A quality diagnosis method of GMAW based on improved empirical mode decomposition and extreme learning machine

Journal of Manufacturing Processes 54 (2020) 120–128

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A quality diagnosis method of GMAW based on improved empirical mode decomposition and extreme learning machine

T

Yong Huanga,b, Dongqing Yanga,b,*, Kehong Wanga,b, Lei Wanga,b, Jikang Fana,b a b

School of Material Science and Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China Key Laboratory of Controlled Arc Intelligent Additive Manufacturing, Nanjing University of Science and Technology, Nanjing, 210094, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Gas metal arc welding CEEMDAN Energy entropy Extreme learning machine

Due to the non-stationary and nonlinear characteristics of arc signal in gas metal arc welding (GMAW), results in the difference of frequency distribution. In this study, a method for evaluate weld quality based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and extreme learning machine (ELM) is proposed. First, the current signal is decomposed into intrinsic mode functions (IMFs) of different frequency bands by CEEMDAN, and then the energy entropy of IMFs is extracted. Because of the energy of each IMF under different weld quality is varies, the energy entropy and normalized energy of IMFs are used as a feature vector to classify the weld quality combined with extreme learning machine (ELM). The result shows that CEEMDAN and ELM can be used to identify the weld quality types of GMAW accurately.

1. Introduction Because gas metal arc welding (GMAW) is affected by various process parameters, the shape and droplet transfer behavior of arc are complex and variable. Its electrical signal is a nonlinear and non-stationary signal, how to extract feature information from electrical signals is the key to analyze welding stability and droplet transfer mode. The traditional method is to construct an evaluation function based on the characteristic of time-domain to diagnose the welding state. Adolfsson et al. [1] used the repeated sequential probability ratio test of voltage signal to monitoring the weld quality in robotic GMAW. Alfaro et al. [2] extracted the auto-correlation function and power spectral of current signal to quantify the droplet transfer mode in GMAW. Kumar et al. [3] combined the probability density distributions of voltage signal and neural network to assess welders' skill. Simpson et al. [4,5] extracted the two-dimensional histogram of voltage and current signal for quality diagnosis and fault detection of GMAW. Wu et al. [6–8] extracted mean value, variance and kurtosis of current signal to assess the weld quality in robotic GMAW. However, the time-domain methods of electrical signals only can analyze from statistical perspective. Due to the welding process is affected by various factors, the physical and chemical processes of arc is very complicated. The time-domain method is gradually difficult to meet the precise analysis of weld quality. Wavelet analysis is an advanced time-frequency analysis method. It can not

only locate high-frequency components in non-stationary signal, but also analyze the low-frequency components and provide local features in the time-frequency domain. Zhang et al. [9] carried out wavelet packet transform to eliminate the pulse interference of voltage signal in the welding of aluminum alloy. Pal et al. [10] applied neurowavelet packet to predict weld joint strength, the results showed that wavelet packet features could obtain more accurately prediction compared to the time-domain features. Chen et al. [11] used wavelet transform to decompose acoustic emission signal into different frequency bands in monitoring of friction stir welding. In recent years, a new adaptive time-frequency analysis method has been developed rapidly, which is empirical mode decomposition (EMD) [12–15], it can decompose the complex signal into a series of intrinsic mode functions (IMFs). He et al. [16] applied EMD to decompose the current signal into a series of IMF in submerged arc welding. Huang et al. [17] employed EMD to eliminate effectively the noise of voltage signal in pulsed gas tungsten arc welding. Yusof et al. [18] used EMD to obtain Hilbert spectral of arc sound signal, and detected the weld porosity defects. Cheng et al. [19] applied EMD to eliminate the noise of near-infrared signal in laser welding, and extracted the energy of different frequency bands to diagnose the defects. However, the local nature of the EMD may produce oscillations with very disparate scales in one mode, it becomes a problem, named as ‘mode mixing’. The complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) [20] proved to be an

⁎

Corresponding author at: School of Material Science and Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China. E-mail addresses: [email protected] (Y. Huang), [email protected] (D. Yang), [email protected] (K. Wang), [email protected] (L. Wang), [email protected] (J. Fan). https://doi.org/10.1016/j.jmapro.2020.03.006 Received 28 December 2019; Received in revised form 29 February 2020; Accepted 2 March 2020 1526-6125/ © 2020 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

