CONTROL OF GMA BUTT JOINT WELDING BASED ON NEURAL NETWORKS

# K. H. Christensen[^1], T. Sørensen[^2]

# ABSTRACT

This paper presents results from an experimentally based research on Gas
Metal Arc Welding (GMAW), controlled by the artificial neural network
(ANN) technology. A system has been developed for modeling and online
adjustment of welding parameters, appropriate to guarantee a high degree
of quality in the challenging field of butt joint welding with full
penetration under stochastically changing boundary conditions, e.g.
major gap width variations. GMAW experiments performed on mild-steel
plates (3 mm of thickness), show that high quality welds with uniform
back-bead geometry are achievable for gap width variations from 0.5 mm
to 2.3 mm - scanned 10 mm in front of the electrode location. In this
research, the mapping from joint geometry and reference weld quality to
significant welding parameters, has been based on a static multi-layer
feed-forward network. The Levenberg-Marquardt algorithm, for non-linear
least square error minimization, has been used with the back-propagation
algorithm for training the network, while a Bayesian regularization
technique has been successfully applied for minimizing the risk of
inexpedient over-training.

# KEYWORDS

GMA welding, butt joint welding with full penetration, open-loop weld
geometry control, neural network modeling, Marquardt algorithm, and
Bayesian regularization.

# 

# 

# INTRODUCTION

Gas Metal Arc Welding (GMAW) is - due to its considerable flexibility,
productivity and weld quality - the most prevalent arc welding process
in industry; but unfortunately also one of the most complex processes.
Basically, the GMAW process involves conductive, convective, radiative
heat and metal transfer, phase transformations among many unknown
disturbances. Accordingly, the GMAW process is a time varying,
non-linear, coupled, multi-variable process whose highly complex
physics, is not fully comprehended neither qualitatively nor
quantitatively. Selecting appropriate welding parameters to get a given
weld quality (i.e. weld geometry), is clearly a non-trivial task.
Furthermore, even minor changes in system dependent parameters, e.g.
joint geometry, heat conduction, etc., from given reference values
necessitate a continuous adjustment of significant welding parameters,
such as welding speed, current, voltage etc. to facilitate a sufficient
quality and shape of a desired weld. Therefore, to handle such
situations in a reasonable way it is appropriate to obtain a
mathematical model that correlate welding process parameters to weld
quality - or vice versa; but obviously, it seems to be a challenging
issue in the field of arc welding automation.

During the past decades, intense research into the area of mathematical
modeling of the complex arc welding processes has been made to increase
the understanding of the effects of the arc welding process parameters
on the weld quality. This extended work includes theoretical studies
based on heat transfer and fluid flow theory etc. as well as empirical
methods based on knowledge collected from specific weld task
experiments. However, the many years of work has proven that the
development of exact and reliable models based on the fundamental
physical laws are extremely complicated if not impossible, and even the
most promising models are typically unsuitable for real-time control
purposes. Even though empirical models inherently have many drawbacks,
such as sensitivity on geometry and material properties, and much more,
they tend to have some advantages in the area of arc welding automation.
Classic regression analysis was applied to welding geometry research in
the late half of the 80\'ties (Ref. 1), while the first step towards the
application of artificial neural network (ANN) was reported a few years
later (Ref. 2). In this, ANN was used to determine the relationship
between significant welding parameters and characteristic weld bead
dimensions for gas tungsten arc welding.

Since the publication of (Ref. 2), a diversity of papers, typically
addressing optimization and control, have been published underlining the
quality of ANN, as a generic tool with a high degree of flexibility for
modeling and control of a great variety of arc welding processes on
different kind of joint geometries, materials, etc. (Ref. 3-8). Some of
the publications, e.g. (Ref. 7-8) show that artificial neural networks
are indisputable alternatives to classic regression analysis.

Still, research on modeling and control of real-life welding based on
ANN techniques are limited and more contributions are needed. Therefore,
in this paper research on the ANN based modeling and control of the GMAW
process, is presented. A model based control system has been developed,
that continuously compensate for gap width variations in butt joint
welding with full penetration by selection and maintenance of the
equipment parameters necessary to achieve a user specified reference
back-bead geometry, which is naturally a considerable factor to the
final weld quality.

After a short introduction of ANN, the paper proceeds with a description
of the general considerations concerning the welding experiments that
have been carried out. Next, the results from these experiments are
presented and discussed together with the applied control strategy, and
finally a conclusion on the work is drawn.

