Detection of crack location and depth in a cantilever beam by vibration measurement and its comparative validation in ann and ga

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 04 Issue: 10 | Oct -2015, Available @ http://www.ijret.org 152
DETECTION OF CRACK LOCATION AND DEPTH IN A CANTILEVER
BEAM BY VIBRATION MEASUREMENT AND ITS COMPARATIVE
VALIDATION IN ANN AND GA
M.S. Mhaske1
, R.S. Shelke2
1
Assistant Professor, Department of Mechanical Engineering, Sandip Foundation’s Sandip Institute of Engineering
and Management, Nashik, Maharashtra, India
2
Assistant Professor, Department of Mechanical Engineering, Sir Visvesvaraya Institute of Technology, Nashik,
Maharashtra, India
Abstract
The presence of a crack is hazardous problem in the performance of many structures and it affects many of the vibration
parameters like Natural frequency and mode shapes. Current research has focused on using different modal parameters like
natural frequency, mode shape and damping to detect crack in beams. This work concentrates on the parameters like Deflection of
a beam, Bending moment and behaviour of stresses. In this work, simulation is carried out by using analysis software ANSYS to
find the change in natural frequencies as well as mode shapes for the cracked and uncracked beam. It is then verified by the
results obtained from ANN controller and Genetic Algorithm. ANN is used to determine location of crack and its depth along with
directions of propagation and Natural frequencies and corresponding mode shapes difference as initial input to calculate the
variation and the vibration parameters. The output from ANN controller is corresponding depth and crack location. outputs from
numerical analysis are compared with output from Experimentation and they have good resemblance to the results predicted by
the ANN controller. Genetic algorithm is an evolutionary type of algorithm which generates the optimized solution to the
problems. It is an iterative process to reach to the final solution. By using this, same results are found and related with the results
of ANN. And finally the results are compared to find the most appropriate approach amongst the two methods.
Keywords— ANN, Crack, Depth, GA
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1. INTRODUCTION
Damage detection by using crack analysis in a mechanical
or civil structure has been a topic of research for last few
decades. For every new researcher, a new method or change
in modal parameters is a way to carry out the detection
procedure of a crack. Damage is a result of crack and crack
changes stiffness of a structure. Due to change in stiffness
dynamic response of a system changes.
Finite Element Method is used to determine properties of a
structure, or by modal analysis. Characteristics of cracked
and uncracked beams are different. Because of this, flaws in
materials can be detected, especially in beams. Crack
formation due to cycling loads tends to fatigue of the
structure and forms discontinuities in the crystal structure of
a beam. When a structure has a crack, its dynamic properties
are observed to be changed drastically. To be specific, crack
reduces stiffness and natural frequencies, and increases
modal damping.
Cracks can initiate major failures in vibrating component.
Therefore, dynamics of cracked structures should be studied
[1]. Specifically, damage due to crack can cause reduction in
stiffness, with a higher reduction in natural frequencies, also
increases the modal damping, and changes the mode shapes
[2].Because of this changes, the crack position from support
as well as edges can be found The reduction in natural
frequencies can be easily noticed . In the research by Kam
and Lee, the finite elements method has been selected to
find the location of a crack and its magnitude for a crack in a
cantilever beam. Also they have verified Natural frequency
of the beam experimentally. The mathematical equations
were derived for the beam with one crack and supported at
both the ends [4] to observe the effect of the crack to the
natural frequency. Dimarogonas and Chondros conducted
many experiments with a cantilever beam made up of
aluminium with a crack [5]. They stated that the experiments
resemble with the mathematical expressions. Formulae were
derived for bending vibrations of an Euler Bernoulli.They
examined the changes in the ratio of crack location to the
beam length and also the ratio of the depth of the crack to
the beam height. They studied the change of natural
frequency of the beam. Rizos et al introduced a method of
amplitudes at two different points in a system vibrating at
only one of its natural frequencies and analytical solution of
its dynamic response. Shen and Chu found the presence of
cracks in a structure by exciting it [9] at different natural
frequencies and used a numerical method for the analysis of
response. Chondros et al. [10] investigated a continuous
vibration theory of a cracked beam for lateral vibration of
cracked Euler–Bernoulli beams with one or two edge cracks.
