See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/338283220
A novel real-time measurement method for dynamic resistance signal in
medium frequency DC resistance spot welding
Article in Measurement Science and Technology · December 2019
DOI: 10.1088/1361-6501/ab6673
CITATIONS
READS
12
290
4 authors:
Zewei Su
Yu-Jun Xia
Shanghai Jiao Tong University
Shanghai Jiao Tong University
3 PUBLICATIONS 57 CITATIONS
10 PUBLICATIONS 99 CITATIONS
SEE PROFILE
SEE PROFILE
Yan Shen
Yongbing Li
Shanghai Jiao Tong University
Shanghai Jiao Tong University
7 PUBLICATIONS 74 CITATIONS
127 PUBLICATIONS 1,834 CITATIONS
SEE PROFILE
Some of the authors of this publication are also working on these related projects:
Magnetically assisted resistance spot welding View project
Resistance spot weld-bonding View project
All content following this page was uploaded by Yu-Jun Xia on 24 June 2020.
The user has requested enhancement of the downloaded file.
SEE PROFILE
Measurement Science and Technology
ACCEPTED MANUSCRIPT
A novel real-time measurement method for dynamic resistance signal in
medium frequency DC resistance spot welding
To cite this article before publication: Ze-Wei Su et al 2019 Meas. Sci. Technol. in press https://doi.org/10.1088/1361-6501/ab6673
Manuscript version: Accepted Manuscript
Accepted Manuscript is “the version of the article accepted for publication including all changes made as a result of the peer review process,
and which may also include the addition to the article by IOP Publishing of a header, an article ID, a cover sheet and/or an ‘Accepted
Manuscript’ watermark, but excluding any other editing, typesetting or other changes made by IOP Publishing and/or its licensors”
This Accepted Manuscript is © 2019 IOP Publishing Ltd.
During the embargo period (the 12 month period from the publication of the Version of Record of this article), the Accepted Manuscript is fully
protected by copyright and cannot be reused or reposted elsewhere.
As the Version of Record of this article is going to be / has been published on a subscription basis, this Accepted Manuscript is available for reuse
under a CC BY-NC-ND 3.0 licence after the 12 month embargo period.
After the embargo period, everyone is permitted to use copy and redistribute this article for non-commercial purposes only, provided that they
adhere to all the terms of the licence https://creativecommons.org/licences/by-nc-nd/3.0
Although reasonable endeavours have been taken to obtain all necessary permissions from third parties to include their copyrighted content
within this article, their full citation and copyright line may not be present in this Accepted Manuscript version. Before using any content from this
article, please refer to the Version of Record on IOPscience once published for full citation and copyright details, as permissions will likely be
required. All third party content is fully copyright protected, unless specifically stated otherwise in the figure caption in the Version of Record.
View the article online for updates and enhancements.
This content was downloaded from IP address 111.186.51.7 on 09/02/2020 at 01:17
Page 1 of 17
Ze-Wei Su1, Yu-Jun Xia1, Yan Shen1, Yong-Bing Li1,2,*
1
cri
pt
A novel real-time measurement method
for dynamic resistance signal in medium
frequency DC resistance spot welding
Shanghai Key Laboratory of Digital Manufacture for Thin-walled Structures, School of
Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, P.R. China
2
State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong
University, Shanghai, 200240, P.R. China
Corresponding author: E-mail address: yongbinglee@sjtu.edu.cn; Tel.: 86-21-34206305
us
*
Abstract
pte
dM
an
Resistance spot welding (RSW) is widely used in auto-body manufacturing, and the weld quality is
critical to ensure the safety and reliability of an automobile structure. The dynamic resistance (DR) signal
is one of the most frequently applied process signals for real-time quality monitoring and control of RSW.
However, the accuracy of DR measurement is highly affected by the inductive component of the secondary
voltage signal. In a medium-frequency direct current (MFDC) RSW system, it is proved that traditional DR
measurement methods such as root mean square (RMS) method and average method fail to eliminate the
interference of the inductance and hardly meet the monitoring requirements. Therefore, a novel real-time
DR measurement method based on forgetting factor recursive least square (FFRLS) algorithm is proposed
and tested under simulated and experimental conditions in this paper. Sensitivity analysis is performed to
optimize the forgetting factor, which is proved as the critical parameter of the novel method to balance the
convergence speed and oscillation amplitude. With the optimized forgetting factor, the error analysis and
comparative study are conducted under different welding modes. Results show that the inductive noise
could be effectively eliminated by the new method. The measurement error of the proposed method is
limited within ± 6 μΩ at a 99.73% confidence level (±3σ) at both constant and time-varying current modes.
This study can pave the way for real-time monitoring and control for the MFDC RSW system.
Keywords: resistance spot welding, medium-frequency direct current, dynamic resistance, real-time
measurement, forgetting factor
ce
1. Introduction
Resistance spot welding (RSW) is the major joining method for car body manufacturing [1], and the weld
quality directly affects the auto-body security and reliability. The quality of RSW is significantly influenced
by various disturbances in the production sites [2], which makes the welding quality inspection critical.
The traditional direct RSW quality inspection methods, such as sampling inspection based on destructive
or non-destructive techniques, are inefficient and can not inspect 100% of welds on a car body. As a result,
the reliable non-destructive technics of RSW quality monitoring by measuring various dynamic signals are
generally proposed, such as dynamic resistance (DR) [3-11], electrode force [12-14] , electrode vibration
signals [15], ultrasonic signal [16-18] and electrode displacement [19-23], to reflect the nugget growth
Ac
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
AUTHOR SUBMITTED MANUSCRIPT - MST-109751.R2
AUTHOR SUBMITTED MANUSCRIPT - MST-109751.R2
pte
dM
an
us
cri
pt
process indirectly. DR monitoring is widely accepted because it is low-cost and can provide rich
information about the nugget formation [24-26]. Since metal melting and solidifying processes occur in the
interface of steel sheets that are not visible, it is challenging to observe nuggets and get the true value of
DR accurately in real-time. Hence, researchers have conducted lots of in-depth studies on DR measurement
methods.
A lot of DR measurement methods were applied to AC RSW equipment . Andrews et al [3] measured
the DR of one cycle or half-cycle with the ratio of the RMS voltage to RMS current. Savage et al [4]
calculated DR by using the instantaneous electrode voltage and welding current at peak current point in
each half-cycle to remove the inductive noise caused by the transformer. Needham et al [27] calculated DR
by the ratio of integrated voltage and integrated current to theoretically eliminate the induced noise.
Yongjoon Cho et al [5] used the process variables, which were monitored in the primary circuit of the
welding machine, to obtain the variation of the dynamic resistance across electrodes. Garza and Das et al
[6,7] use a recursive least square (RLS) method to iteratively calculate the resistance and inductance, which
improved the sampling resolution of the signal. Ling and Wong et al [8,9] used the Hilbert Transform to
monitor the time-varying input impedance signal. Hongjie Zhang and Lijing Wang et al [10,11] proposed
a new measurement method to obtain the complex electrical impedance whose real part reflects the DR
changes and provided more details over time.
In recent years, the technology of the mid-frequency DC (MFDC) inverter has become more mature. The
secondary current of the MFDC RSW has no zero-crossing phenomenon of the welding current, which
provides a good condition for realizing DR monitoring technology [28,29]. The peak value method [4]
cannot be used in medium frequency DC RSW, because the secondary current signal of MFDC RSW does
not have a peak whose derivative is zero. The root means square (RMS) method [3] and the average method
[27] are the most widely used methods to monitor DR used in MFDC RSW controllers. When measuring
the voltage, the impedance of the RSW circuit consists of two parts: the resistance load containing the DR
relating to weld nugget formation, and the inductive reactance caused by the mutual inductance and internal
inductance of the circuit [30]. As a result, DR cannot be measured by merely dividing the voltage by the
current. The measurement accuracies of the traditional methods are highly affected by the inductive
component of the secondary voltage and hardly meet the monitoring requirements.
In this study, a novel real-time measurement method for the DR signal in MFDC RSW is presented,
which can eliminate inductive noise and measure the resistance accurately. Therefore, a measuring system
was built to measure current and voltage signals of MFDC RSW. A sensitivity analysis was conducted to
determine the optimal value of the method key parameter through simulation experiments. Besides, a series
of welding experiments under different welding modes were carried out, and error analysis and comparative
study were conducted to test the measurement accuracy of the new method in measuring the DR of MFDC
RSW.
2. Dynamic resistance measurement system and the equivalent circuit
ce
The real-time electrical signals of welding were required to measure the DR during the RSW process. The
whole experimental system consisted of several parts as shown in Figure 1, including welding controller,
spot welding robot, signal processing equipment and measurement sensors for current and voltage. A
Centerline spot welding robot with a servo gun was used, and the resistance welding controller was a
MEDAR(WTC) MFDC adaptive controller whose working frequency is 1000 Hz. The electrodes used in
the experiments were made of CuCrZr alloy with an end face of 6 mm in diameter. In this study, a
MEATROL Rogowski coil of 0.5% accuracy class was placed on the lower electrode as the current sensor.
Its output signal can be used to obtain the current signal through integration by the signal processing
equipment. The integral constant of the integrator was 20 ms and the sampling frequency was 240 ksps,
which means it can get 240000 samples per second. This Rogowski coil exhibited a strong anti-interference
ability and high measurement accuracy, meeting the measurement requirements of the MFDC RSW
Ac
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 2 of 17
Page 3 of 17
secondary current. Two shielded twisted pairs were installed respectively to the mounting holes on the
upper and lower electrode arms to record the secondary voltage.
a
e
us
d
cri
pt
b
an
c
Figure 1 Experimental equipment and measuring sensors. (a) Welding controller, (b) spot welding robot,
(c) signal processing equipment, (d) Rogowski coil, (e) wire for voltage measurement.
L2
dM
R2
LM
R
Voltage: U
L1
pte
Current: I
The Load Part
The Measurement Part
Figure 2 Equivalent circuit of medium frequency DC resistance spot welding.
ce
A typical equivalent circuit for the load part and the measurement part of secondary circuit of MFDC
RSW is shown in Figure 2, which is equivalent to a resistor-inductor series (RL) circuit model [31-33]. In
the figure, L1 and L2 represent the inductance of the RSW secondary circuit (L1 is the inductance in the
measurement area and L2 is the inductance outside the measurement area), LM is the mutual inductance
generated during the voltage measurement under a time-varying electromagnetic field, R is the resistance
in the measurement area and changes continuously as the nugget is formed, which usually consists of the
contact resistance, the electrode resistance of the electrode and the sheets, and R2 is the total resistance
outside the measurement area. During the RSW process, the welding transformer is used to induce a voltage
as the input source in the secondary circuit. Two or more metal sheets are pressed together by a pair of
electrodes, and the passage of large current heats up the sheets through the resistance according to Joule’s
Law. The voltage U measured by the twisted-pair cablings in the RSW process can be expressed as the
Ac
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
AUTHOR SUBMITTED MANUSCRIPT - MST-109751.R2
AUTHOR SUBMITTED MANUSCRIPT - MST-109751.R2
equation (1), that is available from the equivalent circuit model and composed of a resistive and an inductive
component [30].
U = IR + L
dI
dt
(1)
cri
pt
In the equation, I is the secondary current and L is the total inductance of L1 and M. R is the resistance
load. Due to the total inductance L, DR cannot be calculated by merely dividing the voltage by the current.
3 The novel real-time measurement method for dynamic resistance signal
3.1 Algorithm for calculating dynamic resistance
u = h