**THE MODELING TECHNIQUE: ARTIFICIAL NEURAL NETWORK (ANN)**

Due to their theoretical ability to approximate arbitrary non-linear
mappings, ANN\'s are typically applied when appropriate analytical
models are unknown or extremely complex. In mathematical terms, an ANN
can be characterized as a highly complex, non-linear mapping function,
which in a given domain transforms input to output. Although an ANN
model may be very complex, the basic mathematics is relatively simple.
Modeling with ANN is empirical modeling, and thus a sample database
covering the entire problem domain must be available, similar to
conventional regression analysis. When presented with inputs inside this
domain, but not appearing in the training data, a suitably trained
network will have the ability to generalize well.

The static multi-layer feed-forward network with biases and at least one
sigmoid layer is widely recognized for the capability of approximating
any function with a finite number of discontinuities (i.e. non-linear,
coupled, and multivariable systems such as e.g. the GMAW process
addressed here). In the context of this paper, a feed-forward network of
this type, shown in Figure 1, is applied.

![](media/image1.wmf)

Figure 1: Two-layer feed-forward network, performing the mapping
**y**~2~ = **F**(**x**) : $\Re^{N_{0}} \rightarrow \Re^{N_{2}}$.

The mapping from input to output can be expressed as follows:

$$\begin{array}{r}
y_{0} = x \\
y_{k} = f_{k}(A_{k}y_{k - 1} + b_{k})\text{   for }k = \text{1,2,}\text{.}\text{.}\text{.},n
\end{array}$$

where **x** (*N*~0~ 1) is an input vector, while **y***~k~* (*N~k\ ~* 1)
is an output vector from the *k*\'th layer. The sigmoid-function is
applied as transfer function: **f***~k~*(**s**) = (1+exp(-**s**))^-1^
(*N~k\ ~* 1). **A***~k~* is a weight matrix of dimension *N~k\ ~*
*N~k-~*~1~, **b***~k~* is a bias weight column vector of length *N~k~*,
and *n* is the number of layers.

In this paper the Levenberg-Marquardt algorithm for non-linear least
squares (a standard numerical optimization technique) is used with the
back-propagation algorithm for training the feed-forward neural network.
In (Ref. 9), it has been shown that the Levenberg-Marquardt algorithm is
much more efficient than other known algorithms, when the network
contains less than a few hundred weights, which is the case in this
paper.

Minimizing the risk of inexpedient over-training by use of a so-called
regularization technique (Ref. 10), is more important than guaranteeing
a fast rate of convergence. Instead of minimizing the sum of squared
errors, *F* = *E~D~*, which is the traditional approach for network
training, the objective of this technique is to minimize a performance
function with the following structure (for training based on a set of
weld data of size *m* containing:
{**x**,**t**}~(1)~,{**x**,**t**}~(2)~,...,{**x**,**t**}~(*m*)~):

$F = {\beta E}_{D} + {\alpha E}_{W}$ with ![](media/image2.wmf)

As shown in (Ref. 10), this modification of the performance function -
the addition of the term *E~W~*, representing the sum of squares of the
network weights - will improve network generalization, so that any
modestly oversized network will have the ability to sufficiently
represent the true underlying function. The basic idea of the method,
which consistently produces networks with good generalization abilities,
is that the true underlying function is assumed to have a limited degree
of smoothness, for which reason this method constrains the size of the
network weights. The optimal setting of the regularization parameters,
and , is based on the Bayesian theory, and so this technique is referred
to as Bayesian regularization. Furthermore, it is assumed that the
experimental data are infected by Gaussian noise, and finally, it should
also be noted that input and output, in this paper, are scaled similar
to (Ref. 2):

$$p_{n} = \frac{0\text{.}9 - 0\text{.}1}{p_{\text{max}} - p_{\text{min}}}(p - p_{\text{min}}) + 0\text{.}1$$

where *p*~max~ and *p*~min~ are maximum and minimum, respectively, of
the physical data parameter *p*, and *p~n~* is the scaled parameter
applied to the network.

### GENERAL CONSIDERATIONS CONCERNING THE WELDING EXPERIMENTS

The developed system is based on an ANN model, which facilitates the
mapping from some characteristic features describing the weld quality
and joint geometry to some significant welding equipment parameters. For
that reason, it is assumed that a correlation between the characteristic
features, shown in Figure 2, and significant welding parameters (welding
speed, voltage, and wire feed speed) emerge during welding, by which it
is possible to design and train an ANN model that estimate feasible
welding parameters. Furthermore, it is to be noted that the control
system design is based on the static characteristics of the welding
process.