Determination of the dynamic response of a beam which is
simply supported and has open surface cracks is done by
this cracked beam theory. In this theory, the analysis of
dynamic behaviour of a concrete beam with an edge crack

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was done. The effects of depth and location of a crack on the
modal properties were experimentally determined in order to
identify the depth and location of a crack. This method was
used to give excitations to natural frequencies of the beam.
2. EXPERIMENTATION
When damage or crack occurs in a beam, it modifies the
vibration characteristics of uncracked beam, like the natural
frequencies and mode shapes. The properties of the
uncracked beams are generally referred to the initial records
in detection of crack. It can be determined with the help of
modal tests. If compared to the initial values of
experimentation, any change in the structural parameters
which are measured in the service life of structure shows
damage and it can be used to determine the severity of a
crack as well as its location. Of all the various parameters,
the most widely used parameter is natural frequency and it is
used as a governing parameter of damage in a beam or
structure. Also it can be verified from the modal tests with
great accuracy. If a crack occurs in a beam or structure,
stiffness values and natural frequency values get reduced.
Various instruments are used for experimental analysis of a
crack i.e. Fast Fourier Transform (FFT) analyser, impact
hammer, accelerometer, and many more accessories. The
piezoelectric accelerometer which is unidirectional is used
to find the functions of frequency response. The
accelerometer is mounted with the help of mounting clips on
the beam near crack so that it can capture correct signal. The
beam is excited using an impact hammer. In every test, the
location of impact is kept constant. A gentle tap is given to
the beam with the help of impact hammer. Number of
experiments is performed on a cantilever beam made up of
mild steel having single crack and without crack .The depth
as well as location of a crack is varied along the length of
the beam. Following are the properties of mild steel,
Young’s modulus (E) 2.0 e11 N/m2
Density (ρ) 7950 N/m3
Poisson’s ratio 0.3.
The cantilever beams under experimentation have
rectangular cross section.
The cross sectional area is
0.025 x 0.010 m,
L = 0.25m
Crack depth is represented in terms of (a/h) ratio
Where,
a = depth of crack and
h = height of beam
And crack location is represented in terms of (e) where e is
ratio of location of crack at distance L1 from the support to
the length of the beam L.
The FFT Analyzer is a tool developed for vibration
measurement. It uses impulse execution & either frequency
domain analysis or time domain analysis to give the model
Parameter from the response measurement in real time.
Fig.1 Experimental set up
The variable parameters considered for the experimentation
are 1) depth of a crack & 2)location of a crack from fixed
end of a beam.
For a crack at 25mm, 50mm, 100mm from fixed end of a
beam, depth is varied in order to obtain number of natural
frequencies and change in natural frequencies which is
further useful to obtain network in ANN and population of
GA.
Following are the observations of experimentation. The
readings listed below are selected set of readings.
TABLE I EXPERIMENTAL OBSERVATION OF NATURAL
FREQUENCY
Sr.
No
Location
of Crack
from
Support
L1
(mm)
Depth
of
Crack
a
(mm)
Ratio
(a/h)
E =
L1/L
Natural
Frequency
of beam
F1
(Hz)
Natural
Frequency
of beam
F2
(Hz)
1 25
2 0.2
0.1
446.21 2301.68
3 0.3 458.23 2359.34
5 0.5 496.27 2364.12
2
50
2 0.2
0.2
587.19 2370.93
3 0.3 621.31 2389.24
5 0.5 637.14 2408.51
3 100
2 0.2
0.4
658.96 2413.63
3 0.3 677.33 2456.98
5 0.5 697.67 2487.53
From the readings obtained after experimentation, a
parameter is to be defined or selected for comparison of
results and its validation. And the parameter is ratio of
frequencies. It is the ratio of natural frequency of a cracked
beam to the natural frequency of uncracked beam. For this
ratio a beam without crack is initially checked for first two
natural frequencies in hertz. The values obtained for first
two natural frequencies are 719.61 & 2489.51 respectively.