h =I

us
The recursive least squares (RLS)method, characterized by stronger tracking ability and fast calculation
speed, has been widely used as an adaptive parameter identification method [34-36]. It is less sensitive to
noise and can be measured according to the process. The difference between the actual observed and
calculated values of information can be minimized to estimate the unknown parameters of the model. Thus,
this method is widely used in the field of online parameter identification. Based on the equivalent RL circuit
model of the secondary circuit and equation (1), the voltage of the secondary circuit is expressed as equation
(2):
 R
dI 
，  =  L 
dt 
 
(2)
dM
an
According to equation (2), the discernibility matrix θ consists of the resistance R and the inductance L. h
is the regression matrix constructed from the current I and current differential composition dI/dt. However,
a so-called "data saturation" phenomenon occurs in the RLS method as the data grows, which means that
the information provided by the new data is drowned in the old data and gradually loses effect on the
correction of parameter estimates [37-39]. The gain matrix used to correct the previous discernibility matrix
also gradually decrease until they approach 0, which means the algorithm can no longer effectively correct
the parameter. In order to mitigate this phenomenon, the attenuation factor β (0 ＜ β ＜ 1) is added to reduce
the impact of old data by exponentially weighting the old data. The role of the factor is to reduce the weight
of old data and increase the impact of new data to adapt to the rapid change of time-varying signals. The
model at kth sampling point can be transformed into as equation (3):
  k −1u (1)    k −1hT (1) 

