In automatic and robotic welding with arc oscillations, in order to adapt the trajectory of the welding torch to the real location of the joint of the parts, it is promising to estimate the position of the electrode relative to the welding line based on the current of the welding arc. The significant advantages of using estimators are the absence of additional equipment on the welding torch, as well as the combination of welding and measuring points. The paper proposes a new approach based on the use of an artificial neural network to solve the problem of estimating the position of the electrode relative to the seam line. The quality indicators of the estimation processes have been investigated using mathematical modelling. Neural network, estimator, electrode deviation, welding, arc oscillations, robot Proceedings ITTAP'2023: 3rd International Workshop on Information Technologies: Theoretical and Applied Problems, November 22-24, Proceedings
DEVIATION IN ROBOTIC
One of the main ways of developing automatic and robotic welding systems is the use of tools for
adapting the trajectory of the welding torch [
An alternative to VS are the so-called arc sensors of the position of the electrode relative to the connection line of the welded parts [6]. Such sensors are suitable for welding technologies with transverse oscillations of the arc. It is known that as a result of transverse oscillations of the arc, there are such positive effects as an increase in the width of the seam, a decrease in the penetration depth, and a decrease in overheating of the metal [7-8].
Arc sensors allow the ε̂ estimate of the transverse deviation of the electrode tip from the weld line to be obtained not on the basis of direct measurements, but indirectly, on the basis of measurement of the welding arc current. Essential advantages of the arc sensors include the absence of any extra equipment on the welding torch and combining the welding points with the measurement ones.
Functional dependence of the welding current upon ε under steady conditions in welding fillet, Toverlap or butt joints with groove preparation is of a clearly defined extremal (unimodal) character, resulting from the V-shaped profile of surfaces of the parts joined. Minimum of this functional dependence always falls on the weld line between the parts joined. One of the most common approaches to finding extremum is based on activation of the system using probing oscillations and the method of synchronous detection [9]. Transverse oscillations of the welding torch can be used as the probing oscillations for the case of arc welding. With such oscillations the synchronous detector receives a signal proportional to amplitude of the 1st harmonic of the welding current to obtain the ε̂ estimate [6].
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However, having such an important advantage as the high frequency selectivity under conditions of substantial interference, the method of synchronous detection is not free from certain drawbacks. The latter include the need to adjust the initial phase of the harmonic signal coming to a multiplication link of the synchronous detector, depending upon the phase delay of the 1st harmonic of the welding current in an inertia control object of the extremal system, which (delay) can vary with the unstable parameters of the object. In addition, determination of the amplitude of only the 1st harmonic of the welding current gives no way of obtaining the ε̂ estimate, which is insensitive to variations in the welding process parameters. To do this, it is necessary to determine also the amplitude of the 2nd harmonic of signal [6].
The purpose of this article is to consider a new approach, based on using the artificial neural network (NN), to solving the problem of estimation of the position of the electrode relative to the connection line of the welded parts in welding with arc oscillations.
( ) = ( ) + sin ; = 2 , (1) where A and f are the amplitude and frequency of the torch oscillations, respectively, and is the deviation of the middle position of the electrode from the joining line. The welding current signal i(t) from the current sensor CS is fed to a band filter BF which passes frequencies in a range from f to 2f. In this case the (t) signal of oscillations of the welding current at an outlet of BF will be determined as follows [6]:
torch
Y 0 i(t)
CS
BF
(t) wire (electrode) x
X −
+ CWS the time constant of the welding circuit; = ( − ); = −1√ ⁄ , where de is the electrode 2 diameter, vw is the welding speed and ve is the electrode feed speed. It should be noted here that relationships (1) through (5) are valid on condition of confirmation of a hypothesis of the δ(t) signal being quasi-stationary, i. e. having rather small variations for a period of oscillations of the torch.
As it can be seen from expression (3), upon determining amplitude A1 of the 1st harmonic of the δ(t) signal, we can find the ε̂ estimate of the transverse deviation ε of the electrode tip from the weld line. This was a traditional approach to determination of ε̂, based on the use of the method of synchronous detection to find A1 [9]. The synchronous detector is a device for current averaging the δ(t) × sin( ωt + ϕD) signal, for a period of probing oscillations of where ϕD is the adjusted initial phase determined as ϕD = π2 − β − ϕ1. However, during the welding process there is a probability of variations in some parameters of the welding circuit, such as Rw, M and E. To obtain the ε̂ estimate, which would be insensitive to variations in these parameters, it is necessary also to determine the amplitude of the 2 nd harmonic of δ(t) [6]. Upon meeting the T<Tw condition, where T=1/f is the period of the torch oscillations, by dividing (3) by (4) we will obtain an expression for determination of this estimate: 1 (6) ̂= ℎ ( × 1).