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h1(k−1) − m1k = h1k

important improvement on EMD, achieving a negligible reconstruction error and solving the problem of ‘mode mixing’ for different realizations of signal plus noise. Hassan et al. [21] introduced CEEMDAN and bootstrap aggregating to classify sleep states in electroencephalogram. Han et al. [22] used CEEMDAN and a multi-layer perceptron neural network to diagnose the system fault. Ali et al. [23] used the extreme learning machine and CEEMDAN to forecast significant height of coastal waves. So, it is necessary to combine pattern recognition methods for classification and prediction after signal processing. Extreme learning machine (ELM) is a new single-hidden layer feedforward neural networks (SLFNs) which randomly chooses hidden nodes and analytically determines the output weights of SLFNs [24]. ELM tends to provide good generalization performance at extremely fast learning speed. Tian et al. [25] used local mean decomposition–singular value decomposition and ELM for classification of bearing faults. Xie et al. [26] introduced a novel computer-aided diagnosis system for the diagnosis of breast cancer based on ELM. Mao et al. [27] used ELM to imbalanced fault diagnosis problem. In this study, CEEMDAN is applied to the arc information analysis of GMAW. First, the electrical signal is decomposed into a series of IMF by CEEMDAN, and then the welding state is diagnosed by energy entropy of IMFs. When the welding state changes, the normalized energy of IMFs will change in each frequency band, the normalized energy component and energy entropy of IMFs are extracted to identify the weld quality with ELM. The paper is organized as follows: Section 2, EMD, CEEMDAN and energy entropy of IMFs are introduced. Section 3, the energy entropy of IMFs is calculated under different welding stability. Section 4, ELM theory is introduced, the normalized energy component and energy entropy of IMFs are combined with ELM for weld quality classification. Section 5, the conclusions are given.

Then it is set to

The first component c1 should contain short period components of the signal. (5) Separate c1 from x(t) to get: (5)

r1 = x(t) − c1

The r1 repeats above steps as the original signal to obtain a second IMF component c2, and then repeats the above steps n times to obtain n IMF components:

r1 − c2 = r2 ⎫ ⋮ r(n−1) − cn = rn ⎬ ⎭

(6)

If rn is a monotonic function, the above process stops and the IMF cannot be extracted at this time. Summarizing formulas (5) and (6), we end up with: n

x(t) =

∑ cj + rn (7)

j= 1

The signal x(t) can be decomposed into n IMF modes and a residual rn. The IMF components (c1, c2, …, cn) contain frequency band components from high frequency to low frequency. Each frequency band contains different frequency components that vary with the signal, and rn represents the trend term of the signal x(t). 2.2. CEEMDAN CEEMDAN method obtains the IMF by adding the adaptive white noise as well as the computation of the unique signal residual to overcome the deficiency of EMD, it makes the reconstructed signal almost identical with the original signal. CEEMDAN method not only overcomes the existing mode mixing phenomenon of EMD, but also reduced the reconstruction error. The operator Ej (∙) is defined as the j -th mode component obtained by EMD. Let ωi be white noise with N (0,1) . If s (n) is the original data, ∼ the k -th IMF of CEEMDAN be IMFk , so the algorithm is described as below: 1) The signal s (n) + ε0 ωi (n) is decompose by EMD I realizations to obtain their first modes and compute the first IMF:

2.1. EMD The EMD stems from an assumption that any signal consists of different simple intrinsic modes. The extrema of mode is the same as the zero crossing. There is only one extreme point between successive zero crossings, each mode is independent of the other modes. In this way, the signal can be decomposed into a series of IMF. Among them, the IMF is defined as follows: 1) In the whole data, the number of extreme points and zero crossings must be equal or at most 1 difference. 2) At any data point, the mean of the local maximum envelope and the local minimum envelope must be 0. An IMF represents an inherent oscillation mode, not just a simple harmonic form. By definition, any signal can be decomposed by EMD as follows: (1) Extract all local maxima of the signal, and use cubic spline interpolation to fit all local maxima points to obtain the maxima envelope. (2) Fitting all local minima points to obtain the local minima envelope, all data points between the maximal envelope and the minimal envelope. (3) Let the mean value of the maximum value envelope and the minimum value envelope be m1, and the difference between the original signal x(t) and m1 be the first component h1.

