Analysis of vibration signal responses on pre induced tunnel defects in friction stir welding using wavelet transform and empirical mode decomposition

J.Rai ,T.Balusamy ,R.Raj Jawahar

a Vinayaka Mission’s Kirupananda Variyar Engineering College,Salem,India

b Department of Mechanical Engineering,Government College of Engineering,Salem,India

c Department of Mechanical Engineering,Dynamech Design Solutions,Chennai,India

ABSTRACT Among many condition-monitoring systems in welding operation,Defect identification is an important method to ensure the precision in finishing operation.Friction stir welding is a solid state welding process used to join two metals without the use of electrode at lower temperatures.The aim of this present work is to identify and localize the tunnel defect in aluminum alloy and measure the distance of the defect zone in the time domain of the vibration signal during Friction stir welding.The vibration signals are captured from the experiments and the burst in the vibration signal is focused in the analysis.A signal-processing scheme is proposed to filter the noise and to measure the dimensional parameters of the defect area.The proposed technique consists of discrete wavelet transform(DWT),which is used to decompose the signal.The enveloping technique is applied on the decomposed zero padded signal.The continuous wavelet transform(CWT)has been implemented on detailed signal followed by a time marginal integration(TMI)of the CWT scalogram.Empirical mode decomposition(EMD)is used to replace the detailing coefficients from DWT with Intrinsic Mode Function(IMF).Statistical parameters such as mean,kurtosis,S.D and crest factor have been extracted from the final filtered signal for validating the defect welds from the control defect free welds.Results produced were found to be that kurtosis is 7.4402 for tunnel defect induced weld and 3.3862 for defect free welds.As the increase in kurtosis value predicts the defect zone impact in the signal.The measurement of the defect zone of the cut 1(voids)and cut 2(tunnel grooves)in correlation with the processed signal is found to produce a much redundant results with an error rate of 0.02.

1. Introduction

Friction stir welding(FSW)is a solid-state joining technique that has expanded rapidly since its development in 1991 and has found applications in a wide variety of industries,including aerospace,automotive,railway,and maritime.The FSW process exhibits a number of attractive advantages when compared to other welding processes,perhaps the most significant of which is the ability to weld alloys that are diffciult or impossible to weld using fusion welding techniques.FSW is also an energy efficient process that requires no filler material and,in most cases,does not require the use of a shielding gas.The development of a failure diagnostic system for welding operations based on vibration signal processing has been an active area of research for more than two decades.A reliable online condition monitoring system is desired in industries to provide accurate fault diagnostic information about mechanical systems to prevent the machinery performance degradation,malfunction or even catastrophic failures.An ability to detect rising defects in the welding process has been contributed significantly in prevention of catastrophic failures in the work-piece.Fault diagnosis can be categorized as defect identification,defect localization,defect size measurement and defect pattern classification [1].During the last few years, a significant progress in analytic modeling,instrumentation for vibration measurement along with the signal processing techniques have made possible to examination of defect signature from vibration signals of machines.Parey and Tandon have introduced the analytical model,based on an impact velocity model relating measurable vibration signal to the defect size on the gear tooth flank.The dynamic impact velocity model provides the relationship between the overall acceleration level with defect size and rotational speeds of gear pair[2].The well-established conventional parameters such as crest factor,kurtosis,power spectrum and cepstrum estimation,time-domain averaging and demodulation,have been proven to be adequate in fault detection.However,the main drawback is that they are based on the assumption of stationary of the analyzed vibration signal[3].In the process of diagnosis by many investigators,kurtosis is found suitable in identifying the defect signatures of rotating machinery.Barszcz et al.have identified another statistical spectrum technique,i.e.,spectral kurtosis,for detection of a tooth crack in the planetary gear of a wind turbine[4,5].Combet and Gelman have proposed optimal denoising,using Wiener filter based on the spectral kurtosis methodology,to enhance the small transients in gear vibration signals,in order to,detect local tooth faults such as spitting at early stage[6,7].Cheng et al.have observed the novelty of generalized demodulation of time-frequency analysis in fault diagnosis.This is particularly suitable for the processing of multicomponent amplitude-modulated and frequency-modulated(AM-FM)signals,because it can decompose a signal into a set of single-component signals whose instantaneous frequency may carry the defect signature[8].Zheng et al.have investigated a new approach of gear fault diagnosis based on continuous wavelet transform.They have concluded that the bi-orthogonal continuous wavelet transform is able to generate a finer time-scale resolution than orthogonal wavelet transform,which is more suitable for extracting the signature of a mechanical fault[9].One can find from literature is that the time-frequency methods are effective tools for analyzing diagnostic signals and have been widely used to describe machine condition[10].Dalpiaz et al.have explained in their report about the gear condition monitoring by vibration analysis based on time-frequency and cyclo-stationarity analysis. They have reestablished the fact that the wavelet transform is effective in crack detection[11].Belsak and Flasker have investigated the wavelet de-noising methods in defining local changes in vibration signal of faulty gear.Wavelet function matches signal burst very well at certain scales and from the resultant coefficient spectrums it is possible to reveal impulses hidden in noise signals[12].Rafiee and Tse have presented a novel time-frequency based feature recognition system using autocorrelation of continuous wavelet coefficients(CWCs)for gear fault diagnosis[13].From above literature study,it is concluded that the wavelet transform generates very effective time frequency spectrum to analyze the nonstationary vibration signal from a rotating system.Moreover,the suitability of time frequency spectrum in precise defect localization on the weld zone is discussed in present analysis.

