# Sample Entropy-Based Approach to Evaluate the Stability of Double-Wire Pulsed MIG Welding

Authors: Ping Yao; JiaXiang Xue; Kang Zhou; XiaoJun Wang
Journal: Mathematical Problems in Engineering
 (2014)

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## Abstract

According to the sample entropy, this paper deals with a quantitative method to evaluate the current stability in double-wire pulsed MIG welding. Firstly, the sample entropy of current signals with different stability but the same parameters is calculated. The results show that the more stable the current, the smaller the value and the standard deviation of sample entropy. Secondly, four parameters, which are pulse width, peak current, base current, and frequency, are selected for four-level three-factor orthogonal experiment. The calculation and analysis of desired signals indicate that sample entropy values are affected by welding current parameters. Then, a quantitative method based on sample entropy is proposed. The experiment results show that the method can preferably quantify the welding current stability.


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## Body

## 1. Introduction

Double-wire pulsed MIG welding is used prevalently in current industrial occasions, such as engineering machinery, coal mining, and ship building. For achieving better operation efficiency and gaining satisfactory welding operation, appropriate process control methods need to be used [1–3]. Electric signals contain a lot of information reflecting the welding performance and welding quality; online measuring of the corresponding electric signals can do a lot of useful things, such as power factor correction [4, 5] and fault diagnosis [6, 7]. Analyzing and processing this information can help us to improve welding stability and to objectively assess welding performance.For decades, a lot of relative researches were taken to use the electrical signals to analyze the welding process and improve the production. Luksa and Rymarski evaluated welding quality by analyzing the changes of electric signals [8]. Shinoda et al. found that splashes result in unstable electric signals and affect welding quality [9]. Hermans and den Ouden found that welding process stability is directly relative to weld pool oscillation [10]. Quinn et al. evaluated welding quality by setting stable current thresholds [11]. Adolfsson et al. studied a repetition sequential probability ratio algorithm. This algorithm can detect small sudden changes in electric signals [12]. Klimov et al. designed a new method of collecting current signals in the welding. By means of the method, current signals of ERW were collected for welding quality evaluation [13]. Šoštarić et al. indicated that online monitoring of the welding process by electric signals is feasible after comparing the quality of online monitoring signals and oscilloscope-acquired signals [14]. He et al. assessed the stability of submerged arc welding by analyzing current signals with Lyapunov exponent [15]. Xue et al. analyzed the effects of current and voltage on welding stability from the perspective of statistics and spectrum [16, 17]. Li et al. and Chen et al. established a multi-information acquisition system to collect a variety of electrical signals for analyzing the welding process [18, 19]. Chen et al. considered that relatively stable welding process can be obtained only under optimum operations conditions by analyzing the effect of current waveform on the stability of short circuiting transfer process [20].Hence, using electrical signals in welding production process is very usual in reality. However, present studies of welding current signals mainly focused on time domain and frequency domain. In practical production occasion, current signals change in chaos. In other words, the actual process is typically nonstationary and random. Hence, in addition to the features of time domain and frequency domain, nonlinear features of welding current should also be concerned further by researchers.There were some relative researches focused on the issue of nonlinear features of the welding current. Entropy is a common function which is used to describe the system state. It is used to calculate system disorder phenomena. In recent years, researchers have made some studies about welding process stability by means of approximate entropy (ApEn). ApEn was proposed by Pincus for overcoming the difficulty in solving the entropy in chaos [21–24]. Pincus and Kalman found that the ApEn of arc voltage increases with the increase of wire feed speed in GMAW [24]. Cao et al. analyzed the relationship between ApEn (and its standard) and the stability of short circuit transfer of CO2 welding [25, 26]. Nie et al. used neural network to predict the ApEn of P-MIG welding of aluminum alloy and achieved good results [27]. Zhang et al. evaluated adaptive control results by ApEn and found that smaller ApEn leads to better adaptive control [28].The study showed that there is a certain relationship between the entropy and stability of welding signals, but the consistency is relatively poor due to being affected by various data length and embedding dimension. In 2000, Richman and Moorman proposed a new time series complexity measurement method on the basis of ApEn-sample entropy (SampEn) [29]. Moreover, SampEn reduces ApEn errors, and better consistency and accuracy can be gained with faster computing speed [30].Current researches of the SampEn focus on the biomedical field [31–33] and gain better achievements in the analysis of atrial fibrillation electrocardiograms [34]. An intelligent prognostic for battery health based on SampEn feature of discharge voltage was also proposed [35].The study showed that the usage of SampEn electrical stability analysis is feasible. Experimental results show that the SampEn method can accurately quantify the stability of the welding process. Hence, it has great potential in research and quality analysis of welding mechanism.The rest of this paper is organized as follows. In Section2, the flow of Richman’s algorithm is stated. The relation between sample entropy and stability of welding signals is explored in Section 3. Also, in Section 4, the effect of different current variables on the other variables on the SampEn is illustrated in detail. To validate the proposed method, a new evaluating current stability is given in Section 5, and then the actual experiments and corresponding analysis are provided subsequently.