I

1 ∼ ¯ 1 (n) IMF1 (n) = ∑ IMF1i (n) = IMF I i=1

(8)

2) In the first stage (K = 1), the first signal residual is calculated: ∼ r1 (n) = s (n) − IMF1 (n) (9) 3) I realizations are performed (i = 1,2, …, I ) . In each realization, the signal r1 + ε1 E1 (ωi (n)) is decomposed until their first EMD mode obtained. Based on the calculation, the second modal component (second IMF) is computed as follows: I

1 ∼ IMF2 (n) = ∑ E1 (r1 + ε1 E1 (υi (n))) I i=1

(10)

4) For the remainder of each stage, i.e. k = (2, ...,K ) , we calculate the k residual. Step 3 is repeated, and the k + 1 modal component is calculated as follows:

(1)

∼ rk (n) = rk − 1 (n) − IMF (n)

Ideally, if h1 is an IMF, then definition h1 is the first IMF of x(t). (4) If h1 is not an IMF, h1 repeats the steps (1)-(3).

h1 − m1 = h11

(4)

c1 = h1k

2. EMD, CEEMDAN and energy entropy of IMFs

x(t) − m1 = h1

(3)

(11)

I

1 ∼ IMF(k + 1) (n) = ∑ E1 (rk (n) + εk Ek (υi (n))) I i=1

(2)

After k times of repeated screening, h1k becomes an IMF.

(12)

5) Step 4 is executed until the obtained residual signal no longer 121

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carry out any IMF, and the standard condition is that no IMF can be extracted from residual as well as the number of extreme points is no more than two. At the end, the number of all modal components is K . The final residual signal is: K

rK (n) = s (n) −

∼

∑ IMFk k=1

(13)

Thus, the original signal sequence s(n) is finally decomposed into: K

s (n) =

∼

∑ IMFk + rK (n) k=1

(14) Fig. 2. Current signal of GMAW.

2.3. Energy entropy of IMFs + 80 % Ar, the wire diameter of 1.2 mm, the contact tip-to-work distance (CTWD) of 15 mm, the torch angle of 90° and specimens of Q235 steel plates of 400 × 200 × 6 mm3. The sampling rate of arc current signal is 10 KHz.

Due to the IMF components contain frequency band components from high frequency to low frequency. When the frequency distribution of a complex signal changes, and the energy of each frequency band of CEEMDAN will also be different. Based on the information entropy theory, the energy entropy of IMFs of CEEMDAN is proposed. The signal is decomposed by CEEMDAN to obtain a series of IMF and a residual rn. The energy components corresponding to IMFs are E1, E2, E3, E4, …, En. Due to the orthogonality of the IMF components, the residual component can be ignored. The total energy of IMFs is equal to the energy of the original signal. Since the IMF components contains different frequency component, the E={E1, E2, …, En} is correspond to the energy distribution of IMFs in different frequency component. The energy entropy of IMFs can be expressed as:

3.2. EMD and CEEMDAN of welding current signal In order to compare the decomposition effect of EMD and CEEMDAN of current signal, the 4096 data is selected for analysis (Fig. 2). According to the proposal of CEEMDAN, ε0 and I are very important parameters. The appropriate value of ε0 is 0.01 to 0.5, and a larger I would prolong the algorithm running time. Considering the actual calculation conditions, the parameters are selected for ε0 = 0.2 and I = 200 . The IMFs of EMD and CEEMDAN are shown in Fig. 3. The maxima peaks of imf1-4 correspond to the moment of arc droplet transfer, and the peaks interval reflects the uniformity of droplet transition. The imf5-8 show a certain period reflects the main characteristics of droplet transition which from arcing to short-circuiting of welding. Comparing the IMFs, CEEDMAN has more IMFs than EMD. The imf 3-8 is calculated by fourier transform, the frequency of imf 3-8 of CEEMDAN is significantly more concentrated (Figs. 4 , 5 ). Clearly, the CEEMDAN can more effectively obtain frequency components of signals, and the IMFs are concentrated in a certain frequency than the EMD.

n

Hen = −∑ pi ∙log(pi)

(15)

i= 1

where, pi = Ei/ E , E=

n ∑i= 1 Ei .

