NEURAL NETWORK BASED ESTIMATOR OF THE ELECTRODE
                         DEVIATION IN ROBOTIC WELDING WITH ARC OSCILLATIONS
                         Bogdan Pryymaka, Mykola Zhelinskyia, Mykola Ostroverkhova, Oleksiy Khalimovskyya
                         a
                                Igor Sikorsky Kyiv Polytechnic Institute, 37, Prospect Beresteiskyi, Kyiv, 03056, Ukraine


                                             Abstract
                                             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.

                                             Keywords 1
                                             Neural network, estimator, electrode deviation, welding, arc oscillations, robot

                         1. Introduction
                             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 [1]. The analysis of literary sources shows that today such
                         means are most often visual sensors (VS) [2-4]. According to the signal of the VS, the trajectory of the
                         welding torch is adapted to the real location of the joint of the parts [2, 3]. In [4], the possibility of using
                         a VS to assess the quality of welds is considered. The prospects for using artificial intelligence methods
                         in welding operations with visual sensors are highlighted in [5].
                             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, T-
                         overlap 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].

                         Proceedings ITTAP’2023: 3rd International Workshop on Information Technologies: Theoretical and Applied Problems, November 22–24,
                         2023, Ternopil, Ukraine, Opole, Poland
                         EMAIL: b.i.pryymak@gmail.com (A. 1); mykola.zhelinskyi@gmail.com (A. 2); n.ostroverkhov@hotmail.com (A. 3);
                         o.khalimovskyy@ukr.net (A. 4)
                         ORCID: 0000-0001-7680-8565 (A. 1); 0000-0003-4862-1802 (A. 2); 0000-0002-7322-8052 (A. 3); 0000-0003-3672-8530 (A. 4)
                                          ©️ 2023 Copyright for this paper by its authors.
                                          Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
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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 1 st 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 2 nd 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.

2. Method for estimation of the electrode deviations
    Fig. 1 schematically shows the system of welding with arc oscillations. The welding current source
WCS is connected to parts welded and the welding torch. Voltage is in the welding torch fed through a
sliding contact to the welding wire which serves as the consumable electrode. During the welding
process the torch is brought into oscillation in a direction across the weld line. That is, in the system of
the X – Y coordinates with a centre on the weld line, where the Y axis is parallel to a longitudinal axis
of the electrode extension and the X axis is normal to the weld line, the current position of the electrode
tip is determined as follows:
                                𝑥(𝑡) = 𝜀(𝑡) + 𝐴 sin 𝜔 𝑡; 𝜔 = 2𝜋𝑓,                                       (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]:




                                                               i(t)                 (t)
                                                                           BF



                                                                 CS
                                        torch


                                                           wire
                                                        (electrode)
                                        Y

                                                                     −         +
                                            0            X                CWS
                                                    x
                                                

Figure 1: Schematic of the system for welding with arc oscillations
                    𝛿(𝑡) = 𝐴1 cos( 𝜔𝑡 − 𝛽 − 𝜙1 ) + 𝐴2 sin( 2𝜔𝑡 − 𝛾 − 𝜙2 ),                          (2)
where A1 and A2 are the amplitudes of the 1 and 2 harmonics of the δ(t) signal, respectively;  and
                                              st     nd

 are the phase shifts of these harmonics due to dynamics of the welding circuit; ϕ1 and ϕ2 are the phase
delays of the above harmonics in the filter. Values in (2) are found from the following formulae:
                                             𝐴𝐾𝐸 𝑡ℎ(𝜇𝜀)                                             (3)
                                    𝐴1 =                      ;
                                          𝑅𝑤 √1 + (𝜔𝑇𝑤 )−2

                                                 𝐴2 𝐾𝐸𝜇                                                 (4)
                               𝐴2 =                                   ;
                                      4𝑅𝑤 𝑐ℎ2 (𝜇𝜀)√1 + (2𝜔𝑇𝑤 )−2

                            𝛽 = 𝑎𝑟𝑐𝑡𝑔(𝜔𝑇𝑤 );       𝛾 = 𝑎𝑟𝑐𝑡𝑔(2𝜔𝑇𝑤 ),                                    (5)

where M is the slope of electrode melting rate characteristic depending upon the welding current; E is
the intensity of the electric field in the arc column; R w is the welding circuit resistance; Tw=Rw/EM is
                                                    𝜋−𝛼
the time constant of the welding circuit; 𝐾 = 𝑡𝑔 (      ); 𝜇 = 𝑑𝑒 −1 √𝐾𝜋𝑣𝑤 ⁄𝑣𝑒 , where de is the electrode
                                                     2
diameter, vw is the welding speed and v e 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
       π
ϕD = − β − ϕ1 . However, during the welding process there is a probability of variations in some
       2
parameters of the welding circuit, such as R w, 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       𝜇𝐴 𝐴1                                               (6)
                                       𝜀̂ =    𝑎𝑠ℎ ( × ).
                                            2𝜇       2 𝐴2
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.

