Very
important to most users of MATLAB, toolboxes allow you to learn and apply specialized
technology. Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems. Areas in which
toolboxes are available include signal processing, control systems, neural networks, fuzzy
logic, wavelets, simulation, and many others.
For our project, we must use ―wavelet toolbox‖ to analysis signal and ―neural network
toolbox‖ to classify the types of partial discharge.
Wavelet toolbox:
Wavelet Toolbox™ software extends the MATLAB®
technical computing
environment with graphical tools and command-line functions for developing wavelet-based
algorithms for the analysis, synthesis, denoising, and compression of signals and images.
Wavelet analysis provides more precise information about signal data than other signal
analysis techniques, such as Fourier.
The Wavelet Toolbox supports the interactive exploration of wavelet properties and
applications. It is useful for speech and audio processing, image and video processing,
biomedical imaging, and 1-D and 2-D applications in communications and geophysics.
There are two ways to use CWT (continuous wavelet transform) and DWT (discrete
wavelet transform). The first one is using command lines and the second one is using graphic
user interface of wavelet toolbox.
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6.4.2 Use command lines for the wavelet analysis.
The first step is launch MATLAB software:
Fig. 6.4.2.1: MATLAB’s interface I.4.2.1
The figure 6.4.2.1 shows the interface of MATLAB. There are 4 important parts:
I- Content of current folder
II- Interface used for typing command
III- Workspace: all variables and data which is used or created during the work
IV- History of all command typed
Second step of analysis process is to import data (signal captured from oscilloscope) to
MATLAB. Realize this by clicking to ‗menu‘ button, choose ‗import data‘, go to the folder
which contain the data of partial discharge signal and choose the data that we want to import.
The data will appear in the part III of MATLAB‘s interface
I II
III
IV
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Fig. 6.4.2.2: import the data ‘x1’
The figure above shows the importation of data ‗x1‘ to Matlab. The dimension of this
data is 10004 as mentioned above. We must exclude four first values before stating wavelet
analysis.
To exclude these four values we type this command in the part II of Matlab‘s
interface:
>> x1=x1(5:10004,:);
Fig. 6.4.2.3: exclude 4 first values of data
Now the data contain only 10000 values and we can start the wavelet analysis.
Continuous wavelet analysis
To realize the wavelet analysis, we use 2 command lines:
COEFS = CWT(S,SCALES,'wname','plot')
Where S is the name of signal example x1 in our case
SCALE is the range of scale that we want use for CWT example 1:20 (from 1 to 20)
Wname is the name of wavelet used for the analysis example db1, sym2 etc… [5]
‗plot‘ is one option to plot the coefficients generated by continuous wavelet transform
We can type >>help cwt to get more information about this command
This command sends back to us the coefficients of CWT
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For each wavelet analysis, the choice of wavelet is very important. Each wavelet will
give us a different result (because each segment of signal will be compare avec the shifted and
scaled version of wavelet). The suitable wavelet for one analysis is the one which is able to
generate the most coefficients with high value. In other word, suitable wavelet for the analysis
of one signal is the one which is correlated with the signal to analysis. So to choose the
suitable wavelet, we calculate the correlation coefficient between the wavelets and the signal.
The one, which give the best result, is the suitable wavelet. For our partial discharge signals,
db6, db7, sym7, sym8 can give good results and the Symlets 8 (sym8) was chosen as the best
compromise between the different similarity measures [9].
Fig. 6.4.2.3: symlets wavelet order 8
Once we have finished selecting the wavelet, we can realize our wavelet analysis
>>a=cwt(x1,1:60,‘sym8‘,‘plot‘);
We use this command line to realize continuous wavelet transform of ‗x1‘ with sym8
wavelet for scale coefficients coming from 1 to 60. All coefficients are saved in variable ‗a‘.
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Fig. 6.4.2.4: CWT of x1 using sym8 wavelet
In the figure 6.4.2.4, we can see the waveform of x1 and also the wavelet coefficients
of x1. For the high variation part of x1, we found that its corresponding coefficients are higher
than others part of signal. So with this we have also the information about frequency and time.
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Discrete wavelet analysis
To realize a discrete wavelet analysis, we can use the following command line:
[C,L] = WAVEDEC(S,N,'wname') for multi-level DWT
Where S is the name of signal to analysis
N is the level of decomposition
‗wname‘ is the type of wavelet used for analysis
We can type >>help wavedec to get more information about this command
This command will give us 2 variables C and L. What do these means?
C contains the coefficients of approximations and details. L contains the length of
coefficients of approximations, coefficients of details and signals.
Fig. 6.4.2.5: two level decomposition of a signal with 100 samples.
Figure 6.4.2.5 shows a simple example of DWT of signal with 100 samples. At first
level, there are 50 coefficients of approximation cA1 and 50 coefficients of detail cD1. At
second level, there are 25 coefficients of approximation cA2 and also 25 coefficients of detail
cD2.
In this case L will be a vector with 100 components. The 25 first components are the
coefficients of cA2, the 25 following components are coefficients of cD2 and the 50 last
components are coefficients of cD1.