3. Experiment and analysis 3.1. Experimental condition Based on the correlation between welding parameters and weld quality, the GMAW test under different welding parameters is carried out. The equipment is consists of a Yaskawa Motoman robot and a RD350 welding machine which made by Kalerda corporation of china (Fig. 1), the common welding conditions: the shielding gas of 20 % CO2

3.3. Energy entropy of IMFs in different welding status When the welding state changes, the time-frequency domain

Fig. 1. The experiment equipment of GMAW. 122

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Fig. 3. IMFs of EMD and CEEMDAN.

CEEMDAN. It can be seen that the energy entropy of EMD and CEEMDAN can basically reflect the state change of the welding process, but only relying on the energy entropy is not enough to classify the weld quality (surface porosity, good formed, poorly formed and wider weld).

distribution of the arc current signal also changes. Figs. 6(a) 7(a) 8(a) 9(a) show different weld quality, such as surface porosity, good formed, poorly formed and wider weld. Table 1 shows the process parameters of those weld quality. The 4096 data points of current signal are selected separately Figs. 6(b) 7(b) 8(b) 9(b), and the time-frequency distribution of current signal are very different Figs. 6(c) 7(c) 8(c) 9(c). The welding current signals are decomposed by EMD and CEEMDAN, and energy entropy of IMFs is shown in Table 2. When the welding process is various, the energy is different in each frequency band, resulting in changes in energy entropy. The difference of the mean of energy entropy (E(Hen) ) is small, and EMD has lower energy entropy than

4. The classification based on CEEMDAN and ELM 4.1. ELM The single-hidden layer feed-forward neural network (SLFN) has

Fig. 4. Frequency spectrum of imf 3-8 of EMD. 123

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Fig. 5. Frequency spectrum of imf 3-8 of CEEMDAN.

Fig. 6. The surface porosity and local current signal. ∼ N

been broadly utilized in many fields because of its approximation ability in non-linear mapping. However, SLFN has the disadvantages of slow training speed, easy to fall into the local minimum and sensitive to the selection of learning rate. A new learning algorithm for singlehidden layer feed-forward neural networks which is named extreme learning machine (ELM) is proposed recently (Fig. 10). The research shows that a single-hidden layer neural network with N hidden neurons can learn N different observations for nearly any non-linear activation function with any small error, achieves much faster learning speed and better generalization ability with the smallest training error and weights of SLFN than traditional learning algorithms. Suppose learning N arbitrary different instances (x i , ti ) , where x i = [ x i1, x i2 ,…, x in ]T ∈ Rn , and ti =[ti1, ti2 ,…, tim ]T ∈ Rm , standard single∼ hidden layer feed-forward networks with N hidden neurons and activation function g(x) are mathematically modeled as a linear system:

∑ βi g (wi ∙xj + bi) = oj , i=1

j = 1, …, N (16)

where wi =[wi1, wi2 ,…, win ]T denotes the weight vector connecting the i-th hidden neuron and the input neuron, βi =[βi1, βi2 ,…, βim ]T denotes the weight vector connecting the i-th hidden neuron and output neurons, oi =[oi1, oi2 ,…, oim ]T is the output vector of the SLFN, and bi represents the threshold of the i-th hidden neuron. wi ∙x j represents the inner product of wi and x j . If the SLFN with N hidden neurons with activation function g (x ) is able to approximate N distinct instances (x i , ti ) with zero error means that:

Hβ= T where

124

(17)

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Fig. 7. The good formed and local current signal.

