20120140503021

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 3, March (2014), pp. 191-201, © IAEME
191
COMPARISON OF ANN ALGORITHMS TO DETECT THE SATURATION
LEVEL IN THE MAGNETIC CORE OF A WELDING TRANSFORMER
Rama Subbanna .S1
, Lahari .J.N1
, Usha Rani .K.R1
, Dr. Suryakalavarthi .M2
1
Department of Electrical and Electronics Engineering,
St. Martins Engineering College, Hyderabad.
2
Department of Electrical and Electronics Engineering,
Jawaharlal Nehru Technological University, Hyderabad.
ABSTRACT
This paper concerns with performing an analysis of different ANN algorithms used to detect
the magnetization level in the magnetic core of a welding transformer. The magnetization level
detector is a significant element of a middle-frequency direct current (MFDC) resistance spot
welding system (RSWS). The circuit of resistance spot welding system comprises of an input
rectifier, an inverter, a welding transformer and a full wave rectifier which is mounted on the output
of the welding transformer. The resistances of secondary winding and characteristics of rectifier
diodes could be marginally different. These variances can cause DC component in welding
transformer’s iron core flux density, which causes an increment in the iron core saturation with the
vital impact on transformer’s primary current, where spikes appear in the current waveform, which
leads to over-current protection turn off of the entire system. To prevent above-mentioned
phenomena the welding system control must detect the magnetic core saturation level. Formerly, an
Artificial Neural Network based detector was implemented to detect the saturation level. In this
paper, we will examine four different ANN algorithms that can be applied, evaluate them and then
adopt which is the finest algorithm based on aspects such as computational time, root mean square
error, gradient obtained and algorithm complexity. Four algorithms in total were assessed including
Resilient-Back propagation, Levenberg-Marquardt, Gradient-Descent and Bayesian Regularization.
Keywords: Welding Transformers, Hysteresis, Artificial Neural Network Algorithms and
Controllers.
INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN ENGINEERING
AND TECHNOLOGY (IJARET)
ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
Volume 5, Issue 3, March (2014), pp. 191-201
© IAEME: www.iaeme.com/ijaret.asp
Journal Impact Factor (2014): 7.8273 (Calculated by GISI)
www.jifactor.com
IJARET
© I A E M E

192
INTRODUCTION
This paper presents the best possible algorithm to detect the saturation level in the magnetic
core of a welding transformer. This is done by taking into account parameters such as computational
time, algorithm complexity, gradient obtained and mean square error of ANNs. The magnetization
level detector is a significant component of middle-frequency direct current (MFDC) resistance spot
welding system(RSWS), in which the welding current and the flux density present in the welding
transformer’s magnetic core are controlled by two hysteresis controllers[1]. The resistance spot
welding systems described in different comprehensions [2]-[5], have many applications in the
automotive industry. Although the alternating or direct currents (dc) can be utilised for welding this
paper deals with the RSWS (Fig. 2) with dc welding current. The resistances of the two secondary
windings R2, R3 and characteristics of the rectifier diodes, connected to these windings, can
marginally vary. References [6]-[9] show that all these small differences combined lead to an
increased dc component in welding transformer’s magnetic core flux density. This causes a rise in
magnetic core saturation which affects the primary current i1of the transformer, where current spikes
appear, which ultimately lead to the over-current protection turn-off of the entire system. However,
the problematical current spikes can be stopped either passively [6] or actively [7]-[9]. Closed-loop
control of the welding current and magnetic core flux density can be employed to prevent the current
spikes actively. Hence, the welding current and density must be calculated. Rogowski coil is usually
used for the measurement of the welding current [10] and Hall sensor or a probe coil wound around
the magnetic core can be used to measure the magnetic core flux density. The flux density value in
the Hall sensor is obtained by analogue integration of the voltage induced in the probe coil [7].
Integration of the induced voltage might be defective due to the unidentified integration constant in
the form of residual flux and drift in analogue electronic components. By using the closed-loop
compensated analogue integrator the drift can be kept under control [9].An innovative, two
hysteresis controllers based control of the RSWS, where current spikes are prevented actively by the
closed-loop control of the welding current and flux density in the welding transformer’s magnetic
core, is presented in [9]. This requires measurement of the welding current, instead of measured flux
density, only the data about magnetization level in the magnetic core is essential. Few methods tested
on welding transformer’s magnetic core, that can be applied for magnetization level detection are
presented in [7]-[8]. All these methods employ Hall sensor or probe coils which make them
unsuitable for applications in industrial RSWS, because of the comparatively high sensitivity on
vibrations, high temperatures and mechanical stresses. To conquer all these problems, an ANN based
magnetic core magnetization level detector was presented previously in [10]. The measured
transformer’s primary current is its only input. The ANN based magnetic core magnetization level
detector is trained to identify the waveform of the current spikes, that appear in the primary current
when the magnetic core is about to reach the saturation region. When the spike is detected, the ANN
target signal enables the transformer supply voltage to change direction which also changes the
magnetic flux density consequently. In this manner, the ANN detector controls the system and
prevents the over-current protection switch-off. This paper analyses the four different ANN methods
employed, including a comparative study of each and finally decides the best method based on the
different parameters used.
ARTIFICIAL NEURAL NETWORK
The inspiration for the neural networks came from examination of central nervous systems. In
an artificial neural network, simple artificial nodes, called "neurons" are connected together to form a
network which resembles a biological neural network.