2 2 2 As is seen, here there are no parameters depending upon variations in the welding process conditions. Therefore, we will take expression (6), which allows determination of the ε̂ estimate of the electrode deviation from the weld line, which is robust to variations in the welding circuit parameters, as the basis for the development of the NN-based estimation device.
In building the device for estimation of the lateral electrode deviation, the task was to obtain current values of the estimate every half-period of the torch oscillation, i. e. determine ε̂ with a period of T0=T/2. Fig. 2 shows a block diagram of the NN-based estimator for ε. The diagram comprises two pulse elements with a closing period of T0 and T1.
Kn
T1
T0 TDU x
y NN
CU ˆ
Operation of these elements is synchronized between each other and T1=T0/N, where N is an integer. The welding current oscillation signal δ(t) comes to the estimator input. Upon passing a link with the rate-fixing coefficient Kn, this signal becomes such that | δ̄(t)| ≤ 1. The rate-fixed signal δ̄(t) is sampled in time with a period of T1 and comes to the time delay unit TDU. The N-dimensional vector , the components of which are N of the last values of the sampled signal δ̄ (nT1), n = 0,1,2, . .. , is formed in the TDU. Vector sampled with a period of T0 comes to the input of NN, where the two-dimensional vector is determined, whose components are values of the amplitudes of the 1st and 2nd harmonics of the δ̄ signal. The ε̂ estimate of the electrode deviation from the weld line is determined in the deviation computation unit CU according to (6). Therefore, according to the described principle of operation of the estimator, it can be seen that the signal at its output will be determined discretely by the T0 sampling period and the certain time delay. neuron in the hidden layer is determined as: ℎ = ( ∑ + ) , ( ) = 1 − −2 1 + −2
. = ∑ ℎ
+
where xi is the i-th input of NN, bj is the bias of the j-th neuron in the hidden layer (in Fig. 3 the neuron biases are not shown) and f(∙) is the activation function of the type of a hyperbolic tangent: Output of the m-th neuron in the output layer ym is the weighted sum of the input signals hj and the biases bm
The feedforward NN, having only one hidden layer with a certain number of neurons contained in it, is known to be capable of approximating a wide range of continuous non-linear functions at a preset accuracy. In this case the minimum required number of neurons in the hidden layer is determined heuristically, based on the tolerated approximation error.
The purpose of teaching (training) the multi-layer feedforward network consists in finding weight factors of couplings and neuron biases. The method of error backpropagation is employed most (7) (8) (9) frequently to train this type of NN. This method belongs to the supervision type of the teaching methods. The main point of this method is that an error arising during training, which presents a difference between the actual and preset values of the network output, is re-distributed by varying the coefficient of coupling between the network layers in a direction from the output to input of NN to minimize the total network error. An improvement in the backpropagation algorithm is described [10]. This improvement made it possible to substantially increase the rate of teaching the networks. So, it is this Levenberg-Marquardt modification that we use in our work.
To train the network, we formed arrays of 500 values of its output vector and the preset output vector . Dimensionality of the input vector was assumed to be equal to dim ( )=N=20. Arrays of the vectors ( ) = [ 1( ), 2( ), . . . , 20( )] ; ( ) = [ 1( ), 2( )] , = 1,500 were determined as: ( − 1)
( ) = 1( )cos ( − − 1 + ( )) (10) 2 ( − 1)
+ 2( )sin ( − − 2 + ( )) , = 1,20 where y1, y2, ∆β and ∆γ are the random, uniformly distributed values within their variation ranges. In the hidden layer of NN were selected 13 neurons and this network was being trained for 1200 epochs.
The computation experiments involving a mathematical model of the system were conducted to determine qualitative indicators of the processes of estimation of the electrode position with respect to the weld line. The following parameters of the welding process were selected for modelling:
M=0.35 mm/A·s; E=2 V/mm; Rw=0.2 Ohm; de=1.2 mm; ve=45 mm/s; vw=5 mm/s; K=1; A=2 mm; f=5Hz.
Phase shifts of the welding current oscillation signal due to BF were assumed to be ϕ1=-0.8 rad and ϕ2=1.6 rad. During the modelling process the δ(t) signal was found using expressions (1) through (5). In the model of the estimator the time delay caused by NN computer emulation and performance of mathematical operations was ignored.