## 2. Algorithm

In this work, Richman’s algorithm is used. First of all, algorithm process is introduced as follows.Given a sequence number withN points u(1),u(2)⋯u(N) as original data. When embedding dimension is m and m+1, before N-m, vectors need to satisfy the following condition: m-dimensional vector Xm(i) is meaningful when 1≤i≤N-m.(1)
Form vector sequences of sizem:
(1)Xm(i)=[u(i),u(i+1),u(i+m-1)],dddddddi=1,2,…,N-m+1.(2)
Define the distance betweenXm(i) and Xm(j)(d[Xm(i),Xm(j)]) as the absolute maximum difference between their scalar components:
(2)d[Xm(i),Xm(j)]=max⁡k=0⋯m-1(|u(i+k)-u(j+k)|).(3)
For a givenXm(i), count the number of j  (1≤j≤N-m,j≠i), denoted as Nm(i), such that the distance between Xm(i) and Xm(j) is less than or equal to r. Then, for 1≤i≤N-m,
(3)Brm(i)=Nm(i)N-m.(4)
DefineBrm(i) as
(4)Bm(r)=∑i=1N-m+1Bim(r)N-m+1.(5)
Increase the dimension tom+1:
(5)Xm+1(i)=[u(i),u(i+1),u(i+m)],kkkkkkkki=1,2,…,N-m.(6)
CalculateNm(i) as the number of Xm+1(i) within r of Xm+1(j), where j ranges from 1 to N-m(j≠i). Then, Brm+1(r) is defined as
(6)Brm+1(r)=Nm(i)N-m-1.(7)
SetBm+1(r) as
(7)Bm+1(r)=∑i=1N-mBim+1(r)N-m.(8)
Finally, SampEn can be defined as(8)SampEn(m,r,N)=lim⁡⁡{-In⁡[Bm+1Bm(r)]},
which is estimated by the following statistic:
(9)SampEn(m,r,N)=-In⁡[Bm+1Bm(r)].From step(1) to step (7),ir shows that SampEn calculation requires determining three parameters, which are m, r, and N, where different m and r correspond to different SampEn. Presently, there are no theories guiding how to assign values to m and r. In the current study, the usual assigned value of m was 1 or 2, and the value of r was 0.1 to 0.5 times of the standard deviation of raw data. Lake et al. thought that the SampEn distribution is normal when m is smaller and r is larger, and small amount of lost data points does not affect the entropy calculation [36].Consequently, in this paper, the SampEn is calculated under the following conditions:(10)m=2,r=0.07,N=2000.


## 3. SampEn and Stability

To explore the relation between sample entropy and stability of welding signals, four current signals which have the same parameters but different stability are chosen to do the calculation of SampEn and its corresponding standard deviations (SD). Four signals of different stability are selected. Their parameters are as follows: 33.3% of pulse width (% of period, PW), 380 A of peak current (Ip), and 100 A of base current (Ib) and of frequency (f). Wavelet analyzer is used to capture current signals; its presentation is shown in Figure 1. From signal 1 to signal 4, the stability decreases in turn.Current waveform: (a) signal 1, (b) signal 2, (c) signal 3, and (d) signal 4.
(a)
(b)
(c)
(d)SampEn calculation results are shown in Figure2. SampEn values of signal 1 and signal 2 are relatively small and have little difference, while SampEn value of signal 3 is more stable and larger than the preceding two signals. The magnitude changes of signal 4 are much larger than the preceding three signals.Figure 2
Calculation results of SampEn.Figure3 shows the SampEn averages (AVG) and SD of 20 calculations; SD reflects the degree of deviation from the average of SampEn sequence. As shown in Figure 3, SD of signal 4 is about twice those of the preceding three signals, which shows that the stability of signal 4 is diverse at different time. Comparing Figures 1, 2, and 3, it is found that the more stable the signal, the smaller the AVG and SD. This is because the randomness, irregularities, and SampEn on the time series decrease.Figure 3
AVG and SD of SampEn.


