NEURAL NETWORK ANALYSIS FOR EVALUATING WELDING
PROCESS
K. C. Kirn, A. Chertov and R. Gr. Maev
Department of Physics, University of Windsor, Ontario N9B 3P4, Canada
ABSTRACT. In this research, the back propagation neural network (NN) model traditionally used
for letter recognition was used for estimating the nugget size. For this, seven kinds of data series were
prepared. Before the neural network calculation, all input parameters and target parameter (nugget
size) were normalized. The estimated nugget size was affected on the normalized constant and middle
layer. In order to increase the relationship between the actual nugget size measured from the peel test
and the estimated nugget size calculated from NN analysis, the normalized constant and the number
of middle layer were chosen by trial and error. By the trained NN, we can achieve almost 90% of the
relationship between actual and estimated nugget size. The trained NN can achieve almost a 90%
correlation between actual and estimated nugget size. Also, two kinds of simulation were performed
to find which input parameter gave the strongest effect on the nugget size. As a result of the
simulation analyses, it was clarified which one of the sets of input parameters are the most important
factor in achieving a strong correlation.
INTRODUCTION
Ultrasonic NDE during last decades are used as a powerful method for inspection
and monitoring of welds. The possibility of using ultrasound as an in-line measurement
method is especially beneficial because it can realize a continuous cycle for process
monitoring and feedback. During the process, elastic properties of welded metals undergo
significant changes due to heating and melting. In previous research, embedded watercooled broadband ultrasonic transducers were installed into both a pedestal and scissors
spot welder. The setup allowed for acquiring data during welding by using throughtransmitted and reflected pulsed wave modes.
The analysis of the experimental data produced a number of interesting features
[1,2]. The relationship between the Maximum Time Of Flight (MTOF) and actual nugget
size measured from the peel test showed a strong correlation of about 80%. Such a
relationship allows us to estimate the nugget size based on only one parameter, - MTOF,
without peeling. To increase the reliability of the estimated nugget size higher then 80%,
the nugget size should be estimated from multi input parameters, including MTOF as well
as welding current, welding cycles and etc. To do this, two methods have been proposed: a
multi-regression method and a neural network method. The former is profitable when
regressors have a wide range of distribution. In our case, some regressors do not have a
wide range of distribution. For a multi input parameter case such as this one, the neural
network analysis was used.
In this research, the back propagation neural network model, traditionally used for
letter recognition, was used for estimating nugget size. For this, seven kinds of data series
were prepared. Three series were obtained from a pedestal resistance spot welder and four
series were obtained from a scissors resistance spot welder. Before neural network
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/S20.00
608
calculations, all input parameters and the target parameter (nugget size) were normalized.
The estimated nugget size depends on the divided normalization constant and the middle
layer. Thus, in order to increase the correlation between the actual nugget size measured
from the peel test and the estimated nugget size calculated from NN analysis, the
normalization constant and the number of the middle layer were chosen by trial and error.
The trained NN can achieve an almost 90% correlation between actual and estimated
nugget size. Also, two kinds of simulation were performed to find which input parameter
gave the strongest effect on the nugget size. From the simulation result, it is known that the
number of input parameters is the most important factor in achieving a strong correlation.
RESISTANCE SPOT WELDING ELECTRODE BUILT-IN ULTRASONIC
TRANSDUCERS TECHNOLOGY
In previous research, a Resistance Spot Welding (RSW) monitoring system for
quality control was developed in which an ultrasonic transducer with a cooling system is
built. The experimental system built in previous work is schematically shown in Figure 1.
The system included a pedestal and scissors resistance spot welder, two embedded 4MHz
broadband ultrasonic transducers, and a data acquisition system consisting of a USD-15
pulser-receiver (Krautkramer's) and a TDS-520 digitizing oscilloscope (Tektronix). The
measurement setup also contained a WS25 welding current monitor (Robotron), a PC
interfaced with the welder via a relay block, and connected via a GPIB port to the TDS520. The transducers were incorporated into welding electrode adapters providing housing
and at the same time keeping the electrode cooling flow nearly unperturbed. This required
a number of vias for the coolant installed around the transducer. The ultrasonic pulse
repetition frequency was 300Hz that allowed for sending through the weld and receiving 5
ultrasonic waveforms per cycle. During the process 200 waveforms were routinely
acquired and stored in the TDS520 flash memory and consequently uploaded to the PC.
