EMD- PNN based welding defects detection using laser-induced plasma electrical signals

Journal of Manufacturing Processes 45 (2019) 642–651

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EMD- PNN based welding defects detection using laser-induced plasma electrical signals ⁎

Yiming Huanga, Shuaishuai Houa, Shufeng Xub, Shengbin Zhaoa, Lijun Yanga, , Zhifen Zhangc,

T ⁎

a

Tianjin Key Laboratory of Advanced Joining Technology, School of Materials Science and Engineering, Tianjin University, Tianjin, 300350, China Shanxi Taigang Stainless Steel Co., Ltd, Taiyuan, 030000, China c School of Mechanical Engineering, Xi’an Jiao Tong University, Xi’an, 710049, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Laser welding Plasma electrical signal Wavelet packet transformation Empirical mode decomposition Probabilistic neural network

The plasma electrical signal has gained extensive attention for characterizing the behavior of the laser-induced plasma due to the advantages of easy acquisition and feedback control. In this paper, the electrical signals were measured by a passive probe based on the principle of plasma sheath effect. To explore the mutation characteristics of plasma electrical signals during defect generation in laser deep penetration welding, wavelet packet transform (WPT) and empirical mode decomposition (EMD) were used to compress data and extract features, respectively. Based on the analysis of the time-frequency spectrum of a typical plasma electrical signal, the approximate coefficients of 0˜390 Hz frequency range were reconstructed. The residual term which characterizes the change trend of electrical signal was obtained by the further adaptive decomposition. For better identifying weld defects, another two statistical features, mean value and standard deviation, were extracted by carrying out statistical analysis in the time domain. The feature database is built with above features and used as inputs of the predictive model based on the probabilistic neural network (PNN). The result showed the average prediction accuracy was as high as 90.16% when recognizing five statuses of weld seam, including sound weld and four kinds of weld defects.

1. Introduction As an advanced material processing technology, laser welding has been widely used in automobile, aerospace and other industrial production process. Unlike the traditional arc welding, laser welding uses laser beam as the energy carrier to transmit energy. In laser deep penetration welding process, a keyhole is formed in the molten pool. At the same time, the superheated metal evaporates to form plasma, which erupts from the keyhole. It has been well recognized that the interaction between laser and material has an important influence on welding quality [1–3]. Therefore, the study of laser induced plasma is of great significance to the quality control of welding process. In recent years, researchers have made a series of studies focusing on the geometry shape of the plasma by using visual sensing [4–6]. By means of high-speed imaging, Brock et al. [7] observed the dynamic shape of the metal vapor plume during the laser deep penetration welding process and proposed a formation model of vapor plume which indicated the generation of the vapor plume was determined by the keyhole dynamics. You et al. [8,9] established a multi-sensing system and realized an evaluation of the laser welding process by analyzing the

⁎

intensity of visible light and the size of laser-induced metallic plasma. Although visual sensor can provide abundant morphological information of the plasma, it still has the deficits of complex instrumental design and insufficient image processing speed. In fact, the nature of the plasma that it is composed of a large number of free electrons and positive ions determines that there is an intrinsic relationship between its electrical properties and welding quality [10]. During keyhole plasma arc welding, Zhang et al. [11] measured the electrical effect of the plasma cloud and used it to detect the state of the keyhole for keyhole process control. In recent year the plasma charge sensor has been applied in the laser welding process. By designing a detection system based on a passive electrical probe, Bi et al. [12] measured electrical signals and calculated the electron temperature of the plasma in the laser welding. Furthermore, Zhao et al. [13] found that there were obvious differences in frequency characteristics of electric signals between thermal conduction laser welding and deep penetration laser welding. It can be seen that the detection method based on a passive electrical probe is suitable for laser induced plasma in violent fluctuation state. However, its research on the application of welding quality monitoring needs to be further

Corresponding authors. E-mail addresses: [email protected] (L. Yang), [email protected] (Z. Zhang).

https://doi.org/10.1016/j.jmapro.2019.08.006 Received 4 June 2019; Received in revised form 27 July 2019; Accepted 3 August 2019 Available online 13 August 2019 1526-6125/ © 2019 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