1.1. Defects in friction stir welding process

FSW defects may be of any orientation,size,or shape.However,like arc welding,the process moves in a linear fashion,usually at a constant rate along the jointline,and therefore has a similar tendency to produce defects,which propagate for some length and have their major dimension parallel to the travel direction.When discussing methods of detection,it is helpful to divide FSW defects into inclusions,volumetric defects,and non-volumetric(laminar)defects.When discussing the mechanical and structural significance of defects it can be useful to additionally classify by non-surface breaking(interior)and surface breaking(face or root).Flash is produced by displacement of material from the face(tool-side surface)of friction stir welded components[14].Things like insufficient forging pressure,excessive travel speed,inappropriate tool design,or an overly worn tool may cause the formation of voids[15,16].Voids and Tunnel defects(single voids extending longitudinallyalong the weld)can be found in FSW under non-ideal process conditions.Tunnel defects are important because they can have significant mechanical effects and can be difficult to detect by nondestructive testing(NDT),often being narrowand lacking in volume.According to the literature,depending on location and extent,Tunnel defects can have significant effects on mechanical properties,including fatigue life,impact strength,root bend survival,and through-thickness load-bearing capacity.The mechanical effect of a tunnel defect is dependent primarily on its penetration depth and width.The effects on tunnel defect were found to be more prominent.In the present work,an experiment is carried out with a customized test setup,where the tunnel defect is introduced in the aluminum 6082 alloy(6 mm thick plate).The generated vibration signal is captured and is used for fault diagnosis.A signal-processing scheme is desired and proposed to identify and localize the defect in time domain. Towards this, the signal processing technique denoises the vibration signal using un-decimated wavelet transform(UWT).In order to extract time-frequency representation from denoised signal,the Morlet wavelet transform(MWT)has shown to be very effective.The smoothed instantaneous power spectrum is achieved by integrating time-frequency spectrum in time domain.The measurement of the distance between two-tunnel defect zones is carried out using inverse CWT graph.In the proposed method,an attempt is also made to replace denoised signal from UWT with Intrinsic Mode Function(IMF)generated from Empirical Mode Decomposition(EMD).The experimental analysis is presented in subsequent part of the paper.

