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INTERNATIONAL JOURNAL OF in Engineering and Technology (IJARET), ISSN 0976 – International Journal of Advanced Research ADVANCED RESEARCH IN ENGINEERING AND Volume 5, Issue 3, March (2014), 6480(Print), ISSN 0976 – 6499(Online)TECHNOLOGY (IJARET)pp. 191-201, © IAEME ISSN 0976 - 6480 (Print) ISSN 0976 - 6499 (Online) IJARET Volume 5, Issue 3, March (2014), pp. 191-201 © IAEME: www.iaeme.com/ijaret.asp Journal Impact Factor (2014): 7.8273 (Calculated by GISI) ©IAEME www.jifactor.com 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. 191 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 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. 192 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 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. 193 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 2. Gradient Descent: 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=JTJ And the gradient can be computed as G=JTe 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- [JTJ+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. 194 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 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. 195 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 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 196 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 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 Figure 2(a): Target signal of ANN with Figure 2(b): Best training performance GD algorithm 197 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 3) Levenberg-Marquardt Figure 3(a): Target signal of ANN with Figure 3(b): Best training performance LM algorithm 4) Bayesian Regularization Figure 4(a): Target signal of ANN with Figure 4(b): Best training performance 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/ RP GD LM BR parameters Computational 00:18 00:15 01:03 1:04 time(sec) Gradient 0.0523 0.0172 0.00256 0.150 Performance(MSE) 0.00373 0.0103 0.00348 0.00443 198 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 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. REFERENCES 1. K. Deželak, J. Pihler, G. Štumberger, B. Klopčič and D. 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Herawati Yusuf, “The Influence of Air Gaps at 0.4 Duty Cycle on Magnetic Core Type ‘E’ to Increase the Efficiency of Cuk Converter”, International Journal of Electrical Engineering & Technology (IJEET), Volume 4, Issue 2, 2013, pp. 71 - 80, ISSN Print : 0976-6545, ISSN Online: 0976-6553. 22. Rama Subbanna.S, Kamalakar.K.S.K. and Dr. Suryakalavarthi.M, “Fuzzy Logic Approach to Control the Magnetization Level in the Magnetic Core of a Welding Transformer”, International Journal of Electrical Engineering & Technology (IJEET), Volume 4, Issue 3, 2013, pp. 19 - 28, ISSN Print : 0976-6545, ISSN Online: 0976-6553. 200 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 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. 201