Ir thermography

ELECRICAL SYSTEM FAULT DIAGNOSIS USING
INFRARED THERMOGRAPHY
A PHASE-I PROJECT REPORT
Submitted by
PRIYADHARSINI. S (090107126063)
SHIYAM DHARSAN.R.P (090107126077)
SUJITH KUMAR.B (090107126084)
YOGAPRIYA.M (090107126097)
In partial fulfilment for the award of the degree
of
BACHELOR OF ENGINEERING
in
ELECTRONICS AND COMMUNICATION ENGINEERING
SRI SHAKTHI INSTITUTE OF ENGINEERING
AND TECHNOLOGY,
COIMBATORE-641062
ANNA UNIVERSITY : CHENNAI-600 025

TABLE OF CONTENTS
CHAPTER
NO.
TITLE PAGE NO.
LIST OF FIGURES
ACKNOWLEDGMENT
i
ii
ABSTRACT iii
1.
2.
INTRODUCTION
1
2.1 Introduction 3
2.2 Thermography 4
2.3 Advantages of thermography 5
2.4 Limitations and disadvantage of thermography 6
2.5 2.5 Spectral distribution of radiation intensity of black
Body using Planck’s equation
6
2.6 2.6 Infrared Thermography in Condition Monitoring of
Electrical Equipment
7
2. 2.7 Thermographic camera 8
2.8 Most common errors in thermographic measurement 11
2.9 Finding Hot Spots 11
2.10 Challenges Faced During Infrared
Thermography Of Electrical Equipment
11
3. LITERATURE SURVEY 17
4. PROJECT DESCRIPTION
4.1 Block diagram of the system used for inspection of
equipment
20
4.2 Input Image
4.3 SIFT Algorithm
21
5. SIMULATION RESULT AND CONCLUSION

5.1Simulation result 24
REFERENCES 26

NAME OF THE FIGURE
1.Thermogram of loose connection
2.Thermal image of electrical contact
3.Electromagnetic spectrum
4.FLIR i7 camera
5.Block diagram of the system used for inspection
of equipment
Output
PAGE NO.
5
9
10
11
12
24

ABSTRACT
An automatic diagnosis system is proposed in this project for a more and more
important issue, preventive maintenance. Every year, various workplace accidents
happen due to undesirable maintenance. No matter how stringent the rules governing
the maintenance of electrical equipment may be, it is always a challenge for the power
industry due to the large number of electrical equipment and the shortage of
manpower. In this project, an automatic diagnosis system for testing electrical
equipment for defectsis proposed. Based on non-destructive inspection, infrared
thermography is used to automate the diagnosis process. Thermal image processing
based on statistical methods and morphological image processing technique are used
to identify hotspots, the reference temperature and cause for defects. The problematic
area is captured using thermal camera. The repeated objects are detected by using
feature detection algorithm like SIFT. Once the repeated objects are identified, their
real time temperature are measured using thermal software. By comparing the real
temperature of repeated objects, the fault area is localised and the reason for fault is
identified using Artificial Neural Network. Here we used Levenberg – Marquardt
Algorithm which comes under Back Propagation technique. The thermal diagnosis
system to be implemented by this project can be used at the various power facilities to
improve inspection efficiency as the reason for the defect can be identified.

CHAPTER-1
INTRODUCTION
In the power system, there are many kinds of electrical equipments such as circuit-
breaker, transformer, lightningarrester, capacitor, current and potential transformer,
bushing, and insulator and so on. These equipment play animportant role in power-supply
system. Unfortunately, some nasty faults often happen to the electrical equipment because
of a variety of reasons, and they are seriously imperilling the safe operation of electric
power production.Therefore, a great cost is paid for preventive test to remove hidden
dangers in power system. In recently years, withthe fast development of infrared
technology, infrared thermography technique is in great advantages of diagnosing electrical
equipment with faults. By means of getting the thermography of electrical equipment
withouttouching, one can judge whether the equipments is in good or not by analyse the
thermal distribution of these equipment. It is proved by practice that infrared thermography
diagnosis has become the necessary andeffective supplementary measure of the preventive
test to the electrical equipment.
It can be divided into two kinds of faults attribute according to the location of the
faults of electricalequipment, the external and internal faults. Asfar as infrared
thermography diagnosis, the external faults showmainlythe overheatof connectors, and they
are easy to be discerned. However, the internal faults are difficult to bepenetrated because
internal faults are much more complex. To find out the internal faults, one must know the
law of the internal faults attribute to the relation of their infrared thermography
characteristics. The internal faults of the electrical equipment can be divided into loose
connection or contact of internal conductors and inferiority in insulation and other faults. In
order to know the law of infrared thermography diagnosis to electrical equipment with
internal faults, on the basis of the electrical equipment simulation test and the experience by
infrared thermography diagnosis to a great many substations, we sum up a few technique
problems of infrared thermography diagnosis to the electrical equipment, with internal
faults and show some typical examples thermographies of electrical equipment with
internal faults.

By automating the inspection process, the problem of time wastage and manual
involvement in the inspection process can also be done away with. Thus, this project
proposes an automatic diagnosis system fo1r testing electrical equipment for defects. For
this purpose Scale invariant feature transform (SIFT) algorithm is used. The defective parts
are detected by determining which of these areas on the infrared images are with higher
temperatures than the normal prescribed levels. Inspection results are classified into
different categories depending on the levels of temperatures detected that tell the power
companies the seriousness of each situation in each of these areas.
Thermal inspection of the electrical equipment can reveal various types of problems
in electrical installations. In recent years, the use of thermal imaging or infrared
thermography has become an important tool in preventive and predictive maintenance. It is
a useful method for inspecting the condition of electrical equipment. Thermal imaging
inspection is well known as a non-contact measurement technique where the inspection can
be done without interrupting or shutting down the operation of a system. It is a safe, reliable
and very cost-effective approach for a maintenance programme.

CHAPTER 2
INFRARED
THERMOGRARHY

CHAPTER 2
2.1.Introduction
In 1800, astronomer Sir William Herschel discovered infrared, and thus began
the exploration of the science of thermography. Sir William designed and created his own
telescopes - becoming very familiar with lenses, mirrors and light refraction. His
thermography research began with the knowledge that sunlight was made up of all the
colours of the spectrum, and that it was also a source of heat, so he set out to determine
which colours were responsible for heating objects. The first thermography experiment
utilized a prism, paperboard, and thermometers with blackened bulbs where the
temperatures of the different colours were measured. As sunlight passed through the prism,
Sir William observed an increase in temperature as he moved the thermometer from violet
to red in the rainbow created by the light. Herschel noted that the hottest temperature was
actually beyond red light, and that the radiation causing this heating was invisible. He
called this invisible radiation “calorific rays." Today, we refer to the light/energy as
infrared, and the measuring of the heat emitted as thermography.
Infrared Thermography is simply a picture of heat. All the bodies emit energy from
their surface as electromagnetic waves, which magnitude is directly related to their
temperature. The hotter the object is, the more energy it tends to radiate. Such temperature
settles the wavelength of the emitted energy, the colder the object is, the higher its
wavelength will be, whereas the hotter it is, the lower its wavelength will be. This last case,
is the one of the infrared energy, non visible to the human eye, but visible by means of an
infrared camera.