C, in this case, is a vector of 4 components. The first component is the length of cA2 (number
of values of cA2 =25). The second component is length of cD2 (its value must be equal to the
first one). The third is length of cD1 (50) and the last one is length of S (100).
L= [a1 a2 …a25 a26 …a50 a51 … a100]
C= [25 25 50 100]
cD1 cD2 cA2
100
50 50
25 25
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Fig. 6.4.2.6: approximation and details of discrete wavelet transform 3 levels
This figure shows the decomposition at level 3 of signal ‗x1‘. We can see three details
(D1, D2, D3) and latest approximation (A3). The details contain the high frequencies
information (noise in this case) and approximation contains low frequencies information. We
can see that A3 is original signal without noise.
With 2 vectors C and L, we can reconstruct the coefficients of approximations and details of
each level via the following command lines:
cA3 = appcoef(C,L,'sym8',3); for the coefficients of approximations
cD3 = detcoef(C,L,3); for the coefficients of details
All information about this type of wavelet analysis is given in Wavelet toolbox (p.72 to
p.76).
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6.4.3 Using Graphic User Interface of wavelet toolbox
Another useful way to realize wavelet transform is to use Graphic User Interface of
wavelet toolbox. We don‘t have to type any command line to realize the analysis. All can be
done with windows and buttons.
The first step is to open the Graphic User Interface of wavelet by typing the following
command line:
>>wavemenu
Fig. 6.4.3.1: Graphic User Interface of wavelet toolbox
A window, like figure 6.4.3.1, will be opened. In this window, there are many type of
wavelet transform. For our case, we focus only on Wavelet 1-D (Discrete wavelet transform
1D) and continuous wavelet 1-D.
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Continuous wavelet transform (continuous Wavelet 1-D)
We can use the continuous wavelet analysis by clinking to the ‗Continuous Wavelet 1-
D‘ button of ‗wavemenu‘ figure. The following figure will be opened.
Fig. 6.4.3.2: CWT with Graphic User Interface
Wavelet analysis becomes very simple with Graphic User Interface (GUI). The Figure
6.4.3.2 shows the continuous wavelet transform with GUI. The continuous wavelet will be
realized via following steps:
Import data from ‗file‘ button.
Choose the family of wavelet that we want to use for the analysis.
Choose the range of scale.
Push ‗Analysis‘ button. The results will be shown as the figure 6.4.3.2
The figure 6.4.3.2 shows the coefficients of CWT of one partial discharge signal with
‗sym8‘ for scale come from 1 to 60.
We can also export the result of wavelet analysis from GUI to workspace and save it to
computer (See more details in Wavelet toolbox tutorial [5]).
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Discrete wavelet transform (Wavelet 1-D)
We can use the discrete wavelet transform by clicking to the ‗Wavelet 1-D‘ button of
‗wavemenu‘ figure. The following figure will be opened.
Fig. 6.4.3.3: DWT with graphic user interface.
The figure above shows the analysis of DWT via graphic user interface. The discrete
continuous wavelet will be realized via following steps:
Import data via ‗file‘ button. The signal will be plot on the first axe of Wavelet 1-D (s
in Figure 6.4.3.3).
Choose the kind of wavelet that we want to use ( sym8 in this example) and level of
decomposition (6 in this example)
Click to ‗analyze‘ button to get all coefficients of details and approximation
In this example, we took a discrete wavelet transform of one partial discharge (s) to
level 6 with sym8 wavelet. It gives us all details (d1 to d6) and approximation at level 6 (a6).
We can also export results from GUI to workspace and save them to computer. (See more
details in Wavelet toolbox tutorial more details).
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Conclusion
Wavelet analysis is a powerful processing tool to extract all information about signal.
The Matlab helps us to realize this analysis simpler. For our project, we use the discrete
wavelet analysis to generate details and approximation coefficients. Sym8 wavelet is used for
analysis thanks for the correlation between this one and partial discharge signal [6]. Our
signal has 10000 samples and the maximum level that we can decompose our signals is 9
(log2N-3=9) so we decompose all partial discharge data into 9 levels. The coefficients of
details and approximation will be used to classify all kind of partial discharge. The following
chapter will give more details about utilization of these coefficients.
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7 Artificial Neural Network (ANN)
The goal of our project is find out the defect in the transformer via the waveform of
partial discharge (PD) signals captured by oscilloscope. The PD signals will be analyzed by
discrete wavelet transform to generate wavelet coefficients. After, these coefficients will be
compared with a library to identify the kind of partial discharge.
Fig. 7.1: Process of recognition
To realize this recognition, two things are required Feature extraction and Feature
classification. In our project, DWT is used for the feature extraction and artificial neuron
network is used for method classification (Feature classification).
Feature extraction
Any pattern which can be recognized and classified possesses a number of
discriminatory attributes or features. Thus, the first step in any recognition process is to
consider the problem of what discriminatory features to select and how to extract these
features from the patterns. It is quite clear that the number of features needed for successful
classification depends on the discriminatory quality of the chosen features. The tools used for
selection of feature vector (a set of selected features) are generally application dependant.