## 4. Parameters Effects

Double-wire pulsed MIG welding has more different parameters when compared to other types of welding operation. For different electrical signals which serve different welding occasions, it is insufficient to only compare their SampEn values; the effect of different current variables on the SampEn is required to be focused on.In order to analyze the parameters’ effects on evaluation results, the orthogonal experiment was carried out in this work, and we choose four factors, which are PW,Ip, Ib, and f, and these four factors are chosen as research subjects. For each factor, three levels are selected from small to large. L9 (34) orthogonal table is used. Using Matlab Simulink establishes a simulation model to generate 9 desired signals. Then, SampEn values of the 9 desired signals are calculated. Corresponding experimental arrangement is shown in Table 1.Table 1
Orthogonal arrangement and results.
Number
PW/%
I
p/A
I
b/A
f/Hz
AVG
1
50
450
100
150
0.0305
2
50
300
80
100
0.0202
3
50
200
50
50
0.0101
4
33
450
80
50
0.0090
5
33
300
50
150
0.0275
6
33
200
100
100
0.0181
7
20
450
50
100
0.0147
8
20
300
100
50
0.0074
9
20
200
80
150
0.0222Table1 shows that the variation of the current parameters has certain impacts on SampEn values. In Table 1, maximum SampEn value is 0.0305, while minimum SampEn value is only 0.0074, which means that there is large difference between them. Range analysis results are shown in Table 2.Table 2
Range analysis of AVG.
SampEn
PW
I
p
I
b
f
AVG1
0.0608
0.0542
0.056
0.0802
AVG2
0.0546
0.0551
0.0514
0.053
AVG3
0.0443
0.0504
0.0523
0.0265
Min
0.0148
0.0168
0.0171
0.0088
Max
0.0203
0.0184
0.0187
0.0267
Range
0.0055
0.0016
0.0015
0.0179The frequency has the largest impacts on results among these four factors, and its corresponding range value is 0.0179. With the change inf levels, the AVG rapidly reduces from 0.0802 to 0.0265; followed by the PW, the corresponding range value is 0.0055; Ip and Ib have little effect on the results, and their corresponding range values are 0.0016 and 0.0015, respectively. In Table 1, the desired signals have the same stability; however, their SampEn values are different. Hence, the effects of current parameters on SampEn values should be considered when SampEn is used for quantifying current signals stability.SampEn values change with parameters because varying patterns of time series are different under different parameters. For example, when frequency is higher, time series change more quickly; so the probability of appearance of a new model increases in the same data segment, and its corresponding SampEn values are also bigger.


## 5. Evaluation Method

According to the researches described in Sections3 and 4, not only the electrical signals but also the parameters’ values can affect the SampEn. Hence, to further objectively evaluate the electrical signals and exclude the influence of different parameters on SampEn, a new method, which is used to evaluate the current stability of double-wire pulsed MIG welding, is designed in this paper.


### 5.1. Method

(1)
The SampEn stability evaluation index of single current (CSI) is calculated as follows:(11)CSI=AVG-AVGIAVGI×SD-SDISDI,
where AVG and SD represent averages and standard deviations of original signals SampEn, whileAVGI and SDI represent averages and standard deviations of desired signals SampEn.
(2)
Calculate subindex of double-wire (DI1):
(12)DI1=α×max⁡⁡(CSI1,CSI2),
whereα represents weighting factor, which is generally determined based on wire and other conditions, while CSI1 and CSI2 represent stability evaluation indexes of leading current and trailing current, respectively.
(3)
Calculate subindex of double-wire (DI2):
(13)DI2=(1-α)×min⁡⁡(CSI1,CSI2).
(4)
Calculate SampEn evaluation index of double-wire (DCSI):(14)DCSI=DI1+DI2.