The radiation measured by the infrared camera depends not only on the temperature
of the object but also on its emissivity. The radiation coming from the surrounding area and
reflected on the object also influences the measuring. Therefore, to measure the temperature
accurately, besides the effects of different sources of radiation that interact with the object,
other variables such as emissivity, distance between the camera and the object scanned,
environment temperature and humidity, must also be considered. In addition, due to the
characteristics of the infrared radiation, to detect any overheating by IR scans, the heat
generated must be “directly” in sight of the thermographer.
2.2 Thermography
Thermography is one of the most powerful tools available for electrical maintenance.
With professional training and some experience a thermographer can quickly locate high
resistance connections,load imbalance and overloads while the system is in operation. This
can all be accomplished without direct contact to the energized system.
Electrical inspections have typically produced remarkable returns, with documented
returns of 30 to 1 on the part of a major industrial insurer. Prevention of catastrophic failure
and unscheduled outages often results in cost savings far in excess of the cost of the test
equipment and program.
Today’s economic climate, however, demands even greater assurances for reliability
from maintenance thermographers from past. Experience can reveal the inspection
program’s successes and limitation.
Some limitations to thermographic tests of electrical equipment are quite obvious.
Some problems are inherent to laws of physics and must be lived with or worked around.
Others are related to environmental or operating conditions. The latest infrared test
equipment is no longer a limiting factor; it will do more than usually needed. But
inadequate data collection procedures and a poor understanding of how to use the
information gathered are very much limiting factors.

IR film is sensitive to infrared (IR) radiation in the 250°C to 500°C range, while the
range of thermography is approximately -50°C to over 2,000°C. So, for an IR film to show
something, it must be over 250°C or be reflecting infrared radiation from something that is
at least that hot. Night vision infrared devices image in the near-infrared, just beyond the
visual spectrum, and can see emitted or reflected near-infrared in complete visual darkness.
Starlight-type night vision devices generally only magnify ambient light.
Figure:1 Thermogram of loose connection
Infrared thermography is generally classified in two types, passive and active
thermography,
In passive thermography, the temperature gradients are present in the materials
and structures under tests naturally. One of the applications of passive thermography is for
preventive and predictive maintenance.
In active infrared thermography, the sample is heated by an external controlled
heat sourceand its surface temperature is monitored as a function of time through changes
of emittedinfrared radiation.
2.3 Advantages of thermography
 It shows a visual picture so temperatures over a large area can be compared
 It is capable of catching moving targets in real time
 It is able to find deteriorating, i.e., higher temperature components prior to their failure

 It can be used to measure or observe in areas inaccessible or hazardous for other
methods
 It is a non-destructive test method
 It can be used to find defects in shafts, pipes, and other metal or plastic part.
 It can be used to detect objects in dark areas
2.4 Limitations and disadvantages of thermography
 Quality cameras often have a high price range (often US$6,000 or more)
 Images can be difficult to interpret accurately when based upon certain objects,
specifically objects with erratic temperatures, although this problem is reduced in active
thermal imaging
 Accurate temperature measurements are hindered by differing emissivities and
reflections from other surfaces
 Most cameras have ±2% accuracy or worse in measurement of temperature and are not
as accurate as contact methods
 Only able to directly detect surface temperatures
2.5 Spectral distribution of the radiation intensity from a black body using Planck
equation
Planck derived the law as in equation (1), which describes the spectral distribution of
theradiation intensity from a black body where the emissivity of the surface, ε is equal to 1
(Holst, 2000).
𝜀𝜆𝑏 =
𝐶1
𝜆5(𝑒
𝐶2
𝜆𝑇 −1)
𝑊
𝑚2−𝜇𝑚
(1)
Where 𝜀𝜆𝑏 is the black body monochromatic radiation intensity, C1 (3.7411 x108 W-
μm4/m2) and C2 (1.4388 x104 μm-K) are the first and second radiation constants
respectively; λ is the wavelength of the radiation being considered and T is the absolute

temperature of the blackbody. By integrating Planck’s law over the entire spectrum (λ = 0
to ∞), the total hemispherical radiation intensity is obtained.
𝜀 𝑏 = 𝜎𝑇4
(2)
where ζ is the Stefan–Boltzmann constant (5.67051 x 10-8 W/m2K). It has to be pointed
out that equation (2) describes the radiation emitted from a black body which is the
maximumvalue radiated by a body at a given temperature. Real objects almost never
comply with thislaw although they may approach the behaviour of a black body in certain
spectral intervals.A real object generally emits only a part ελ of the radiation emitted by a
black body at thesame temperature and at the same wavelength. By introducing the
quantity,
𝜺 =
𝜺 𝝀
𝜺 𝝀𝒃
(3)
which is called the spectral emissivity coefficient, equation (2) can be rewritten for real
bodies by simply multiplying its second term by ελ. When averaged over all wavelengths,
the total power density for a non-black body object is [1]
𝑒𝑚𝑖𝑠𝑠𝑖𝑣𝑖𝑡𝑦 = 𝜀𝜎𝑇4
(4)
2.6 Infrared Thermography in Condition Monitoring of Electrical Equipment
All electrical devices are usually rated for power, which indicates the amount of
energy that the devices can conduct without being damaged. If the device is operated at a
power above its specifications, the excess power can reduce the device's life cycle and
efficiency. Basically, faults in electrical power system can be classified into few categories,
i.e., poor connection, short circuit, overloading, load imbalance and improper component
installation. In most cases, the major cause of overheating in utility components is the
change in resistance due to loose connection. The loose connection causes electricity to use
smaller area of the defective connection than required for proper current flow and therefore,
increases the resistance and temperature of the connection. Any problem, which
accompanies a change in resistance of the equipment, causes it to consume morepower than
the intended load.