The principle of the data acquisition is given in Figure 2. Each waveform contained 250
Frame i
TDS520
FIGURE 2. Data acquisition principle.
FIGURE 1. Experimental setup.
609
8
6
Middle Layer
Logistic Hidden Layer
y = 0.0415x - 4.3101
2
R = 0.7804
W1
5
4
3
2
Error < 0.00001
Target Value
Error > 0.00001
Calculate new W1 and W2 by
Back propagation Method
1
0
150
Training End
W2
….
……..
……
……
……..
……
.
….
….
….
….
….
Actual N ugget Size(m m )
7
170
190
210
230
250
Input Layer : 106 or 206
Logistic Output Layer
M axim um TO F(ns)
FIGURE
FIGURE 3.
3. Peel
Peel test
test vs.
vs. MTOF
MTOF variation.
variation.
FIGURE
FIGURE 4.
4. The
The explanation
explanation of
of used
used neural
neural network
network
model.
model.
samples
have been
been processed
processed in
in order
order to
to
samples taken
taken at
at aa 100MHz
100MHz sampling
sampling rate.
rate. The
The waveforms
waveforms have
obtain
processing included
the peak-to-peak
peak-to-peak
obtain amplitude
amplitude and
and phase
phase information.
information. The
The processing
included the
amplitude
amplitude monitoring,
monitoring, TOF
TOF measurements
measurements and
and Fourier
Fourier Transform
Transform methods.
methods. Among
Among these
these
parameters,
the
MTOF
shows
strongest
correlation
to
the
nugget
size;
Figure
shows this
this
parameters, the MTOF shows strongest correlation to the nugget size; Figure 33 shows
relationship.
the nugget
nugget size
size without
without peeling.
peeling. But,
But,
relationship. From
From this
this relationship,
relationship, we
we can
can estimate
estimate the
in
weld quality
quality will
will be
be affected
affected by
by the
the
in this
this case,
case, we
we used
used only
only one
one parameter,
parameter, MTOF.
MTOF. The
The weld
weld
thickness, waveform
waveform
weld current,
current, number
number of
of cycles,
cycles, electrode
electrode force,
force, specimen
specimen thickness,
information
neural network
network
information and
and etc.
etc. To
To use
use all
all these
these parameters
parameters as
as input
input parameters,
parameters, the
the neural
analysis
was
used.
analysis was used.
BACK
BACK PROPAGATION
PROPAGATION NEURAL
NEURAL NETWORK
NETWORK MODEL
MODEL
To
propagation neural
neural network
network model
model used
used
To estimate
estimate nugget
nugget size,
size, we
we used
used the
the back
back propagation
in
the neural
neural network
network model.
model. This
This
in letter
letter recognition.
recognition. Figure
Figure 44 shows
shows the
the explanation
explanation of
of the
neural
layer. All
neural network
network model
model included
included aa logistic
logistic hidden
hidden layer
layer and
and logistic
logistic output
output layer.
All
weighting
rate was
was 0.1
0.1 and
and
weighting functions
functions were
were initialized
initialized by
by random
random variables.
variables. The
The training
training rate
maximum
was 0.00001
0.00001 because
because the
the
maximum training
training number
number was
was 5000
5000 times.
times. The
The RMS
RMS error
error limit
limit was
general
by about
about
general nugget
nugget size
size isis under
under 10mm
10mm and
and the
the nugget
nugget size
size (target
(target value)
value) is
is divided
divided by
1000
of weighting
weighting connection
connection w,
w1
1000 during
during the
the simulation.
simulation. The
The equation
equation for
for the
the calculation
calculation of
and
and w
w22 at
at the
the hidden
hidden layer
layer and
and output
output layer
layer were
were as
as follows.
follows.
wnew, 2 = wold , 2 − η ⋅ δ 1 ⋅ f
__
O
/•
(1)
/ -I \
where,
where, wwnew
is weight
weight connecting
connecting after
after adjusting
adjusting the relation between neuron cells i and j,
Mew2
, 2 is
w
η is
wold
is weight connecting
connecting before adjusting the relation between neuron cells i and j,j, t|
old, 22 is
training
1 −-output
) and
training rate,
rate, δS1l isis delta
delta notation(
notation(δS1l ==output
output ×x ((1
output)) ×xerror
error)
andffisisthe
theactivation
activation
function.
function.
wnew,1 = wold ,1 − η ⋅ x ⋅ δ 2
(2)
where, xx isis the
the input
input parameters
parameters and
and δ822 is
is delta
delta notation(
notation(<?