### 5.2. Experiment

For validating the above method, corresponding experiments were conducted. A self-developed inverter welding machine is used for pulsed MIG welding. Q235 steel (δ=4.0 mm) is used as bead on plate welds. Welding wire is H08Mn2Si (Φ=1.0 mm). The shielding gas is pure argon, and the flow rate is 15 L/min. Figure 4 shows the experimental platform.Figure 4
The platform of experiment.Three double-wire current signals of different parameters and stability are selected for studying. Figure5 shows the real-time current waveforms of stable signal to unstable signal, where ILeading is the abbreviation of leader wire current, while ITrailing is the abbreviation of trailing wire current. These corresponding parameters are in Table 3.Table 3
Signal parameters.
Signals
PW/%
I
p/A
I
b/A
f/Hz
ILeading1
28.57
310
66
47.6
ITrailing1
28.57
270
70
47.6
ILeading2
39.13
305
70
86.9
ITrailing2
39.13
252
68
86.9
ILeading3
31.25
380
100
62.5
ITrailing3
31.25
310
90
62.5Double-wire current signals: (a) stable, (b) relatively stable, and (c) unstable.
(a)
(b)
(c)The current waveforms of ILeading1 and ITrailing1 in Figure5(a) are regular and stable. On the contrary, the current waveforms in Figure 5(b) are relatively bad; especially greater spikes appear in the rise and fall in ILeading2, which means that there are greater overshoots, while ITrailing2 is relatively good. The stability of current waveforms in Figure 5(c) deteriorates; in ILeading3, large breaking arc appears at 2000 ms, spikes can be seen in the base time from 2020 ms to 2110 ms, the peak current begins to increase when the value achieves the 2120 ms; the stability of ITrailing3 is even worse, because the current is unable to reach a given value.


### 5.3. Analysis

According to the method described in Section5.1, the value of α in (11), (12) is assumed as 0.75, and the results are shown in Table 4. As it can be found, CSI changes with the variation of current. The current waveforms of ILeading1 and ITrailing1 are regular and stable, which is corresponding to small CSI. The stability of ILeading2 is not as good as ILeading1; hence, its corresponding CSI is larger. ITrailing2 is relatively stable; therefore, its corresponding CSI is close to ITrailing1. The stability of ILeading3 deteriorates, and the corresponding CSI further increases. Moreover, ITrailing3 is very unstable; its CSI is also much larger than the others. Experiments show that CSI can truthfully reflect the stability of welding electrical signals.Table 4
Signal parameters and quantitative results.
Signal
AVG
AVG
I
SD
S
D
I
CSI
DI1
DI2
DCSI
ILeading1
0.0198
0.0072
0.0049
0.0026
1.5206
—
0.3802
1.5408
ITrailing1
0.0204
0.0072
0.0048
0.0026
1.5476
1.1607
—
ILeading2
0.0539
0.0151
0.0124
0.0053
3.4534
2.5900
—
3.0005
ITrailing2
0.0432
0.0151
0.0100
0.0053
1.6421
—
0.4105
ILeading3
0.0340
0.0099
0.0116
0.0035
5.6308
—
1.4077
12.7091
ITrailing3
0.0570
0.0099
0.0146
0.0035
15.0685
11.3014
—DCSI of stable signal is only 1.5408 and DCSI of signal 2 is about twice that of stable signal, which indicates that the stability of signal 2 deteriorates. DCSI of signal 3 is 8.25 times the DCSI of signal 1, which indicates that signal 3 is very unstable. By this method, the stability of double-wire welding current is effectively distinguished. However, the present study sample size is so limited; hence, it is necessary to further study the robustness and the selection rule of weighting coefficientsα.


## 5.1. Method

(1)
The SampEn stability evaluation index of single current (CSI) is calculated as follows:(11)CSI=AVG-AVGIAVGI×SD-SDISDI,
where AVG and SD represent averages and standard deviations of original signals SampEn, whileAVGI and SDI represent averages and standard deviations of desired signals SampEn.
(2)
Calculate subindex of double-wire (DI1):
(12)DI1=α×max⁡⁡(CSI1,CSI2),
whereα represents weighting factor, which is generally determined based on wire and other conditions, while CSI1 and CSI2 represent stability evaluation indexes of leading current and trailing current, respectively.
(3)
Calculate subindex of double-wire (DI2):
(13)DI2=(1-α)×min⁡⁡(CSI1,CSI2).
(4)
Calculate SampEn evaluation index of double-wire (DCSI):(14)DCSI=DI1+DI2.