According to a thermographic survey, it was found that 48% of the problems were
found in conductor connection accessories and bolted connections. This is mainly resulted
from the loose connection, corrosion, rust and non-adequate use of inhibitory grease. On the
other hand, 45% of the thermal anomalies appear in disconnectors contacts. Mostof the
anomalies are due to deformations, deficient pressure of contact, incorrect alignment of
arms and dirtiness. Only 7% of the problems were found in electrical equipment.
Another major cause of overheating in electrical components within the structure is
overloading. Through IRT camera, the sign of overloading can be seen clearly even if the
cable was located deep into the concrete where the red region which has high temperature
value covered all parts of the components or cables. By utilizing IRT technology, the
thermal image will clearly indicates the problematic area. The suspected area can be easily
identified and interpreted. Nevertheless, in some cases, the interpretation of thermographic
image cannot be done directly except for an experienced and qualified thermographers.
2.7 Thermographic cameras
A thermographic camera or infrared camera is a device that forms an image using
infrared radiation, similar to a common camera that forms an image using visiblelight.
Instead of the 450–750 nanometer range of the visible light camera, infrared cameras
operate in wavelengths as long as 14,000 nm (14 µm). In 1929, Hungarian physicist
Kalman Tihanyi invented the first infrared-sensitive (night vision) electronic television
camera for anti-aircraft defense in Britain. The first conventional IR camera, the
"Evaporograph", was declassified around 1956.
Thermal imaging cameras convert the energy in the infrared wavelength into a
visible light display. All objects above absolute zero emit thermal infrared energy, so
thermal cameras can passively see all objects, regardless of ambient light. However, most
thermal cameras only see objects warmer than -50°C.

Figure 2: Thermal image of electrical contact
Theory of operation
All objects (even cold ones) radiate heat in the form of infrared energy. As an
object heats up, it radiates more energy, and the wavelength gets shorter. Infrared radiation,
visible light and ultraviolet light are all forms of energy in the electromagnetic spectrum.
The only difference is their wavelength.
Figure 3:Electromagnetic spectrum
The human eye can only see a small range of colours in the electromagnetic
spectrum. These light waves range in length from 0.4 to 0.7 microns. If an object gets hot
enough, the energy will reach the visible range and the object will be “glowing” red, like
the burner on an electric stove. Fortunately, infrared imaging systems can detect infrared
energy long before it reaches the visible stage.
The camera-like device then converts these invisible light waves into a graphic
image that is displayed on a monitor. Modern infrared cameras also provide actual
temperature readings, and store the data, so that the information can be later used to

produce a report. However, gathering the information is the easy part. The real work and
value is what the thermographer can do with the data that is gathered. As in any form of
non-destructive testing, the interpretation of the finding takes both education and
experience.
FLIR camera
The FLIR i7 thermal imaging camera is an extraordinary tool for detecting
structural problems (or potential problems) with heavy equipment, motors, pumps,
buildings, circuit breakers, cooling systems, and much more .
When equipment and/or structural integrity begins to malfunction, all heck can
break loose, often resulting in a loss of productivity or worse, bodily harm.
Professionals and homeowners alike can take comfort in knowing that a powerful
diagnostic tool like the FLIR i7 thermal imaging camera can save them from this fate by
detecting miniscule temperature variations.These variations can quickly and easily identify
any pipe or duct leaks, cracked or loose seals, electrical failures, mechanical breakdowns,
moisture issues, insulation scarcity, and so much more. With the help of FLIR i7 infrared
camera , the problem in contractor repairs, heating and cooling systems, pumps, circuit
breakers, transformers, motors, building structures can be identified.
Figure 4: FLIRi7 camera
The FLIR i7 thermal imaging camera is at the high end of entry level IR
cameras. With a resolution of 120 x 120 pixels, this particular camera can be used to
identify a variety of structural and mechanical problems before they escalate into full-blown

crises. The compact size of the FLIR i7 camera, along with its light 12-ounce body and
ultra powerful infrared capabilities, make it among the most sought-after thermal imaging
units in today's marketplace. The unit boasts a visually appealing 2.8" LCD color display,
and can store up to 5000 high-quality JPEG images. Additionally, the i7 is incredibly
accurate. It has an accuracy of plus or minus 2 percent, along with a temperature
measurement sensitivity of 0.1 degrees C. This is essential for monitoring the condition of a
thermally sensitive target.
2.8 The most common errors in thermographic measurements
To accurately measure the temperature distribution on the body of electrical machines, it
is necessary to separate the influence of wished sources from disturbances that have to be
compensated. In order to do this automatically, the camera must be informed of the
following parameters:
 the atmospheric temperature,
 the distance between the object and the camera,
 the relative humidity,
 the emissivity of the object.
2.9 Finding the "Hot Spots"
Infrared thermography is a non-destructive technique for detecting “hot spots,”
which are temperature differentials that may indicate problems such as loose electrical
connections or excessive friction in machinery and mechanical systems. Other uses for this
technique include finding defective or leaky steam traps and clogged steamed lines, as well
as many other conditions which can lead to failure or energy loss.
Infrared thermography utilizes a camera-like device which views a large area at
a time, senses infrared emissions and converts the emissions into a visual display. Large
quantities of equipment are scanned while in operation, so production need not be

interrupted. Trouble spots can be pinpointed quickly, saving labour and cost and targeting
plant maintenance resources where they are needed.
2.10 Challenges Faced During Infrared Thermography of Electrical Equipment
When performing an infrared inspection of an electrical system it is important to realize
that all of the radiation leaving a surface is not due solely to the temperature of the surface.
Unless knowledge, understanding and caution are applied during the analysis portion of the
inspection, documentation and interpretation may result in the false conclusion that a fault
does or does not exist.Wesum up a few technique problems of infrared
thermographydiagnosis to the electrical equipment, with internalfaults andshow some
typical examples thermographies of electrical equipment with internal faults. They are loose
connection or contact of Internal conductors,Inferiority in Internal Insulation of Electrical
Equipment, etc.,
Loose connection or contact of internal conductors
It will lead to the resistance increasing and overheat in the action of the current
when some internal conductors arein loose connection or contact. The heat power conforms
to the low of P=I’R (where P is the heat power, I is thecurrent passes through the conductor,
and R is the contact resistance of the conductors). Although the heat source ofthis kind of
faults is in the internal of equipment, the external of equipment will show overheat
somewhere because of the action of the thermal transmission. Therefore, compared with
the thermography of normal equipment, the thermography of this kind of faults will show
the characteristic of local overheat somewhere of the equipment. This kind of faults often
take place in the contacts of circuit-breaker and primary internal connection of current
transformer and bushing and cable splice in internal connection of conductors. this kind of
faults can be found out by the Characteristic of their thermographies
a) Loose contact of internal contacts of short coil circuit
The loose contact of internal contacts of short coilcircuit-breaker shows mainly
the loose contact of the uppercontact or intermediate contact. Either of them will lead