The first computation experiment simulated the next practical situation. During welding with arc oscillations, the torch moves along the weld so that the path of its middle position ε(t) is a straight line, but the angle between ε(t) and the weld line is equal to 0.2 rad. At the time t=0, where ε(t)=-4 mm, the δ(t) signal is fed to the input of the estimator. Processes occurring in this case are shown in Fig. 4,a, where are depicted the ε(t) (curve 1) and ̂ε(t) (curve 2) signals. It can be seen from this figure that after the first period T0, where the adequate input vector of the network is just being formed, the ˆ(t) 0.5 -0.5 -1 0 , p.u.
4 c 1 2 3 5 6 7 t, s FigureF4i:g.P4r.oPcreoscseessseoscoccucrurrirningginintthhee eessttiimmaattoor ratalti nlienaeralyrlvyavryairnyginεg: aε:–aes–tiemsattimionatoiofnε;ofbε–; bam–palimtupdelistuodfes (t) of harmonics of the currehnatr manodnicthseoifrtehsetcimuraretnetsa;ncd–thseigirneasltiδm̄(att)es; c – signal
. signal at the output of the estimator with a small-time delay almost copies the ε(t) signal within its variation range.
Fig. 4,b shows actual values of amplitudes (in per unit – p. u.) of the 1st (curve 1) and 2nd (curve 3) harmonics of the δ̄ signal and the corresponding estimates of amplitudes of these harmonics (curves 2 and 4), while Fig. 4,c shows the δ̄(t) signal. It can be seen from these Figures that NN is characterized by a rather high accuracy of functioning.
The next experiment was in modelling, similar to that in the first experiment, of the process of estimation at ε(t)=3sin(πt). Fig. 5 shows the ε signal (curve 1) and the ε̂ estimate (curve 2).
The latter experiment consisted in investigation of the process of estimation of the electrode deviation at ε varying following the exponential law. Approximately the same character of variation in ε will persist in the weld tracking system closed by the ε̂ signal, providing that the controller of this system is synthesized to ensure the well-damped transient processes. Fig. 6 shows the ε signal with an amplitude of 2 mm (curve 1), varying following the exponential law, and the estimate of this signal (curve 2). 1 2 1 2 3 4 5 t, s
Analyzing the modelling results shown in Fig. 4-6, one can note that the estimator thus built provides a high accuracy of estimation of the electrode deviation from the weld line, with a variation in the deviation following different functional dependencies and within different ranges.
There is another important advantage of using NN for estimation of ε. Under certain conditions of the welding process, such as those involving short circuiting of the arc gap, some noise ξ(t) may be present at the output of BF. In this case, if we use the model of such a noise in preparation of the network teaching data arrays, we can train NN so that it becomes adapted to the effect of this noise.
In robotic welding with arc oscillations, in order to adapt the trajectory of the welding torch to the actual location of the connection of parts, it is promising to use arc sensors that estimate the position of the electrode relative to the welding line based on the current of the welding arc.
A new approach based on the use of an artificial neural network is proposed to solve the problem of estimating the position of the electrode relative to the seam line.
A two-layer feedforward neural network with a 20-13-2 type architecture was used to construct the electrode deviation estimator. Based on the welding current signal, the estimator evaluates the relative position of the electrode twice during the arc oscillation period.
Mathematical modelling shows that the estimation processes are characterized by a sufficiently high accuracy indicators. 6. References [6] G.A. Tsybulkin, Arc sensing systems for welding robots, Stal, Kyiv, 2011, 145 p. (in Russian). [7] Singh, P. K., Patel, D., Prasad, S. B. (2016). Development of vibratory welding technique and tensile properties investigation of shielded metal arc welded joints. Indian Journal of Science and Technology, Vol. 9(35), pp. 1–6, doi: 10.17485/ijst/2016/v9i35/92846. [8] Luo, Y., Zhang, Z.L., Zhou, C.F. et al. (2017) Effect of oscillation parameters of narrow groove MAG welding on weld formation. J. Hebei Univ. Sci. Technol, 38, 6. https://doi.org/10.3390/app13095519. [9] G.A. Tsybulkin, Adaptive control in arc welding, Stal, Kyiv, 2014, 171 p. (in Russian). [10] Hagan M.T. and Menhaj M.B. Training Feedforward Networks with the Marquardt Algorithm // IEEE Trans. Neural Net., vol. 5, 1994, №6, pp. 989-993.