 

(3)

=
  (k )
pte
  k − k u ( k )    k − k hT ( k ) 

 

  k −1hT (1) T   k −1hT (1)  

 

 ( k ) = 
 

  k − k hT (k )    k −k hT (k )  
 
 

−1
  k −1hT (1) T   k −1u (1)  

 


 

  k −k hT (k )    k −k u (k )  
 
 

(4)
ce
Based on the modified circuit equation (3), the calculation formula (4) of the identification matrix θ(k),
which represents the resistance and inductance of the kth sampling point, can be obtained. The resistance
R and the inductance L of the secondary circuit are estimated based on the current I and voltage u provided
during welding. Then the covariance matrix P(k) is defined as equation (5), which demonstrates the
relationship between P(k) and P(k-1) to service for subsequent iterations, where α = β2 is defined as the
forgetting factor.
Ac
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 4 of 17
Page 5 of 17
-1
    k − 2 hT (1) T   k − 2 hT (1)  

 

 

 2 


T



=  
+ h( k ) h ( k ) 

T
T

 

    h (k − 2)    h (k − 2)  

T
T



   h (k − 1)   h (k − 1)  


 

=  P −1 (k − 1) + h(k )hT (k ) 
=
-1
cri
pt
  k −1hT (1) T   k −1hT (1)  

 





P(k ) = 
  hT (k − 1)    hT (k − 1)  

 

 hT (k )   hT (k )  


-1
1
P(k − 1)h(k )hT (k ) 
I
−
P(k − 1)
  hT (k ) P(k − 1)h(k ) +  
(5)
T
  k −1u (1) 




  k − k u (k ) 


an
  k −1hT (1) 




 (k ) = P(k )
  hT (k − 1) 


T
 h (k ) 
us
The discernibility matrix is transformed into equation (6) with the covariance matrix P(k) and shows the
relationship between θ(k) and the matrix on the previous point θ(k-1). The previous discernibility matrix is
used to get the new one by correcting the error between the observed matrix u(k) and the predicted value
hTθ(k-1).
dM
= P(k )  P −1 (k − 1) (k − 1) + h(k )u (k ) 
=  I − P(k )h(k )hT (k )   (k − 1) + P(k )h(k )u (k )
=  (k − 1) + P(k )h(k ) u (k ) − hT (k ) ( k − 1) 
(6)
K(k), which is called the gain matrix and indicates the degree of correction for errors, is calculated by
equation (7). The larger the gain matrix K(k), the stronger the correction effect.
K ( k ) = P ( k ) h( k )
1
P(k − 1)h(k )hT (k ) 
I
−
P(k − 1)h(k )
  hT (k ) P(k − 1)h(k ) +  
P (k − 1)h(k )
= T
h (k ) P (k − 1)h(k ) + 
pte
=
(7)
ce
Finally, the forgetting factor recursive least square (FFRLS) algorithm used to decouple the resistance
and inductance values of the kth sampling point is summarized as above equations where 0 ≤ α ≤1.

  (k ) =  (k − 1) + K (k ) u (k ) − hT (k ) (k − 1) 

P(k − 1)h(k )