to overheat of the circuit-breaker, but their pattern of theoverheat are different. When the
upper contact is in loosecontact, the infrared thermography shows the temperature of its
header is the highest, then the basal stump flange,and the intermediate porcelain bushing is
the lowest.
b) Loose connection of primary internal connection of current transformer
When the primary internal connection of the currenttransformer is in loose
connection, it will lead to currenttransformeroverheat under the action of the current.
Thethermography of the current transformer shows thecharacteristic of the header of the
current transformer isoverheat while the porcelain body is almost normally.
c) Loose connection of the internal outlet terminal of high- voltage bushing header
When the internal outlet terminal of bushing header isin loose connection, it will
lead to the bushing headeroverheat under the action of the current. The thermography
of the bushing shows the characteristic of the bushingheader is the heating center while the
body of the porcelainbushing is basically in normal.
d) Loose connection of internal conductors of cable splice
When a phase of cable splice is in loose connection of internal conductor, the
cable splice will be overheat. Thethermography of the cable splice will show the
characteristic of local overheat, and the heat centre is in the forked of the phase.
Inferiority in Internal Insulation of Electrical Equipment
Under the action of high-voltage, some electrical equipment will overheat
because of their inferiority of internal insulation; the heat power conforms to the law of
𝑃 = 𝑈2
. 𝜔. 𝐶. 𝑡𝑔. 𝛿
(Where P is the heat power, U is the voltage, 𝜔is the angle frequency, C is the capacitance
of the equipment, and the 𝛿is the angle of dielectric loss), the electric test of this kind of
fault generally shows the dielectric loss increasing. These kinds of faults often happento the

equipment such as potential and current transformer. Coupling condenser, cable splice
deliquescence and deviation of post insulator.
a) Inferiority in internal insulation of potential transformer
When a phase of the potential transformer is inferior in internal insulation, its
thermography will show thecharacteristic of whole body overheat in comparison withthe
other phases moreover, there is not a remarkableoverheat center on its body but the
temperature of its headeris a little higher than that of the porcelain body.
b) Inferiority in internal insulation of current transformer heating and there
When a phase of the current transformer is inferior in internal insulation, its
thermography will show thecharacteristic of whole body overheat in comparison with
the other phases, there is not a remarkable overheat Centreon its body but the temperature
of the header is higher thanthat of its porcelain body.
c) Inferiority in internal insulation of coupling condenser
When a phase of the coupling condenser is inferior ininternal insulation, its thermography
will show thecharacteristic of whole body overheat in comparison with the other phases
moreover, its whole body is almost homogeneous heating and there is not a overheat centre.
d) Insulation deliquescence of the cable splice
When the cable splice is deliquesced because of local damage or poor sealed, the
thermography of the cable splice will show the characteristics of whole body overheat or
local overheat. When whole insulation of the cable splice is deliquesced, the thermography
of the cable splice shows characteristics of whole body overheat.
e) Deviation of post insulator
Sometimes the post insulator may deviate from insulation and give out abnormal heat
because of fail in manufacturing and technology or porcelain aging in the long time. The
thermography of the post insulator shows the characteristic of whole body overheat.

Other faults
Some faults of electrical equipment are rather particular. For example, some electrical
equipment with oilfor insulator dielectric may lack of oil or low oil level, sometimes the oil
level is pseudo or false oil level. Thiskind of fault is difficult to be found by common
electrical test, but it is very effective for infrared thermography tofind out. As electrical
equipment are with normal heat because of power consumption and the oil of electrical
equipment is the carrier of heat. Therefore, when the oil level is lower, the thermography of
the equipment willshow characteristic of the mark of oil level separatrix with temperature
lower above and higher below. This kind of fault often happens to the equipment such as
coupling condenser and potential transformer and oil bushing of transformer. In addition,
some equipment give out unbalanced or abnormal heat distribution because of their internal
components being damped, this kind of faults often happen to the equipment such as all
sorts of arrester.
a) Lack of oil in coupling condenser
The oil level of coupling condenser with lack of oil is often lower for several
skirts, this kind of fault can be seen from its thermography when the high sensitivity of the
thermo vision is selected. Moreover, there is a clear temperature gradient in oil level.
b) Lack of oil in potential transformer
When a potential transformer is lack of oil or low oillevel, its thermography will show
the characteristic ofseparatrix with dimer above and brighter below, theseparatrix indicates
the true oil level. This kind of fault canbe seen from its thermography when the high
sensitivity ofthe thermo vision is selected.
c) Lack of oil in bushing of transformer
When a bushing of transformer is lack of oil or low oillevel, its thermography
will show the characteristic ofseparatrix with dimer above and brighter below, theseparatrix
indicates the true oil level. This kind of faultscan be seen from its thermography when the
highsensitivity of the thermo vision is selected. Moreover, thereis a clear temperature
gradient in oil level.

d)Dampness in internal components of arrester
When the internal components of arrester is dampedbecause of poor sealed or
porcelain damage, the resistance of the internal components will be abnormal,
thecharacteristic of its thermography is subject to the structure of the arrester. Generally
speaking, when wholecomponents of the arrester are damped, its thermographywill show
the characteristic of whole body overheat bycomparison with other phases. When local
components ofthe arrester are damped, its thermography will show thecharacteristic of local
overheat and local dimer (lower temperature) by comparison with other phases, it
shouldtake notice that in the latter case, the location of the dampis just in the dimer of the
thermography.
CHAPTER 3
LITERATURE REVIEW

Soib Taib , Mohd Shawal Jadin,Shahid Kabir-“Thermal Imaging For Enhancing
Inspection Reliability : Detection and Characterization”
The role of non-destructive testing (NDT) is to ensure integrity, and in turn,
reliability of equipment or structure. Besides, NDT can also monitor in-service
degradation and to avoid premature failure of the equipment/structures and prevent
accidents as well as savehuman life. Up to now, NDT has been used in various fields
of applications such as the inspection of electrical power plant, substation, storage
tanks, bridges, aircraft, pressurevessel, rail, pipeline and so on. Human eyes can only
see light in the visible spectrum, ranging from about 400 nm to a littleover 700 nm.
The electromagnetic spectrum is a band of all electromagnetic waves
arrangedaccording to frequency and wavelength. As shown in Fig. 1, the wavelength
spectrum ofinfrared light ranges from about 1 mm down to 750 nm. All objects emit
energy proportionalto its surface temperature. However, the energy radiated can only
be detected by an infrareddetector that depends on the emissivity coefficient of the
surface under measurement. The Stefan-Boltzmann law describes the total
maximumradiation that can be released from a surface. Since thermal imaging systems
only respondto a small portion of the spectrum, it is necessary to introduce Planck’s
blackbody law. Infrared thermography is generally classified in two types, passive and
active thermography. In active thermography, the relevant thermalcontrasts are