## 5.2. Experiment

For validating the above method, corresponding experiments were conducted. A self-developed inverter welding machine is used for pulsed MIG welding. Q235 steel (δ=4.0 mm) is used as bead on plate welds. Welding wire is H08Mn2Si (Φ=1.0 mm). The shielding gas is pure argon, and the flow rate is 15 L/min. Figure 4 shows the experimental platform.Figure 4
The platform of experiment.Three double-wire current signals of different parameters and stability are selected for studying. Figure5 shows the real-time current waveforms of stable signal to unstable signal, where ILeading is the abbreviation of leader wire current, while ITrailing is the abbreviation of trailing wire current. These corresponding parameters are in Table 3.Table 3
Signal parameters.
Signals
PW/%
I
p/A
I
b/A
f/Hz
ILeading1
28.57
310
66
47.6
ITrailing1
28.57
270
70
47.6
ILeading2
39.13
305
70
86.9
ITrailing2
39.13
252
68
86.9
ILeading3
31.25
380
100
62.5
ITrailing3
31.25
310
90
62.5Double-wire current signals: (a) stable, (b) relatively stable, and (c) unstable.
(a)
(b)
(c)The current waveforms of ILeading1 and ITrailing1 in Figure5(a) are regular and stable. On the contrary, the current waveforms in Figure 5(b) are relatively bad; especially greater spikes appear in the rise and fall in ILeading2, which means that there are greater overshoots, while ITrailing2 is relatively good. The stability of current waveforms in Figure 5(c) deteriorates; in ILeading3, large breaking arc appears at 2000 ms, spikes can be seen in the base time from 2020 ms to 2110 ms, the peak current begins to increase when the value achieves the 2120 ms; the stability of ITrailing3 is even worse, because the current is unable to reach a given value.


## 5.3. Analysis

According to the method described in Section5.1, the value of α in (11), (12) is assumed as 0.75, and the results are shown in Table 4. As it can be found, CSI changes with the variation of current. The current waveforms of ILeading1 and ITrailing1 are regular and stable, which is corresponding to small CSI. The stability of ILeading2 is not as good as ILeading1; hence, its corresponding CSI is larger. ITrailing2 is relatively stable; therefore, its corresponding CSI is close to ITrailing1. The stability of ILeading3 deteriorates, and the corresponding CSI further increases. Moreover, ITrailing3 is very unstable; its CSI is also much larger than the others. Experiments show that CSI can truthfully reflect the stability of welding electrical signals.Table 4
Signal parameters and quantitative results.
Signal
AVG
AVG
I
SD
S
D
I
CSI
DI1
DI2
DCSI
ILeading1
0.0198
0.0072
0.0049
0.0026
1.5206
—
0.3802
1.5408
ITrailing1
0.0204
0.0072
0.0048
0.0026
1.5476
1.1607
—
ILeading2
0.0539
0.0151
0.0124
0.0053
3.4534
2.5900
—
3.0005
ITrailing2
0.0432
0.0151
0.0100
0.0053
1.6421
—
0.4105
ILeading3
0.0340
0.0099
0.0116
0.0035
5.6308
—
1.4077
12.7091
ITrailing3
0.0570
0.0099
0.0146
0.0035
15.0685
11.3014
—DCSI of stable signal is only 1.5408 and DCSI of signal 2 is about twice that of stable signal, which indicates that the stability of signal 2 deteriorates. DCSI of signal 3 is 8.25 times the DCSI of signal 1, which indicates that signal 3 is very unstable. By this method, the stability of double-wire welding current is effectively distinguished. However, the present study sample size is so limited; hence, it is necessary to further study the robustness and the selection rule of weighting coefficientsα.


## 6. Conclusions

The relationship between SampEn and the current stability is studied. The results show that the more stable the current, the smaller the value and the standard deviation of SampEn under the same parameters. When welding current parameters are different, SampEn values are also different. Therefore, the welding current parameters’ impacts should be considered when evaluating the welding stability. Then, a method of quantifying the stability of double-wire welding process based on SampEn is designed. The method puts forward a new idea for the quantitative evaluation of the welding process. The research is important for in-depth study of the law of the welding process and its stability mechanism.



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