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TABLE II: RESULTING FREQUENCY RATIO
Sr.
N
o
Location
of Crack
from
Support L1
(mm)
Depth
of Crack
a
(mm)
Frequenc
y Ratio
FC/F1
Frequency
Ratio
FC/F2
1 25
2 0.62 0.92
3 0.64 0.95
5 0.69 0.95
2
50
2 0.81 0.95
3 0.86 0.96
5 0.89 0.97
3 100
2 0.92 0.97
3 0.94 0.99
5 0.97 0.99
3. ARTIFICIAL NEURAL NETWORK
Artificial Neural Networks (ANN) has been widely used as
a reliable tool for determination and classification of faults
in a machine or a structure. It can give solutions for inverse
variation problems in fault detection as it is well prepared
for the recognition of pattern and excellent capabilities of
interpolation.
ANN gives a methodology to classify the problems which
are related to the non-linear problems, provided that they
can be represented in terms of input patterns, and it can also
eliminate the complications by conventional methods of
computation.
It has a set of data as inputs and the possible expected
outputs are calculated by setting up a formulated and
reference linearity between the set of inputs and the
respective outputs. The relation between input data and
output is not specified but it has to be obtained. Once the
process of mapping between input and output is understood,
the outputs can be easily obtained. It ultimately increases the
efficiency of complete design. The purpose of using the
neural network is only to calculate the outputs of all the
neurons from network. Every output as a neuron is to be
considered as a function of the sum of the inputs plus a bias.
In the figure only one neuron is taken into consideration.
The techniques like artificial neural network, Fuzzy logic
and Genetic algorithm are widely used to predict the life of
various components. Also they are used to optimize and
minimize the errors occurred in the natural frequencies
determined by various approaches like numerical simulation
and experimental analysis. Genetic algorithms are basically
dependent on the natural genetics and the nature selection of
defined problems. Large, discrete and non linear type of
modeling can be done using such techniques. Even the
conventional methods fail sometimes to provide proper
outputs; in such cases use of the genetic algorithm gives
desired results. Genetic algorithm uses every error to
evaluate the fitness and fineness of every individual step in
the available population. Genetic algorithms are used for
various optimizations and it is proven as an excellent
solution even for very difficult problems related to
optimization. The current work includes Genetic Algorithm
as a solution to validate the crack detection problem with
experimental results [28]. The artificial neural network is an
evolutionary algorithm which is used for simulation for
various cases [29]. The Current work concentrates on the
application of ANN to determine the location and depth of a
crack. The ANN requires a set of input data to proceed for
the simulation. Hence the provided input is successive mode
shapes and the corresponding natural frequencies of a
cracked beam. The cantilever beam under study has cracks
at several locations from the supports and various values of
depths are also considered. This Search technique uses most
of the data for calculation and rest is kept aside for
validation which is done further. Along with the
experimental results natural frequencies and mode shapes
are obtained with the help of finite element method. The
results of FEM are used to run ANN. The network proceeds
towards the parameters for calculation by its algorithms. It
then selects the Major input parameter on its own form the
available data. It performs various iterations to eliminate the
errors and reaches to the solution [31]. The network has
number of layers for calculation. According to the given
inputs, when a system enters single crack, network sets up
two layer network. Similarly for two cracks it sets up a three
layer network and so on. The errors go on decreasing with
the increase in number of layers. Number of layers can also
be selected manually. Lesser the errors more are the
accuracy in outputs.
Fig. 2 Schematic network of ANN
According the topology of artificial neural network
mentioned in the diagram shown above and the listed
procedure, Readings required for the validation are obtained
by creating a network in software known as GMDH Shell.
It has given tremendous resemblances of values with the
reference values.

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TABLEIII: RESULTS BY ANN
Sr.
No
Location of Crack from
Support L1
(mm)
Ratio
a/h
E = L1/L
1 25
0.19
0.110.31
0.53
2
50
0.18
0.190.31
0.52
3 100
0.21
0.420.33
0.51
It is a computational method and has a very large number of
simple processing units called as neurons. Every neuron is
assigned with a significant value as input when it is in the
initial layers and outputs when it is in the cross over
network.
