Application of Continuous Wavelet Transform based on Fast Fourier Transform for the Quality Analysis of Arc Welding Process

SMAW (Shielded Metal Arc Welding) and GMAW (Gas Metal Arc Welding) are two of the most prominent welding processes commonly utilized in almost all types of modern industries. Among various aspects of these processes, some of the important parameters that govern the quality of the final weld product are the skill level of welders, welding consumables, and the role of shielding gases (in GMAW). Currently, the role of these parameters in determining the quality of the welded product is examined by evaluating the final weld produced and not by investigating how these factors actually affect the welding process. This is an indirect way to evaluate such welding parameters, which are both time-consuming and expensive. During the actual welding process, random variations in arc signals (voltage and current) take place. These dynamic variations are so short and rapid that ordinary ammeters and voltmeters cannot monitor the rate of such variations. However, the reliable acquisition of such variations and its subsequent analysis can provide very useful information in determining the quality of the final weld product. In this study, arc voltage and current were acquired at 100,000 samples/sec, filtered and subsequently analyzed using Continuous Wavelet Transform based on Fast Fourier Transform (CWT-FFT) technique to evaluate welding skill, welding electrodes (in SMAW process), and the effect of shielding gases (in GMAW process). Results thus obtained clearly differentiated the skill level of different trainee welders and welding electrodes in the SMAW process and the effect of shielding gases and arc current in the GMAW process. Very good correlation among the obtained results, its weld bead and weld pool images were observed. Hence, this research proposes a simple yet effective methodology to evaluate the arc welding process parameters using CWT-FFT


Introduction
Arc welding is one of the most commonly and widely used welding process in almost all types of modern industries for joining various ferrous and non-ferrous metals. Due to its inherent merits like the ease of use, versatility, flexibility, and low maintenance cost this process finds its application in fabricating almost everything we see around us like buildings, bridges, locomotives & coaches, general machinery, defence equipment etc. This process has many variants (like SMAW, GMAW, GTAW etc.) and the primary differences between these processes are the methods by which the molten metal is protected from the atmosphere [1]. Due to its unpredictable arc behaviour and complicated modes of metal transfer, arc welding has stochastic characteristics and therefore, dynamic fluctuations in arc voltage and current were observed during actual welding. The quality of the final weld product depends heavily on various welding parameters that create these random fluctuations. Consequently, if these variations that occur during the actual welding process are suitably acquired and processed then, the effect of various arc welding parameters like the skill of welders, the role of shielding gases and consumables etc on the final weld product can be understood in a much better way than it is done at present. However, such dynamic variations in arc voltage and current occur for very short intervals of time. Therefore, to record such variations, a high-speed data acquisition and monitoring system (along with relevant sensors), capable of acquiring arc variations at the same rate as they occur should only be used. In order to establish an effective weld monitoring system, many researchers have used techniques like visible light imaging Recently, a general-purpose and commonly available DSO has also been used to establish an effective weld monitoring system [21][22][23].  [33][34][35][36][37][38] the authors have used the denoising property of the wavelet transform to denoise the noisy welding signal by maintaining a soft threshold and subsequently extracting various process parameters to evaluate the welding process.
In the present study, welding signal (arc voltage and current) and weld pool image were acquired using a highspeed Digital Storage Oscilloscope (DSO) and a high-speed camera set up. Subsequently, evaluation of the welder's performance, welding electrodes in the SMAW process and the role of shielding gases in a GMAW process were done by analyzing the resultant welding signals. The analysis presented in this work was carried out using both statistical and CWT based signal processing techniques. Detailed analysis on the results thus obtained and their practical implications are suitably delineated in this paper. But, before proceeding to experimental setup details, a brief description of the methodologies of Continuous Wavelet Transform based on Fast Fourier Transform (CWT-FFT) technique used in this study is given below.