= δS11×xhx(l
—hh)xw
δ2 =
h×(1−
) × w22).). In the
where,
calculations, first
first ww22 was
was calculated
calculated and
and next
next w
Wj1 was calculated.
calculated. That is, the
the weighting
weighting
calculations,
connection of
of hidden
hidden layer
layer w
w1l is
is calculated
calculated from
from the weighting connection of output layer
connection
This isis called
called the
the back
back propagation
propagation model.
model. According
According to the training, the RMS error
ww22.. This
becomes
smaller.
becomes smaller.
610
ESTIMATION OF NUGGET SIZE BY NEURAL NETWORK METHOD
For neural network training, seven kinds of data series were prepared. Three series
were obtained from the pedestal resistance spot welder. The specimens had thicknesses of
0.8mm, 1 mm and 2 mm respectively. Four data series were obtained from the scissors
resistance spot welder. The specimens had a thickness of 0.8 mm, 1mm, 1.2 mm and 1.8
mm respectively. From the seven series of data, three series include 106 parameters
including; number of welding cycles, welding pressure, welding current, maximum time of
flight (MTOF), time to the MTOF, specimen thickness and wave form information.
The remaining four series of data include 206 parameters including the above mentioned
parameters. All input parameters were normalized. The estimated nugget size was
changed according to this normalized value and the number of the hidden layer. The best
normalized value and hidden layer was sought. Figure 5 shows how did we calculate the
normalized constant for output value in a case of 0.8mm thick samples obtained from a
scissors machine.
The vertical axis of Figure 5 (a) shows how the square of the correlation coefficient
between the actual and estimated nugget size varied according to the change of the
normalized value. The vertical axis of Figure 5 (b) shows the linear dependency between
the actual and estimated nugget size according to the change of the normalized value. In
this case, the normalized value does not have an effect on the estimated nugget size. Thus,
two hundred was chosen as the normalizing constant.
Figure 6 shows how the number of the middle layer was chosen. From Figure 6, we
know the R-square value smoothly decreased as the number of the middle layer increased.
Thus, eight was chosen as the best number of middle layer because it was possible to get a
good R-square value and there is a small variance between the minimum and maximum
values.
0.8
0.3
~0
100 200 300 400 500 600 700 800 900 1000
'0
________Normalized Constant______________
(a) R-square vs. normalized constant
100 200 300 400 500 600 700 800 900 1000
Normalized Constant
(b) Linearity vs. normalized constant
FIGURE 5. Calculation of divided value in target value
611
1i
11
0.9
Ktoit_.
0.9
1
0.8
0.8
0.9
0.9
0.9
1
0.8
0.8
0.9
0.7
0.7
0.8
0.6
£,0.6
0.7
§ 0.5
0.5
0.6
J 0.4
0.4
0.5
0.3
0.3
0.4
0.2
0.2
0.3
0.1
0.1
0.2
0
0.1
° 00
0.7
0.7
0.8
6
0.6
0.7
0.5
g* 0.5
0.6
0.4
0.4
0.5
0.3
0.3
0.4
0.2
0.2
0.3
0.1
0.1
0.2
0
0.1
° 00
0
0
Linearity
Linearity
R square
R square
i °-
10 20
20
10
30 40
60
70
30
40 of50
50
60 layer
70 80
80 90
90 100
100
Number
Middle
10
30
40 50 60
80 value
90 100
(a) R-square
R-square
vs. 70
divided
(a)
vs.
divided
value
Number
of Middle
layer
20
Number of Middle layer
0
0
(a) R-square vs. divided value
10
10
20
20
30
40
50
60
30
40of Middle
50 layer
60 70
70 80
80 90
90 100
100
Number
Number
of
Number
of Middle
Middle layer
layer
10
20 30 40
50
60 70
80
(b)
vs.
divided
value
(b) Linearity
Linearity
vs.
value
Number
of Middle
layer layer
Number
ofdivided
Middle
90
100
(b) Linearity vs. divided value
FIGURE 6.