Journal of Manufacturing Processes 45 (2019) 642–651

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plane with an angle of 45 ° to the workbench moving direction and its endpoint was 2 mm away from the interaction point between laser and material. It is worth noting that a water-cool device was installed in the probe to resist high temperature conducted by the plasma. Since the acquired electrical signal was very weak which cannot be directly transmitted to the recording instrument, a signal modulation circuit was designed to amplify the electrical signal. The electrical signal was recorded by a data acquisition card USB-6211 from National Instruments at a sampling frequency of 100 KHz and stored in the industrial personal computer (IPC). 2.2. Measuring principle of plasma electrical signal It is known that the materials melt rapidly and gasify strongly, producing high-temperature metal vapor when the high-energy density laser beam acts on the surface of the material. Moreover, the hightemperature metal vapor dissociates, generating a compact laser-induced plasma between the laser nozzle and the workpiece. When the probe is placed into the electrically neutral plasma, a certain density of negative charge will accumulate on the surface of the probe under the effect of plasma sheath. Since the plasma is in a local thermal equilibrium state, the negative potential measured by the probe can be expressed by the following formula [14]:

Fig. 1. The schematic diagram of the experimental system.

(1)

Us = −(KT /4e ) In (mi / me )

deepened. This paper aims to propose a method of on-line quality monitoring for laser deep penetration welding based on the plasma electrical signals. Using a passive electric probe, electrical signals of plasma are collected and analyzed. Moreover, the weld state can be distinguished by extracting effective features of electrical signals. Finally, the prediction of weld defects is realized based on probabilistic neural network, which is helpful to realize online defect control.

Where, Us is the sheath voltage, K denotes the Boltzmann constant, T is the electron temperature, e is an electron charge, and mi and me are positive ion mass and electron mass, respectively. A typical plasma electrical signal collected by a passive probe is shown in Fig. 2(a). It can be seen that the electrical signal has random and non-stationary characteristics. It is worth mentioning that the collected electrical signal is amplified in 6.4 times by the conditioning circuit. The noise signal for no-load stage is analyzed, as shown in Fig. 2(b). It is obvious that there is a direct current (DC) component in the original noise signal. Therefore, the DC component should be removed in the subsequent data processing. The details of the electrical signal after removing the DC component are shown in Fig. 2(c). It can be seen that the sheath voltage signal collected by the probe has oscillation characteristic, which is caused by the time-varying temperature of the plasma ejected from the keyhole. The generation principle is shown in Fig. 2(d). Laser-induced plasma is composed of a large number of positive ions, electrons and neutral particles. When the passive probe enters the plasma, electrons gathering on the probe surface result in a − φ potential. To investigate the frequency characteristics of the electrical signal, Fourier transform is performed on the signal to transform it into a series of data composed of sine waves with different amplitudes and frequencies. The sine waves ranging from 0 to 2500 Hz are displayed in Fig. 2(e) with a three-dimensional image. The amplitude spectrum is obtained by intercepting the positive half z-axis of the image with a front view. It can be seen that the maximum amplitude is concentrated in the range between 285 and 355 Hz.

2. Experimental system and detection principle 2.1. Experimental setup The experimental system was composed of three parts, i.e., laser welding module, travelling mechanism module and electrical signal acquisition module, as shown in Fig. 1. The bead-on-plate welding was carried out on the 4 mm-thickness 304 stainless steels with a dimension of 200 mm-length × 60 mm- width. The experiments were conducted by a Nd: YAG laser (JK2003SM, GSI) with a maximum power of 2 KW under the continuous wave mode. The laser radiation was transferred by an optic fiber and focused on the base metal surface through a lens with a focal length of 160 mm. Welding parameters were listed in Table 1. The focus with a spot diameter of 0.6 mm is 1 mm below the surface of the base metal. In order to minimize the absorption, refraction and scattering effect of the laser-induced plasma on the laser energy, a side blowing shielding gas of pure argon was employed with a flow rate of 25 L/min. The travelling mechanism module was controlled by a three-dimensional numerical control platform. Before welding, the laser head is adjusted to keep perpendicular to the base metal which was mounted on a workbench. During welding, the laser head was kept still while the workbench was driven in a direction which was opposite to that of welding process. A passive probe made of copper was used to acquire the electrical signal of laser-induced plasma. The probe was mounted in the Y–Z

3. Processing methods of electrical signals As can be seen from Fig. 2, the voltage of plasma electrical signals changes regularly in the range from 0 to -7 v when the welding bead is well formed. However, due to its complex fluctuation and abundant data, it is difficult to extract evident characteristics corresponding to welding quality. Therefore, it is necessary to conduct data mining on