![](media/image3.wmf) ![](media/image4.wmf)

Figure 2: The process model maps weld quality and joint geometry into
welding parameters.

To perform the described experimental validation, a PC-based welding
system has been established, consisting of a welding machine, a two-axis
table system, and a laser vision system, which is applied for real-time
seam tracking and online gap width measurement. The joint geometry is
scanned 10 mm in front of the welding torch. A schematic diagram of the
system is shown in Figure 3, while technical specifications relevant for
the experiments are given in Table 1.

![](media/image5.wmf)![](media/image6.jpeg){width="1.1236111111111111in"
height="1.5083333333333333in"}

Figure 3: Structural diagram of the experimental system.

  ------------------------- ---------------------------------------------
  Joint type                Butt weld (without backing)

  Plate material            Mild steel (S235)

  Plate thickness           3 mm

  Plate dimensions (LW)     330 50 mm

  Power supply              Constant voltage machine

  Wire type                 EN440 -- G3Si1

  Wire diameter             Ø1.2 mm

  Shielding gas             Mixture: 92 % Ar and 8 % CO~2~

  Gas flow rate             15 l/min

  CTWD                      10 mm

  Welding torch orientation Horizontal (PA) with a travel angle of 90
                            degrees
  ------------------------- ---------------------------------------------

Table 1: Technical specifications for the experiments conducted (CTWD:
Contact Tip to Workpiece Distance).

#### OPEN-LOOP CONTROL STRATEGY

The experimental investigation of the applicability of ANN in an
open-loop control strategy contains two steps: (1) To verify that the
proposed ANN model based on static weld data in fact can fit the
characteristics of the weld task in a suitable way. (2) To examine the
applicability of the static ANN process model in an open-loop control
system controlling a dynamic process.

![](media/image7.wmf)

Figure 4: The developed process model applied to an open loop control
system.

According to (1) the applicability of the developed process model
(Figure 4), in terms of precision and robustness, has been demonstrated.
A series of GMAW experiments has been conducted to obtain the decisive
knowledge about how the significant welding parameters affect the
back-bead geometry, given different joint geometries. Consequently, a
total of 39 quality welds have been made, and the welding parameters
have been selected within the domain of useable parameters, when parts
to be welded are fixed to produce given constant gap widths within a
prescribed interval. During the welding process, the gap width is
scanned 10 mm in front of the welding torch following the centerline of
the gap, while the back-bead width and height have been measured
afterwards. The relatively few experiments have been carried out in an
unsystematically way for gap widths within the interval of 0.0-2.3 mm
(Table 2), and the main objective of the experiments has been to
maintain homogenous back-bead geometries, as shown in Figure 5.

Obviously, different sets of welding parameters for a given gap width
can produce identical back-bead geometries. Therefore, for later use of
the weld data it is crucial to perform these preliminary experiments
with a certain degree of attention to the aim of this original research.

+-----+---------+---------+---------+---------+---------+---------+
| W   | Wire    | Voltage | Welding | Gap     | Ba      | Ba      |
| eld | feed    |         | speed   |         | ck-bead | ck-bead |
|     | speed   | \[V\]   |         | width   | width   | height  |
| No. |         |         | \[m     |         |         |         |
|     | \[      |         | m/min\] | \[mm\]  | \[mm\]  | \[mm\]  |
|     | m/min\] |         |         |         |         |         |
+-----+---------+---------+---------+---------+---------+---------+
| 8   | 3.8     | 19.0    | 325     | 1.00    | 3.70    | 1.00    |
+-----+---------+---------+---------+---------+---------+---------+
| 16  | 5.0     | 21.0    | 375     | 0.40    | 2.80    | 0.60    |
+-----+---------+---------+---------+---------+---------+---------+
| 25  | 2.8     | 18.0    | 310     | 2.00    | 3.70    | 0.85    |
+-----+---------+---------+---------+---------+---------+---------+
| 26  | 3.0     | 18.0    | 350     | 1.60    | 2.80    | 0.40    |
+-----+---------+---------+---------+---------+---------+---------+
| Min | 2.8     | 18.0    | 300     | 0.00    | 1.50    | 0.25    |
+-----+---------+---------+---------+---------+---------+---------+
| Max | 5.8     | 22.0    | 375     | 2.30    | 5.10    | 2.70    |
+-----+---------+---------+---------+---------+---------+---------+

Table 2: Four out of 39 experiments are shown with the boundary limits
of each parameter. The considerable variation of the gap width obviously
implies major changes in wire feed speed and voltage.