6. Calculation
Calculation of
number of
FIGURE
of number
of middle
middle layer
layer
FIGURE 6. Calculation of number of middle layer
Next, in
in order
order to
to look
look for
for the
the best
best normalized
normalized value
an input
Next,
value for
for an
input value,
value, the
the same
same procedure
procedure
was
carried
out,toFigure
Figure
shows
thenormalized
result. In
case,
region
and
end
was
out,
77 shows
the
result.
In this
this
case,
the
initialvalue,
regionthe
andsame
end region
region are
are
Next,carried
in order
look for
the best
value
forthe
an initial
input
procedure
unstable
and
the
middle
region
is
stable.
The
maximum
input
value
was
460
and
was carried
7 shows
this maximum
case, the initial
are
unstable
andout,
theFigure
middle
regionthe
is result.
stable.InThe
inputregion
value and
wasend
460region
and the
the
normalized
value
should
be
biggeristhan
than
this
value,
therefore,
five
was
chosen.
By
unstable and
the should
middlebe
region
stable.
maximum
value was
and the
normalized
value
bigger
this The
value,
therefore,input
five hundred
hundred
was460
chosen.
By
this
method,
the
normalized
value
in
the
input
and
output
values,
and
the
number
of
the
normalized
should be bigger
value,
five hundred
chosen.
this
method,value
the normalized
value than
in thethis
input
andtherefore,
output values,
and thewas
number
of By
the
middle
layer were
were
chosen.
11 shows
result.
this method,
the normalized
value
in thethis
input
and output values, and the number of the
middle
layer
chosen. Table
Table
shows
this
result.
middle layer were chosen. Table 1 shows this result.
TABLE 1
1 Divided
Divided value
value and
TABLE
and number
number of
of middle
middle layer.
layer.
TABLE 1 Divided value and number of middle layer.
Divided Value in target value
Number of Middle layer
0.8
(P)
200
10
1
(P)
200
10
Divided Value in input value
800
1200
Thickness, mm
1
0
1
(S)
200
9
1.2
(S)
200
10
1.8
(S)
200
10
800
500
600
900
900
1
0.9
11
0.8
0.9
0.7
0.8
0.6
0.7
0.5
£,0.6
0.6
0.4
|
0.5 0.5
0.3
^0.4
0.4
0.2
0.3
0.1
0.2
0
200 400 600 800 1000 1200 1400 1600 1800 2000
0.1
Normalized
Constant
Normalized
Constant
0
1200
1400 1600
1600 1800
1800 2000
2000
200 400 vs.
600normalized
800 1000 1200
1400
(b) Linearity
constant
Normalized
Constant
Normalized
Constant
_______Normalized
Constant_______________
Linearity
Linearity
R square
R square
0.9
11
0.8
0.9
0.9
0.7
0.8
0.8
0.6
0.7
0.7
0.5
0.6
0.6
0.4
' 0.5
0.5
0.3
0.4
0.4
0.2
0.3
0.3
0.1
0.2
0.2
0
0.1
0.1
200
10
0.8
(S)
200
8
2
(P)
200 400 600 800 1000 1200 1400 16001800 2000
Normalized
Constant
Normalized
Constant
200
600normalized
800 1000
100012001400160018002000
200 400vs.
1200
1400 16001800 2000
(a) R-square
constant
Normalized Constant
________Normalized
Constant______________
Normalized Constant
(a)
(a) R-square vs. normalized constant
(b) Linearity vs.
vs. normalized
normalized constant
constant
FIGURE 7. Calculation of normalized constant in input value.
FIGURE 7. Calculation of normalized constant
constant in
in input
input value.
value.
612
Estimated Nugget S ize(mm
Estimated Nugget S ize(mm
Estimated
EstimatedNugget
NuggetSSize(mm
ize(mm
66
5.5
5.5
55
66
5.5
5.5
55
=0.78x
0.78x +
+0.8895
0.8895
yy =
22 = 0.7804
RR =
0.7804
4.5
4.5
44
y=
+ 0.4602
y 0.888x
= 0.888x
+ 0.4602
2
R R=20.9322
= 0.9322
4.5
4.5
44
3.5
3.5
3
3
2.5
2.5
2.5
2.5
3.5
3.5
3.5
4.5
5.5
4.5
5.5
4.5
5.5
Actual Nugge S ize(mm)
3.5
3.5
3
3
2.5
2.5
2.5
2.5
6.5
6.5
Actual
ActualNuggeSize(mr$
Nugge S ize(mm)
3.5
4.5
5.5
3.5
4.5
5.5
3.5
4.5
5.5
Actual Nugget S ize(mm)
Actual
ize(rm1
S ize(m
m)
Actual Nugget
Nugget S
6.5
6.5
(a) Least
Least Square
Square Method
(b)
Neural Network
Method
(a)
Method
(b)
(b) Neural
Neural Network
Network Method
FIGURE 8. Comparison of estimated nugget size by least square method and estimated nugget
sizesize
by by
neural
FIGURE
nugget
neural
FIGURE 8. Comparison of estimated nugget size by least square method and estimated nugget
size by
neural
network
network
network
Estimated
Nugget
S ize(mm
Estimated
Nugget
S ize(mm
Here, P stands for pedestal welder machine and S stands for scissors welder
Here,
P stands for pedestal
pedestal welder
welder machine and S stands for scissors welder
machine. Using these parameters, the neural networks were trained. After training, the
machine.