Table 1 Process parameters used in laser welding. Laser power (W)

Welding speed (mm/s)

Spot diameter (mm)

Defocusing distance (mm)

Gas flow rate (L/min)

1400

6–12

0.6

−1

25

643

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Fig. 2. (a) A typical electrical signal of plasma (with welding speed 12 mm/s); (b) noise acquired before welding and DC-offset removed noise signals; (3) a detail of electrical signal corresponding to the rectangular box in Fig. 2(a); (d) schematic diagram of measuring principle; (e) frequency spectrum of Fig. 2(a).

length of 2 N. The waveform defined by three parameters can be obtained:

the plasma electrical signals with different weld states which are obtained under various welding parameters. On the basis of retaining the original data structure and information, the intuitive and effective features are extracted. The technical processing scheme selected in this paper consists of two parts, including data compression based on wavelet packet transform (WPT) and feature extraction based on empirical mode decomposition (EMD). The traditional multi-resolution analysis divides the frequency band of the signal by exponential interval. Therefore, the frequency resolution in the low frequency sub-band is better than that in the high frequency sub-band. The signal containing a lot of detailed information cannot be decomposed and represented. This method is not suitable for the analysis of plasma electrical signals considering the its variation characteristics. Wavelet packet transformation developed on the basis of multiresolution analysis can provide a more detailed analysis for the signal [15,16]. It further decomposes the detail coefficients which are not divided in the multi-resolution analysis, leading to a finer equalwidth interval. The method improves the time-frequency resolution and performs better time-frequency localization analysis on the signal containing a large amount of medium and high frequency information. Wavelet packets are defined as follows. For a given function sequence Wn (x ), nεN , which consists of the following two equations:

Wj, n, k (x ) = 2−j /2Wn (2−jx − k )

Where, n∈ N, (j, k ) ∈ k is the local time parameter, j denotes the decomposition scale, n is the node number corresponding to the scale of the wavelet packet tree. For each scale j , the possible values of n are 0, 1, …, 2 j − 1. The waveforms Wj, n, k (x ), k εZ are identified as wavelet packets determined by W0 (x ) = φ (x ) . It can be seen that the wavelet packages are a set of functions Wj, n (x ) with certain relation including scale functions and wavelet functions. Assuming f(t) is a time signal, P jn (t ) is wavelet packet coefficient corresponding to Wj, n (x ) . Wavelet packet decomposition can be expressed as follows:

2

∑

h (k ) Wn (2x − k )

k=0

(2)

2N − 1

W2n + 1 (x ) =

2

∑ k=0

g (k ) Wn (2x − k )

P00 (t ) = f (0)

(5)

P j2+n1 (t ) = HP jn (t )

(6)

P j2+n1+ 1 (t ) = GP jn (t )

(7)

Where, G and H are the wavelet packet decomposition filters, related to the scaling function and wavelet function, respectively. On this basis, the characteristics of wavelet packet coefficients are analyzed to determine the way of signal reconstruction. After data compression performed by wavelet packet transform, the electrical signals still maintain non-stationary characteristic. In order to investigate the state of the signal when a drastic change occurred, the time-frequency domain analysis should be carried out to obtain the overall view and localization results of the electrical signal in the timedomain and frequency-domain. Although wavelet packet transform can achieve this goal, the optimal features is hard to be obtained since the wavelet packet basis cannot be changed once it is determined due to the

2N − 1

W2n (x ) =

(4)

Z 2,

(3)

Where, W0 (x ) = φ (x ) is the scale function, W1 (x ) = ψ (x ) is the wavelet function, h (k ) and g (k ) are a set of conjugate mirror filters with the 644

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Fig. 3. The algorithm flow diagram of feature extraction.