Over the past couple of decades, several different approaches have been adopted for the
choice of features in PD pattern recognition. These different approaches can be broadly
grouped into the following methods/tools:
PD signal Captured by
oscilloscope
Feature extraction
Feature classification
Classification methods
Reference
Result
Kind of partial discharge
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statistical methods
pulse shape parameter approach
signal processing tools (Fourier transform, wavelet transform)
image processing tools and time-series approach
So these are some principal methods for feature extraction. Their details can be found
in [14].
Classification method
Once the feature vector is created, it will be sent to a classification method to
recognize the kind of defect that is the source of corresponding partial discharge. There are
quite a good number of classifiers available in the literature for pattern recognition. The
various approaches are based on: decision functions, distance functions, likelihood functions,
artificial neural networks, trainable classifiers etc. All the different classifiers proposed for PD
may be grouped as distance classifiers, statistical classifiers, ANN-based classifiers and fuzzy
logic based classifiers [15].
In this project, the signal processing tools with discrete wavelet transform is chosen for
feature vectors extraction and ANN (Artificial neural network) is chosen for classification
method. In the next chapter, the artificial neural network will be talked more in details and
also how the feature vectors are used.
7.1 Introduction of artificial neural network
An artificial neural network is a system based on the operation of biological neural
networks, in other words, is an emulation of biological neural system. Why would be
necessary the implementation of artificial neural networks? Although computing these days is
truly advanced, there are certain tasks that a program made for a common microprocessor is
unable to perform; even so a software implementation of a neural network can be made with
their advantages and disadvantages.
Advantages:
A neural network can perform tasks that a linear program can not.
When an element of the neural network fails, it can continue without any problem by
their parallel nature.
A neural network learns and does not need to be reprogrammed.
It can be implemented in any application.
It can be implemented without any problem.
Disadvantages:
The neural network needs training to operate.
The architecture of a neural network is different from the architecture of
microprocessors therefore needs to be emulated.
Requires high processing time for large neural networks.
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Another aspect of the artificial neural networks is that there are different architectures,
which consequently requires different types of algorithms, but despite to be an apparently
complex system, a neural network is relatively simple. There are 2 popular architectures:
Feed-forward neural networks, where the data from input to output units is strictly
feed-forward. The data processing can extend over multiple (layers of) units, but no
feedback connections are present, that is, connections extending from outputs of units
to inputs of units in the same layer or previous layers.
Fig. 7.1.1: Feed-forward neural network
Recurrent neural networks that do contain feedback connections. Contrary to feed-
forward networks, the dynamical properties of the network are important. In some
cases, the activation values of the units undergo a relaxation process such that the
neural network will evolve to a stable state in which these activations do not change
anymore. In other applications, the changes of the activation values of the output
neurons are significant, such that the dynamical behavior constitutes the output of the
neural network (Pearlmutter, 1990).
Fig. 7.1.2: Recurrent neural networks
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So the principal of all neural networks is: we put one set of value in inputs, the neural network
will take some calculation (depend on parameters of the neural network) and we obtain one
set of value in output. This method is very powerful for the classification.
All introduction and definition of neural network is given in the Annex 5. In summary, to
creating a neural network, we need the following steps:
Collect data for neural network
Extract the feature vectors
Define the number of input layer, output layer and hidden layer (if necessary)
Initial weights and bias between each connexion of ANN
Train the neural network to find the right values of weights and bias
Use the neural network
Return to our project, our goal is to identify the kind of partial discharge thanks to
information come from partial discharge signal. The process of our project is:
The discrete wavelet transform gives the feature vectors which are coefficients of
details and approximation (see chapter discrete wavelet transform). These feature vectors will
be sent to the input of neural network. The output of neural network is the kind of partial
discharge (kind of defect) corresponding to the inputs.
The neural network used for our project is Perceptron. The training algorithm is back-
propagation. The next chapter will talk in details the Perceptron neural network and also back-
propagation algorithm.
7.2 Perceptron neural network
Fig. 7.2.1: Simple Perceptron with one input and one output
Collect data from
oscilloscope
Feature extraction
DWT
Artificial neural
network
Kind of partial
discharge
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Perceptrons are the simplest architecture to learn when studying Neural Networking.
It‘s a kind of Feed-forward neural networks. Since making connections of perceptrons into
a neural structure is a bit complicated, let‘s take a perceptron by itself. A perceptron has a
number of external input pattern, one internal input (called a bias b), an activation function,
and one output. In the figure 7.2.1, you can see a picture of a simple perceptron with only one
external input unit (p), one weight (w) one activation function (f), one output (a) on the left
and the same with one bias (b) on the right. It resembles a neuron.
Fig. 7.2.2: Complete scheme of simple Perceptron
Figure 7.2.2 shows the complete scheme of a simple Perceptron with one input layers
and one output layers.
Usually, the input values are boolean (just two possible values 1 and 0, true and false),
but they can be any number. The outputs of the Perceptron can have value from 0 to 1 (it‘s
depend for activation function chosen).