induced by an external stimulus. The passive method has beenwidely applied in
diverse areas such as production, predictive maintenance, medicine,detection of forest
fire, thermal efficiency survey of buildings, road traffic monitoring,agriculture and
biology, detection of gas and in NDT.
Early prevention of electrical power failures is veryimportant since power
interruptions can have serious impacts on the social and economic activities of a
country. To ensure acontinuous power supply, the reliability of electrical
powerequipment must be checked regularly. Abnormalities in the equipment will
occur when their internal temperatures exceed their limits. Consequently, the
overheating of electrical equipment can lead to subsequent failure of the equipment
and can potentially result in unplanned outages, injury and fire hazard. In addition, the
efficiency of an electrical grid reduces prior to failure; thus energy is spent generating
heat, causing unnecessary loss. The common problems regarding thermal anomalies in
electrical installations are loose or poor connections, unbalanced loads, short circuits,
overloading andcracks or defects in the equipment body. Basically, there are two ways
to analyse the thermal characteristics in electrical equipment. The first is
thequantitative evaluation, which is to measure the exact real temperature value of an
object. However, these measurements are relatively difficult to obtain; in order to
determine the real and accurate temperature value, the true emissivity value mustbe
identified by considering the effects of ambient conditions and atmospheric
attenuation. The second is the qualitative measurement, which considers the relative
temperature valueof a particular hotspot with respect to other equipment in a similar
environment. This method, which employs the ΔT criteria, is widely used to evaluate
electrical equipment. The qualitative measurement is the most suitable method for
evaluating the thermal condition of electrical equipment; therefore, all similar and
identical structures within the thermal image should be grouped together. For
detecting the regular structure of electrical equipment, the tasks can be broken down
into three separate steps:
a) Detecting the interesting feature points in the thermalimage with specific
descriptors.

b) Comparing all the features and matching them withthe most similar and closest
distance points.
c) Segmenting the regions of interest.
Ying-Chieh Chou , Leehter Yao-“Automatic diagnostic system of electrical
equipment using infrared thermography."
The repair and maintenance of equipment at important facilities has been a
primary area of concern. Of these facilities, the repair and maintenance of equipment
at power transmission facilities is listed as a task with the highest priority because our
abilities to continue to enjoy the quality of life we are enjoying now depend solely on
the continuous operation of this equipment in the future. Power installations are
usually located in every corner of small villages and big cities. This is because
electricity has to be provided to wherever the consumers are conducting their indoor
or outdoor activities, leading to tens of thousands of such facilities. The repair and
maintenance of a facility can be classified under three different categories: when
equipment malfunction, time–based, and condition-based maintenance. The most
popular one is condition-based maintenance, also known as preventive maintenance.
Infrared thermography technique is widely used in preventive maintenance for the
advantage of carrying out quick, accurate, and wide area inspections by telemetry.
With this technique, defective parts can be detected through simple observation of
infrared images and there is no need to shut down the operation of a facility to look
inside the equipment for inspection. Infrared thermography technology is a technology
that uses infrared sensors and optical lenses in a constructed electrical circuitry to
capture images of thermal objects based on temperature variations. Infrared thermal
camera stores the infrared pictures of thermal objects as thermal images that the
human can see in order to understand the inside conditions of the objects. With the
images, inspectors can analyse the temperature variations of thermal objects to lookfor
defective parts. Infrared thermography technology is a non-destructive inspection
technique. The inspection can be conducted efficiently by keeping a distance from the
inspected equipment. There is no need to halt equipment operation while an inspection

is going on. Since the collection of information for inspection is by telemetry,
hazardous operations can be avoided . For these reasons, Infrared thermography is
widely used for many applications involving preventive maintenance.
J.Rantala.D.Wu,A.Salerno,G.Busse – “Thermal Imaging for Qualitative Based
Measurements of Thermal Anomalies in Electrical Components”
Temperature change in materials can be induced with mechanical
vibration where thethermo-elastic effect and hysteresis effect are involved. The
thermo-elastic effect is the dominating mechanism in metals. In polymers, however,
the hysteresis loss dominatesalready at low amplitudes, as is obvious from their
high acoustic or mechanical damping. The enclosed area corresponds to the
dissipated energy which is converted into heat. Delamination can occur in the
manufacturing process of wood-based panels with coatingmaterials such as veneer.
These defects have to be detected in an early stage. A sample shown in was
investigated Between the 0.5 mm veneer layer and substrate there are several holes
and two embedded sheets: a piece of teflon film in the middle and an aluminium film
at the right bottom corner. All these defects can be clearly detected in the
phase and amplitude image. The quality of polymer materials may suffer from
boundary effects. Therefore one is interested to detect boundaries or their changes.
One example is welding of polymers. Areas of disband are inherent sources of
weakness which result in failure under load. In the middle of the sample there is an air
gapbetween two bonded parts. Defects were shown up in the phase and amplitude
image whenultrasonic waves are coupled into the sample. The contrast of phase and
amplitude image ismuch better than in a thermographic image. Intact boundaries are
also essential for coated materials where the outer layers are supposed to have
some special functions, e.g. improved resistance to wear, corrosion, or heat.In these
cases one is interested to monitor local variations of thickness or to detect areas of
disband where the loss of adhesion may later on result in failure. A metal sample with
ceramic coating on a metal substrate was inspected by using lock-in

vibrothermography. Adelamination area on the upper edge of the sample is
detected. In the phase image the beginning of the delamination can be seen clearly.
CHAPTER 4
PROJECT DESCRIPTION

CHAPTER 4
PROJECT DESCRIPTION
4.1 Block Diagram of the System Used for Inspection of Equipment
Process
Under
Diagnostic
Data
Acquisition
Using IR
Camera
Finding
Repeated
Objects
Fault
Classification
Using
ANN/SVM
Data
Bank
Type Of Fault
Normal
Abnormal