with the frequency band of 400 Hz when carrying out the frequency sub-band decomposition of equal width. For the collected signals, the sampling frequency is 100 KHz. According to Nyquist sampling theorem, the maximum analysis frequency is 50 KHz. To acquire the desired frequency sub-band, at least 7 layers of wavelet packet transformation should be performed. In view of the good regularity of Daubechies wavelet, the db5 wavelet is selected considering the order of vanishing moment and the computational cost as well. According to the binary tree theory, a complete binary tree consists of a large number of subtree structures. Thus, it is necessary to set a criterion to obtain the optimal wavelet packet tree. In this paper, the Shannon entropy is chosen as the information cost function. Furthermore, the wavelet packet tree with the minimum cost function value of wavelet packet coefficients is taken as the optimal tree structure with a fast bottom-up search method. The calculation formula of the Shannon entropy M (P ) of the wavelet packet coefficient is as follows:

non-adaptive characteristic. As a time-frequency analysis method proposed in recent years, EMD has significant advantages in dealing with non-linear and non-stationary signals [17,18]. It can filter out the inherent mode of signal and realize the extraction of the mode function, whose envelope is symmetric with respect to zero and whose numbers of extrema and zero crossings differ by at most one. It should be noted that the signal may be excessively extracted in adaptive decomposition, resulting in an excessive number of intrinsic mode functions (IMF). In this case, the last several IMFs can be combined with the residual term to represent the change trend of the signal. In this paper, due to the large number of data sampling points collected by the high sampling frequency, the obtained eigen modal functions will be redundant. Therefore, a stop criterion of the iterative solution process is set in the solving process, that is, the maximum number of IMFs should not exceed 12. The algorithm flow diagram of feature extraction for plasma electrical signals is shown in Fig. 3. Considering that the residual term may have the same value in different weld states, which is not good for classification and recognition of weld states. The reconstructed electrical signals were statistically analyzed, and the characteristic values such as average value and standard difference were obtained to describe the weld state in detail.

M (P ) = −

∑

(P jn )2log (P jn )2

j, n ∈ N

(8)

The structure of the optimal tree is calculated according to the above method and shown in Fig. 4(a). The time-frequency spectrum of the signal is shown in Fig. 4(b). It is worth mentioning that the wavelet packet coefficients are arranged from small to large according to their frequency distribution in Fig. 4(b), rather than the natural number of sequential nodes. Since the wavelet packet coefficient can describe the nature of the signal and represent the amount of energy carried by the signal, the weight of decomposed signals in the original signal can be measured by the energy ratio of the wavelet packet coefficient in the node of the optimal tree. In view of the difference in the scale of each node in the optimal

4. Results and discussion 4.1. Compressed electrical signals As shown in Fig. 2(e), the energy distribution of the signal is mainly concentrated in the range from 0 to 1200 Hz. The frequency with the maximum energy is within 400 Hz. Therefore, the signal was divided

Fig. 4. Results of wavelet packet transformation: (a) optimal wavelet packet tree; (b) time-frequency spectrum of the plasma electrical signals. 645

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Fig. 5. The energy distribution of leaf nodes in optimal tree: (a) three-dimensional view; (b) two-dimensional view from Y–Z plane in (a).

tree, there is a difference in the number of samples covered by each node. The energy ratio is calculated after reconstructing the wavelet packet coefficients in this paper. The results are shown in Fig. 5(a). The color in the figure indicates the energy ratio of each leaf node. To facilitate observing the results, the data is projected on the X–Z plane, as shown in Fig. 5(b). As can be seen from the figure, node [7 0] accounts for 95.29% of the total signal energy, effectively representing the original signal. Therefore, the subsequent data analysis focuses on the reconstructed signal corresponding to the [7 0] node.

−5.19–−4.26 V when the welding seam is good. Since the plasma electrical signal is affected by the eruption of plasma in the keyhole, associated with the key hole size, the dynamic behavior of the molten pool flow, its frequency is a function of time. Therefore, the instantaneous frequency reflecting the time-varying regularity of signal frequency is applied to describe transient frequency characteristic of electrical signals in the local point. The instantaneous frequency can be solved as follows: for a random time series X (t ) , Hilbert transformation is performed on it, and Y (t ) can be obtained as:

4.2. Analysis of EMD results

Y (t ) =

A series of welding experiments were conducted according to the parameters in Table 1. Furthermore, welding seams containing defects were selected to analyze as well as the corresponding plasma electrical signals. As shown in Fig. 6, it is a welding seam obtained with the welding speed of 10 mm/s. Besides, there are electrical signals acquired synchronously and compressed signals by wavelet packet transform. It can be seen that the absolute value of the electrical signal is smaller than that of the normal weld when the defect of poor fusion occurs on the surface of the weld. In order to study the frequency characteristics of the signal and extract specific features, empirical mode decomposition was performed on the compressed signal to obtain eleven IMFs and one trend term, as shown in Fig. 7. As can be seen from the figure, all IMFs are timevarying signals which are symmetric around the X-axis. Among them, the amplitudes of IMF1, IMF2 and IMF3 are smaller than that of the noise signals collected in idler circuit, while the amplitudes of IMF4 are close to the noise signals. Therefore, it is inferred that IMF4 represents the noise signal of the acquisition circuit, while IMF1-IMF3 represent high-frequency oscillation signals in the circuit. The amplitudes of from IMF5 to IMF9 are of the same order of magnitude, slightly larger than those of IMF10 and IMF11, reflecting the characteristics of plasma oscillation. The residual term reflects the variation trend of plasma electrical signals. When the fusion is poor, the residual term value is between −4.16 and −3.28 V. The value belongs to the range of

Where, PV is the Cauchy principal value. X (t ) and Y (t ) are combined into a conjugate complex pair, the analytic solution is Z(t):

1 PV ⎛ π ⎝

+∞

∫−∞

X (τ ) d (τ ) ⎞ τ−π ⎠

(9)

Z (t ) = X (t ) + iY (t ) = a (t ) eiθ (t ) Where, a (t ) =

X 2 (t ) dθ (t )

+

Y 2 (t )

, θ (t ) =

(10) Y (t ) arctan( X (t ) ) .

The instantaneous

frequency is ω = dt . According to the above method, the instantaneous frequencies of each IMF are obtained as shown in Fig. 8. In this figure, every IF corresponds to each IMF component. As can be seen, the instantaneous frequencies of the first three IMFs all fluctuate in the level of 104 Hz l, with strong high-frequency characteristics. The IMF4 component mostly fluctuates in the range from 0 to 5000 Hz and reaches 104 Hz in the local range, which is characterized by the noise. The fluctuation ranges of IMF5 and IMF6 are 0–2000 and 0–1000 respectively, which are consistent with the plasma oscillation characteristics reported in existing studies [19,20]. The frequency fluctuation of IFM7 and IMF8 is small, in the range of 200˜500 Hz, which is consistent with the reported keyhole oscillation characteristics [21]. The remaining three instantaneous frequencies are in the band of 0–200 Hz, reflecting the disturbance in the welding process, which may also be caused by the excessive decomposition of EMD. The last figure in the lower right corner reflects the time-frequency characteristics of the compressed plasma electric signal in the whole welding process. From the perspective of amplitude, it can be seen that the energy is mainly concentrated in the band of 0–100 Hz. By empirical mode decomposition, signals in different frequency domains can be separated, with clear physical meanings clarified. In addition, the features representing the state of welding seams can be obtained. To verify the effectiveness of the proposed method, a quantitative comparative analysis has been conducted. The analysis shows the trend features obtained by WPT are seriously affected by the number of decomposition layers and the kind of the wavelet basis. As shown in the Fig. 9, the red and yellow lines represent the trend features reconstructed by the approximate coefficient from the WPT with the decomposition of 12 layers. It can be seen that the features obtained by different wavelet bases are different. A large amount of trial and error is required to determine the decomposition layer number and wavelet basis corresponding to the best feature. In addition, the features obtained are not as obvious at signal mutation as those obtained by WPT-

Fig. 6. The appearance of a welding seam (with welding speed 10 mm/s) and corresponding plasma electrical signals. 646

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Fig. 7. IMF components and residual term obtained by EMD.

EMD method, as shown in the rectangular box in the figure. Therefore, obtaining features directly from WPT is not an ideal choice for acquiring features. Compared with the results obtained by EMD, the time of obtaining the trend by WPT-EMD is reduced by 1 time. Moreover, conducting WPT on electrical signals in advance can avoid the interference of other factors on trend characteristics to the greatest extent. The results show that WPT-EMD is the optimal method for feature extraction in this application.

4.3. Various joint statuses Using the same method, a variety of weld defects obtained under other welding conditions were analyzed. As shown in Figs. 10(a) and 11 (a), there are three defects, namely discontinuity weld seam, weld width mutation and fish-scale weld. Here, discontinuity weld seam indicates that the weld width is inconsistent. As can be seen from the figures, the plasma electrical signals have different representations for different defects. In Fig. 10(a), the weld seam spanned three states, including discontinuity of welding seam, transition state, and well-

Fig. 9. Comparative analysis of feature extracted methods.

formed weld. However, there is still the problem of welding surface quality even when the welding seam is well formed. The plasma electrical signal has an abrupt change at the corresponding position.