193
Figure 1: Artificial neural network
ALGORITHM
The threshold function of the units is modified to be a function that is continuous derivative,
the sigmoid function. The use of the sigmoid function gives the extra information necessary for the
network to implement the back-propagation training algorithm. Back-propagation works by finding
the squared error (the Error function) of the entire network, and then calculating the error term for
each of the output and hidden units by using the output from the previous neuron layer. The weights
of the entire network are then adjusted with dependence on the error term and the given learning rate.
Training continues on the training set until the error function reaches a certain minimum. If the
minimum is set too high, the network might not be able to correctly classify a pattern. But if the
minimum is set too low, the network will have difficulties in classifying noisy patterns.
In order to perform a supervised learning we need a way of evaluating the ANN output error between
the actual and the expected output. A popular measure is the mean squared error (MSE) or root mean
squared error (RMSE):
MSE = Σ(yi – oi )2
(1)
RMSE = (MSE)1/2
(2)
Where yi is the predicted value, oi is the observed value, and n is the number of data set.
As previously mentioned, there are numerous algorithms, which can be used for training ANNs.
The following algorithms were used in this study to train ANNs:
1. Resilient Back propagation:
Multilayer networks typically use sigmoid transfer functions in the hidden layers. These
functions are often called "squashing" functions, because they compress an infinite input range into a
finite output range. Sigmoid functions are characterized by the fact that their slopes must approach
zero as the input gets large. This causes a problem when you use steepest descent to train a
multilayer network with sigmoid functions, because the gradient can have a very small magnitude
and, therefore, cause small changes in the weights and biases,
even though the weights and biases are
far from their optimal values. The purpose of the resilient back propagation (RBP) training algorithm
is to eliminate these harmful effects of the magnitudes of the partial derivatives.

194
2. GradientDescent:
This algorithm is one of the most popular training algorithms in the domain of neural
networks. It works by measuring the output error, calculating the gradient of this error, and adjusting
the ANN weights and biases in the descending gradient direction. Hence, this method is a gradient
descent local search procedure. This algorithm includes different versions such as standard or
incremental back propagation (IBP):the network weights are updated after presenting each pattern
from the learning data set, rather than once per iteration; batch back propagation (BBP): the network
weights update takes place once per iteration, while all learning data pattern are processed through
the network; quick propagation (QP): QP is a heuristic modification of the back propagation
algorithm. It is proved much faster than IBP for many problems. QP is also defined as: mixed
learning heuristics without momentum, learning rate optimized during training.
3. Levenberg-Marquardt:
The Levenberg-Marquardt algorithm was designed to approach second-order training speed
without having to compute the Hessian matrix. When the performance function has the form of a
sum of squares, then the Hessian matrix can be approximated.
H=JT
J
And the gradient can be computed as
G=JT
e
Where J =Jacobian matrix, which contains first derivatives of the network errors with respect to the
weights and biases, and e=vector of network errors. The Jacobian matrix can be computed through a
standard back-propagation technique that is much less complex than computing the Hessian matrix.
Xk+1=Xk- [JT
J+µI]-1
JT
e.
4. Bayesian Regularization:
Bayesian regularized artificial neural networks (BRANNs) are more robust than standard
back-propagation nets and can reduce or eliminate the need for lengthy cross-validation. Bayesian
regularization is a mathematical process that converts a nonlinear regression into a "well-posed"
statistical problem in the manner of a ridge regression. The function ‘trainbr’ can train any network
as long as its weight, net input, and transfer functions have derivative functions. Bayesian
regularization minimizes a linear combination of squared errors and weights. It also modifies the
linear combination so that at the end of training the resulting network has good generalization
qualities. This Bayesian regularization takes place within the Levenberg-Marquardt algorithm. Back-
propagation is used to calculate the Jacobin jX of performance with respect to the weight and bias
variables X. Each variable is adjusted according to Levenberg-Marquardt,
jj = jX * jX
je = jX * E
dX = -(jj+I*mu) je
Where E is all errors and I is the identity matrix.
The adaptive value mu is increased by mu_inc until the change shown above results in a
reduced performance value. The change is then made to the network, and mu is decreased
by mu_dec.