All of the inputs (including the bias) have weights attached to the input patterns that
modify the input values to the neural network. The weight is just multiplied with the input.
There is another structure of Perceptron which is Multi-layers Perceptron.
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Fig. 7.2.3: Multi-layers perceptrons
The principal of multi-layer Perceptron (Figure 7.2.3) is the sample than simple
Perceptron. But with multi-layers Perceptron, there are 3 layers (input layers, hidden layers
and outputs layers). For some applications which are not possible with simple Perceptron, the
multi-layer Perceptron can give a better result. For our case, we use multi-layer Perceptron
The activation function is one of the key components of the Perceptron as in the most
common neural network architectures. It determines, based on the inputs, whether the
Perceptron activates or not. There are several activation functions like sigmoid function, step
function (threshold), linear function.
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Fig. 7.3.4: Activation functions of ANN
Figure above shows some activation functions frequently used and their symbols. For
each activation function, we can obtain a different result at the output of neural network.
Example, function threshold (‗pas unitaire‘) give only 2 values at the output (0 or 1). For
others functions, we can obtain a value coming from 0 to 1. For our artificial neural network,
sigmoid function is chosen.
7.3 The back-propagation algorithm
The back-propagation is a training algorithm used to adjust weight and bias of an
artificial neural network feed-forward (Perceptron in our case). When we create the neural
network, the weight and bias are initialized with random values. The back-propagation
algorithm will modify these weights and bias in order to minimize means square errors
between the inputs and outputs of neural network. To realize training with back-propagation,
an input vectors and a target vectors is needed.
To realize the training with back-propagation, we must differentiate 3 terms:
Input vectors: they are the vectors will be sent to inputs layer of neural network
Output vectors: they are the values at the output of neural network when the input
vectors is put in inputs layers (they are real values)
Target vectors: it‘s is the values that neural network must give at output when input
vectors is put in inputs layers (they are perfect values or target values).
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For example ‗p‘ is input vectors of neural network, ‗t‘ is target vectors of neural
network and ‗a‘ is the output vectors of neural network. The goal is minimize the cost
function F (means square errors) which is defined as:
Where Q is number of inputs vectors used for training phase. This minimization can
be done thanks to delta rules:
The algorithm LMS (Least Mean Squared) estimates the kth iteration the mean
square error e² by calculating the derived of mean square errors based on the weight and the network. Thus:
For j= [1…R] .R is the length of input vector
So we have equation
We can simplify the expression above by
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This means that the weights and biases of the network must change
Where α is the learning rate. In the case of multiple neurons, we can write
The expression (7.3.1) is the most important expression that we must to keep. The
following steps are needed for the training with back-propagation
Collect data for training (input vectors and target vectors)
Choose the learning rate α
Put each input vector to input layer
Calculate the output vector
Find out the error between target vector and input vector
If there is errors between target vector and input vector and this error is superior than
an accepted value, modify the weights and bias thanks to expression (7.3.1)
Repeat these steps until all errors are inferior to the accepted value.
This is the back-propagation used to train neural network feed-forward (Perceptron in
our case).
7.4 Artificial neural network created for partial discharge classification
To classify all kind of partial discharge, the multi-layer Perceptron is used. This
Perceptron contains:
One inputs layer
One output layer
One hidden layer
The activation functions used are sigmoid function
Inputs layer
The number of inputs layer is equal to length of feature vectors [17]. According to the
beginner of this chapter, we use discrete wavelet transform to extract feature vectors. Our
original signals have 10000 samples. We will decompose our signal up to level 9 with discrete
wavelet analysis. After this analysis, we will find 10000 coefficients of approximation (cA9)
and details (from cD1 to cD9). If these coefficients used directly for feature vector, the inputs
layer will have 10000 neurons. As we discussed before, one disadvantage of neural network is
‗Requires high processing time for large neural networks‘ (see chapter 7.1). So with 10000
neurons in inputs layer, computer needs a lot of time to make the calculations. So we need
reduce the number of neuron at inputs layer (the number of components of feature vector).
(7.3.1)
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By researching on the internet, we decided to use statistical method to reduce the
number of components of feature vector described in [9] [14]. The principal idea of this
method is that we will calculate four coefficients of statistic (means, variance, skewness, and
kurtosis) for all coefficients of details and approximation of each level.
For example x=[x1,x2,x3,…,xN], the definition of these four coefficients of statistic of
x are:
These coefficients can have expressions below:
Where η is means of x, ζ is variance of x, γ is skewness of x and κ is kurtosis of x
We calculate all means, variance, skewness and kurtosis of all details (from cD1 to
cD9) and approximation (cA9). In final, we can reduce to 40 (statistical coefficients of 9
levels of details and 1 level of approximation) of 10000 coefficients of DWT. Now, the
feature vectors have 40 components in place of 10000 components.
So with discrete wavelet transform and statistical method, we obtain the feature
vectors of 40 components. The inputs layer has 40 neurons
Hidden layer
Hidden layer is the intermediate layer between input layer and output layer. There
isn‘t formula to calculate the number of neuron of this layer. We must try with different
values and choose the values which give the best results. For our experience, with 20 neurons
(7.3.2)
(7.3.3)
(7.3.4)
(7.3.5)
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at hidden layer, we obtain a good result so we decided to create the neural network with 20
neurons at hidden layers.