(8)
 K (k ) = T
h
(
k
)
P
(
k
−
1)
h
(
k
)
+



1
T
 P(k ) =  I − K (k )h (k )  P(k − 1)


The FFRLS method for resistance measurement was proposed with the algorithm. The flow chart of the
new method is shown in Figure 3, where M is the total number of sampling points and T is the cycle time
corresponding to the carrier frequency. The regression matrix h(k) is built from the secondary current I and
the relevant current differential dI/dt. The voltage value at the kth sampling point in the welding process
Ac
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
AUTHOR SUBMITTED MANUSCRIPT - MST-109751.R2
AUTHOR SUBMITTED MANUSCRIPT - MST-109751.R2
cri
pt
needs to be collected as the observation matrix u(k). During the measurement process, the forgetting factor
α was used to prevent the information being incorporated into the old data. The regression matrix h(k) is
initialized as zero, while the gain matrix K(k) and the covariance matrix P(k) are both initialized as the
identity matrix. Based on the error between the observation matrix u(k) and the result value calculated by
the regression matrix h(k), the gain matrix K(k) and the covariance matrix P(k) is calculated. Then, the
discernibility matrix θ(k) is obtained by correcting the previous discernibility matrix. As the new
observation data is introduced periodically, the FFRLS method decouples the inductance and resistance at
every sampling point through iteration, and then output discernibility matrix per cycle time T. Through
continuous iterative correction within a cycle, the estimated values of dynamic resistance and inductance
within a cycle are obtained. As shown in each subfigure of Figure 9 and Figure 12, the FFRLS method
could measure resistance accurately in MFDC RSW and met the monitoring requirements.
Start
us
Initialize forgetting factor α,
covariance matrix P(0), and
identification matrix θ(0)
an
Input voltage u(k), current I(k)
Calculate current differential dI(k)/dt
dM
Construct observation matrix h(k)
Calculate covariance matrix P(k),
gain matrix K(k), and
identification matrix θ(k)
k = k+1
pte
k = nT, (n = 1,2,3...)
N
Y
Output identification matrix θ(k)
ce
N
k>M
Y
End
Figure 3 Flow chart of the FFRLS method
3.2 Determination of optimal forgetting factor by sensitivity analysis
Ac
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 6 of 17
The forgetting factor α used in the FFRLS method is the key to avoid incorporation of the new data into
the old data. If the forgetting factor decreases, the tracking ability of the system will become stronger to
track the variation of resistance in time but be more sensitive to noise. If the value of the forgetting factor
becomes larger, the oscillation amplitude will decrease, but the tracking ability of the system will be
Page 7 of 17
i (t0 + t ) =
UM 
U
+ i (t0 ) − M
R 
R
 − Lt
  e
R
cri
pt
weakened. Therefore, the optimal forgetting factor needs to determine by sensitivity analysis so that the
tracking ability is guaranteed and noise interference is reduced. A series of simulated welding experiments
were carried out for sensitivity analysis and test the algorithm's ability to decouple resistance and inductance.
Since the changes of the transformer leakage inductance and the transformation ratio can be equivalent to
a change in the input voltage waveform, they can be ignored in the simulation because they have less effect
on the algorithm verification and forgetting factor optimization. The simulation was conducted using circuit
balance equations where inversion period is set as T, the duty cycle is S, the peak value of the secondary
voltage is UM, the initial moment is t0, the current is i, the dynamic resistance is R and the inductance is L.
Based on the set values, the currents are obtained by circuit balance equations. When (n-1)T ≤ t0+t ≤ (n1)T+TS, the magnitude of the obtained current is:
(9)
When (n-1)T+TS ≤ t0+t ≤ (n)T, the magnitude of the obtained current is:
R
− t
L
Resistance: R
Voltage: U
Current: I
(a)
20
dM
Total inductance: L
Current I (kA)
25
15
Voltage U (V)
an
us
(10)
i (t0 + t ) = i (t0 )  e
The obtained current signal (after applying noise) and the set voltage signal can be used to simulate the
welding experiment to select an optimal forgetting factor and to test the algorithm's ability to decouple
resistance and inductance. In the simulation experiments, the secondary voltage peak was 5 V, welding
time is 40ms, the resistance was 100 μΩ, and the total inductance L that is made up of the circuit inductance
in the measurement area L1 and the mutual inductance LM was 0.2 pH. The inversion period was set as 1ms
and 240 points were sampled in one period. A step current signal from about 10 kA to 20 kA was generated
to the simulated welding with the duty cycle of the voltage changed from 20% to 40% at 20 ms in the
experiments. ±20 A simulate sinusoidal noise was applied to the current during resistance measurement.
20kA
10
10kA
5
0
0
8
16
24
Time (ms)
(b)
32
40
6
5V
S = 0.2
S = 0.4
4
2
0
0
8
16
24
Time (ms)
32
40
(c)
pte
Figure 4 Simulation result of secondary signal when welding with the time-varying current. (a) Secondary circuit model,
(b) secondary current, (c) secondary voltage. S is the duty cycle
ce
The different forgetting factors were tested and analyzed in this study, as shown in Figure 5. When the
forgetting factor is smaller than 0.98, the FFRLS method can track the resistance variation in time, but it is
particularly sensitive to noise. When the forgetting factor is 0.95, the maximum error caused by noise can
even reach 80 μΩ. If the forgetting factor exceeds 0.98, the DR curve became smoother with the increase
in the forgetting factor, and the tracking ability is weakened. An 8 ms delay even occurs at the beginning
of welding with the forgetting factor 0.99. Besides, the FFRLS method could also accurately measure the
inductance component. The error of inductance would continue to decrease as the forgetting factor
continues to increase. When the forgetting factor is 0.98, the maximum error of resistance measurement is
about 0.4 μΩ with a 2 ms delay, and the maximum error of inductance measurement is 1.2 pH.
Ac
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
AUTHOR SUBMITTED MANUSCRIPT - MST-109751.R2
AUTHOR SUBMITTED MANUSCRIPT - MST-109751.R2
101.0
2 ms
8
16
24
Time (ms)
(a)
32
2 ms
99.0
0
40
210
8
16
24
Time (ms)
(b)
32
40
40 pH
180
FFRLS
True
165
8
16
24
Time (ms)
(d)
32
40
Inductance (pH)
201.00
195
150
0
99.5
0.2 μΩ
100.0
99.5
99.0
0
8 ms
8
24
16
Time (ms)
(c)
32
40
201.00
200.25
199.50
198.75
FFRLS
True
1.2 pH
198.00
0
200.25
199.50
0.45 pH
8
16
24
Time (ms)
(e)
32
198.00
0
40
FFRLS
True
198.75
us
80
0
80 μΩ
100.0
FFRLS
True
100.5
cri
pt
120
0.4 μΩ
100.5
Resistance (μΩ)
160
101.0
FFRLS
True
Inductance (pH)
FFRLS
True
Resistance (μΩ)
Resistance (μΩ)
200
Inductance (pH)
8
16
24
Time (ms)
(f)
32
40
10.00
9.824
dM
tRMSE (μΩ)
9.75
an
Figure 5 The resistance and inductance measured at different forgetting factors.
(a) Resistance at forgetting factor 0.95, (b) resistance at forgetting factor 0.98, (c) resistance at forgetting factor 0.99,
(d) inductance at forgetting factor 0.95, (e) inductance at forgetting factor 0.98, (f) inductance at forgetting factor 0.99.
9.50
0.75
0.498
0.50
0.727
0.473
0.440
0.25
pte
0.00
0.95
0.96
0.97
0.98
Forgetting factor
0.99
Figure 6 The tRMSE of DR curves with different forgetting factors.
ce
In resistance measurements, the error of the method defined as the tRSME is calculated by equation (11)
to evaluate accuracy of the new methods, where the M is the total number of sampling points in a DR curve
and e(i) is the error between the measured value and the true value at ith sampling point.
tRSME =
1
M
M
 e(i)
2
(11)
i =1
The optimal forgetting factor was obtained by comparing tRSME with different forgetting factors.
Furthermore, the tRMSE with the forgetting factor from 0.95 to 0.99 is showed in Figure 6. When the
forgetting factor is 0.98, the value of tRMSE reaches a minimum of 0.44 μΩ. Moreover, the high
convergence rate of the new method means that this method can realize real-time tracking and accurately
feedback the variation of resistance in the RSW process. The process of determining the optimal forgetting
factor is actually to find the balance point between the convergence speed of the algorithm and the ability
Ac
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 8 of 17
Page 9 of 17
to resist noise interference. The forgetting factor is only related to the sampling parameters of the
monitoring equipment, is not needed to be changed to cater to the new welding condition. From the results
of simulated welding, the optimal forgetting factor 0.98 meets the actual RSW monitoring requirements
with a sampling frequency of 240 ksps.
cri
pt
4. Error analysis for the new method
4.1 With the constant current mode
us
The effectiveness and reliability of the traditional DR measurement methods were tested in the welding
experiments. The RMS method [3] and the average method [27] measures the resistance of one cycle
according to Ohm's law, and the voltage and current of one cycle should be measured first. The time of one
cycle is 1ms, and 240 data points are used for resistance recognization in one cycle. The RMS voltage of
one cycle Urmst and the RMS current of one cycle Irmst are simultaneously calculated by equation (12) where
T represents the cycle time corresponding to the carrier frequency, i represents the instantaneous current,
and u represents the instantaneous voltage. The average current of one cycle I and the average voltage of
t
one cycle
Ut
as equation (13) is used to calculate the resistance of one cycle
.
an
Rt = U t / I t
Rt
1
1 2
u 2 dt , I rmst =
i dt