Using these parameters, the neural
machine.
neural networks were trained. After
After training, the
nugget sizes were estimated. Figure 8 shows how much the correlation was enhanced by
nugget
sizes
were
estimated.
Figure
8
shows
how
much
the
correlation
was enhanced by
nugget
were
utilizing the neural network method.
utilizing
the
network
method.
utilizingFrom
the neural
neural
network
this figure, it is seen that the correlation between the actual nugget size and
From this
figure,
thatimproved
the correlation
nuggetissize
and
figure,
correlation
the actualmethod
the estimated
nugget
sizeit is
is seen
greatly
and thisbetween
neural the
network
very
the
estimated
nugget
size
is
greatly
improved
and
this
neural
network
method
is
the
estimated
nugget
very
effective in predicting nugget size. We applied this method all to datum. Figures. 9-10
effective
in result.
predicting
size.
applied between
this method
all toand
datum.
Figures.
effective
predicting
9-10
shows this
Figurenugget
9 shows
the We
relationship
the actual
estimated
nugget
shows
this
result.
Figure machine.
9 shows Figure
the relationship
the actual
and estimated
result.welder
relationship
size for
pedestal
10 shows between
the relationship
between
the actualnugget
and
size
for pedestal
machine.
shows the
relationship
between
the actual
and
pedestal
welder
machine.
Figure
estimated
nuggetwelder
size for
scissors Figure
welder 10
machine.
From
these results,
it is seen
that the
estimated
nugget
size
for
scissors
welder
machine.
From
these
results,
it
is
seen
that
estimated
scissors
welder
machine.
From
correlation between the estimated nugget size and the actual nugget size is almostthe
correlation
size byand
actual
nugget
size isgives
almost
consistantlybetween
90% andthe
the estimated
nugget sizenugget
estimated
thethe
neural
network
analysis
a
consistantly
90%than
andthat
the estimated
nugget size
estimated
by the
neuralTable
network
analysis
gives a
better reliability
by the
least square
method.
2 shows
how much
better
reliabilityisthan
that estimated by the least square method. Table 2 shows how much
better
the correlation
enhanced.
the correlation is enhanced. 7.5
7.5
6.5
7.5
5.5
6.5
4.5
5.5
3.5
4.5
2.5
3.5
1.5
2.5 1.5
1.5
1.5
y = 0.9396x + 0.2981
2
R = 0.9525
y = 0.9396x + 0.2981
2
R = 0.9525
3.5
3.5
3.5
4.5
5.5
Actual Nugget S ize(mm)
4.5
5.5
4.5
5.5
6.5
7.5
6.5
6.5
7.5
Actual
Nugget S
Size(mT$
Actual
Nugget
ize(mm
)
(a) Specimen
thickness
0.8mm
(a) Specimen thickness
0.8mm
9.5
y = 0.8574x + 0.7721
2
R = 0.8803
Estimated Nugget S ize(mm
Estimated Nugget S ize(mm
Estimated
NuggetNugget
S ize(mm
Estimated
S ize(mm
7
7.5
6.5
67
6.5
5.5
56
4.5
5.5
45
3.5
4.5
34
2.5
3.5
32.5
2.5
2.5
y = 0.9334x + 0.432
2
R = 0.9436
8.5
9.5
7.5
y = 0.8574x + 0.7721
2
R = 0.8803
y = 0.9334x + 0.432
2
R = 0.9436
8.5
6.5
7.5
5.5
6.5
4.5
5.5
3.5
2.5
2.5
3.5
4.5
5.5
Actual Nugget S ize(mm)
3.5
3.5
4.5
4.5
5.5
5.5
6.5
6.5
(b) Specimen
thickness
1mm
S ize(mm)
Actual Nugget
Nugget Size(nTTt
Actual
7.5
7.5
4.5
2.5
2.5
3.5
2.5
2.5
4.5
6.5
Actual Nugget S ize(mm)
4.5
4.5
6.5
6.5
(c) Specimen thickness
2mm
Actual
)
Actual Nugget
Nugget SSize(mm
ize( mrO
8.5
8.5
(b)
thickness
(c) Specimen
thickness
(b) Specimen
thickness
1mm
2mmmachine.