Output layer
The output layer is the answer of neural network when there is a value (a feature
vector) put on input layer. The number of neuron of this layer is equal to the number of defect
that we have. If we have 3 defects (3 kind of partial discharge) the number of neuron of output
layer is 3. Now the question is how neural network will answer?
It‘s very easy, for each time, only one output (one neuron) of output layer is activated
(1) and others output is deactivated (0). For example the neural network has 3 outputs which
correspond to 3 types of partial discharge (type 1, type 2, type 3), the feature vectors of partial
discharge type 1 is put on input layer and in output of neural network, the output type 1 is
equal to 1 and others outputs are equal to 0. So we can conclude that this signal is type 1.
Test our analysis method.
To test our analysis method, we use 3 transformers with 3 differences defects. These
transformers are shows in the following figure:
Fig. 7.4.1: Transformers with different defects
The figure 7.4.1 shows transformers with different defects in inside. Type 1 is a voltage
transformer where the defect is resistor fat QZ13. Type 2 is also a voltage transformer where
the defect is resistor coated silicon. Type 3 is a current transformer with vacuum bladder. For
each type of defect, we captured 110 data. 100 data will be used to train the neural network
with back-propagation algorithm. Once the neural network is trained, we use 10 last data to
test our neural network.
In this test, we try to classify these 3 types of defects. So the output layer of our neural
network has 3 neurons.
Type 1 Type 2 Type 3
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Fig. 7.4.2: Perceptron created for our classification
The figure 7.4.2 shows the configuration of neural network used for our project. Once
it‘s created, we must train the neural network to make sure that it works correctly. For training
phase, we use the back-propagation algorithm and we must create the matrix of data and
target matrix for training phase. So what are these matrixes?
The matrix data for training phase is a matrix which contains all feature vectors of
partial discharge signals that we know which type they belong. See example below to
understand
A = x1 y1 z1
x2 y2 z2
x3 y3 z3
. . .
. . .
. . .
x40 y40 z40
So A contains 3 feature vectors x, y, z that we know in advance which type of partial
discharge they belong. For example x is type 1, y is type 2 and z is type 3.
The target matrix is the matrix which contains the answer (output desired, target
output) of each feature vectors in matrix of data used for training phase. For example, with
matrix of data which has 3 feature vectors x, y, z like the example above. The target data
corresponding to matrix A for training phase is:
T= 1 0 0
0 1 0
0 0 1
The first column of T shows that the first feature vector of A is type 1. The second
column of T shows that the second feature vector of A is type 2 and the third shows that the
third feature vector of A is type 3.
For training phase, we must have a matrix of data with a lot of feature vectors in order
to give a good result. As mentioned before, we use 100 data of each type of partial discharge
for training phase. We have 3 kind of defect so we captured totally 300 signals for training
phase. And the dimension of our data matrix is 40x300. The target matrix for training phase
x y z
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has a dimension of 3x300. These matrixes can be created thanks to matlab code in the Annex
6.
Once we created the data matrix and target matrix for training phase, we can create the
neural network and train this neural network thanks to neural network toolbox of Matlab.
These following steps must be respect to create, train and use the neural network thanks to
graphic user interface of neural network tutorial:
Type this command code in matlab windows >>nprtool. The following figure will be
opened
Fig. 7.4.3: graphic user interface of neural network toolbox
Click Next to proceed. The Select Data window will be opened. Select data matrix for
‗Inputs‘ and target matrix for ‗Targets‘ as the figure 7.4.4
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Fig. 7.4.4: data matrix and target matrix selection
When we finish the data selection, click Next to go to the Validation and Test Data
window.
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Fig. 7.4.5: Validation and Test Data window
Validation and testing data sets are each set to 15% of the original data. With these
settings, the input vectors and target vectors will be divided into three sets as follows:
80% are used for training.
10% are used to validate that the network is generalizing and to stop training
before over-fitting.
The last 10% are used as a completely independent test of network
generalization.
More details about this are given in ‗neural network toolbox tutorial‘ [17] (page 3-10).
Click next to continue
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Fig. 7.4.6: Network architecture
Choose the number of hidden layer (in our case it‘s is 20) and Click next to open the
train network window
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Fig. 7.4.7 Train network
Click ‗Train‘ to train our neural network. It will try to modify all weights values in
order to get a good result with data matrix and target matrix. The following window
will be opened.
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Fig. 7.4.8: Neural network training
So this figure shows the structure of neural network and also how neural network is
trained. We can click to the ‗Confusion‘ button to open the following window which is used
to see the performance of neural network
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Fig. 7.4.9: confusion table
This figure gives all confusion during the training phase, validation phase and test
phase. The neural network will be more performance if there are less confusions in training
phase validation phase and test phase [17]. In our case, there aren‘t confusions in any phase.
So our neural network is very performance.
Once the neural network is created and trained, we must save this neural in order to
able to test after.
