SPECIAL ISSUE PAPER 123

Application of wavelet transform of acousticemission and cutting force signals for tool conditionmonitoring in rough turning of Inconel 625gK Jemielniak*, J Kossakowska, and T UrbanskiFaculty of Production Engineering, Warsaw University of Technology, Narbutta, Poland

The manuscript was received on 5 March 2010 and was accepted after revision for publication on 8 June 2010.

DOI: 10.1243/09544054JEM2057

Abstract: Nickel-based superalloys are widely used in the aircraft industry since they are excep-tionally thermal resistant, retaining their mechanical properties at temperatures of up to 700 ◦C.On the other hand, since they are very difficult to machine, tool life is typically short and canfinish abruptly. As catastrophic tool failure can destroy an expensive workpiece, automatic toolcondition monitoring (TCM) has become particularly critical. This paper presents an applica-tion of the wavelet packet transform (WPT) for extracting useful TCM features from the cuttingforces and acoustic emission (AE) signals during rough turning of Inconel 625. New, improvedmethods of signal feature (SF) relevancy evaluation were proposed based on determination andcorrelation coefficients. Out of several SFs calculated from bandpass signals, the most useful forTCM were automatically selected. The selected features were used for tool condition monitoring.

Keywords: tool condition monitoring, cutting forces, acoustic emission, wavelet transform

1 INTRODUCTION

For many years, difficult-to-machine alloys havecaused serious problems in the aviation and othermanufacturing industries. Nickel-based superalloysare widely used in the aircraft industry since theyare exceptionally thermal resistant, retaining theirmechanical properties at temperatures of up to700 ◦C [1]. However, they are very difficult-to-cutmaterials due to their high shear strength, work-hardening tendency, inclusion of highly abrasivecarbide particles in the microstructure, strong ten-dency to weld and form a built-up edge, and lowthermal conductivity [2, 3]. Tool wear is not repeat-able and has a tendency to end catastrophically bychipping or breakage. Thus, tool wear monitoringplays a very important role in guaranteeing undis-turbed production machining of nickel-based alloyslike Inconel 625.

Tool and process condition monitoring has beenone of the most important focuses of research efforts

*Corresponding author: Faculty of Production Engineering,Warsaw University of Technology, Institute of ManufacturingTechnology, Narbutta 86, Warsaw 02-524, Poland.email: k.jemielniak@wa.home.pl

for more than 20 years. An excellent summary of earlywork on this topic can be found in reference [4]. Muchresearch has been done since then, and there aremany commercially available tool condition moni-toring systems [5]. However, these are generally notconsidered to be sufficiently reliable for broad appli-cations. Most of these systems apply ‘one process–onesignal feature’ strategies. On the other hand, it is com-monly agreed that reliable tool wear evaluation basedon one signal feature (SF) is impossible, because anyfeature depends not only on the tool wear but alsoon a variety of other process parameters with ran-dom natures. Therefore, the relationship betweentool wear and a measured value is very complex andhas a statistical nature, rather than a strictly pre-dictable one. Hence, the key issue in tool conditionmonitoring (TCM) is finding multiple signal featurescorrelated with tool condition [6]. Various methodsfor tool wear monitoring have been developed, mostof which are based on acoustic emission (AE), cuttingforces, and vibrations [5–7]. Many approaches havebeen taken to analyse these signals. Over the past 15years, the wavelet transform has become one of theemerging and fast-evolving mathematical and signalprocessing tools. It has been used for surface metrol-ogy [8], chip form monitoring [9], and grinding wheel

