The aim of this work is to develop and evaluate a novel method to detect the magnetization level in the magnetic core of a welding transformer. It is based on an Artificial Neural Network (ANN) and requires only the measurement of the transformer's primary current. The magnetization level detector is a substantial component of a Middle-Frequency Direct Current (MFDC) Resistance Spot Welding System (RSWS), where the welding current and the flux density in the welding transformer's magnetic core are controlled by two hysteresis controllers [1].

The resistance spot welding systems described in different realizations [2]-[7], are widely used in the automotive industry. Although the alternating or Direct Currents (dc) can be used for welding, this work focuses on the RSWS (Figure 1) with dc welding current. The resistances of the two secondary windings R2, R3 and characteristics of the rectifier diodes, connected to these windings, can slightly differ. References [8]-[11] show that combination of these small differences can result in increased DC component in welding transformer's magnetic core flux density. It causes increasing magnetic core saturation with high impact on the transformer's primary current i1, where current spikes eventually appear, leading to the overcurrent protection switch-off of the entire system. However, the problematic current spikes can be prevented either passively [8] or actively [9]-[11].

When the current spikes are prevented actively, closedloop control of the welding current and magnetic core flux density is required. Thus, the welding current and the magnetic core flux density must be measured. While the welding current is normally measured by the Rogowski coil [12], the magnetic core flux density can be measured by the Hall sensor or by a probe coil wound around the magnetic core. In latter, the flux density value is obtained by analogue integration of the voltage induce in the probe coil [9]. Integration of the induced voltage can be unreliable due to the unknown integration constant in the form of remnant flux and drift in analogue electronic components. The drift can be kept under the control by the use of closed-loop compensated analogue integrator [11].

An advanced, 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 [11]. This solution requires measuring of the welding current, while instead of measured flux density only information about magnetization level in the magnetic core is required. Some methods are tested on welding transformer's magnetic core, that can be applied for magnetization level detection as presented in [9], [10]. All these methods are required in Hall sensor or probe coils which make them less interesting for applications in industrial RSWS, due to the relatively high sensitivity on vibrations, mechanical stresses and high temperatures. In order to overcome these problems, an ANN based magnetic core magnetization level detector is introduced in this work. Its only (single) input is the measured transformer's primary current. The ANN, based on the magnetic core magnetization level detector, is trained to recognize the waveform of the current spikes, which appear in the primary current when the magnetic core is approaching the saturated region. Upon detection of a spike, the ANN target signal makes it possible for the transformer supply voltage to change the direction which also changes the magnetic flux density accordingly. This way, the system is controlled using the ANN detector and over-current protection switch-off is prevented.

Before the ANN can be applied, its structure must be defined first, and then the ANN must be trained using an appropriate learning method [10], [13], [14]. In this paper, the ANN structure appropriate for saturation detection in the transformer's magnetic core and the appropriate learning methods are found with the help of a properly built dynamic model of the RSWS [8], [15]. The mentioned dynamic model includes models of the hysteresis controllers [11] and the ANN based magnetization level detector. The well-known trial and error method was used for defining ANN structure. It is shown that the three-layer ANN with 30 neurons in the first layer, 7 neurons in the second layer, and 1 neuron in the third layer, gives acceptable results. The ANN is trained by the resilient back-propagation rule, where the measured and calculated samples of transformer's primary current, with different known levels of saturation in the magnetic core, are used. The calculated and measured results presented in this paper, shows that the proposed ANN based magnetic core magnetization level detector can be used as a part of the discussed RSWS, improving performances of the entire system.

The RSWS, shown in Figure 1, consists of an input rectifier, an H-bridge inverter, a single phase transformer and a fullwave output rectifier [11]. The three-phase Alternating Current (AC) voltages u1, u2, u3, supplied from the electric grid, are rectified in the input rectifier in order to produce the direct current (dc) bus voltage. This voltage is used in the H-bridge inverter, where different switching patterns and modulation techniques can be applied, to generate ac voltage uH, required for supply of the welding transformer. The welding transformer has one primary and secondary windings. They are marked with indices 1, 2 and 3 respectively. The currents, the number of turns, the resistance and the leakage inductances of the primary and secondary welding transformer's windings are denoted by i₁, I₂,I₃, N₁, N₂, N₃, R₁, R₂, R₃ and Lσ₁, Lσ₂, Lσ₃. The effects of the eddy current losses are accounted by the resistor R_fe,R₁ and L₁ are the resistance and inductance of the load. The output rectifier diodes D₁ and D₂ are connected to both transformer's and secondary coils. They generate the dc welding current i₁ which has a dc value a few times higher than the amplitudes of ac currents i₂ and i₃ that appear in the transformer's secondary coils without the rectifier diodes.