FIGURE 9. The relationship
between
the actual
and estimated nugget
size for pedestal
welder
FIGURE 9. The relationship between the actual and estimated nugget size
size for
for pedestal welder
welder machine.
machine.
613
5.5
5
4.55
y = 0.9369x + 0.2572
2
R = 0.9379
y = 0.9369x
+ 0.2572
R = 0.9379
2
5
4.5
4.5
4
3.5
3
4
3.5
2.53
3.5
3
2.5
2
22
2
33
4
4
Actual Nugget
Nugget
S ize(m
m)
3 Actual
4 S
ize(mr}
Actual Nugget S ize(mm)
5
6
5
6
3
2.5
2.5 2.5
2.5
(a) Specimen thickness 0.8mm
y = 0.9459x + 0.2492
2
R = 0.9589
y = 0.9459x
+ 0.2492
2
R = 0.9589
2.5
2.5
3.5
4.5
5.5
3.5
4.5
5.5
3.5 Nugget
4.5 S ize(mm)
5.5
Actual
tetual
Nugget
Size(rmt
Actual Nugget S ize(mm)
6.5
6.5
7.5
7.5
Estimated
Nugget
S ize(mm
Estimated
Nugget
S ize(mm
(a) Specimen
thickness 0.8mm
(a)
Specimen thickness
0.8mm
Estimated
Nugget
S ize(mm
Estimated
Nugget
S ize(mm
y = 0.888x + 0.4602
R = 0.9322
y = 0.888x
+ 0.4602
2
R = 0.9322
5
5.5
3.54
7.5
7.5
6.5
6.5
5.5
5.5
4.5
4.5
3.5
3.5
2.5
2.5
1.5
1.51.5
1.5
6
5.5
6
2
4.5
4
Estimated
Nugget
S ize(mm
Estimated
Nugget
S ize(mm
Estimated
Nugget
S ize(mm
Estimated
Nugget
S ize(mm
5.5
3.5
4.5
5.5
3.5
4.5
5.5
ize(mm) 5.5
3.5 Actual
4.5 SSJze(nrr$
Actual Nugget
Nugget
Actual Nugget S ize(mm)
6.5
6.5
(b)
(b) Specimen
Specimen thickness
thickness 1mm
1mm
(b) Specimen thickness 1mm
8.5
8.5
7.5
7.5
6.5
6.5
5.5
5.5
4.5
4.5
3.5
3.5
2.5
2.5 2.5
2.5
y = 0.8951x + 0.4898
2
R = 0.9011
y = 0.8951x
+ 0.4898
2
R = 0.9011
3.5
3.5
4.5
5.5
6.5
4.5
5.5
6.5
4.5 Nugget
5.5 S ize(mm
6.5 )
Actual
A:tual Nugget Size(rm$
Actual Nugget S ize(mm)
7.5
7.5
8.5
8.5
(c) Specimen
Specimen thickness
thickness 1.2mm
(d)
Specimen
thickness
1.8mm
(c)
1.2mm
(d) Specimen
Specimen thickness
thickness1.8mm
1.8mm
(c) Specimen
thickness
1.2mmand estimated(d)
FIGURE 10.
The
relationship
between
the
actual
nugget
size
for
scissors
welder
machine.
FIGURE
10.
The
relationship
between
the
actual
and
estimated
nugget
size
for
scissors
weldermachine.
machine.