4.2 Input Image
The input image is the infrared image that is captured on the Thermal camera during
inspection. When the thermal images are captured inappropriately, the image colour can
appear too bright or too dark and monotonous. These thermal images with flaws tend to
increase the amount of mistakes inspectors made by making wrongful judgements during an
inspection In order to avoid this, it is suggested that thermal images that do not show vivid
distinction between the main objects and their backgrounds must not be included in an
inspector report.
Thermal images, or thermograms, are actually visual displays of the amount of
infrared energy transmitted and reflected by an object. As there are many sources of
infrared, it is difficult to get the accurate temperature of an object using this method.
The inputs are detected by the feature extraction technique like SIFT, SURF, MSER
etc., out of which sift is most commonly used. The SURF algorithm is derived from the
SIFT algorithm. The SURF algorithm is more efficient than SIFT because the number of
iterations are reduced in SURF. The sift algorithm is used to find the repeated objects in a
system.
The input is obtained from the images of a thermal camera which gives of a
thermogram of the image being captured. Thermographs are converted from colour domain

to gray scale domain in order to reduce the computational complexity. The defect region
in thermographs is highlighted by Image enhancement which is done with averaging
Gaussian filters. Image segmentation by edge detection is performed on those thermographs
with suitable filters. After which post processing (dilation, region growing and erosion) is
done to remove the undesirable region. Dilation is performed on the edge detected image to
bridge the gap between each pixel; region growing is performed on the dilated image to
differentiate the region of interest pixels from the background pixels; erosion is performed
on the region filled image to isolate the defect or the region of interest.
The input image is given to the neurons in the artificial neural network. The input
layers pass on the node input to the hidden layer where the processing is done. After the
processing, the output is obtained in the output layer with errors eliminated to a maximum
extent.
4.3 SIFT Algorithm
The detection step of SIFT algorithm is based on difference of mean (without
interpolation). This algorithm is used to find the repeated objects and the stable points by
diluting the image. Following are the major stages of computation used to generate the set
of image features:
1. Scale-space extrema detection: The first stage of computation searches over all scales and
image locations. It is implemented efficiently by using a difference-of-Gaussian function
to identify potential interest points that are invariant to scale and orientation.
2. Key point localization: At each candidate location, a detailed model is fit to determine
location and scale. Key points are selected based on measures of their stability.
3. Orientation assignment: One or more orientations are assigned to each keypoint location
based on local image gradient directions. All future operations are performedon image
data that has been transformed relative to the assigned orientation, scale, andlocation for
each feature, thereby providing invariance to these transformations.

4. Keypoint descriptor: The local image gradients are measured at the selected scalein the
region around each keypoint. These are transformed into a representation thatallows for
significant levels of local shape distortion and change in illumination.
This approach has been named the Scale Invariant Feature Transform (SIFT), as it
transforms image data into scale-invariant coordinates relative to local features.
4.4 SURF Algorithm:
SURF (Speeded Up Robust Feature) is a robust local feature detector, first presented
by Herbert Bay et al. in 2006, that can be used in computer vision tasks like object
recognition or 3D reconstruction. It is partly inspired by the SIFT descriptor. The standard
version of SURF is several times faster than SIFT and claimed by its authors to be more
robust against different image transformations than SIFT. SURF is based on sums of 2D
Haar wavelet responses and makes an efficient use of integral images.
It uses an integer approximation to the Hessian blob, which can be computed extremely
quickly with an integral image (3 integer operations). For features, it uses the sum of the
Haar wavelet response around the point of interest. Again, these can be computed with the
aid of the integral image. The speed of SURF algorithm is same as that of SIFT but the
quality is less when compared to SIFT.
Matching Features:
Repeating structures are present in almost every image of electrical
installations. This is due to the fact that electrical installations often are made in a very
structured and symmetrical way. Another factor is the presence of a three-phase system,
where there will be at least three similar copies of most components. Such repeating
structures can be considered as an indication of the existence of multiple similar objects in
the image. If working properly, similar objects ought to have the same temperature. If not,
you can conclude that the function of the installation is not optimal. Thus, by comparing
temperature properties of regions with the same geometric appearance, conclusions on the
function of the installation can be made.

To be able to find a repeating pattern in an image one approach is to identify
distinctive features in the image, describe the features and compare them with each other to
find similar regions within the image. If a number of such matches are found in the image
you can further investigate the mutual properties between the matches to strengthen the
hypothesis of a repeating structure. An indication of a repeating structure from matching
feature points is if pairs of matching points have the same relative translation. To be able to
use the detected SIFT features to repeating structures in the image the descriptors of the
points must be compared to detect similar image regions.
Although the SIFT descriptors are scale invariant only features of the same scale are
compared. If the detail in the image is detected as a feature at a certain scale the
corresponding detail in a similar object will be detected at the same scale. This cannot be
true always because of the discreteness of the concept of scale nearly identical details in an
image can appear as a feature of adjacent scales.
The strategy of considering pairs of features with a sufficiently small mutual distance as
being similar is not very reliable. It will generate many false matches if the threshold is
chosen too high and will miss many true matches if the threshold is chosen too low.
4.5 Artificial Neural Network
Artificial neural network (ANN) is an artificial model of real neural networks which
refers to the vast networks of interconnected neural cells that exist in the brains of animals
and humans. These neural cells act as summations, collecting the sum of the inputs to the
neural cells and sending a corresponding output onwards to the next neural cells. The
connections between neurons, or neural cells can vary in size. The difference in size of the
connections leads to varying levels of the signals being transmitted among cells, giving
varying relevance to the signals transmitted. The neurons of the brain are replaced by
nodes, and are connected by weights.

A network can consist of any number of nodes, arranged in any kind of pattern. In our
project, a feed-forward back propagation network is used, which consist of three or more
layers of nodes. The first layer is the input layer, which has nodes depending upon the
number of input. The last layer is the output layer which consists of as many nodes as there
are outputs from the system. The hidden layer lies in between these two layers which
consist of an arbitrary number of nodes. The number of nodes in the hidden layers must be
chosen for individual network as it affects the behaviour of the network. The weight of each
node is updated during a training phase and this updating of the nodes can be done in many
different ways using training algorithms. Common for all training algorithm that uses
supervised learning is that the output of the system is compared to a specified target output,
and the error between these two is used to update the weights.
4.6.Applications of artificial neural networks
The utility of artificial neural network models lies in the fact that they can be used to
infer a function from observations and also to use it. Unsupervised neural networks can also
be used to learn representations of the input that capture the salient characteristics of the
input distribution and more recently, deep learning algorithms, which can implicitly learn
the distribution function of the observed data. Learning in neural networks is particularly
useful in applications where the complexity of the data or task makes the design of such
functions by hand impractical.
The tasks to which artificial neural networks are applied tend to fall within the following
broad categories:
 Function approximation, or regression analysis, including time series predictionand
modelling.
 Classification, including pattern and sequence recognition, novelty detection and
sequential decision making.
 Data processing, including filtering, clustering, blind signal separation and
compression.
Application areas of ANNs include system identification and control (vehicle
control, process control), game-playing and decision making (backgammon, chess, racing),