If the result is satisfied, click next in train network windows. If the result isn‘t
satisfied click ‗retrain‘ to realize training (each training will give the differences
weights i.e. news results).
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Fig. 7.4.910: save result window
When the result is satisfied, we must save this neural, click to ‗Save Results‘ to save
the neural network to ‗workspace‘. His default name is ‗net‘. We can change this
name as we want.
Now the neural network is created and trained. We can use our neural network. How
to use this neural network?
The diagram above shows the wave to test/use our neural network. This network is
created to recognize 3 type of partial discharge. So now we will captured new signals of these
3 types of partial discharges (which is not use for training phase) and test to see if the neural
network arrive to recognize the type of partial discharges of these signal or not.
Captured data from
oscilloscope Signal with
10000 samples
Feature vectors extraction thanks
to DWT and statistical
method
Neural network
trained
Kind of partial
discharge
identified
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For each type of partial discharge, we captured 10 news signals. These signals will be
processed by DWT (discrete wavelet transform) and statistical method to obtain their 40
components used for input of neural network.
To test the neural network, we use this command:
>>sim(net,x1)
Where net is the name of neural network saved in workspace of Matlab and x1 is the feature
vector of signal that we want to test.
Fig. 7.4.11: test the neural network with the signal type 1
The figure 7.4.11 shows the test for the signals type 1. We can see that the first
component of output is 0.9998 which is very higher than others components of output, it
indicate that the signal belong to type 1.
Fig. 7.4.12: Test the neural network with the signal type2
The figure 7.4.12 shows the test for the signals type 2. We can see that the first
component of output is 0.9993 which is very higher than others components of output, it
indicate that the signal belong to type 2.
Fig. 7.4.13: Test the neural network with the signal type 3
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The figure 7.4.13 shows the test for the signals type 3. We can see that the first
component of output is 0.9993 which is very higher than others components of output, it
indicate that the signal belong to type 3.
For each kind of defect, 10 data was captured to test the neural network. These data
can be recognized without confusion. So the neural network created is very performance for
classification these 3 types of defect.
If we have more defect in the transformer, we must just captured the data of these new
defects and re-create (with larger layers in output) and re-train the neural network. After, the
neural network could recognize these defects.
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8 Graphic User Interface (GUI)
During our project, Matlab software was used to realize all our analysis (discrete
wavelet transform, statistical method and also artificial neural network). These analyses
require the knowledge about Matlab software and also utilization of command lines in
Matlab. It could be difficult for someone who wants to understand and use our method. To
help user to use our method simpler, we decide to create a graphic user interface which realize
our analysis method with window and button (not command line).We program this graphic
user interface in Matlab thank to GUIDE (Graphic User Interface development environment).
GUIDE, the MATLAB graphical user interface development environment, provides a
set of tools for creating graphical user interfaces (GUIs). These tools greatly simplify the
process of designing and building GUIs. We can use the GUIDE tools to perform the
following tasks:
Lay out the GUI.
Using the GUIDE Layout Editor, we can lay out a GUI easily by clicking and
dragging GUI components—such as panels, buttons, text fields, sliders, menus, and so
on—into the layout area. GUIDE stores the GUI layout in a FIG-file.
Program the GUI.
"GUIDE automatically generates a MATLAB program file that controls how the GUI
operates. The code in that file initializes the GUI and includes function templates for
the most commonly used callbacks for each component—the commands that execute
when a user clicks a GUI component. Using the MATLAB editor, we can add code to
the callbacks to perform the functions you want.
Graphic User Interface created for the partial discharge recognition
To realize an analysis with Graphic User Interface of partial discharge, we need these
following steps
Open Matlab software
Change the current folder to the ‗partial discharge‘ folder (this folder contain the
program of graphic user interface of partial discharge).
Type >>partialdischarge at the command line and the following window will be
opened
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Fig. 8.1: Graphic User Interface of partial discharge
This window is the Graphic User Interface of partial discharge that we create to
analyze the partial discharge signals thanks to DWT and neural network. In this window we
can:
Click to images to visit the website of TRENCH Company and INSA
Click to ‗help‘ button to open ‗Help Partial Discharge‘ window. It will generate the
pdf files which explain how to use DWT, neural net work and also how to use this
Graphic User Interface. Choose the document that you want to read and click ‗Ok‘
button, this document will be opened.
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Fig. 8.2: Help Partial Discharge Analysis window.
Click to Start Analysis to start our analysis. The following window will be opened
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Fig. 8.3: graphic user interface of partial discharge analysis
Figure above shows the graphic user interface (GUI) of our partial discharge analysis process.
With this GUI, we can:
Create new neural network with new data and use the neural network created
Choose one neural network exited from a folder and utilize the neural network chosen
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Create new neural network with new data
This chapter shows each steps to create a new neural by using our process.
The first step is to collect the data needed for the analysis (the waveform data of each defect).
These data is captured from oscilloscope via computer connection (see the chapter Artificial
Neural Network).