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DYNAMIC MODEL OF SPOT WELDING SYSTEM
The resistance spot welding system is schematically shown in figure. It comprises of an
input rectifier, an inverter, a single phase welding transformer and a full-wave rectifier mounted on
the transformer output. The three-phase supply voltages are first rectified by the input rectifier and
then smoothed to produce the direct current (DC) bus voltage. The H-bridge inverter uses the(pulse
width modulation)PWM technique to generate AC supply voltage in primary of the transformer[11].
A centre aligned PWM is used to obtain the required transformer supply voltage u. The transformer’s
secondary winding has two equal coils which are connected to the output diode rectifier. A special
connection of the transformer’s secondary coils with the diodes is important to reach the required
value of the DC welding current in the given time. Rogowski coil measures the welding current,
which is usually in the range 10kA and 30kA [12]. InFig.2uu, uv and uw denote the AC voltages
supplied from the electric grid, while UDC is the DC bus voltage at the output of the input rectifier.
The H-bridge inverter is composed of the IGBT transistors S1 to S4 and corresponding diodes DH1 to
DH4. U denotes the transformer’s primary coil AC supply voltage generated by the H-bridge inverter.
Subscripts 1,2and3 are used to denote all variables and parameters related to the primary coil and to
the two secondary coils of the transformer, respectively. N1, N2 and N3 are the number of turns, i1, i2
and i3 are the currents, Lσ1, Lσ2 and Lσ3 are the leakage inductances, and R1, R2, and R3 are the ohmic
resistances of corresponding coils of the transformer. RFe represents the iron core losses of the
transformer while TR is an ideal transformer with non-linear magnetizing characteristic. The output
rectifier diodes are denoted with D1 and D2, iL is the DC welding current, while RL and LL are the
ohmic resistance and the inductance of the RSWS load. The spot welding system ensure a high
output power, where as small size of welding transformer with mounted rectifier is preferred. Power
losses are very high because of high currents in the system. The diodes of the full-wave output
rectifier contribute to major losses. The transformer with mounted rectifier is water-cooled, which
requires an intricate design of the whole system. In the existent understanding of the transformer
(schematic presentation is shown in Fig2) there are different resistances of output branches of
transformer marked with R2 and R3. Moreover, even the characteristics of output rectifier diodes D1
and D2 can be different. The full-wave rectification on the output of the transformer is used to obtain
the necessary short rise time and a high magnitude of the welding current iL which is significant for
quality of welding.
Fig2: Schematic representation of a resistance spot welding system
The outcomes of simulations, attained by the dynamic model of the RSWS, demonstrate that
small difference in resistances R2, R3 and in characteristics of the rectifier diodes D1 and D2 can
cause unbalanced time behaviour of the magnetic core flux density B and the current spikes in the
primary current i1, shown in Fig.3. The a) graph in Fig.3 shows the variation of flux with time. It can
be observed that after a definite point, the flux begins to increase and reaches the saturation level.

196
The b), c) and d) graphs in Fig.3 illustrate the variation of primary current in different time scales. As
the core begins to saturate and the flux increases beyond the limits, the current spikes start to appear
in the welding transformers primary current. From Fig. 3(c), it can be clearly observed that the spikes
begin to appear at around 0.075s. These spikes start to gradually grow with time and finally become
adequate to cause over-current protection turn-off of the entire welding system. In order to avert this,
first these spikes must be detected using an appropriate method and then the detected spikes are
suppressed.
Fig.3: (a) Time Behaviour of Flux Density
(b)
(c) (d)
Fig.3: (b), (c) and (d) Time behaviour of primary current i1