T T
T T
1
1
U t =  udt , I t =  idt
T
T
T T
Rrmst = U rmst / I rmst U rmst =
(12)
(13)
dM
Although it is hard to get the true value of the DR, it’s obvious that the DR remains basically unchanged
when welding with no sheet, and the accurate value can be obtained by the volt-ampere characteristic curve.
The welding experiments were carried out with constant current and no sheet was placed between the
electrodes. The secondary current was set to 4 kA to 13 kA in turn, and the welding time was 150ms. When
welding with constant current, voltage and current remain approximately unchanged during the welding
process. The volt-ampere characteristic curve of the RMS method and the average method was drawn with
the value over all time such as Urms and Irms, whose slope was the resistance of the measurement area, as
shown in Figure 7. The value over all time, such as Urms and U , could be calculated by the average of the
value of one cycle during the whole welding process, such as Urmst and U t .
3300
RMS
Average
Voltage over all time U (mV)
pte
3000
2700
The RMS method：
U = 71.156 I + 2298.3
2400
ce
Ac
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
AUTHOR SUBMITTED MANUSCRIPT - MST-109751.R2
600
I
U
300
0
0
The average method：
U = 51.716 I + 7.7009
2
4
6
8
10
Current over all time I (kA)
12
Figure 7 The volt-ampere characteristic curves measured by the RMS method and the average method.
AUTHOR SUBMITTED MANUSCRIPT - MST-109751.R2
cri
pt
The volt-ampere characteristic curve measured by the RMS method has a broad intercept (1082.3 mV),
indicating that there is a sizeable error caused by inductance in the resistance measurement of the RMS
method. By contrast, the intercept of the volt-ampere characteristic curves measured by the average method
(7.7 mV) is approximately zero following the pure resistance load law, so the slope of the curve calculated
by the average method (51.716 μΩ) is considered as the conventional true value of the measuring area
resistance. Furthermore, the RMS current differential dI/dt of one cycle is never zero, so the inductive
component of voltage in equation (1) always exists and is greater than 0. The resistance of one cycle Rrmst
calculated by dividing the voltage by the current simply always contains inductive noise. However, the
average current differential dI/dt of one cycle changes negatively with an exponential decay to zero, and
the average of the inductive components in the secondary voltage also decays negatively with time when
the current is constant. As a result, the resistance of one cycle Rt measured by the average method is almost
accurate.
100
Current I
Lower electrode
1.72 μΩ
30
60
90
120 150
Time (ms)
(b) Welding current: 5 kA
Average
FFRLS
1.31 μΩ
4
5
6
pte
0.0
51.716 μΩ
dM
tRMSE (μΩ)
0.5
40
an
(a)
1.0
60
20
0
2.0
1.5
FFRLS
Average
80
us
Resistance (μΩ)
Upper electrode
7
8
9
10
Current (kA)
11
12
13
(c)
Figure 8 The results when welding with no sheets and constant currents. (a) Schematic diagram for the RSW process,
(b) resistance when welding current: 6 kA, (c) the tRMSE of the FFRLS method and the average method
ce
Following the RSW theory, the temperature of the secondary circuit is small when welding with no sheet,
and the resistance value of the measurement area should remain stable at the true value. The tRSME of the
FFRLS method and the average method at different current from 4 kA to 13 kA are compared to analyze
the accuracy of the new method when the current is constant, as shown in Figure 8 (c), where the true value
is replaced by the conventional true value. Only the data of the 10-150 ms is employed for the tRMSE
calculation. The maximum tRSME of the FFRLS method compared to the conventional true value is 1.31
μΩ, less than the maximum value of the average method 1.72 μΩ. As an example, the DR curves of the
FFRLS method and the average method are almost stable at the conventional true value of the measuring
area resistance 51.716 μΩ when welding with the constant current 5 kA, as shown in Figure 8 (b). The
results show that the new method and the average method can both eliminate the inductive noise to measure
Ac
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 10 of 17
Page 11 of 17
the resistance of one cycle. As a result, when welding with the constant current mode, the measurement
accuracy of the new method and the average method are both better than the RMS method.
From the error analysis theory, the population standard deviation and probability limit error are calculated
for random error evaluation of the new method. The population standard deviation σ can be estimated by
(14)
cri
pt
1 l
 (tRMSE( p))2
l − 1 p =1
=
where tRMSE(p) is used to represent the random error of the pth measured series and l is the total number
of measured series. Thus, the population limit error can be calculated by multiplying the confidence
coefficient by the population standard deviation, where the coefficient usually takes 3 for a 99.73%
confidence level (±3σ). It can be calculated that the random errors are 0.958 μΩ and the probability limit
error of the DR curves measured by the FFRLS method is mainly distributed in ±3 μΩ when welding with
the constant currents mode.
Upper electrode
150
Steel sheets
90
60
30
0
60
tRMSE: 1.825 μΩ
an
dM
Resistance (μΩ)
FFRLS
Average
30
60
90
Time (ms)
120
150
(b)
150
Resistance (μΩ)
(a)
120
90
30
0
Lower electrode
150
120
FFRLS
Average
us
Resistance (μΩ)
Current I
FFRLS
Average
120
90
tRMSE: 1.969 μΩ
60
tRMSE: 1.116 μΩ
30
60
90
Time (ms)
120
(c)
150
30
0
30
60
90
Time (ms)
120
150
(d)
pte
Figure 9 The resistance when welding with steel sheets and constant currents. (a) Schematic diagram for the RSW
process, (b) welding current: 6 kA, (c) welding current: 9 kA, (d) welding current: 12 kA.
ce
Additionally, two uncoated DP590 high strength steel sheets that were 0.8 mm in thickness and had a
tensile strength of ≥ 590 MPa were used to test the error of the methods with a constant current. The
chemical composition of the steel is given in Table 1. The welding experiments under three current levels
(6 kA, 9 kA, 12 kA) were performed where the electrode force was set as 2.6 kN and the welding time as
150 ms. The tRMSE between the measured resistance value and true value is analyzed to test the method