For example we have 3 defects which can produce the partial discharge phenomena. So we
want classify this 3 types of defects. The first thing we must do is create 3 samples which
represent these 3 defects. We measure the partial discharge of these 3 samples. For each
sample (each type of defect), we capture several measurement (example 20 or 50
measurement for each sample) to computer. Normally with Tektronix oscilloscope, the
measurement will be saved in ‗isf‘ format. We put all measurement of the same sample in a
folder specific.
Fig. 8.4: folders where all measurement are saved
In the figure above, we can see 3 folders which contain the measurements of 3 samples. Each
folder contains the measurements of one sample (the ‗isf‘ files).
The second step is to select the data to GUI of partial discharge. Open GUI of partial
discharge and use the ‗select data for a new neural network‘ to select data.
Fig. 8.5: select data to create a new neural network
To select the data to create a new neural network, we must following these steps:
Enter the total number of defect that you want to classify in case ‗total number of
defect (3 in our example)
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You enter the type of defect that you want to select now (1 or 2 or 3 in our example) in
the case ‗Type of defect‘. These numbers must be entered with care because it will
change completely our result.
Click ‗Data Select‘ to select the data. A select window will open and we go to the
folders where there are the data of the type of defect typed in case ‗type of defect‘.
Fig. 8.6: Window used to select data
Click ‗Ouvrir‘ to select data (in the figure 8.6, ten data of defect type 1 are selected)
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Fig. 8.7: Data selected
Figure 8.7 shows the result of selection of data type 1. In case ‗Description‘ we will see the
dimension of matrix input is 10000x10 because we selected 10 data of defect type 1 (each
data has 10000 values). The matrix output is created for the neural network. The case ‗Display
data‘ displays all data select for analysis. We repeat these steps to select data for others type
of defect.
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Fig. 8.8: data of all 3 types of defect selected
Figure 8.8 shows that the data of 3 types of defect are selected (10 data of each type of defect
are selected). The matrix input contains the waveform data (see type of data).
The third step is use wavelet analysis to create the feature vector data corresponding for each
waveform data. Use the case ‗Wavelet analysis‘ to realize this step. In this case, we can
choose different type of wavelet for analysis (the wavelet symlet 8 is recommended). When
we finish the choice of wavelet, we click to the ‗Wavelet Analysis‘ button to realize the
discrete wavelet transform at level 9 (see Chapter Wavelet transform).
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Fig. 8.9: Wavelet analysis withi GUI of partial discharge
The figure 6 shows the result of wavelet analysis. In case ‗description‘ we can see that the
dimension of input matrix is 40x30 in place of 10000x30 in figure 8.8. The input matrix
contains now feature vector data. This is the result of wavelet analysis + statistical method
(see Feature Vector in Chapter Artificial Neural Network). The box ‗Display data‘ displays
the coefficients of new input matrix. Now we have the input matrix and output matrix for
neural network. The next step is to create the neural network.
Use the case ‗Neural Network analysis‘ to create new neural network. Our neural network has
3 layers
Input layer configured by input matrix
Output layer configured by output matrix
Hidden layer configured by user. So you must enter the number of hidden layer to
create new neural network (20 is recommended by our experience)
When we entered the size of hidden layer, we need to click the ‗create new neural‘ button to
create a neural network. A neural network will be created and a window will be opened.
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Fig. 8.10: Neural network training
This figure shows the result of training phase. Click ‗confusion‘ button to see the result of
neural network (see neural network toolbox or chapter Artificial Neural Network to have
more information). If the result is not good, click ‗create new neural‘ button again to retrain
the neural network. If the result of neural network is good, we can close the ‗Neural Network
Training‘ window (figure 7) and use this neural now.
Now when the network was created, we can:
Save this neural network to our current folder by typing the name that you desire to
save in box ‗name of neural network to save‘ and click ‗save the neural network‘
button. A mat file will be create in our current folder and contains the new neural
network.
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We can use directly this neural network to test by clicking ‗choose data for test‘ in
‗Test Panel‘ box. This button will allow us to select new data for test. For example we
want to know one object which has which type of defect. We must captured some
partial discharge data of this object from oscilloscope (We must capture several data,
only one data is not accepted because with more data, the result will be more
accurate).We select these data thanks to ‗choose data for test‘ and after the result will
be appear in ‗Description‘ box.
Fig. 8.11: Select data for test
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Fig. 8.12: Result of test
Figure 8.12 shows the result of test with some data of type 1 (we selected 5 data of defect type
1). The ‗Description‘ box shows that the defect is the type 1. So the neural network works.
The ‗Display data‘ shows the feature vector of all data selected for test.
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Choose one neural network existed from a folder and utilize the neural network chosen
To choose a neural network existed from a folder, we use the ‗choose an existed neural‘
button (Figure 8.12). This button allows us to select one neural created before.
Fig. 8.13: Select a neural network existed before.
This figure shows the window used to select a neural network. We go to the folder which
contains the neural network that you want to select. We choose the network and click ‗Ouvrir‘
(In figure 8.13, net1 was chosen). The neural network will be import to workspace of Matlab.
Now we can use this neural network to test. To analyze with this neural network, you use the
‗choose data for test‘ button like the chapter before.