197
RESULTS AND DISCUSSION
In each of the mentioned ANN training algorithms, the only input to the ANN is the primary
current of the welding system obtained from the above presented dynamic model. Based on whether
there is a spike occurring or not, the output of the ANN is obtained. Whenever, a spike is detected,
the output of the ANN is set to 1. Then, a Hysteresis Controller which operates in union with the
ANN based detector performs a closed-loop control of the transformers’ primary voltage. With this,
the flux and hence the primary current are reduced and brought back within their operating limits.
Whenever a spike is detected, the transformers’ primary voltage reverses its polarities and hence the
flux changes its direction towards the other peak. The simulations for each of the training algorithms
of the ANN were executed by considering the architecture of three layered network with 30 neurons
in the input, 7 neurons in the hidden layer, 1 neuron in the output layer. In this paper, four different
training algorithms were analysed and studied based on parameters such as computational time, best
training performance, gradient etc. Also, the best method was suggested based on these parameters.
The results of the target signal and the best performance for each method has been shown below.
1) Resilient Back Propagation
Figure 1(a): Target signal of ANN with Figure 1(b): Best training performance
RBP algorithm
2) Gradient Descent
GD algorithm

198
3) Levenberg-Marquardt
LM algorithm
4) Bayesian Regularization
BR algorithm
The table (1) below shows the training times, gradients and the root mean squared errors for
each of the algorithms for the architecture 30-7-1.
Table 1: Table depicting a comparison of training times (s), RMSE values and gradients for the
three algorithms for an ANN with the architecture 30-7-1
Method/
parameters
RP GD LM BR
Computational
time(sec)
00:18 00:15 01:03 1:04
Gradient 0.0523 0.0172 0.00256 0.150
Performance(MSE) 0.00373 0.0103 0.00348 0.00443

199
Based on the parameters, computational time, gradient descent method gives the least value
of all the four methods. Resilient back propagation method gives the next best value. Levenberg-
Marquardt and Bayesian Regularisation methods take comparatively more time for computation.
When gradient is taken into account, Levenberg-Marquardt algorithm has the least gradient of all
followed by Gradient Descent, Resilient back propagation and Bayesian Regularisation. The
performance given in terms of Mean Squared Error is least for LM method and highest for GD. By
taking all these parameters into consideration and assessing them, it can be observed that the LM
method is the most suited method for detecting the saturation level in the magnetic core of a welding
transformer. RBP is an easier method to employ due to lesser computational time and relative
algorithm complexities.
CONCLUSION
The main objective of this work is compare four training algorithms that can be employed to
detect the saturation level in the magnetic core of a welding transformer and to bring about the best
suited method considering numerous factors such as computational time, mean squared error,
gradient and algorithm complexity. Based on analysis the following conclusions have been obtained:
• Levenberg-Marquardt algorithm gave the least RMSE value and also the least gradient
compared to all the four methods.
• The Gradient Descent method gave the highest RMSE value which is not a desired quality.
• The Resilient Back propagation algorithm gave RMSE values close to the Levenberg-
Marquardt algorithm and the output signal obtained was close enough to the required target
signal.
Considering all the factors such as RMSE, computational time, algorithm complexity and the
gradients obtained, it is concluded that the Resilient Back Propagation algorithm is the most suitable
method that can be employed to detect the saturation level in the magnetic core of welding
transformer and Levenberg-Marquardt can be considered as the next best.
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AUTHOR’S BIBLIOGRAPHY
Rama Subbanna,S. graduated from Jawahalal Nehru Technological University in
the year 2003. M.Tech from Jawahalal Nehru Technological University, Hyderabad,
in the year 2006. Currently, He is pursuing Ph.D from Jawahalal Nehru
Technological University, Anatapur, India. Presently, he is working as Assistant
Professor in St.Martin’s Engineering College. His research includes Transformer,
Controllers, ANN Techniques and Fuzzy Logic Methods.
Lahari,J.N. is a final year student of B.Tech in Electrical and Electronics
Engineering at St. Martins Engineering College, J.N.T.U-Hyderabad. Her research
interests are mainly concerned with applications of Power Systems and Electrical
Machines with artificial intelligence techniques.
Usha Rani,K.R. is a final year student of B.Tech in Electrical and Electronics
Engineering at St. Martins Engineering College, J.N.T.U-Hyderabad. Her research
interests includes Fault location and detection in power system network and
Electrical Machines.
Dr. Suryakalavathi,M. graduated from S.V.University, Tirupati in the year 1988 .
M.Tech from S.V.University, Tirupati in the year 1992. Ph.D from J.N.T.University,
Hyderabad in the year 2006 and Post Doctoral from CMU, USA. She is presently
professor of Electrical and Electronics Engineering department, J.N.T.U.College of
Engineering, Hyderabad. She presented more than 50 research papers in various
national and international conferences and Journals. Her research area includes High
Voltage Engineering, Power Systems, Artificial Intelligence Methods.

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