Fig. 8. Instantaneous frequency corresponding to each IMF and Hilbert-Huang spectrum. 647

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Fig. 10. Data acquired with welding speed of 8 mm/s: (a) weld seam and corresponding plasma electrical signal; (b) denoised electrical signal; (c) the residual term of EMD.

input layer, hidden layer, summation layer and output layer, shown in Fig. 13. The input layer is used to receive training sample data, so the number of neurons is equal to the dimension of the sample, and its function is to pass the data to the hidden layer. The number of neurons in the hidden layer is the same as the number of training samples. Each neuron node the hidden layer has a center. The determination of the center takes the form of random selection from the input sample data. After determining the center, in order to prevent the radial basis function from being too pointed or too flat, the smoothing factor is calculated according to the formula below:

Wavelet packet transform and empirical mode decomposition were carried out successively for the purpose of compressing and extracting features from the electrical signals of the plasma. The characteristics of the electrical signals representing the defects were obtained, as shown in Fig. 10(b). When discontinuous weld defects appear, the trend term value of the electrical signal is in the range of −5.15–−5.46 V. Subsequently, it is observed in Fig. 11(a) that the absolute value of the electrical signal increases sharply in the case of weld width mutation, while the absolute value of the electrical signal increases and decreases periodically in the case of fish-scale weld. The processing results of electrical signals in Fig. 11(a) is shown in Fig. 11(b). The trend characteristic value corresponding to weld width mutation is between −4.69 and −5.27 V, and the trend characteristic value corresponding to fish-scale weld pass is between −4.26 and −4.59 V. By the observation of above data, it can be seen that different defect has different value range in the residual term of EMD. However, there exists intersection between the sound weld and weld width mutation as well as Fish-scale weld. For this reason, time-domain statistical analysis was carried out on the original electrical signals. It is observed from Fig. 2 that there were 5 troughs for every 1000 points on average. Thus, statistical analysis is conducted at an interval of 200 points. The mean value, standard deviation, kurtosis and skewness of the voltage signal were calculated. 100 sets of feature samples of different weld states were selected by ascending counts, shown in Fig. 12. It can be seen that the mean value and standard deviation shown in Fig.12(a) and (b) are better for the discrimination of weld state than kurtosis and skewness in Fig.12(c) and (d). Therefore, three feature values, including mean, standard deviation and residual term, were selected as input vectors to build the prediction model of weld state.

σ=

dmax 2N

(11)

Where, dmax represents the maximum distance between the selected centers, N is the number of hidden nodes. At this point, the distance between the input data and the center is calculated, and the value is output through the radial basis function. The calculation equation is as follows:

Фij = exp ⎛⎜− ⎝

‖xk − x ij ‖2 ⎞ 2σ 2

⎟

⎠

(12)

Where, Фij is the output of j th neuron of i th category in the hidden layer, x ij indicates the j th center of i th category, xk represents the input k th sample. It is worth mentioning that, each neuron in the hidden layer has been divided into a certain category due to the characteristic of supervised learning in PNN network. The function of summation layer is to average the output of neurons belonging to the same category in the hidden layer, as shown in the following formula: L

vi =

∑ Фij /L j=1

4.4. Prediction based on Probabilistic neural network

(13)

Where, vi represents the output of class i in the summation layer, L represents the number of neurons in class i . Therefore, each neuron in the summation layer corresponds to a category which only connects with the corresponding category in the hidden layer. The output layer has only one neuron, and the maximum value in the summation layer is taken as the output category:

Neural network has been widely used in the monitor and control of welding process [22,23]. As a deformation form of radial basis neural network, probabilistic neural network integrates density function estimation and Bayesian decision theory, which can solve the pattern classification problem well [24]. The model structure is composed of

Fig. 11. Data acquired with welding speed of 12 mm/s: (a) weld seam and corresponding plasma electrical signal; (b) denoised electrical signal; (c) the residual term of EMD. 648

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Fig. 12. Statistic features: (a)mean; (b) standard deviation; (c) skewness; (d) kurtosis.