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9 Conclusion
For the measurement part, with the filter created, we arrive to eliminate the 50 Hz
signal. Without this signal, the partials discharges are simpler to captured and simpler to
analysis.
The problem of reflexion and oscillation frequency modifies our partial signal signals.
And we can obtain wrong signals. By adapting the impedance in function of coaxial cable we
eliminate the reflexion phenomena and by reducing the loop of measuring circuit we can
attenuate the oscillation frequency.
The discrete wavelet transform is chosen to analysis partial discharge signal because it
gives us all information about time and frequency. This analysis is more suitable than Fourier
transform for the type of partial discharge which is the signals with very fast variation in a
very short time.
The statistical method is used to reduce the number of coefficients used for neural
network. It will reduce the analysis time of neural network and also gives more accurate
results (so many coefficients require many weight and the neural network becomes more
difficult to train).
The neural network classifier is chosen thank to its advantages, the Perceptron neural
network is used for the analysis. The back-propagation is used to train our neural network.
The results of neural network created for 3 types of partial discharge are 95% so the neural
network works perfectly. So the problem now is just to identify all type of defect can be take
place in the transformer. Create the samples which have only one defect a time. Test these
samples and training the neural network with more output (more type of defect) and after we
can use this neural network to identify an unknown defect in the transformers.
During this final year project, we has discovered a lot of new theory about the
difficulties of measurement process, the problem of transmission at high frequencies, the
wavelet analysis and also the neural network which are very important for our professional
life in the future.
We want to thank Mr MINKER, Mr SMIGIEL our supervisors. They help us a lot to
understand many thing and also to solve all problem that we had during our project. We want
also to thank all people in TTT department of TRENCH Company for their help during our
project.
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References
[1] Hans Edin, ―Partial Discharge Studied with Variable Frequency of the Applied
Voltage‖, 2001, pp. 12.
[2] E. Kuffel, J.Kuffel, W.S. Zaengl, High Voltage Engineering – Fundamentals – Second
Edition, 2000
[3] Guide for Partial Discharge Measurements in Compliance to IEC 60270 – December 2008
[4] Cours 1998 de C. Brielmann Leitungstheorie, G. S. Moschytz, U. Brugger et J. Rosenblatt
– ‗Transmission sur lignes‘
[5] ‗Wavelet toolbox‘- Matlab -http://www.mathworks.com/help/toolbox/wavelet/
[6] ‗Standing wave‘- http://en.wikipedia.org/wiki/Standing_wave
[7] ‗Wavelets and Filter Banks‘, by Strang and Nguyen, P.1
[8] ‗Wavelets and Filter Banks‘, by Strang and Nguyen, P.91
[9] D. Evagorou, A. Kyprianou, P.L.Lewin, A. Stavrou, V. Efthymiou, A.C. Metaxas, G.E.
Georghiou ‗Feature extraction of partial discharge signals using the wavelet packet transform
and classification with a probabilistic neural network‘- IEEE, p.8
[10] ‗Wavelet tutorial‘ http://polyvalens.pagespersoorange.fr/clemens/wavelets/wavelets.html
[11] Sheng, Y. ‗WAVELET TRANSFORM’. In: The transforms and applications handbook.
Ed. by A. D. Poularikas. P. 747-827. Boca Raton, Fl (USA): CRC Press, 1996. The Electrical
Engineering Handbook Series.
[12] Mallat, S. G. ‗A THEORY FOR MULTIRESOLUTION SIGNAL DECOMPOSITION:
THE WAVELET REPRESENTATION’. IEEE Transactions on Pattern Analysis and Machine
Intelligence, Vol. 11, No. 7 (1989), p. 674- 693.
[13] Burrus, C. S. and R. A. Gopinath, H. Guo. ‗INTRODUCTION TO WAVELETS AND
WAVELET TRANSFORMS, A PRIMER’. Upper Saddle River, NJ (USA): Prentice Hall, 1998
[14] N. C. Sahoo, M. M. A. Salama. ‗Trends in Partial Discharge Pattern Classification:A
Survey’. p3 –p7
[15] N. C. Sahoo, M. M. A. Salama. ‗Trends in Partial Discharge Pattern Classification:A
Survey‘. P7 –p12
[16] http://www.learnartificialneuralnetworks.com/#Intr
[17] Neural network toolbox tutorial, http://www.mathworks.com/help/toolbox/nnet/
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[18] D. Evagorou, A. Kyprianou, P.L.Lewin, A. Stavrou, V. Efthymiou, A.C. Metaxas, G.E.
Georghiou ‗Feature extraction of partial discharge signals using the wavelet packet transform
and classification with a probabilistic neural network‘- IEEE, p.8
[19] Standard IEC 60270:2000-12 ―High-voltage test techniques – Partial discharge
measurements‖. Publication of Dr. MINKNER
[20] A coaxial shunt 14 ohms. The R&D department borrowed it from Prof. Ing. A.
RODEWALD from the university of applied Sciences in Muttenz/BL/CH
[21] Wavelet transform: http://en.wikipedia.org/wiki/Wavelet_transform
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