Fig. 8. The poorly formed and local current signal.

the hidden layer output matrix H has been fixed at random. Hence, the process of training a single-hidden layer feed-forward neural network is equal to solving a well-established linear system optimization problem which is shown as follows:

⎡ g (w1 ∙x1 + b1) ⋯ g (wNh ∙x1 + bNh) ⎤ ⎥ H (w1, …, wNh, b1, …, bNh , x1, …, xN ) = ⎢ ⋮ ⋮ ⋮ ⎢ g (w ∙x + b )⋯ g (w ∙x + b ) ⎥ 1 N 1 Nh N Nh ⎦ ⎣ (18) T

'

⎡ w1 ⎤ w= ⎢ ⋮ ⎥ , T= ⎢ T ⎥ ⎣ wNh ⎦Nh × m

‖Hβˆ − T‖ = min ‖Hβ − T‖

T

β

⎡ t1 ⎤ ⎢⋮⎥ ⎢ T⎥ ⎣tN ⎦N × m

(19)

Its unique least-squares solution with minimum norm is

βˆ = H †T

H is the hidden layer output matrix of the SLFN. Huang et al. [24] proved that, given arbitrarily small value ε > 0 , if the activation function of the hidden layer in the single-hidden layer feed-forward network is infinitely differentiable, and the number of hidden neurons is less than or equal to the number of data samples, then the input weights and hidden layer biases can be assessed at random, and the single-hidden layer feed-forward network approximates the N training data with ε error, that is to say, ‖Hβ− T‖ ≤ ε . The ELM algorithm randomly assigns the input weights wi and hidden layer biases bi for the SLFN with the infinitely differentiable activation function, thus,

(20)

H†

is the Moore-Penrose generalized inverse of H. For feed-forwhere ward networks, the smaller their output weights are, the better generalization ability they have. The norm of βˆ is the smallest among all the least-squares solutions of the linear system Hβ= T , thus ELM obtains not only the minimum square training error but also the best generalization ability on unseen data samples. The ELM algorithm is outlined as follows: (1) Choose arbitrary value for input weights wi and biases bi of hidden 125

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Fig. 9. The wider weld and local current signal. Table 1 The process parameters of different weld quality. No.

Voltage (U/V)

Current (I/A)

Gas rate (L/min)

Speed (cm/min)

CTWD (mm)

Weld quality

1 2 3 4

16.5 16.5 18.1 27.4

80 80 140 330

1 15 15 15

40 40 40 40

15 15 15 15

Surface porosity Good formed Poorly formed Wider weld

Table 2 The mean E(Hen) and standard deviation δ(Hen) of energy entropy. Method

Value

Surface porosity

Good formed

Poorly formed

Wider weld

EMD

E(Hen)

2.152

2.009

2.123

2.230

δ(Hen)

0.083

0.089

0.131

0.163

E(Hen)

1.9776

1.8964

1.843

2.111

δ(Hen)

0.085

0.034

0.102

0.124

CEEMDAN

Fig. 11. Diagnosis of welding based on CEEMDAN and ELM.

neurons. (2) Calculate hidden layer output matrix H. (3) Obtain the optimal βˆ in the light of equation βˆ = H †. 4.2. Weld quality classification based on CEEMDAN and ELM From the analysis of energy entropy of CEEMDAN, it shows that the energy entropy of CEEMDAN of current signal in different welding state is different, indicating that the energy of each IMF will change when the welding process is unstable. Since the welding stability is closely related to the weld quality, the classification and identification of the weld quality can be performed. In this study, the normalized energy and energy entropy of IMFs of current signal are used as inputs to the ELM, and different weld quality can be identified. A flow chart of a classification method for weld quality based on CEEMDAN and ELM is shown in Fig. 11.

Fig. 10. Architecture of an ELM.

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Constructing a feature vector T from all energy components. (22)

T= E1, E2 , …, En

Normalize T by considering that some energy values are relatively large. n

⎛ E= ⎜∑ Ei) ⎝ i= 1

(23)

Then

T' =

E1 E2 E , , …, n E E E

(24) '

And, the vector T is a normalized vector. Calculating the CEEMDAN energy based on the vector T' . (4) Forming a new vector T1 based on energy entropy and the first m elements of normalized vector T’.