1.2. Underlying theory

1.2.1. Welding tool frequency

Simulations are carried out to verify the effectiveness of the strategy.In this section,the proposed strategy will be applied for the separation of source signals from experimental vibration signals in welding.It is assumed that the measured vibration signal in friction stir welding is a mixture of multiple independent signal sources.These sources consist of signals related to welding tool,spindle rotational frequency and work-piece geometry variation or other disturbances.Stirring frequency and spindle rotational frequency are frequencies of interest,which are useful for condition monitoring of FSW,but usually contaminated by noises like variation of welding conditions,work-piece condition,etc.The objective of this study is to separate signals of interest from the noisy measured signals.It is a well-known fact that,the stirring frequency is computed by multiplying the area of tool pin surface with the spindle rotational speed(Wsin cycles/s or Hz).Stirring gets amplitude modulated with the feed rate on the work piece.The amplitude modulation of the stirring and its harmonics reveal useful information about the defective welding such as misalignment,improper backlash,over loading,material defects such as void and tunnel defect on the work piece[17].The stirring frequency does not reveal a broken,cracked,void in general,except in some rare cases,when the natural frequencies are not measurable.Another parameter,stirring frequency(STF)occurs when the tool is stirred on the aluminum alloy work piece[18],i.e.,STF=[1/(L/U)](1/Ws),whereLis least common multiple,andUis uncommon factor of weld tool.The STF is normally not measurable because the frequency is very low.However,it can be observed in the time domain when the tool is stirred on the defective zone of the aluminum work piece.In the present work,the author attempts to identify the STF using PSD of envelope signal.

1.2.2. Discrete stationary un-decimated wavelet transforms

Wavelet analysis provides a multi-resolution representation of a signal,thus it has great promise for signal feature detection at different scales[19].The discrete wavelet transform(DWT)of a one-dimensional signal is implemented by two-channel sub-band filtering followed by down-sampling the outputs by a factor of two.The two filters,consisting of a low-pass filter and a high-pass filter,constitute a pair of quadrature mirror filter banks.A multi-level decomposition is implemented by applying the same filtering and down-sampling procedure to the low-pass channel output of the preceding level.This type of signal decomposition is known as an un-decimated wavelet transform.The scheme of the un-decimated wavelet transform(UWT)is given as

1.2.3. Zero padding for signal burst identification

Zero padding is a technique defined as appending zero values to the weighted samples prior to the UWT calculation.The appended zero values are treated as additional samples collected at the same rate and therefore extend the measurement time,as shown in:

Where,the zeros are added toMN-1.This procedure results in more accurate sampling of the signal spectrum because,instead ofNspectral samples,MunionNsamples of the same spectrum are available.Note that extending the data with zeros and computing a longer UWT does increase the number of points in frequency domain.This does not break or alter the basic restriction of the effects of aliasing[20].No amount of zero padding can overcome these fundamental limits and the spectrum parameters,such as signal-to-noise ratio level and the spectral leakage level,remain unchanged.

Now,we can obtain the UWT coefficients of the above equation by:

Compared with Eq.(4),we obtain that:

Accordingly,Eq.(5)can be reformulated as:

Wherelandare the integer part and the fractional part of Mλ0,respectively.Similarly,lis returned by the maximum search routine ofx(k).This can formulate the detailing coefficients with high pass filter to be more detailed in considering the further analysis.

1.2.4. Signal enveloping technique

The defective zone of the work-piece with the stirring contact of the welding tool generates the impulse with low amplitude level.This low-level impulse has an amplitude-modulating effect on the vibration signal,which is visible as high amplitude signal burst in time domain.The modulation effect spreads over a wide frequency range because of the short duration of impulse.Envelope analysis is a practical approach for investigation of such signals, where amplitude modulation presents in characteristic frequencies of the system.The envelope detection technique focuses on a narrow band range in the specified frequency band,which is useful for detecting the low-level impulses that are below the noise level in the normal spectrum.Low pass filtering and FFT based Hilbert transform are the most commonly known methods for envelope detection.However,the FFT based Hilbert transform has advantage for its high speed and so,suitable for real time envelope detection.The Hilbert transform of the signalx(t)is defined by an integral transform:

Hilbert transform generates an artificial complex valued signal from the real valuedx(t).An amplitude modulated envelope signalE(t)can be computed as:[18].It is well known that,the envelope is a low frequency signal compared to the original signal.In order to smooth the envelope signal,a band-pass filtering is desired and is implemented in the present analysis.

1.2.5. Morlet wavelet transform

The wavelet transform provides a combination of time and frequency localization,and thus is important for analyzing nonstationary signals. By considering the signal transients as the response of impulse,the time-frequency structure of the Morlet wavelet matches the typical transients best[21,22].Besides,its“box spectrum”is suitable as a filter.The Morlet wavelet is defined as a complex exponential function in the time domain and has a shape of Gaussian window in the frequency domain as follows:

Where Ψ(f)is the Fourier Transform of Ψ(t),ζ is the damping ratio,fmis the center frequency of Morlet wavelet window and τ denotes the time parameter.This Morlet wavelet is used for the continuous wavelet transform of the enveloped signal to define it timefrequency representation for a high frequency signal.