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124 K Jemielniak, J Kossakowska, and T Urbanski

condition monitoring [10]. An interesting review ofmany applications of the wavelet transform in faultdiagnosis and condition monitoring is presented inPeng and Chu [11]. Recently, it is more and more oftenapplied to tool wear monitoring. Kwak [12] applieddiscrete wavelet decomposition to detect tool failureand to conduct the de-noising of the cutting force sig-nal in a turning process. Li and Patri [13] appliedthe wavelet packet transform to tool wear monitor-ing in boring. They used the root mean square (r.m.s.)value of the bandpass of an AE signal to assess the toolstate. Scheffer and Heyns [14] used a wavelet packettransform based on the strain and vibration signal toassess tool wear in turning. Several signal featuresindicative of tool wear were automatically extractedfrom a wavelet packet analysis. A correlation coef-ficient between the feature and the ideal trend wasused for the automatic selection of the best features. Liet al. [15] applied a fast wavelet transform algorithm torecognize the tool wear states in automatic machiningprocessing. They showed that a wavelet analysis basedon this fast algorithm was more sensitive, more reli-able, and faster than a Fourier analysis in recognizingthe tool wear states for different cutting conditions.

The objective of the present study was the appli-cation of improved methods of feature extraction,selection, and integration based on the wavelet trans-form of raw AE and cutting force signals, for tool wearmonitoring in the rough turning of Inconel 625.

2 DISCRETE WAVELET TRANSFORM

The discrete wavelet transform was developed byMallat with a fast algorithm based on the conju-gate quadratic filters [16]. The wavelet transform candecompose a signal into different components in dif-ferent time windows and frequency bands through thewavelet scale function, and scaled and shifted versionsof the mother wavelet. The discrete wavelet transform(DWT) decomposes a signal into the scaling coeffi-cients (approximations A) and wavelet coefficients(details D) by the convolution of the signal and theimpulse responses of the lowpass and highpass filters.The filter’s outputs are subsampled by 2. At the firstlevel, the original signal is decomposed into A1 andD1, and then approximation A1 is decomposed againinto A2 and D2. Generally, the approximations (Aj+1)and details (Dj+1) at level j + 1 can be expressed byconvolutions

Aj+1 [n] =∞∑

k=−∞h

[2n − k

]Aj

[k]

(1)

Dj+1 [n] =∞∑

k=−∞g

[2n − k

]Aj

[k]

(2)

Fig. 1 Three-level wavelet packet transform (WPT) decom-position, where blackened fields indicate the fre-quency band of the original signal

where h and g are the impulse responses of the low-pass and highpass filters respectively, which are dis-crete equivalents to the scaling function and wavelet.

Another type of wavelet transform is the waveletpacket transform (WPT), where the approximationsand details are both decomposed, providing manymore frequency bands (Fig. 1). Since this providesmore opportunities to find useful signal features,it was used in this research. From a mathematicalpoint of view, the structure of the computations ina WPT is exactly an octave-band filter band. Thus, theapproximations and details are bandpass signals (seeFig. 1).

Several wavelet basis function types are available inthe literature. After many experiments with a numberof them, the coiflet 5 wavelet and three-level decom-position WPT were applied because they were themost informative.

3 EXPERIMENTAL SET-UP AND CONDITIONS

The experiments were performed on a turning cen-tre (TKX 50N) equipped with an industrial AE sen-sor (Kistler 8152B121) mounted on the turret and acutting force sensor (Kistler 9017B) mounted underthe turret (see Fig. 2(a)). The tool was a CRSNL3225P12 MN7 with whisker-reinforced ceramicinserts, RNGN 120700T01020 CC670 (Fig. 2(a)). Theworkpieces were impeller cases made of Inconel 625(Fig. 2(b)), and machined with subsequent perpendic-ular cuts from diameter 406 to 268, with the depth ofthe cut ap = 2.5 mm, feed f = 0.2 mm/rev, and cut-ting speed vc = 220 m/min. Three such workpieceswere machined, during which seven tools were wornout. All of the experiments were conducted until theappearance of a drastic decrease in the surface fin-ish (Fig. 2(c)) or burr formation (Fig. 2(d)), whichare indirect criteria for tool life estimation appliedunder factory floor conditions. The tool notch wear(a direct, laboratory criterion for tool life estimation)

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Application of wavelet transform of acoustic emission and cutting force signals 125

Fig. 2 Experimental set-up and tool life criteria: (a) tool andsensors, (b) the workpiece, (c) surface roughness,(d) burrs, and (e) tool wear

was also measured (Fig. 2(e)). As the notch wearappeared on the side of the cutting edge opposite tothat creating the machined surface, it was not corre-lated with the surface finish. It also was not correlateddirectly with the burr formation. All three phenom-ena (notch wear, surface finish, and burr formation)appeared autonomously, making determination ofthe tool life end difficult, subjective, and dependenton the machine tool operator’s experience. Therefore,the application of a TCM system would be very useful.Here, the used-up portion of the tool life (�T ), definedas the ratio of the cutting time as performed so far (t)to the overall tool life span (T ), was used as the toolcondition measure.