pattern recognition (radar systems, face identification, object recognition), sequence
recognition (gesture, speech, handwritten text recognition), medical diagnosis, financial
applications, data mining (or knowledge discovery in databases, "KDD"), visualization and
e-mail spam filtering.
4.7. Neural Network Structure
Neural networks are models of biological neural structures. The starting point
for most neural networks is a model neuron. This neuron consists of multiple inputs and a
single output. Each input is modified by a weight, which multiplies with the input value.
The neuron will combine these weighted inputs and, with reference to a threshold value and
activation function, use these to determine its output. This behaviour follows closely our
understanding of how real neurons work.
Figure 6: A Model Neuron
The description of the structure is given using a network known as the back
propagation network. To build a back propagation network, proceed in the following
W1j
W2j
Wij
sigmoidX2
Neuron
j
X1
yi
xi
uj
Ti

fashion. First, take a number of neurons and array them to form a layer. A layer has all its
inputs connected to either a preceding layer or the inputs from the external world, but not
both within the same layer. A layer has all its outputs connected to either a succeeding layer
or the outputs to the external world, but not both within the same layer.
Next, multiple layers are then arrayed one succeeding the other so that there is an
input layer, multiple intermediate layers and finally an output layer. Intermediate layers,
that is those that have no inputs or outputs to the external world, are called hidden layers.
Back propagation neural networks are usually fully connected. This means that each neuron
is connected to every output from the preceding layer or one input from the external world
if the neuron is in the first layer and, correspondingly, each neuron has its output connected
to every neuron in the succeeding layer.
Figure 7: Backpropagation Network

Generally, the input layer is considered a distributor of the signals from the external
world. Hidden layers are considered to be categorizers or feature detectors of such signals.
The output layer is considered a collector of the features detected and producer of the
response.
4.8. Neural Network Operation
The output of each neuron is a function of its inputs. In particular, the output of
the jth neuron in any layer is described by two sets of equations:
(5)
(6)
For every neuron, j, in a layer, each of the i inputs, Xi, to that layer is multiplied
by a previously established weight, wij. These are all summed together, resulting in the
internal value of this operation, Uj. This value is then biased by a previously established
threshold value, tj, and sent through an activation function, Fth. This activation function is
usually the sigmoid function, which has an input to output mapping as shown in Figure 4.
The resulting output, Yj, is an input to the next layer or it is a response of the neural network
if it is the last layer. Neuralyst allows other threshold functions to be used in place of the
sigmoid described here.
Figure 8: Sigmoid Function

Equation 1 implements the combination operation of the neuron and Equation 2
implements the firing of the neuron. With a predetermined set of weights, a predetermined
set of threshold values and a description of the network structure (that is the number of
layers and the number of neurons in each layer), it is possible to compute the response of
the neural network to any set of inputs.
4.9. Back propagation Network
The difference between the desired response and the actual response, the erroris
determined and a portion of it is propagated backward through the network. At each neuron
in the network the error is used to adjust the weights and threshold values of the neuron, so
that the next time, the error in the network response will be less for the same input.
This corrective procedure is called backpropagation and it is applied continuously
and repetitively for each set of inputs and corresponding set of outputs produced in
response to the inputs. This procedure continues so long as the individual or total errors in
the responses exceed a specified level or until there are no measurable errors. At this point,
the neural network has learned the training material and you can stop the training process
and use the neural network to produce responses to new input data.
W1j
W2j
Wij
Neuron
j
Error
Sigmoid
X1
X2
Xi
Yj
Dj
Tj

Figure 9: Neuron Weight Adjustment
Back propagation starts at the output layer with the following equations:
(7)
and
(8)
For the ith input of the jth neuron in the output layer, the weight wij is adjusted by
adding to the previous weight value, w'ij, a term determined by the product of a learning
rate, LR, an error term, ej, and the value of the ith input, Xi. The error term, ej, for the jth
neuron is determined by the product of the actual output, Yj, its complement, 1 - Yj, and the
difference between the desired output, dj, and the actual output.
Once the error terms are computed and weights are adjusted for the output layer, the
values are recorded and the next layer back is adjusted. The same weight adjustment
process, determined by Equation 7, is followed, but the error term is generated by a slightly
modified version of Equation 8. This modification is:
(9)
Here, the difference between the desired output and the actual output is replaced by
the sum of the error terms for each neuron, k, in the layer immediately succeeding the layer
being processed times the respective pre-adjustment weights.
The learning rate, LR, applies a greater or lesser portion of the respective adjustment
to the old weight. If the factor is set to a large value, then the neural network may learn

more quickly, but if there is a large variability in the input set then the network may not
learn very well or at all.
In many cases, it is useful to use a revised weight adjustment process. This is
described by the equation:
(10)
This is similar to Equation 7, with a momentum factor, M, the previous weight, w'ij,
and the next to previous weight, w''ij, included in the last term. This extra term allows for
momentum in weight adjustment. Momentum basically allows a change to the weights to
persist for a number of adjustment cycles. The magnitude of the persistence is controlled by
the momentum factor. If the momentum factor is set to 0, then the equation reduces to that
of Equation 7. If the momentum factor is increased from 0, then increasingly greater
persistence of previous adjustments is allowed in modifying the current adjustment. This
can improve the learning rate in some situations, by helping to smooth out unusual
conditions in the training set.
As you train the network, the total error, that is the sum of the errors over all the
training sets, will become smaller and smaller. Once the network reduces the total error to
the limit set, training may stop. You may then apply the network, using the weights and
thresholds as trained. It is a good idea to set aside some subset of all the inputs available
and reserve them for testing the trained network.
4.10.Back Propagation Rule (Or) Generalised Delta Learning Rule :
The total squared error of the output computed by net is minimised by a
gradient descent method known as Back Propagation or Generalised Delta rule.
Derivation :
Consider an arbitrary activation function f(x). The derivation of activation function is
denoted by F(x).
Let