CWT-FFT based Methodology
CWT essentially represents the correlation between continuous input signal "x(t)" and a suitable wavelet function shown below.
Here, scale "a" can be transformed to frequency of wavelet "fa " . This clearly indicates that at a=1 and b=0, the wavelet's associated frequency becomes the mother wavelet's characteristic frequency. Therefore the used in a Since, equation 5 describes the inverse wavelet transform, it should be able to reconstruct the original signal if the wavelet coefficients are known. Here, is constant whose value is determined by the type of wavelet similarly, ( , ) is the details function whose value is given by equation (6).
It is evident from equations 8 and 9 that CWT is now just a simple convolution of the signal with the wavelet.
As a result, a CWT can be considered an inverse Fourier transform.
where, Similarly, to the preceding explanation, if the signal is discrete in nature, a Discrete Wavelet Transform may be implemented to analyze the relevant signal to extract various signal parameters. If x(n) is a discrete signal having "N" number of samples, the convolution equation used earlier can be expressed as equation (11). From this equation the DWT can be easily calculated by simply convolving the signal and wavelets for each position value and iterating the same for each scale a as well.
where, DFT of x(n) is given by ^( ), ^ is the DFT of ψ and k is the frequency index.
If fs is the signal sampling frequency with sampling period Δ , then the wavelet function can also be normalized to obtain the unit energy at each and every scale "a" using equation (15).
where, = 2 Δ and the CWT then can also be defined using equation 16 [39].
The methodologies described above were used to analyze the arc welding signal to evaluate various arc welding parameters. As described in [41], in the present work also, the calculations were performed using different  Fig. 1 shows the complete schematic of the experimental setup used in this study. The setup used basically comprises of a data acquisition, welding and a high-speed camera setup. Brief descriptions about these modules are given below.

Data acquisition setup
For all our studies data acquisition was carried out to acquire the instantaneous values of voltage and current by maintaining an identical condition while making bead-on-plate welding on a carbon steel plate using suitable welding consumables. In order to acquire the arc voltage and current, a general-purpose Digital Storage Oscilloscope (DSO7054B) of Agilent Technologies (now Keysight) having a maximum sampling rate of 4 GSa/seconds and bandwidth of 500 MHz was used. DSO7054B has 4 channels with inbuilt AC to DC coupling.
The input impedance of DSO was 50 -1M Ω and an in-depth memory of 8 M-Points. For sensing welding current, Hall Effect based highly sensitive current clamp (600 A DC and 100 A AC) was used. Similarly, in order to sense arc voltage, a differential probe having 500 MHz bandwidth was used. To achieve high Common Mode Rejection Ratio (CMRR) and to match the overall frequency and attenuation response two signal paths along the measurement were provided. The system has an input capacitance of 2.5 pF and a propagation delay of 6.1 ns. Welding duration was set to 20 seconds and arc voltage and current were acquired at 100,000 samples /seconds. The acquired data were then filtered for noise and in turn used for subsequent analysis.

Welding setup
To evaluate the welding skill in the SMAW process, iinstantaneous current and voltage values were recorded by making bead-on-plate welds on carbon steel using an inverter power source and E 7018 electrodes of 3.15 mm diameter. Similarly, in order to compare different welding electrodes by comparing their arc characteristics welding data were acquired from bead on plate welds on carbon plates using basic coated (E 7018, 3.15 mm diameter) and cellulose coated electrodes (E 6010 of 2.5 mm diameter) and an inverter power source.
To investigate the effect of shielding gases in the GMAW process bead-on-plate welding on carbon plate using AWS ER 70S2 wires (of 1.2 mm diameter) were made by varying the shielding gas and current combinations as shown in Table 1. From this table, it can be seen that for each shielding gas, three different current combinations were used to obtain different modes of metal transfer. It should be noted that all welds are prepared using the same welder and machine.