A raw AE (AEraw) signal was acquired with asampling frequency of 2 MHz using a DAQ card,NI PCI 6111. As this sampling frequency producesan enormously large amount of AE data, only0.05 s (100 000 samples) out of every 10 s period wasrecorded and analysed. Two cutting force signals(Fx and Fz) were acquired simultaneously with a sam-pling frequency of 30 kHz using an NI-PCI 6221 DAQcard at the same points of time during 1.66 s (50 000samples). Each cut lasted 96 s. Eight signal recordingstaken from the middle parts of each cut were used forfurther analysis based on wavelet transforms.

4 EXTRACTION AND SELECTION OF SIGNALFEATURES

As the outputs of the wavelet transforms have rel-atively large sizes, informative features must beextracted from the coefficients (bandpass signals).Wavelet coefficients are usually treated as separatesignals, each characterized by the signal features (SFs)used for time domain signals [17]. Here, the following

Fig. 3 Examples of signal features normalized in time (SFT)and lowpass filtered (SFTf ); (a) Fx/DDD,E: energy ofcoefficient DDD of Fx signal; (b) AEAAA,Sk: skew ofcoefficient AAA of AE signal

six signal features were calculated from the three-leveldecomposition WPT coefficients:

(a) effective value (root mean square, r.m.s.);(b) logarithmic energy (E);(c) skewness: the third statistical moment of a distri-

bution (Sk);(d) kurtosis: the fourth statistical moment of a distri-

bution (Ku);(e) ring-down count (Rd): number of times the

signal crosses the threshold level calculated as30 per cent of the maximum–minimum of thewavelet coefficient value during the first mea-surement (first 100 000 samples) for each tool lifeindependently;

(f) pulse width (Pw): the percentage of time duringwhich the signal remains above this threshold.

For three-level decomposition, there are 14 WPTcoefficients and 84 signal features for each signal(AEraw, Fx , and Fz) – altogether 252 SFs. Althoughthe number of signal features was quite large, mostof them were very distorted or barely sensitive to thetool condition. The decision-making algorithm of theTCM system should not be overburdened with thosefeatures, which would cause unnecessary computa-tion or hinder the subsequent classification process.The selected features should be relevant, sensitive tothe tool condition. To measure this relevancy, somemodel of the relationship between the signal featureand the tool wear or used-up portion of the tool life,�T , is necessary. Here, a lowpass filtered SF coursewas accepted as an SF(�T ) model, which made it pos-sible to avoid any uncertain suppositions about themathematical formula of this model. As the filter char-acteristics depend on the number of elements in thefiltered time series, filtering was preceded by the nor-malization of the SF in time to 0–100 per cent of thetool life to SFT. Figure 3 shows examples of the signalfeatures normalized in time (SFT) and lowpass filtered(SFTf ).

Now, the signal feature usability for tool conditionmonitoring can be evaluated using a coefficient of

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126 K Jemielniak, J Kossakowska, and T Urbanski

determination, R2s , which is a statistical measure of

how well the SFTf (�T ) model approximates the realSFT(�T ) relationship

R2s =

∑i (SFTi − SFTav)2 − ∑

i (SFTi − SFTf i)2

∑i (SFTi − SFTav)2 (3)

where∑

i (SFTi − SFTav)2 is the total square sum,∑i (SFTi − SFTf i)

2 is the residual square sum, SFTi andSFTf i are single values of SFT and SFTf respectively(i = 0, . . . , 100), and SFTav is the average value of SFT.