Fig. 14. A typical testing result of the prediction model based on PNN.

posterior probability density to make its output 1 and the output of other neurons 0. After using the training sample data to create the probabilistic neural network, the test sample is input into the network for testing. The probabilities that the test sample belongs to each category are calculated, and the category corresponding to the maximum probability value is output. As mentioned above, the data used for building the predictive model are derived from the data in Figs. 9–12, including residual terms, mean, and standard deviation. The three features were used as input neurons,

Fig. 13. The schematic diagram of PNN.

y = argmax (vi )

(14)

In the actual calculation, the output layer of the network is composed of competitive neurons, whose number is equal to the number of categories. It receives the data of summation layer and makes the threshold discrimination. It means finding a neuron with the maximum Table 2 The typical examples of the training data.

Residual Mean Std Label

1

2

3

4

5

6

7

8

9

10

−5.198 −5.932 0.364 1

−5.201 −5.368 0.294 1

−4.731 −4.259 0.528 2

−4.715 −4.123 0.758 2

−4.338 −3.971 0.299 3

−4.345 −4.613 0.428 3

−3.484 −3.294 1.175 4

−3.488 −4.771 0.947 4

−4.882 −4.884 0.506 5

−4.881 −5.272 0.304 5

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Table 3 The confusion matrix of a prediction result with an accuracy of 91.57%. The predicted class

The actual class

Discontinuous seam Width mutation Fish-scale weld Poor bead Sound weld

Discontinuous seam

Width mutation

Fish-scale weld

Poor bead

Sound weld

30 0 0 0 7

0 32 0 0 2

0 0 30 0 0

0 0 0 38 0

4 2 0 0 22

5 ms and the time used for building the network is within 30 ms, it is expected to realize on-line prediction of welding quality. Since the features were calculated in 5 ms and the time used for building the network is within 30 ms, it is expected to realize on-line prediction of welding quality. 5. Conclusions In this paper, deep penetration laser welding of stainless steels was carried out and electrical signals of the plasma were acquired in synchronization. The conclusions were obtained as follows: 1 A detection system based on the passive probe was established according to the plasma sheath effect. Through this platform, the plasma electrical signal can be measured, which has proven to have a close relationship with the weld seam. 2 The influence of noise jamming caused by equipment circuit on the electrical signal was effectively eliminated through wavelet packet transformation. On this basis, by means of empirical mode decomposition and statistical analysis, a series of features regarding to the weld state were obtained. 3 A prediction model of weld state was built based on the probabilistic neural network, which can identify the welding state with high accuracy and is beneficial to the realization of the feedback control of welding quality.

Fig. 15. Three-dimensional distribution of test data.

of which the typical data is shown in the Table 2. The labels in Table 2 indicate the discontinuous seam, width mutation, fish-scale weld, poor bead and sound weld corresponding to the numbers from 1 to 5. The neurons of the hidden layer were set at 500 according to the set of samples, while the neurons in the summation layer were set at 5 in accordance with the collected weld states. To build the prediction model, two thirds of the samples were used for training and the rest samples were used for testing. Fifty trials were performed and the average accuracy of prediction was 90.16%. A typical testing result is presented in Fig. 14. In order to further understand the recognition ability of the model in each category, the confusion matrix is used to observe the classification performance of five categories in a typical prediction result, as shown in Table 3. Each column represents the prediction category, and the total number of each column represents the number of data samples predicted into this category. Each row represents the true category of the data. The confusion matrix shows that the data points from groups fish-scale weld and poor weld are classified correctly. The four data points belonging to the group discontinuous seam are misclassified into sound weld. Also, seven data points known to be sound weld are misclassified into discontinuous seam. It can be seen that the mistake is mainly made when distinguishing between discontinuous seam and sound weld. This is because that a discontinuous seam is essentially a deficiency, not a defection. In addition, the morphology of a discontinuous seam is similar to that of a sound weld. If this type of deficiency is not taken into account, the prediction accuracy of classification model based on PNN will be greatly improved. The number of the vertical coordinate indicates the above five weld states. To observe the distribution of test data more clearly, samples were visualized in Fig. 15 with X–Z view. Compared with radial basis neural network, probabilistic neural network has a better performance by fusing density function estimation and Bayesian decision theory. In addition, PNN has no local minimum problem that exists in back propagation network with sufficient sample data. Because of its simple learning process, easy training and fast convergence speed, PNN is very suitable for real-time processing. Since the features were calculated in

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