calculation precision, as shown in Figure 9. Because it is difficult to get the true value in actual welding,
the resistance measured by the average method is viewed as the conventional true value to calculate the
tRMSE in actual welding. As shown in the results, the tRMSE is less than 2 μΩ, which means that the
FFRLS method are very similar with the conventional true value and the measurement error of the proposed
method is limited within ± 6 μΩ at a 99.73% confidence level in actual welding. The DR curves measured
by the FFRLS method conforms to the DR change law during RSW: rapid drop, fast rise and slow decline.
The feature extracted from the DR curves are closely related to the welding process and offers more
information for welding quality monitoring. With the increased welding current, significant differences can
be seen; for example, DR variation increases and the DR peak time are advanced. The sudden drop in DR
curves in Figure 9 (d) reflects the RSW expulsion when the current is large. The new method with a higher
Ac
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
AUTHOR SUBMITTED MANUSCRIPT - MST-109751.R2
AUTHOR SUBMITTED MANUSCRIPT - MST-109751.R2
resistance measurement accuracy can assist in exploring the correlation between the DR features and weld
quality indicators.
Table 1 Chemical composition of applied steel sheet (mass%)
Steel grades
C
Si
Mn
0.055
0.507
1.616
P
S
Alt
0.010
0.004
0.048
cri
pt
DP590
4.2 With the time-varying current mode
Current (kA)
dM
an
us
The welding experiments with no sheet were performed to compare the measurement accuracy of the new
method and the average method as the current varies, where the electrode force was set to 2.6 kN. The timevarying current was set to three-stage, and the total welding duration was 150 ms. In the welding
experiments, different times of variation (10 ms, 20 ms and 30 ms) were applied to welding experiments to
analyze the error induced by the current variation as shown in Figure 10 (a), where the three-stage current
was fixed at 9 kA - 6 kA - 9 kA. Besides, different degrees of current variation dI (1.5 kA, 3 kA and 4.5
kA) was set by changing the magnitude of the second stage (7.5 kA, 6 kA and 4.5 kA) as shown in Figure
10 (b), in which the first and third stage was set to 9kA and the time of variation was set to 10ms.
It is proved in this article that the resistance value of the measurement area should remain stable at the
true value when welding with no sheets. Because of the immediacy and invisibility of RSW, the
conventional true value 51.716 μΩ is taken as the true value. The DR curves obtained by the average method
and the FFRLS method are both stables when the current remains constant. As the dt increases from 10ms
to 30 ms, the error of the average method is reduced from 55 μΩ to 16 μΩ, as shown in Figure 11 (b) (c)
(e). It’s also shown in Figure 11 (d) (e) (f) that the error of the average method reaches 27 μΩ as the current
varies by 1.5 kA, and the error increases to about 110 μΩ as the degree of current variation dI increases to
4.5 kA. In general, when the current varies fast and the value of dI/dt increases, the resistance error of the
average method grows larger, while the result of the FFRLS method is stable at 51.716 μΩ.
9
8
7
6
0
dt = 10 ms
dt = 20 ms
dt = 30 ms
25
50
75
100
Time (ms)
dI = 3 kA
125
150
Current (kA)
pte
(a)
9.0
7.5
6.0
4.5
ce
0
dI = 1.5 kA
dI = 3 kA
dI = 4.5 kA
25
50
dt = 10 ms
75
100
Time (ms)
125
150
(b)
Figure 10 The time-varying current with different degrees and times of variation used in the experiments.
(a) Current with times of variation dt, (b) current with degrees of variation dI.
Therefore, the tRMSE between the resistance measured by the FFRLS method and the conventional true
value is calculated to analyze the accuracy of the methods as the current varies. The tRMSE with different
time-varying current modes is shown in Table 2. The tRMSE of the average method reaches a maximum of
28.212 μΩ, while the error of the proposed method is less than 1.997 μΩ. It indicates that the FFRLS
method measures the resistance more accurately than the average method as the current varies. The random
error evaluation of the new method is carried out and the population standard deviation σ are mainly
Ac
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 12 of 17
Page 13 of 17
evaluated with the equation (14), which is distributed in ±1.919 μΩ.The measurement error of the FFRLS
method with the time-varying current mode is mostly smaller than 6 μΩ at a 99.73% confidence level and
meets the monitoring requirements. Furthermore, when welding with time-varying current, the average
value of the current differential dI/dt of one cycle no longer decays with time. As a result, the average
method cannot eliminate the inductive noise and the resistance of one cycle R comes with a large error as
cri
pt
t
the current varies. However, the FFRLS method iterates the current, voltage and current differential dI/dt
of each sampling point and then iterative decouple resistance and inductances effectively regardless of the
existence of dI/dt. As long as the variation information of the sampling point is accurately collected, the
accuracy of the results measured by the FFRLS method is ensured. The measurement system mentioned in
the article can accurately sample the voltage and current signal as the current varies, thus ensuring the
accuracy of the FFRLS method.
50
25
16 μΩ
Lower electrode
30
Resistance (μΩ)
FFRLS
Average
25 μΩ
100
0
27 μΩ
-50
0
30
90
60
Time (ms)
(d)
120
150
120
50 μΩ
50
55 μΩ
0
0
26 μΩ
50
25
30
0
150
FFRLS
Average
dM
50
100
90
60
Time (ms)
(b)
an
(a)
150
75
28 μΩ
0
0
0
Resistance (μΩ)
13 μΩ
FFRLS
Average
us
Current I
75
100
FFRLS
Average
Resistance (μΩ)
Resistance (μΩ)
100
Upper electrode
Resistance (μΩ)
150
30
90
60
Time (ms)
(c)
FFRLS
Average
100
120
150
110 μΩ
50
0
100 μΩ
-50
90
60
Time (ms)
(e)
120
150
0
30
90
60
Time (ms)
(f)
120
150
Figure 11 The resistance measured when welding with no sheet and different time-varying current modes. (a) Schematic
diagram for the RSW process, (b) dI = 3 kA, dt = 30 ms, (c) dI = 3 kA, dt = 20 ms, (d) dI = 1.5 kA, dt = 10 ms, (e) dI = 3
kA, dt = 10 ms, (f) dI = 4.5 kA, dt = 10 ms.
ce
pte
Table 2 The tRMSE with different time-varying current modes
Current modes
mode
dI
dt
(kA)
(ms)
1
3
10
2
3
20
3
3
30
4
1.5
10
5