Figure 1. Schematic presentation of the RSWS [1]

The dynamic model of the RSWS was built based on the schematic presentation, shown in Figure 1. The results of simulations, obtained by the dynamic model of the RSWS, shows a small difference in resistances R₂, R₃ and in characteristics of the rectifier diodes D₁ and D₂ can cause unbalanced time behavior of the magnetic core flux density B and the current spikes in the primary current i , as 1 shown in Figure 2. The a) and b) graphs in Figure 2 shows the same variables in different time scales. The current spikes appear approximately after 0.06s (Figure 2c). After 0.07s the current spikes become high enough to cause the over-current protection switch off of the RSWS.

Figure 2. (a), (b) and (c) Time behavior of primary current [I]

This paper proposes an ANN based detector of magnetization level in the magnetic core. The only input for the proposed detector is the measured welding transformer's primary current i1. Its output signal (Tar.) is set to one when the preset magnetization level in transformer's magnetic core is exceeded. The ANN[13] is a parallel multi-layer information processing structure, with possibility to include an expert knowledge into an existent process. The ANN accumulates knowledge training process, while the effectiveness of the ANN depends on the quality of the training procedure. The fundamental aim of the training procedure is to adjust all weights in the artificial neural network, to obtain minimal deviations between the target and calculated outputs. Before the ANN is used, an appropriate structure and learning method must be defined. This can be attained with the proper dynamic model of the RSWS[8], [15]. Once the model is built, the proper structure of the ANN and the learning method can be easily defined by running simulations with different ANN structures. The trial and error procedure was applied in the testing.

Figure 3. Signals involved in the training process of the ANN

Figure 4. The transformer's primary current i 1 and the ANN output signal Tar

Figure 3 shows the signals involved in the learning process of the ANN. The input learning signal (pattern) of the ANN in the learning process is the absolute value of the transformer's primary current (1 pu =400A) obtained from the RSWS dynamic model. According to the magnetization level in the magnetic core, the output learning signal (target) was set to zero or one. The current spikes in the transformer's primary current clearly show that the magnetic core becomes highly saturated. In that case, the output of the ANN based magnetization level detector must be set to one. Figure 3 shows learning signals during samples 3000 and 3200, while the number of all samples is 4041.

Results of the ANN are very dependent on the ANN net configuration, hence an extensive testing of different net configurations was performed. The proper net structure can be defined with the proper model of a whole system. The high computational effort required for simulations of the whole system forced us to apply the trial and error method in determining the ANN structure, instead of applying optimization techniques. The correlation coefficients between the target signal and calculated outputs were the Root Mean Square Errors (RMSE). The learning were controlled. Based on results of the extensive numerical analysis, the ANN structure with 30 neurons in first, 7 neurons in second and 1 neuron in last layer was chosen (RMSE = 0.0037252). More or less neurons in the first layer gave worse RMSE. In addition to determining the ANN structure, the model was applied also for determining the most appropriate learning rule. From all learning rules tested, the resilient and Levenberg- Marquardt backpropagation algorithms gave the best RMSE values. However, the resilient backpropagation was adopted due to the lowest Computational effort required.

As soon as the structure of the ANN and learning rule is defined, they can be applied on the measured signals, while the ANN trained with the measured signals can be applied as magnetization level detector in RSWS controlled by the advanced hysteresis control. Figure 4 shows output signals from the ANN for two different transformer's primary currents (absolute, per unit value, 1 Pu = 400A) measured on the RSWS. As soon as the ANN, through the characteristic form of the primary current, detects that the magnetization level in the magnetic core is high enough, but still not too high (Figure .2(c)), the value of the ANN output changes, causing change in the polarity of the applied supply voltage. This leads to the change in the sign of the magnetic flux density derivative. The magnetic flux density move in the opposite direction until the ANN detects increased magnetization level again. The polarity of the applied supply voltage is changed again and the complete procedure is repeated.

The aim of this research presents a reliable method for detection of the magnetic core saturation that does not require any additional sensor. The proposed ANN based detector requires measurement of the welding transformer's primary current. With the increasing level of the magnetic core saturation the magnitude of the current spikes in the primary current is increasing, which finally leads to the over-current protection switch-off. The ANN, used in this work, is trained to recognize the waveform of the current spikes which is used for magnetization level detection. The applied ANN contains 3 layers with 30, 7 and 1 neuron in the first, second and third layer, respectively. It is trained by the resilient backpropagation rule using samples obtained by the measurements and the dynamic model of the RSWS. Performances of the trained ANN were evaluated by tests performed with the samples used in the training procedure, and with the newly measures samples. The results of the laboratory tests are very promising and show reliable recognition of the magnetic core saturation.