𝑦−𝑖𝑛𝑘 = 𝑧𝑖 𝑤𝑗𝑘
𝑖
(11)
𝑧−𝑖𝑛𝐽 = 𝑣𝑖𝑗 𝑥𝑖
𝑖
𝑌𝑘 = 𝑓(𝑦−𝑖𝑛𝑘 ) (12)
The error to be minimised is
𝐸 = 0.5 [𝑡 𝑘 − 𝑦 𝑘 ]
𝑘
² (13)
By use of chain rule we have
𝜕𝐸
𝜕𝑤𝑗𝑘
=
𝜕
𝜕𝑤𝑗𝑘
0.5 [𝑡 𝑘 − 𝑦 𝑘]
𝑘
² (14)
=
𝜕
𝜕𝑤 𝑗𝑘
0.5[𝑡 𝑘 − 𝑡 𝑦−𝑖𝑛𝑘 ]²
= -[𝑡 𝑘 − 𝑦 𝑘]
𝜕
𝜕𝑤 𝐽𝑘
𝑓(𝑦−𝑖𝑛𝑘 )
=-[𝑡 𝑘 − 𝑦 𝑘] 𝑓(𝑦−𝑖𝑛𝑘 )
𝜕
𝜕𝑤 𝐽𝑘
(𝑦−𝑖𝑛𝑘 )
=-[𝑡 𝑘 − 𝑦 𝑘]𝑓¹(𝑦−𝑖𝑛𝑘 )𝑍𝑗 (15)
Let us define
δk=-[𝑡 𝑘 − 𝑦 𝑘]𝑓¹(𝑦−𝑖𝑛𝑘 ) (16)
Weights on connections to the hidden unit zj
𝜕𝐸
𝜕𝑣𝑖𝑗
= − 𝑡 𝑘 − 𝑦 𝑘
𝜕𝐸
𝜕𝑣𝑖𝑗
𝑦 𝑘
𝑘
(17)

= − 𝑡 𝑘 − 𝑦 𝑘 𝑓(𝑦𝑖𝑛𝑘 )
𝜕
𝜕𝑣𝑖𝑗
𝑦−𝑖𝑛𝑘
𝑘
= − δ 𝑘
𝜕
𝜕𝑣𝑖𝑗
𝑦−𝑖𝑛𝑘
𝑘
(18)
Rewriting the equation and substituting the values of y-ink
= − δ 𝑘
𝜕
𝜕𝑣𝑖𝐽
( 𝑧𝑗 − 𝑤𝐽𝑘 )
𝑘
(19)
= − δ 𝑘 𝑤𝐽𝑘
𝜕
𝜕𝑣𝑖𝐽
𝑧𝐽
𝑘
= − δ 𝑘 𝑤𝐽𝑘
𝜕
𝜕𝑣𝑖𝐽
𝑓(𝑧𝑖𝑛𝐽 )
𝑘
= − δ 𝑘 𝑤𝐽𝑘 𝑓´(𝑧𝑖𝑛𝐽 )( 𝑥𝑖)
𝑘
δj= − δ 𝑘 𝑤𝐽𝑘 𝑓´(𝑧𝑖𝑛𝐽 )𝑘 (20)
The weight updation for output unit is given by
Δwjk=−α
∂E
∂wjk
(21)
=α[𝑡 𝑘 − 𝑦 𝑘 ]f¹(𝑦−𝑖𝑛𝑘 )𝑧𝑗
=αδk 𝑧𝑗
The weight updation for the hidden unit is given by
Δ𝑣𝑖𝑗 = −𝛼
𝜕𝐸
𝜕𝑣𝑖𝑗
= 𝛼𝑓1
𝑧−𝑖𝑛𝑗 𝑥𝑖 𝛿 𝑘
𝑘
𝑤𝑗𝑘 (22)
=αδj 𝑥𝑖(23)

This is a generalised Delta Rule used in the Back Propagation network during training.
4.11.Back Propagation Learning Algorithm based on Levenberg
Marquardt Algorithm (LM)
Levenberg – Marquardt algorithm is specifically designed to minimize sum-of-square
errorfunctions of the form.
𝐸 = 1/2 𝐾(𝑒 𝐾)2
=1/2 𝑒
2
(24)
Where ek is the error in the kth exemplar or pattern and e is a vector with element ek. If
thedifference between the pervious weight vector and the new weight vector is small, the
errorvector can be expanded to first order by means of a Taylor series.
𝑒 𝑗 + 1 = 𝑒 𝑗 +
𝜕𝑒 𝑘
𝜕𝑤𝑖
𝑤 𝑗 + 1 − 𝑤 𝑗 25
The error function can be expressed as
𝐸 = 1/2||𝑒(𝑗) +
𝜕𝑒 𝑘
𝜕𝑤𝑖
𝑤 𝑗 + 1 − 𝑤 𝑗 ||2
(26)
Minimizing the error function with respect to the new weight vector, gives
𝑤(𝑗 + 1) = 𝑤(𝑗) − (𝑍 𝑇
𝑍)−1
𝑍 𝑇
𝑒 (𝑗)(27)
Where (z)ki =
𝜕𝑒 𝑘
𝜕𝑤 𝑖
Since the Hessian for the sum-of-square error function is
𝐻𝑖𝑗 = 𝜕2
𝐸/𝜕 𝑤𝑖 𝜕 𝑤𝑗 = {(𝜕𝑒𝑘 /𝜕 𝑤𝑖 )(𝜕𝑒𝑘 /𝜕 𝑤𝑖 ) + 𝑒 𝑘 𝜕²𝑒 𝑘 𝜕 𝑤𝑖 𝜕 𝑤𝑗 } (28)
Neglecting the second term, the Hessian can be written as H= ZT
Z

Updating of the weights therefore involves the inverse Hessian or an approximation
there of for nonlinear networks. The Hessian is relatively easy to compute, since it is based
on first order derivatives with respect to the network weights that are easily accommodated
by back propagation. Although the updating formula could be applied iteratively to
minimize the error function, this may result in a large step size, which would invalidated
the linearapproximation on which the formula is based.
In the Levenberg-Marquardt algorithm, the error function is minimized, while the
step size is kept small in order to ensure the validity of the linear approximation. This is
accomplished by use of a modified error function of the form.
𝐸 = 1/2||𝑒(𝑗) +
𝜕𝑒 𝑘
𝜕𝑤𝑖
𝑤 𝑗 + 1 − 𝑤 𝑗 ||2
+ 𝜆||𝑤(𝑗 + 1) − 𝑤(𝑗)||² (29)
where l is a parameter governing the step size. Minimizing the modified error with respect
tow(j+1) gives
𝑤 𝑗 + 1 = 𝑤 𝑗 − (𝑍 𝑇
𝑍 + 𝜆𝐼)−1
𝑍 𝑇
𝑒 𝑗 (30)
very large values of l amount to standard gradient descent, while very small values l of
amountto the Newton method.

CHAPTER 5
RESULT AND CONCLUISON

5.1.SIMULATION AND RESULT:
These are the image in which the repeated objects in an electrical equipment is tested
and its corresponding vector points are found out.

4.4 CONCLUSION:
The repeated objects in an electrical equipment is found by using the SIFT and SURF
algorithms. A new software using Artificial neural network, Fuzzy logic, etc…, will be
developed in the next phase .

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