4.5
10
tRMSE
Average
(μΩ)
14.134
8.321
6.253
6.652
28.212
FFRLS
(μΩ)
1.514
1.826
1.789
1.384
1.997
0.8 mm uncoated DP590 high strength steel sheets were also used to test the effectiveness and reliability
in actual welding with the time-varying current mode, where the electrode force was set to 2.6 kN. Different
degrees of current variation dI (1.5 kA, 3 kA and 4.5 kA) and different times of current variation dt (30 ms,
20 ms and 10 ms) showed in Figure 10 were also applied in the welding experiments with steel sheets.
When the degree of current variation dI is 3 kA and the variation time dt is 30ms, the two curves are almost
the same. It can be seen from Figure 12 (c) (d) (e) (f) that the resistance measured by the average method
and the FFRLS method is significantly different as the current varies. When the degree of current variation
Ac
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
AUTHOR SUBMITTED MANUSCRIPT - MST-109751.R2
AUTHOR SUBMITTED MANUSCRIPT - MST-109751.R2
cri
pt
dI increases or the time of current variation dt decreases, the resistance measured by the average method
has a larger mutation, which especially reaches 120 μΩ when the dI is 4.5 kA and dt is 10 ms. However,
the DR curve measured by the FFRLS method conforms to the law of RSW DR change, and no significant
mutation occurs as the current varies. According to the RSW theory, the resistance measured by the FFRLS
method is more accurate than the result of the average method as the current varies.
In addition, it is difficult to correctly post-processed the mutations caused by the average method.
Expulsion may also lead to a mutation in the resistance signal [40,41]. It is hard to determine whether the
mutation is derived from the expulsion or the time-varying current, especially under the time-varying
current mode. If the post-processing is forced performed through a simple linear interpolation, it may result
in a misdetection of weld expulsion. In addition, post-processing to the results of the average method is
lagging in getting results, which cannot realize the real-time monitoring and control of the current welding.
Therefore, for the field where high accuracy and fast response are not required, the average method can be
used. However, for some high-end scenarios such as welding adaptive control and accurate evaluation of
welding quality, the FFRLS method can path the way for the subsequent studies.
160
40
0
-40
0
Lower electrode
FFRLS
Average
30
(a)
160
80
40
45 μΩ
40 μΩ
0
FFRLS
Average
-40
0
30
60
90
Time (ms)
(d)
120
150
Resistance (μΩ)
120
dM
160
60
90
Time (ms)
(b)
120
40
80 μΩ
0
-40
0
80 μΩ
30
60
90
Time (ms)
(e)
FFRLS
Average
120
150
120
80
20 μΩ
40
0
-40
0
150
120
80
Resistance (μΩ)
80
Resistance (μΩ)
Steel sheets
120
an
Resistance (μΩ)
Current I
us
160
Upper electrode
Resistance (μΩ)
20 μΩ
30
FFRLS
Average
60
90
Time (ms)
(c)
120
150
150
100
120 μΩ
50
0
-50
0
100 μΩ
FFRLS
Average
30
60
90
Time (ms)
(f)
120
150
pte
Figure 12 The resistance measured when welding with steel sheets and the time-varying current. (a) Schematic diagram
for the RSW process, (b) dI = 3 kA, dt = 30 ms, (c) dI = 3 kA, dt = 20 ms, (d) dI = 1.5 kA, dt = 10 ms, (e) dI = 3 kA, dt =
10 ms, (f) dI = 4.5 kA, dt = 10 ms.
5. Conclusion
ce
In this study, based on the forgetting factor recursive least-squares (FFRLS) algorithm, a novel method was
proposed to measure the dynamic resistance (DR) signal in real-time during the MFDC RSW process with
high measurement accuracy. From the experimental analyses, the following conclusions can be drawn:
a) The novel method could decouple resistance and inductance correctly with the optimal forgetting
factor and the measurement error of this new method is limited within ± 6 μΩ at a 99.73% confidence
level (±3σ). Compared to traditional DR measurement methods such as root mean square (RMS)
method and average method, the new method can eliminate the interference of the inductance and
meet the monitoring requirements under different welding modes, including constant and timevarying current modes.
b) The forgetting factor is proved as the critical parameter of the novel method. When the forgetting
factor decreases, the tracking ability of the system becomes stronger but more sensitive to noise.
Ac
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 14 of 17
Page 15 of 17
us
cri
pt
Thus, to balance the convergence speed and oscillation amplitude in the resistance measurement, the
forgetting factor is optimized to 0.98.
c) The resistance measured by the RMS method contains errors caused by the inductive noise, but the
average method can measure DR correctly when the current is constant. The intercept of the voltampere characteristic curve obtained by the RMS method is very large, while the curve obtained by
the average method followed the pure resistance load law and the slope of it can be considered as
the conventional true value.
d) The comparative study has been conducted with the time-varying current mode, and the results show
that the average method cannot eliminate inductance noise as the current varies. The average current
differential dI/dt in an inverter cycle no longer decays with the increase of time, so the inductive
error cannot be eliminated. The faster the current changed, the larger the error became.
The DR curves can be used to monitor the welding process. The FFRLS method can path the way for the
subsequent studies in some high-precision and fast-response application fields such as weld quality
evaluation. Besides, intelligent welding control and other related research can be conducted subsequently.
In this study, only uncoated high-strength steel materials were taken to analyze the performance of the
proposed method, and other emerging steels can be further studied.
Acknowledgments
an
This work is supported by the National Natural Science Foundation of China (Grant Nos. U1564204 and
U1764251) and the National Key Research and Development Program of China (Grant No.
2016YFB0101606-08).
References
ce
pte
dM
[1] Ceglarek D, Shi J and Wu S M 1994 A Knowledge-Based Diagnostic Approach for the Launch of the
Auto-Body Assembly Process J. Eng. Ind. 116 491-499
[2] Zhang Y S, Wang H and Chen G L 2007 Monitoring and intelligent control of electrode wear based
on a measured electrode displacement curve in resistance spot welding Meas. Sci. Technol. 18 867