![](media/image8.wmf){width="3.2020833333333334in"
height="2.2736111111111112in"}

Figure 5: The \'s indicate the back-bead width, for which the solid line
represent the mean value (\<*w~b~*\> = 3.17 mm), while the o\'s and
dotted line represent the back-bead height (\<*h~b~*\> = 0.92 mm).

Based on these experimentally obtained weld data, a static multi-layer
feed-forward network has been trained by supervised learning. The
trained network manages the mapping shown in Figure 4. The selection of
feasible design parameters of the neural network, such as the number of
hidden layers, the number of nodes in each layer, type of activation
function etc., rely on the specific modeling task. In this study, a
two-layer network with a hidden layer containing three neurons and an
output layer containing three neurons as well - according to the number
of outputs - has been selected. All neurons contain the sigmoid transfer
function. Data sets from 33 of these experiments have been used for
network training, while the remaining 6 data sets have been used for
testing the generalization capabilities of the trained network.

The Bayesian regularization technique (Ref. 10) introduces , a so-called
effective number of parameters, which is a measure of the number of
parameters (weights) in the neural network that are effectively used in
reducing the error function. In the network training = 19.52, which is
much less than the 24 weights that appears in the chosen network.
Accordingly, the neural network applied seems to be large enough to
properly represent the true function.

The performance evaluation of the trained network has been based on a
traditional error analysis applied to the training and test data sets,
respectively. Table 3 shows the absolute mean errors for the welding
parameters, and on the basis of these results the trained network seems
to generalize well. Furthermore, to investigate the network performance
in further detail, a linear regression analysis between the network
response and the corresponding measured data sets has been performed.
The result of this analysis is shown in Figure 6, and it appears that
the wire feed speed and voltage correlate well, while the welding speed
does it barely as well. However, it is notable that especially the wire
feed speed has a great influence on the penetration, and consequently,
it is very important that this particular welding parameter is well
correlated. Since the wire feed speed varies between 2.8-5.8 m/min,
while the welding speed only varies 300-375 mm/min, it is concluded that
the influence of the welding speed is much less that the effect of the
wire feed speed in this series of experiments.

+-----------------+-----------------+-----------------+-----------------+
|                 | Wire feed speed | Voltage         | Welding speed   |
|                 |                 |                 |                 |
|                 | \[m/min\]       | \[V\]           | \[mm/min\]      |
+-----------------+-----------------+-----------------+-----------------+
| Training data   | 0.20            | 0.32            | 12.37           |
+-----------------+-----------------+-----------------+-----------------+
| Verification    | 0.35            | 0.41            | 12.36           |
| data            |                 |                 |                 |
+-----------------+-----------------+-----------------+-----------------+

Table 3: The prediction accuracy of the trained ANN is shown by the
absolute mean errors for the welding parameters. It seems as if the ANN
identifies the underlying trends rather than just memorizes the
input/output relations of the experimental data sets.

![](media/image9.wmf){width="2.115972222222222in"
height="2.0458333333333334in"}![](media/image10.wmf){width="1.9965277777777777in"
height="2.0215277777777776in"}![](media/image11.wmf){width="2.236111111111111in"
height="2.0277777777777777in"}

Figure 6: Predicted versus measured welding parameters for the complete
data set. For wire feed speed, voltage, and welding speed, the
correlation coefficients are 0.95, 0.94, and 0.77, respectively.

Simulations of control performance were conducted with the trained
network, and according to Figure 5, the desired back-bead geometry were
set as *h~b~* = 0.75 mm and *w~b~* = 3.0 mm. In Figure 7 and 8 results
from a simulation with significant gap width variations along the
joint - from 0.5 mm to 2.3 mm - are shown. From the photograph shown in
Figure 7, it is seen how the front-bead geometry varies due to the
continuous adjustment of welding parameters. As expected, the front-bead
geometry became larger when the gap width became smaller and vice versa.
From Figure 8, it follows that a uniform back-bead has been obtained,
even though minor local variations of the height, as well as of the
width, appear along the weld. The mean values of the back-bead height
and width are 0.76 mm and 3.19 mm, respectively, and in general, it is
concluded that quality welds, fully competitive with skilled manual
welding, are achievable.

