ORIGINAL ARTICLE
Prediction of the vertical force during FSW of AZ31 magnesium alloy
sheets using an artificial neural network-based model
Alessio D’Orazio
1
•
Archimede Forcellese
1
•
Michela Simoncini
2
Received: 13 May 2017 / Accepted: 22 May 2018
Ó The Natural Computing Applications Forum 2018
Abstract
A multivariable empirical model based on an artificial neural network (ANN) was developed in order to predict the vertical
force occurring during friction stir welding (FSW) of sheets in AZ31 magnesium alloy. To this purpose, FSW experiments
were performed at different values of rotational and welding speeds, and the vertical force versus time curve was recorded
during the different stages of the process by means of a dedicated sandwich dynamometer. Such results were used in the
training stage of the artificial neural network-based model developed to predict vertical force versus time curves. A multi-
layer feed forward ANN, using the back-propagation algorithm, consisting of the input layer with four input parameters
(rotational speed, welding speed, rotational speed to welding speed ratio and processing time), two hidden layers with four
neurons each, and the output layer with the vertical force as output, was built and trained. The generalization capability of
the ANN was tested using a two-step procedure: in the former, the leave-one-out cross-validation method was used whilst,
in the latter, curves not included in the training dataset were taken into account. The low values of the relative error and
average absolute relative error, and the high correlation coefficients between predicted and experimental results have
proven the excellent capability of the artificial neural network in modeling complex shape of the curve and in capturing the
effect of the process parameters on the vertical force without a priori knowledge of the complex microstructural and
mechanical mechanisms taking place during friction stir welding. Finally, the relationship between vertical force and
processing time, at different welding and rotational speeds, was also predicted using the support vector machine algorithm
and the results were compared with those given by the ANN-based model.
Keywords Magnesium alloy Á Friction stir welding Á Vertical force Á Artificial neural network Á Support vector machine
1 Introduction
Friction stir welding (FSW) is a solid state technology that
is getting more attention in several fields of industry. FSW
allows to join metals owing to the mechanical action of a
rotating and translating non-consumable pin tool, inserted
into the workpieces to be welded. The pin tool causes the
workpiece heating due to both friction at the tool–work-
piece interface and stirring of material from the front to the
back of the pin [1–7]. FSW avoids the formation of the
typical defects of the fusion welding technologies, provides
a fine grained microstructure into the stirred zone and
allows to join alloys difficult to be welded or unweldable;
furthermore, the FSW process reduces the energy con-
sumption, material waste and avoids radiations and dan-
gerous fumes [1, 8].
The quality of joint is critically affected by several
parameters, such as tool geometry and material, backing
plate, rotational and welding speeds, tool plunging, work-
piece material and thickness; they, in turn, affect the
monitoring variables, such as workpiece and tool temper-
atures, torque and forces occurring during process. In order
to fully understand friction stir welding for the obtaining of
& Michela Simoncini
michela.simoncini@uniecampus.it
Alessio D’Orazio
a.dorazio@pm.univpm.it
Archimede Forcellese
a.forcellese@univpm.it
1
DIISM, Universita
`
Politecnica delle Marche, Via Brecce
Bianche, 60121 Ancona, Italy
2
Universita
`
degli studi eCampus, via Isimbardi 10,
22060 Novedrate, CO, Italy
123
Neural Computing and Applications
https://doi.org/10.1007/s00521-018-3562-6
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