In order to demonstrate the effectiveness of Morlet time frequency localization,a sample data signal is analyzed using three kinds of wavelets like Haar,Dauebechies and Morlet wavelet.The signal is scaled and transformed for the effective denoising with a series of equally spaced scales ranging from 1 to 32.This scale value stretches the single wavelet to extract the exact source frequency of the embedded feature in the raw data signal.To increase the possibility of matching the center frequency of a scaled wavelet with the frequency of the source signal, a small-scale interval is preferred. However, a small-scale interval leads to increased computational load,as more scales will be involved in the signal decomposition.A trade-off must therefore be made between the accuracy and computational time. Comparing the wavelet transform results using these wavelets as shown in Fig.1,it is apparent that only the Morlet wavelet is effective in extracting the impulsive component from the signal,as illustrated by the similarity in the waveform between the corresponding wavelet coefficient and the impulsive component.The Daubechies and haar wavelets,in comparison,did not fully reveal the characteristics of impulsive component.This clarifies the selection of morlet wavelet as a base wavelet fot the optimal achievement of feature extraction in the signal.

Fig.1.Comparison of scaled coefficients of continuous wavelet transforms using(a)Haar wavelet,(b)Daubechies wavelet and(c)Morlet Wavelet.

1.2.6. Empirical mode decomposition

EMD was developed for analyzing non-stationary signals that commonly exist in many science and engineering fields.Due to its data-driven nature and the strong capability in analyzing nonstationary signals to provide information on localized amplitudes and frequencies,EMD has been proved to be effective for timefrequency analysis in various areas,such as power quality assessment,biomedical signals,mechanical signals,and geographical signals.For oscillation identification,EMD has been applied to analyze transient measurements[23].In EMD-based oscillation identification,a frequency measurement signal can be viewed as a linear combination of short-term frequency fluctuation components and long-term frequency trends.Short-term frequency fluctuations are defined as the evolution feature of frequency measurementsf(t)between local frequency maxima and minima.Subtracting this fast fluctuation component,which is denoted by（t）,from f(t),one can identify the“slower”frequency trendthat supports the short-term frequency fluctuation component,so that

After recursive decompositions,the representation of Eq.(10)the original frequency measurementf(t)becomes:

Thus the intrinsic mode functions are generated through EMD with the fast fluctuation component.The best-fit functions with least signal-noise ratio are found to be the extraction signal.

1.2.7. Time marginal integration reconstruction using ICWT

The Detailing signal(D3)from the UWT is transformed with amorlet wavelet.CWT computes the inner products of the analyzed signal and a set of complex Morlet wavelets.This transform is also called as analytic wavelet transform,because the complex Morlet wavelet is analytic in nature,i.e.,the power spectra of the Morlet wavelet is zero at negative frequencies.The CWT provides both the magnitude and phase information of signals in the time-frequency domain.However,the magnitude information is only desired in current analysis.In order to achieve an effective time frequency resolution,CWT is computed with an analytic wavelet ψ as:

The time frequency resolution depends upon on the time frequency spread of the wavelet atom ψu(yù),s. Continuous wavelet transform defines a local time-frequency energy densityPwD3,which measures the energy of‘D3’in Heisenberg box of each wavelet ψu(yù),scentered at（u,ξ=η/s）:

Where,η is the center frequency,and this energy density is called scalogram.The time marginal integral can be computed by integrating the scalogram along the frequency axis,or the integral of each row of spectrogram.

The time marginal integrals equivalent to the smoothed instantaneous power of the signal.The instantaneous power reveals how the power of the signal changes over time[24-26].