T1 =

Table 3 Comparison of EMD and CEEMDAN. Test sets

Correct number

Accuracy rate

EMD and ELM CEEMDAN and ELM

80 80

71 79

88.75% 98.75 %

The weld quality diagnosis method is given as the following: (1) Collecting welding current signals under four different weld quality Figs. 6(a) 7(a) 8(a) 9(a), which are surface porosity, good formed, poorly formed and wider weld. (2) The current signal is decomposed into a series of IMF by CEEMDAN, and the first m IMF components containing the main weld information are used to extract the characteristic. (3) Calculating the Ei of the IMF components.

Ei =

+∞

∫−∞

|ci (t)|2 dt ⎜⎛ i= 1, 2, …, n⎞⎟ ⎠ ⎝

(25)

(5) The multi-classifier of ELM The ELM is selected as the classifier, and the extracted feature vector T1 of the training sample is taken as the input, and the different weld quality is taken as the output, where pattern 1- surface porosity [1 0 0 0], pattern 2- good formed [0 1 0 0], pattern 3- poorly formed [0 0 1 0], pattern 4- wider weld [0 0 0 1]. (6) Classification of weld quality ELM is a fast classification algorithm, which is very suitable for multi-classifier with a small number of samples. The performance of the classifier depends on hidden neurons and activation function. Through the process test, the weld seam with surface porosity, good formed, poorly formed and wider weld are obtained, its corresponding current signal is collected. The CEEMDAN decomposition is performed for each 4096 points (0.4096 s), and the CEEMDAN energy entropy and the first eight normalized IMF energy are calculated as the input vector of the ELM, and 160 sets of samples are formed. The 80 samples are selected as training samples, and another 80 samples are used as test samples. The performance of the multi-classifier with different number of hidden neurous and activation functions is shown in Fig. 12, the sig function, sin function and radbas function are more suitable for welding diagnosis. When the number of hidden neurous is more than 20, the accuracy of multi-classifier is very high. In this study, the sig function and hidden neurous of 20 are used for the parameter of ELM. The final recognition accuracy of CEEMDAN and ELM is 98.75 % (Table 3), and obtained good classification results than EMD and ELM (Fig. 13).

Fig. 12. The ELM with different hidden neurous and activation functions.

Model

E E1 E2 , , …, m , Hen E E E

(21)

Fig. 13. The classification of welding based on CEEMDAN and ELM. 127

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5. Conclusions

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According to the non-stationary characteristics of current signal in GMAW, a new diagnosis method based on CEEMDAN and ELM is put forward. First, CEEMDAN is used to decompose the current signal. Then ELM is utilized on the processed data in order to determine the weld quality types. When the welding state changes, the energy entropy of IMFs varies as well, which indicates that the energy of each IMF component changes. Therefore, the energy entropy and first eight normalized energy of IMFs are adopted as the ELM input features to identify the the weld quality types. From the theory analysis and experiment results, it can be concluded that: (1) For current signal in GMAW, the frequency of IMFs of CEEMDAN is significantly more concentrated than EMD. (2) The energy entropy of CEEMDAN can basically reflect the state change of the welding process, but is not enough to classify the weld quality. (3) The energy entropy and first eight normalized energy of IMFs as input feature has highly classification for weld quality combined with ELM. Declaration of Competing Interest The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. Acknowledgments This work is supported by the National Natural Science Foundation of China under Grant No. 51805266, 51805265 and 51905273, is gratefully acknowledged. References [1] Adolfsson S, Bahrami A, Bolmsjö G, Claesson I. On-line quality monitoring in shortcircuit gas metal arc welding. Weld J NEW YORK 1999;78:59–. [2] Alfaro SCA, Carvalho GC, Da Cunha FR. A statistical approach for monitoring stochastic welding processes. J Mater Process Technol 2006;175:4–14. [3] Kumar V, Albert SK, Chandrasekhar N, Jayapandian J. Evaluation of welding skill using probability density distributions and neural network analysis. Measurement 2018;116:114–21. [4] Simpson SW. Statistics of signature images for arc welding fault detection. Sci Technol Weld Join 2013;12:556–63. [5] Simpson SW. Signature image stability and metal transfer in gas metal arc welding. Sci Technol Weld Join 2008;13:176–83. [6] Wu CS, Polte T, Rehfeldt D. Gas metal arc welding process monitoring and quality

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