3. The use of NN for estimation of the electrode deviations

   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.


                             T1                   T0
                                                             x                  y                 ̂
                     
              Kn                      TDU                            NN                 CU

Figure 2: Block-diagram of the electrode deviation estimator

  Operation of these elements is synchronized between each other and T 1=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 𝒙, 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 𝒙 sampled with a period of T0 comes to the input of NN, where the two-dimensional
vector 𝒚 is determined, whose components are values of the amplitudes of the 1 st 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 T 0 sampling
period and the certain time delay.
    Fig. 3 shows architecture of the neural network employed, where black circles designate the inputs
of NN and white circles designate the neurons proper. This NN is a feedforward network, comprising
inputs of NN and two layers of neurons, i. e. hidden and output, which we designate by indices i, j, m,
respectively.




                                I                                             O
                                N                                             U
                                P                                             T
                                U                                             P
                                T                                             U
                                S                                             T
                                                                              S




                                                                    Output
                                                       Hidden        layer
                                                        layer
Figure 3: Architecture of the neural network

   Each input of NN is connected to the input of each neuron in the hidden layer via coupling with a
weight factor wij. In turn, the output of each neuron in the hidden layer is connected to the input of each
neuron of the hidden layer via coupling with a weight factor w jm. The hj signal at the output of the j-th
neuron in the hidden layer is determined as:
                                                                                                      (7)
                                     ℎ𝑗 = 𝑓 (∑ 𝑥𝑖 𝑤𝑖𝑗 + 𝑏𝑗 ),
                                                   𝑖
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:
                                                  1 − 𝑒 −2𝜆                                              (8)
                                          𝑓(𝜆) =             .
                                                  1 + 𝑒 −2𝜆
Output of the m-th neuron in the output layer y m is the weighted sum of the input signals h j and the
biases bm
                                       𝑦 = ∑ℎ 𝑤 + 𝑏                                                      (9)
                                        𝑚              𝑗   𝑗𝑚   𝑚
                                               𝑗
     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
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 𝒙 and the preset output
vector 𝐲. Dimensionality of the input vector was assumed to be equal to dim (𝒙)=N=20. Arrays of the
vectors 𝒙(𝑘) = [𝑥1 (𝑘), 𝑥2 (𝑘), . . . , 𝑥20 (𝑘)]𝑇 ; 𝒚(𝑘) = [𝑦1 (𝑘), 𝑦2 (𝑘)]𝑇 , 𝑘 = 1,500 were determined as:
                          𝜋(𝑖 − 1)                                                                    (10)
   𝑥𝑖 (𝑘) = 𝑦1 (𝑘) cos (            − 𝛽 − 𝜙1 + 𝛥𝛽(𝑘))
                             𝑁
                                                2𝜋(𝑖 − 1)
                                     + 𝑦2 (𝑘) sin (        − 𝛾 − 𝜙2 + 𝛥𝛾(𝑘)) , 𝑖 = 1,20
                                                   𝑁
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.

4. Results of modelling
   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 ε̂(t) (curve 2) signals. It can be seen from this figure that after
the first period T0, where the adequate input vector 𝒙 of the network is just being formed, the ̂( t )

       ε,̂ (mm)                                               A 1 , A 2 , Â 1 , Â 2 (p.u.)
  4                                                       1



  2                                                     0.5



  0                                                       0

                                                                                                    1
                                          1                                                         2
 -2                                                    -0.5
                                          2                                                         3
                                                                                                    4

 -4                                                      -1
   0           2          4           6       t, s         0              2               4     6       t, s
                          a                                                               b
            , p.u.
   1



 0.5



   0



-0.5



  -1
       0              1          2              3             4               5            6            7          t, s
                                                             c
FigureFig.4.
      4: Processes   occurring
             Processes occurringininthe
                                     the estimator
                                         estimator atatlinearly
                                                         linearly  varying
                                                                varying  ε: aε:–aestimation
                                                                                  – estimation of ε; ofbε;
                                                                                                         –b – amplitudes
                                                                                                           amplitudes of
of harmonics of the current   and their    estimates;    c –their
                                                             signal   ̄
                                                                      δ(t) c – signal     ( t )
                          harmonics    of the current and         estimates;
       .
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).
                                         ε,̂ (mm)
                                     4
                                                                                    1
                                                                                    2
                                     2



                                     0



                                  -2



                                  -4
                                    0               1        2            3         t, s
Figure 5: Estimation of harmonic varying
                              Fig.5.     in ε of harmonic varying in ε
                                     Estimation

   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).
                                   ε,̂ (mm)
                             3

                             2             1
                                           2
                             1

                             0

                             -1

                             -2

                             -3
                               0       1       2      3      4       5    t, s
Figure 6: Estimation of exponential
                              Fig.6. varying in εof exponential varying in ε
                                     Estimation

    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.

5. Conclusions
    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.

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