1.2.8. Statistical validation

The statistical parameters such as the crest factor and the kurtosis are well established to realize the impulses in a time domain vibration signal due to the defect in the welding zone. The formulation of these statistical parameters is tabulated in Table 1.The crest factor corresponds to the ratio between the crest value and the R.M.S.value of the signal[27]with‘N’the number of samples taken within the time domain signalx(n).The kurtosis is used to analyze the distribution of the vibratory amplitudes contained in a time domain signal.Mathematically it can be expressed as:

WhereM4is the fourth order statistic moment,M2is the second order statistic moment,and μ is the mean of the signal.The kurtosis and the crest factor are two parameters sensitive to the shape of the signal.The computation of the mean value of the instantaneous amplitudes of the signal raised to the power of four gives a considerable weight to high amplitudes of the kurtosis.The crest factor attenuates the impact of an isolated event with high crest amplitude that only takes into account the crest amplitude of this event.Therefore the kurtosis is acknowledged as a better indicator than the crest factor.Another statistical parameter,i.e.,signal to noise ratio(SNR),which helps in identifying noise level introduced due to defect.The SNR is the inverse of coefficient of variation(Cv),i.e.SNR=1/Cvwith the relation;Cv=r/|l|,where r is standard deviation of the signal.The absolute mean value is taken to ensure that theCvwill be always positive.However,the performance of these parameters is re-evaluated in the proposed signal-processing scheme.

2. Experimentation

Preliminary experiments were carried with the suitable feed rate,axial force and rotational speed of the Friction stir welding machine. An optimum welding condition (rotational speed of 1100 rev/min,axial force of 11 KN,traverse feed rate of 100 mm/min)is shown in Table 2.The experimental setup of the Friction stir welding machine is shown in Fig.2.The fixture was provided with the necessary fasteners for fixing the six-degree of freedom of the processed plates.The material subjected to stir welding is an aluminum alloy(AA 6082),with a 6 mm thickness plate.The chemical composition of aluminum alloy is shown in Table 3.The plates were welded with rectangular samples of 150 mm×75 mm with a non-conventional cylindrical pin tool,made of high-speed steel(HSS M2).The diameter of the tool shoulder is set to be 16 mm and the pin diameter is set to 4 mm as shown in Fig.3.The tool pin was positioned at center of joint line.A data acquisition system with a piezo-electric accelerometer(CE-P41),an A/D conversion card(DAQ2213)and an industrial computer were used to collect experimental vibration signals from the welding process.Vibration signals were acquired with a sampling rate of 5507 Hz.Friction stir-welding experiments were carried out with the defect and defect free conditions.The instrumentation and its range accuracy were shown in Table 4.

Table 1Signal characterization and statistical conditions.

Table 2Welding parameters and dimensions.

2.1. Proposed method

The proposed architecture is shown in Fig.4.The proposed method elaborates the acquisition of signals from the welding condition(spindle rotation speed of 1100 rev/min,plunge depth of 5.5 mm and feed rate of 100 mm/min),which will be used to study the vibration signal separation.A typical vibration signal with their power spectral plot a defect and defect free weld is shown in Fig.5(a)to Fig.5(d).Initially the source signal is separated from its nonlinearity and Gaussian noise using undecimated wavelet transform based on zero padding technique.The zero padding helps to segregate the detailing coefficients with a high pass filter by considering the signal source linearity as shown in Fig.6 to Fig.8.The DWT decomposition can be expressed as A3+D3+D2+D1.The detail coefficient D1,D2,D3 is shown in Fig.8(a)to Fig.8(c),respectively.In this case,spindle rotational frequencyfris about 64.5 Hz (corresponding to the spindle speed of 1100 rev/min),which is considered as the minimum frequency of interest in friction stir welding.Welding frequency fwis about 256.2 Hz(4fr)with a cylindrical pin weld tool, which can be considered as the maximum frequency of interest in friction stir welding (max finterest=1?4fw;64.5 Hz).The sampling frequencyfsis 5507 Hz,which is set to be higher above 4 maxfinterest.Also,Morlet wavelet function is selected for wavelet decomposition(its center frequency is 0.66667 Hz).According to Eq.(20)and Eq.(21):

Table 3Chemical composition of the work piece.

The maximum scaleLmaxand the minimum scaleLminare expressed asLmax=56.91 andLmin=14.33.

Fig.2.Experimental photography of the Friction stir welding with data acquisition system.