![](media/image12.png){width="2.946527777777778in"
height="2.2819444444444446in"}![](media/image13.wmf){width="3.01875in"
height="2.279861111111111in"}

Figure 7: A test weld and its measured gap width variation.

![](media/image14.wmf){width="3.2020833333333334in"
height="2.3159722222222223in"}![](media/image15.wmf){width="3.2020833333333334in"
height="2.3159722222222223in"}

Figure 8: Back-bead height and width according to the simulation shown
in Figure 7.

# CONCLUSION

Physical experiments have shown that the weld bead geometry is extremely
sensitive to gap width variations in GMA butt joint welding with full
penetration, and consequently, a continuous adjustment of welding
parameters is essential for the realization of a uniform back-bead
geometry. An open-loop control strategy, based on neural network
technology, was experimentally investigated and applied successfully to
this particular weld task.

In fact, a series of laboratory based experiments shows, that it is
possible to apply static data to train an ANN to obtain a model of the
GMAW process, and that the model is feasible for high quality, open-loop
butt joint welding with full penetration of 3 mm plates with variations
in the gap width from 0.5 to 2.3 mm.

Unfortunately, the weld quality has proven to be quite sensitive to
changes in welding conditions (not only the gap width), and since it is
expensive, impractical, and often impossible to sustain constant welding
conditions in an industrial environment, the open-loop control strategy
is typically too vulnerable to be applied in such disturbing
surroundings. For that reason future work will be focused on development
of a closed-loop control system based on online monitoring and control
of the weld quality.

# REFERENCES

1.  Raveendra, J., Parmar, R.S.: Mathematical models to predict weld
    bead geometry for flux cored arc welding, Metal Construction, Vol.
    19 Issue 1, pp. 31R-35R, 1987.

2.  Andersen, K., Cook, G.E., Karsai, G., and Ramaswamy, K.: Artificial
    Neural Networks Applied to Arc Welding Process Modeling and Control,
    IEEE Transactions on Industry Applications, Vol. 26 No. 5, pp.
    824-830, 1990.

3.  Lim, T.G., Cho, H.S.: Estimation of weld pool sizes in GMA welding
    process using neural networks, Proceedings of the Institution of
    Mechanical Engineers, Part I (Journal of Systems and Control
    Engineering), Vol. 207 Issue 1, pp. 15-26, 1993.

4.  Chan, B., Pacey, J., and Bibby, M.: Modelling Gas Metal Arc Weld
    Geometry Using Artificial Neural Network Technology, Canadian
    Metallurgical Quarterly, Vol. 38 No. 1, pp. 43-51, 1999.

5.  Chen, S.B., Lou, Y.J., Wu, L., and Zhao, D.B.: Intelligent
    Methodology for Sensing, Modeling and Control of Pulsed GTAW: Part
    1 - Bead-on-Plate Welding, Welding Journal -- Including Welding
    Research Supplement, Vol. 79 Issue 6, pp. 151s-163s, 2000.

6.  Chen, S.B., Zhao, D.B., Wu, L., and Lou, Y.J.: Intelligent
    Methodology for Sensing, Modeling and Control of Pulsed GTAW: Part
    2 - Butt Joint Welding, Welding Journal - Including Welding Research
    Supplement, Vol. 79 Issue 6, pp. 164s-174s, 2000.

7.  Di, L., Chandel, R.S., Srikanthan, T.: Static Modeling of GMAW
    Process Using Artificial Neural Networks, Materials and
    Manufacturing Processes, Vol. 14 No. 1, pp. 13-36, 1999.

8.  Lee, J., Um, K.: A comparison in a back-bead prediction of gas metal
    arc welding using multiple regression analysis and artificial neural
    network, Optics and Lasers in Engineering, Vol. 34 Issue3, pp.
    149-158, 2000.

9.  Hagan, M.T., and Menhaj, M.B.: Training Feedforward Networks with
    the Marquardt Algorithm, IEEE Transactions on Neural Networks, Vol.
    5 No. 6, pp. 989-993, 1994.

10. Dan Foresee, F., and Hagan, M.T.: Gauss-Newton Approximation to
    Bayesian Learning, 1997 IEEE International Conference on Neural
    Networks, Vol. 3, pp. 1930-1935, 1997.

[^1]: ^\*^ Department of Mechanical Engineering, Technical University of
    Denmark, DK-2800 Kgs. Lyngby, Denmark

[^2]: ^\*^