FIGURE 10. The relationship between the actual and estimated nugget size for scissors welder
TABLE 2
2 Comparison of
estimated nugget
size
method
and
estimated
nugget
size
by
neural
TABLE
size by
by least
least square
square method
method and
and estimated
estimatednugget
nuggetsize
sizeby
byneural
neural
TABLE 2 Comparison
Comparison of
of estimated
estimated nugget
nugget size
by
least
square
network
network
network
Thickness, mm
Least Square Method
Neural Network Analysis
2(P) 0.8(S) 1(S) 1.2(S)
0.8(P) 1(P)
94.1% 73.5% 88.9% 65.3% 78% 61.3%
95.3% 88% 94.5% 90.4% 94.2% 95.7%
1.8(S)
76.7%
90.1%
Also, in
order to
know which parameter gives
strong
effect
on
the
estimated
nugget
Also,
gives strong
strong effect
effect on
onthe
theestimated
estimatednugget
nugget
Also, in
in order
order to know which parameter gives
size
in
NNA,
a
computer
simulation
was
performed
according
to
the
changes
of
input
size
according to
to the
the changes
changes ofof input
input
size in
in NNA,
NNA, aa computer
computer simulation was performed according
parameters. First,
one
parameter
was
omitted.
(Figure
11(a))
The
horizontal
axis
(1-7)
parameters.
First,
one
parameter
was
omitted.
(Figure
11
(a))
The
horizontal
axis
(1-7)
parameters. First, one parameter
11(a)) The horizontal axis (1-7)
represents the
the omitted
omitted number
of
lines
and
in
case
of
8,
200
wave
forms
were
omitted.
represents
number
of
lines
and
in
case
of
8,
200
wave
forms
were
omitted.
represents the omitted number
case of 8, 200 wave forms were omitted.
Input parameter = 206
Input parameter = 206
1
11
0.9
0.9
0.9
0.8
0.8
0.8
0.7
,0.7
0.7
0.6
> 0.6
0.6
0.5
!0.50.5
0.44
at 0.4
°0.3
0.3
0.3
0.2
0.2
0.2
0.1
0.1
0.1
0
0
20
20
: * * • * * v\
R-square
Value
R-square
Value
R-square
Value
R-square
Value
1
11
0.9
0.9
0.9
0.8
0.8
0.8
0.7
o 0.7
0.7
0.6
> 0.6
0.6
0.5
|
0.5 0.5
0.4
0.4
3*0.4
0.3
0.3
0.3
0.2
0.2
0.2
0.1
0.1
0.1
0
01
2
3
4
5
6
7
4
11
22The number
33 of 4omitted
55
66
77
input
parameter
Thenumber
numberof
ofomitted
omitted input
input parameter
parameter
The
8
88
(a) R-square vs. the number of omitted input parameter
(a) R-square
R-square vs.
vs. the
the number
number of
of omitted
omitted input
(a)
input parameter
parameter
FIGURE 11. The consideration of input parameter.
FIGURE 11.
11. The
The consideration
consideration of
of input
input parameter.
parameter.
FIGURE
614
40
40
60 80 100 120 140 160 180 200
60
60
80 100
100
120 140
140 160
160 180
180200
200
The80
number
of120
input
parameter
The
Thenumber
numberofofinput
inputparameter
parameter
(b) R-square
R-square vs. the
the number of
of input parameter
parameter
(b)
(b) R-squarevs.
vs. thenumber
number ofinput
input parameter
So, the number of data was 205 (1-7) and 6 (8). From this result, the number of
input parameter effects on the correlation is observed. To confirm this, a computer
simulation corresponding to the number of input parameters was performed and results are
shown in Figure 1 l(b)
Figure 11 (b) shows the number of input parameters had a strong effect on the
correlation. The more input parameters, the better correlation will be achieved. To increase
this correlation, degradation of electrode tip and misalignment will be considered in the
future.
CONCLUSION
By the back propagation neural network method, the nugget size was estimated and
the correlation between the actual nugget size and estimated nugget size was almost
consistently over 90%.
We know that the nugget size estimated by the neural network analysis gives a
better reliability than that estimated by the least square method.
The number of input parameters has a strong effect on the correlation between the
actual and estimated nugget size such that the more input parameters, the better correlation.
To use this method in an actual factory some parameters should be added, for
example, degradation effect or misalignment effect. So, in the future, we will consider
these two effects.
ACKNOWLEDGMENTS
The work described in this paper was supported by Canadian NSERC Grant # CRD
223099-98. The authors also would like to thanks senior specialists of Marketswitch Inc.,
Dr. V. Fishman and Dr. A. Reynberg for helpful discussions and various consultations.
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