Hence the scale valuea,is found to be(a=14,15…55,56);with an increment of interval(1).The decomposed D-3 signal is used to identify the defect zone with the continuous wavelet transform based on time-frequency representation.The signal is enveloped to study its detailed characteristics of the cut with its temporal zone.After signal enveloping,the signal is reconstructed using inverse continuous wavelet transform as shown in Fig.9.To validate the reconstructed source signal,the empirical mode decomposition is applied on the source signal with its intrinsic mode functions(IMF1,IMF2,IMF3)as shown in Fig.10(a)to Fig.10(c).The intrinsic mode function is compared with the ICWT-D3 signal to find it's limiting,signal to noise ratio for the data redundancy.Statistical features such as(mean,kurtosis and crest factor)have been obtained to compare the welding process for defect and defect free welds.

Fig.3.Tool and Work piece dimensions.

3. Results and discussion

From the PSD spectrums,it is noticed that the stirring frequency of 256.2 Hz is present with lower amplitude along with the modulated resonant frequencies with higher amplitude for both defect free and tunnel defect induced work piece.Another distinct observation is that the additional prominent frequency spikes are present at lower frequency of 20 Hz with tunnel defect induced work piece.This explains that the defect generates at lower frequency vibration signals of high amplitudes.

Fig.4.Architecture of the proposed system.

In line with the proposed method,an un-decimated wavelet transform(DWT)up to level-3 is carried out on the vibration signal from the defective weld.From experimental analysis,it is found that the Morlet is the most effective mother wavelet for the current analysis due to its bi-orthogonal properties.The wavelet scalogram of the DWT-D3for the defect free signal is shown in Fig.11(a).It could be observed that the contour streaks of the scalogram in defect free signal is minimal when compared with the tunnel defect induced scalogram as shown in Fig.11(b).The PSD spectra of the defect free and tunnel defect induced signals are shown in Fig.11(b)and(d).From these PSD spectrums,one can notice that the DWT introduces a lot of additional low frequency signal components,i.e.between 1 Hz and 800 Hz in detail coefficients during decomposition,which is due to its translation invariant property.From Fig.11(b),it could be observed that the welding frequency is obtained at 256.2 Hz.This frequency is matched with the frequency observed in Fig.11(d).Also the separated component of the defect 1 and defect 2 induced frequency could be observed at 20.5 Hz and 10.25 Hz.

The Detailing zero padded D3 signal carries all frequency components that belong to the raw signal.So,for the current experiment,the D3 signal presents adequate de-noising capability of DWT and is more suitable for further analysis.Subsequently,for more precise defect identification and localization purpose,the enveloping technique is implemented on the vibration signal.The envelope extraction is done using a center frequency of 0.667 Hz,which is the most prominent frequency component visible in the PSD of the vibration signal of tunnel defect zone.The span of 25 Hz is set to cover the second prominent spike 10.25 Hz.The extracted envelope is shown in Fig.12.Now,from the envelope signal,one can observe that the spikes are prominent due to the vibration bursts present in the signal due to the defect.The PSD of the envelope has the maximum spike at 256.2 Hz,which is almost equalto the observed stirring frequency of 256.4 Hz.In ICWT of Fig.12,significant spikes occur almost in the exact time of the tunnel defect with a very much little variation.Each spike carries two prominent consecutive peaks,which are due to tunnel defect induced as cut 1 and 2.These peaks introduce ambiguity in the measurement,which provides the motivation for a next level of signal processing.The additional x-axis is introduced with a scale factor of(distance with respect to time)to convert the time scale to the feed rate of the welding process.From Fig.12,it is observed that two spikes occur in an interval of 20 mm as shown in Fig.12,which interprets the two defective zones on the welding process.Nevertheless,the envelope signal is too noisy to correlate the defect precisely.

Table 4Instrumentation.

Fig.5.(a-d)Time and frequency of Defect free signal and Defect signal.

Fig.6.Detail 1-coefficient(zero padded)plot of defect signal.

Fig.7.Detail 2-coefficient(zero padded)plot of defect signal.

Fig.8.Detail 3-coefficient(zero padded)plot of defect signal.

Fig.9.Detailed spectrum of burst identification Reconstructed ICWT of D3 enveloped signal.

Fig.10.(a-c)Intrinsic mode decomposed function signal(imf1,imf2,imf3).