4. GENETIC ALGORITHM
The Genetic algorithm is a technique which deals with
science of genetic. Every genetic algorithm has to pass
through the three basic steps namely reproduction,
Crossover and Mutation. To start with the algorithm, an
initial population is to be generated. Every member of the
population is called as chromosome and it is a binary string.
The elements of the chromosomes in particular are called as
genes. In order to solve a problem of any kind, initially a
code is to be generated for every string. The string variables
are used to calculate the results in terms of an objective
function. Once the objective function is defined,
Chromosomes are to be assigned and selected for the
reproduction process. Every genetic algorithm has a fitness
value and it is defined in terms of more number of
reproductions. A linear scaling method gives good fitness
values. So it can be used in many cases. The crossover
process begins after the process of reproduction. Number of
crossovers is obtained with the sets of reproduction values.
And the various points of crossover are selected. The
chromosomes of initial process are termed as parent
elements and the binary strings are called as children or
offspring elements. Last process with the strings is Mutation
process. By the provided codes in the algorithm some of the
chromosomes are alternately changed like O is replaced by
1, or vice versa. This is a very rare process, and hence done
at a low rate.
The four evolutionary elements of Genetic Algorithm are:
1. Selection: It is the process to select the parent strings and
it has a direct proportion of performance of strings with total
performance.The method used for selection is called as
wheel of fortune.It’s a random process.
2. Crossover: It is the process of interaction and mating of
the input parent elements to exchange their individual
strings.
3. Mutation: It Deals with the interacted parent strings to
generate the offspring or children elements possessing the
properties or output strings for both the parent strings.
It has a great convergence toward the solution.
4 Encoding: It is the mapping process to identify the
behaviour of artificial string from the available strings.
Fig.3 Graph representing Relative Crack Location by
Population of GA
Its Easy enough to encode the data for further validation.
The only thing is to have trained in codes of Mat lab.So, the
values of parameters are to be found out by using the
procedure enlisted above. And it is supported and verified
by a software KEEL and Mat Lab. KEEL is a software tool
to assess evolutionary algorithms which can also be used
with the codes similar to mat lab.
TABLE IV : COMPARISON OF CRACK PROPERTIES BY
EXPERIMENTATION, ANN AND GA
S.
N.
Locatio
n of
Crack
from
Suppor
t
L1
(mm)
Ratio
a/h
(Expt)
Ratio
a/h
(ANN)
Ratio
a/h
(GA)
E =
L1/L
(Expt)
E =
L1/L
(ANN)
E =
L1/L
(GA)
1 25
0.2 0.19 0.2
0.1 0.11 0.10.3 0.31 0.31
0.5 0.53 0.5
2
50
0.2 0.18 0.19
0.2 0.19 0.20.3 0.31 0.3
0.5 0.52 0.5
3 100
0.2 0.21 0.2
0.4 0.42 0.410.3 0.33 0.31
0.5 0.51 0.5
5. RESULTS AND CONCLUSION
1. For a vibrating shaft or a structure, the only parameter
which can be used for various analyses is the natural
frequency of vibration.
2. The Calculation terms for this work were depth of a

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crack from surface and its location from fixed support.
3. It is first found with the help of an experimental set up
and then validated with the help of modern search
techniques like Artificial Neural Network and Genetic
algorithm.
4. Validation of experimental results with ANN has an
acceptable resemblance. The indicative figures can state
it in 1% to 3% of the comparison.
5. Further it has been observed that GA also generates a set
of population as an output to achieve almost all the
values with a variation of 1%.
6. Thus, It can be stated from the work that GA can be the
Accurate search method to obtain desired results for
vibrating structures or beams.
6. ACKNOWLEDGMENT
I would like to thank hereby all the anonymous researchers,
scientist for their valuable assistance.
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Detection of crack location and depth in a cantilever beam by vibration measurement and its comparative validation in ann and ga