[3] Bhattacharya S and Andrews D R 1974 Significance of Dynamic Resistance Curves in Theory and
Practice of Spot Welding Weld. Met. Fabr. 42 296-299.
[4] Savage W, Nippes E F and Wassel F A 1978 Dynamic Contact Resistance of Serial Spot Welds Weld.
J. 57 43-50.
[5] Cho Y, Rhee S, Technology 2000 New technology for measuring dynamic resistance and estimating
strength in resistance spot welding Meas. Sci. Technol. 11 1173.
[6] Garza F J and Das M 2000 Identification of time-varying resistance during welding IEEE Instrum.
Meas. Technol. Conf.
[7] Garza F J and Das M 2001 On real time monitoring and control of resistance spot welds using dynamic
resistance signatures IEEE Mid. Sym. Cir. Sys.
[8] Ling S F, Wan L X and Wong Y R 2010 Input electrical impedance as quality monitoring signature
for characterizing resistance spot welding NDT&E Int. 43 200-205.
[9] Wong Y R and Xin P 2014 A New Characterization Approach of Weld Nugget Growth by Real-Time
Input Electrical Impedance Engineering 06 516-525.
[10] Wang L, Hou Y and Zhang H 2016 A new measurement method for the dynamic resistance signal
during the resistance spot welding process Meas. Sci. Technol. 27 095009.
[11] Zhang H, Hou Y and Tao Y 2018 Welding quality evaluation for the resistance spot welding using the
time-varying inductive reactance signal Meas. Sci. Technol. 29.
[12] Johnson K I and Needham J C 1972 New Design of Resistance Spot Welding Machine for QualityControl Weld. J. 51 338-351.
[13] Podrzaj P, Polajnar I and Diaci J 2004 Expulsion detection system for resistance spot welding based
on a neural network Meas. Sci. Technol. 15 592.
Ac
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
AUTHOR SUBMITTED MANUSCRIPT - MST-109751.R2
AUTHOR SUBMITTED MANUSCRIPT - MST-109751.R2
ce
pte
dM
an
us
cri
pt
[14] Kang Z and Cai L 2014 Study on effect of electrode force on resistance spot welding process J. Appl.
Phys. 116 2823-2830.
[15] Wang X F, Li Y B and Meng G X 2011 Monitoring of resistance spot weld quality using electrode
vibration signals Meas. Sci. Technol. 22 045705.
[16] Martín Ó, López M and Martín F 2007 Artificial neural networks for quality control by ultrasonic
testing in resistance spot welding J. Mater. Process. Technol. 183 226-233.
[17] Martín Ó, Tiedra P D and López M 2009 Quality prediction of resistance spot welding joints of 304
austenitic stainless steel Mater. Des. 30 68-77.
[18] Hua L, Wang B and Wang X 2019 In-situ ultrasonic detection of resistance spot welding quality using
embedded probe J. Mater. Process. Technol. 267 205-214.
[19] Chang H S, Cho Y J and Choi S G 1989 Proportional-integral Controller for Resistance Spot Welding
Using Nugget Expansion J. Dyn. Syst., Meas., Control 111 332-336.
[20] Wang H, Zhang Y and Chen G 2009 Resistance spot welding processing monitoring based on electrode
displacement curve using moving range chart Measurement 42 1032-1038.
[21] Lovro K, Polajnar I and Diaci J 2011 A method for measuring displacement and deformation of
electrodes during resistance spot welding Meas. Sci. Technol. 22 067002.
[22] Chen J Z and Farson D F 2004 Technology. Electrode displacement measurement dynamics in
monitoring of small scale resistance spot welding Meas. Sci. Technol. 15 2419-2425.
[23] Chen J Z and Farson D F 2006 Modeling small-scale resistance spot welding machine dynamics for
process control Int. J. Adv. Des. Manuf. Technol. 27 672-676.
[24] Cho Y and Rhee S 2003 Experimental study of nugget formation in resistance spot welding Weld. J.
82 195-201.
[25] Ouafi A E, Bélanger R and Méthot J 2011 Artificial neural network-based resistance spot welding
quality assessment system Int. J. Metall. 108 343-355.
[26] Chied C S 2002 Investigation of monitoring systems for resistance spot welding Weld. J. 81 195s-9s.
[27] Needham C 1983 Measurement of the Resistance at High Alternating Current Weld. Inst. 1-6.
[28] Xia Y J, Zhang Z D and Xia Z X 2015 A precision analogue integrator system for heavy current
measurement in MFDC resistance spot welding Meas. Sci. Technol. 27 25104-25111.
[29] Kang Z and Cai L. 2011 Improvement in control system for the medium frequency direct current
resistance spot welding system Am. Control Conf.
[30] Wei L, Cerjanec D and Grzadzinski G A 2015 A Comparative Study of Single-Phase AC and
Multiphase DC Resistance Spot Welding J. Eng. Ind. 127 583-589.
[31] Klopcic B, Dolinar D and Ctumberger G 2008 Advanced Control of a Resistance Spot Welding System
IEEE Tran. Power Electron. 23 144-152.
[32] Ma Y, Wu P and Xuan C 2013 Review on Techniques for On-Line Monitoring of Resistance Spot
Welding Process Adv. Mater. Sci. Eng. 1-6.
[33] Kang Z and Yao P 2017 Review of Application of the Electrical Structure in Resistance Spot Welding
IEEE Access 5 25741-25749.
[34] Lee D, Morf M and Friedlander B 1981 Recursive least squares ladder estimation algorithms IEEE
Trans. Acoust., Speech, Signal Process. 29 627-641.
[35] Han L, Sheng J, Ding F 2009 Recursive least squares identification for multirate multi-input singleoutput systems Am. Control Conf. 5604-5609.
[36] Bobrow J E, Murray W 1993 An algorithm for RLS identification parameters that vary quickly with
time IEEE Trans. Autom. Control 38 351-354.
[37] Vahidi A, Stefanopoulou A G and Peng H 2005 Recursive least squares with forgetting for online
estimation of vehicle mass and road grade: theory and experiments Veh. Syst. Dyn. 43 31-55.
[38] Paleologu C, Benesty J and Ciochina S 2008 A Robust Variable Forgetting Factor Recursive LeastSquares Algorithm for System Identification IEEE Signal Process. Lett. 15 597-600.
[39] Lu L, Zhao H and Chen B 2016 Improved-Variable-Forgetting-Factor Recursive Algorithm Based on
the Logarithmic Cost for Volterra System Identification IEEE Trans. Circuits Syst. 63 588-592.
[40] Xia Y J, Su Z and Li Y 2019 Online quantitative evaluation of expulsion in resistance spot welding J.
Manuf. Processes 46 34-43.
Ac
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 16 of 17
Page 17 of 17
ce
pte
dM
an
us
cri
pt
[41] Dickinson D W, Franklin J E and Stanya A 1980 Characterization of Spot Welding Behavior by
Dynamic Electrical Parameter Monitoring Weld. J. 59 170.
Ac
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
AUTHOR SUBMITTED MANUSCRIPT - MST-109751.R2
View publication stats