High speed camera setup
To visualize the metal transfer behavior of welding electrodes and correlate the same with the acquired electrical signal a Fastcam MC2.1 photon focus high speed camera with suitable filters and illumination were used. This camera setup had a maximum capture speed of 10,000 frames/sec with the minimum shutter opening time of 1/100,000s. Please note that in this study, metal transfer images of various welding electrodes were captured at 5000 frames/sec. Photograph of the DSO based high speed data acquisition, welding and high-speed camera imaging setup is shown in Fig. 2.  Fig 4 (b) shows the voltage PDD made by a skilled welder, from this figure it is clear that for a good weld made with E 7018 type of basic electrode, voltage PDD should have two distinct and widely separated regions 1, 2 and should have least variations in region 3 (Fig. 4 (b)). On the other hand, the voltage PDD obtained from an unskilled welder in Fig. 4 (a) reveals that an untrained welding personal will have significantly lesser values of region 1 and 2 with large random variations in region 3 (Fig. 4 (a)). Therefore, it is clear that a good welder must have wider region 2 (steady state welding duration) and narrower region 3 (duration of unstable welding). To validate the hypothesis presented just now the bead image and its corresponding radiographs (for skilled and unskilled welders) are shown in Fig. 5. Comparing, Fig. 4    In order to really confirm the results obtained above in grading the skill levels of trainee welders, similar analysis needs to be performed on larger sets of trainee welders. Therefore, 20 passing out trainee welder from a weld training institute were examined by monitoring the welding durations of region 2 and 3 as proposed above and their corresponding rankings are tabulated in Table 2. The ranking obtained in turn were correlated with the current practice of ranking the welding skill using PDD analysis [21][22] and by performing the visual examinations of their final weld bead. From this table and referring to Fig. 7, a very good correlation between the proposed and current practice of weld skill classification were noticed.

Evaluation Welding Consumable
For evaluating the welding electrodes high speed data acquisition and camera setup described in section 3 was used to acquire welding voltage and current and to capture the metal transfer behavior in E 7018 and E 6010 types of welding consumables. High speed camera image in Fig 8 clearly depicts the metal transfer behavior in such electrodes, it is observed that in E 7018 types of basic electrodes short circuit types of metal transfer is predominant whereas in cellulosic electrodes (E 6010 types), both short circuit and spray modes of metal transfer were noticed. This observation was in agreement with those reported in [22]. To study the arc behavior of the individual electrodes their metal transfer characteristics were correlated with their voltage PDDs (Fig 8). In this correlation the region of short circuit and spray transfer in E 7018 and E 6010 electrodes respectively can be easily seen.  Similarly, in addition to short circuit the duration of spray mode of metal transfer happening only in E 6010 electrodes were also observed to be around 1 second. These results were also correlated with the time domain analysis (oscillogram) of the arc voltage signals acquired during actual welding process and a very good correlation were observed between them.

Effect of Shielding Gases in GMAW Process
In a GMAW Process, depending on the composition of shielding gases and current combinations, the metal transfer mechanism can be either short circuiting, globular, or spray type [44]. Therefore, to know their exact behavior, we have used different gas compositions ( Table 1) to find out whether changing modes of metal transfer can be correlated with its corresponding voltage and current signal. Fig. 9 represents the scalogram (using CWT-FT method) of the voltage PDD obtained for GMAW-P when 80 % Ar and 20 % CO2 gas composition was used. We can see from this figure that at around 200 A, the duration of the first peak (or short circuit transfer) is around 3 seconds. Due to considerable duration of short circuit metal transfer spatter of molten droplets around the welded area may occur before separating from the wire on account of a mild explosion which takes place due to an increased current [45]. Therefore, many spatters can be noticed in its bead image shown in Fig 10 (a). With increasing current (from 200 A to 220 A) significant decrease in short circuit metal transfer duration was noticed (~2 seconds) and consequently the spatter around the weld also decreased. A further increase in current (at around 300 A), first peak of voltage PDD or the short circuit metal transfer duration totally disappeared ( Fig. 9 (c)). Because for 80 % Ar and 20 % CO2 gas composition, at around 300 A, spray mode of metal transfer start dominating [45]. Note that spatter around the welded area has significantly decreased now ( Fig. 10 (c)). Results and the trends just now mentioned were in correlation with the time domain analysis of the shielding gas composition of 80 % Ar and 20 % CO2 (see Fig. 12 (a).) CO2 gas mixtures (Fig. 9) Results just now presented are once again is in agreement with the time domain analysis of the 100 % Ar shielding gas composition shown in Fig. 12 (b).

) 150 A and (2) 200 A in GMAW process
It is evident from the above discussions that a CWT-FFT based analysis on welding signals can easily differentiate various modes of metal transfer in the GMAW process. Hence, by monitoring the duration of various process parameters in the scalogram of a GMAW-P voltage PDD, the role of shielding gas composition on arc characteristics and the current above which spray transfer occurs can be studied.

Conclusion
In this work, the application of CWT-FFT to evaluate welding skill and welding consumables in the SMAW process and to study the effect of shielding gases with varying currents in the GMAW process are studied.