In order to reduce this ambiguity in manual demarcation process,another approach is proposed.The CWT is implemented with the help of a complex Morlet wavelet as the mother wavelet.The CWT transform is carried out up to scale 42 and the resultant scalogram in terms of intensity is shown in Fig.12,which is a kind of time-frequency representation.From the CWT spectrum,one can observe that the vibration bursts due to the defect weld generates much lower frequency components(in the range of 0 Hz-25 Hz).The defect is identified in the spectrum as higher intensity stripes.In order to achieve more precise understanding the time marginal approach(ICWT)of the enveloped D3 spectrum is computed.Now,the Time marginal approach graph shows two major spikes,predominately.The two major spikes represent the contact of the two defective zone of the work-piece in stirring.Manual demarcation is done on the Time marginal graph to measure the distance between the two defective weld zones as shown in Fig.13.In order to validate the D3 signal with less redundancy,i.e.,using the Empirical Mode Decomposition(EMD).In view of this,DWT of the proposed method was compared with EMD signal.For the purpose of comparison,the envelope ofD3is over-lapped on envelope of IMF after normalization.From the figure,one can notice that the IMF2 is very close to the envelope of D3 based on SNR.With much redundancy of the IMF2 signal with D3 signal have some deviation in the translation of time scale.This is due to the CWT transform,which translates the time scale. Time marginal approach is used to integrate the time scale with the perfect match on the amplitude level for the ICWT reconstructed D3 signal.The signal decomposition level with respect to its range frequency is shown in Table 5.The generated Time marginal graph of the D3 is shown in Fig.13.The de-noising capability of EMD is re-established and also found equally suitable for the proposed technique as shown in Fig.14.

Fig.11.(a-d)Time-frequency,Time-amplitude,PSD plots of the final extracted signal of DEFECT FREE AND CUT CONDITION.

Fig.12.Enveloped CWT of the Detailed D3 signal(time-frequency plot).

Fig.13.Time marginal reconstruction of the enveloped D3 and Imf2 signal.

Table 5Signal decomposition level with respect to its frequency range.

The average of statistical quantities such as RMS value,Standard deviation(SD),crest factor(CF),signal to noise ratio(SNR),and Kurtosis for the vibration signals from both the stages of the experiments are computed and tabulated below in Table 6.From Table 6,one can observe that the RMS,SD and SNR values are decreasing whereas crest factor and kurtosis values are increasing with the inclusion of the defect.This indicates the presence of the defect.Kurtosis parameter increases almost three times with the defective and is re-established as most suitable statistical parameter for tunnel defect identification.

4. Conclusion

Fig.14.Image of the Defect weld with comparison to their respective analyzed signal.

Table 6Statistical parameter validation.

The experimental analysis presented here re-establishes the fact that kurtosis is the most suitable for the statistical parameter to identify the defect.The defect localization is observed with the implementation of the proposed signal-processing scheme.The Detail coefficients, from the un-decimated wavelet transform(DWT),have shown to be most suitable to de-noise the signal.The details coefficients are observed to be redundant,for further analysis.In order to extract time-frequency information,the continuous wavelet transform(CWT)has been implemented.Time marginal transform (ICWT) of CWT scalogram provided the smoothed instantaneous power of the signal in time domain.The abscissa of the Time marginal graph is mapped onto the defect zone distance of the work piece and is correlated with induced defects in the time domain.Moreover,the Empirical Mode Decomposition(EMD)is found to be equally effective as DWT.Summarizing,the proposed method is suitable and reliable in measuring the cut distance between the two-tunnel defects of the aluminum alloy work-piece using vibration signal in the time domain.The defects present in weld have tendency to produce sudden change in features of vibration signals.The final D3 plots contain abrupt changes in signal,which correspond to presence of defects.The implementation of statistical tool on detail coefficients localizes the abrupt changes more evidently.Statistical values such as kurtosis(stirring zone)is found to be increased in defect induced weld when compared with defect free weld.R.M.S(feed force)is found to be decreased in case of defect-induced weld.This means the feed force decreases on defect-induced area.Crest factor(Defect zone predictor)is found to be decreased with the defect-induced weld.As the defect zone reduces the amplitude of the signal.In case of defect free welds the vibration signal generated are smooth and there are no abrupt changes in the signal,which distinguishes the processed signal of defective weld from that of defect free weld.