As mentioned above, seven tools were worn out(seven tool lives obtained) during the experiments. Itwas decided to use the first three for the TCM systemtraining, while the other four were used for testingthe tool condition monitoring accuracy. Thus, averagevalues of R2

s were calculated and used as the first crit-erion for automatic SF selection. These SFs, for whichaverage values of R2

s > 0.4 were assumed to be sat-isfactory, correlated with the tool condition (smoothenough). Figure 3 presents an example of a signal fea-ture that was accepted at this stage (Fx/DDD,E: energyof coefficient DDD of Fx signal, R2

s = 0.98) and a fea-ture that was rejected as poorly correlated with thetool condition (AEAAA,Sk: skew of coefficient AAA of AEsignal, R2

s = 0.35).The second criterion for an SF selection was its

repeatability. Another coefficient of determination,R2

r , was used for this purpose for signal features thatmet the first criterion

R2r =

∑j∑

i

(SFTf ji − SF3Tfav

)2 − ∑j∑

i

(SFTf ji − SFTfavi

)2

∑j∑

i

(SFTf ji − SF3Tfav

)2

(4)

where SFTf ji is the value of SFTf at the ith point (i =0, . . . , 100) and jth tool life ( j = 1, . . . , 3), SFTfavi =13

∑j SFTij is the average SFTf at the ith point, and

SF3Tfav = 1303

∑j∑

i SFTij is the average of all of theSFTf values for three tool lives.

The signal features that were sufficiently repeatable(R2

r > 0.6) were selected for further consideration.Figure 4 presents examples of accepted (repeatable)and rejected (not repeatable) SFs.

Array SFTfav(�T ) of 101 signal feature values nor-malized in time (0–100 per cent of �T ), filtered, andaveraged is now considered to be a representation ofthe signal feature–used-up portion of tool life.

Every SF, even those well correlated with tool wear,can sometimes be disturbed randomly. Therefore,the number of features should be sufficiently high tocover these possible random disturbances of any SF.On the other side, the selected signal features shouldnot be strongly correlated with each other, to avoid

Fig. 4 Signal feature repeatability evaluation: (a) acceptedSF – Fz/AD,Pw, pulse width of coefficient AD of Fz sig-nal (R2

r = 0.81), (b) rejected SF – AEAAD,rms, effectivevalue of coefficient AAD of AE signal (R2

r = 0.29)

Table 1 The numbers of useful signal features obtainedfrom different signals

AE Fx Fz

R.m.s. 0 2 1Energy 1 0 1Skewness 0 0 0Kurtosis 1 3 3Ring-down count 0 0 2Pulse width 0 0 1� 2 5 8

repeating the same information or giving the samephenomenon too much importance [18–20]. The fol-lowing procedure was adopted to eliminate similarSFs. All of the signal features selected so far weresorted into descending order, according to their R2

rvalues. Then, the first (best) was selected and corre-lation coefficients r2 between this SF and every otherwere calculated. SFs with r2 > 0.75 were rejected astoo correlated with the best one. From among theremaining signal features, again the best one wasselected, and the SFs correlated with it were rejected.This procedure was repeated until no signal featuremeeting the R2

r > 0.6 criterion remained.The procedure described above, wavelet transform

and signal feature calculation, selection, and elimina-tion, was performed fully automatically without anyintervention by the operator. Finally, out of 252 signalfeatures only 15 were left that were considered usefulfor tool condition monitoring: Fx/DDD,rms, Fx/ADA,Ku,Fz/D,Ku, Fz/AD,Pw, Fz/DAA,Rd, Fx/DAA,rms, Fz/DAA,Ku,Fz/DA,Rd, Fz/AD,Ku, Fz/DDD,rms, AEDDA,E, Fx/DAA,Ku,AEDD,Ku, Fx/ADD,Ku, and Fz/DA,E. It is worth noting thatthe most effective SFs were obtained from the Fz signal(8 SFs). The Fx signal was not much worse (5 SFs),while the AE signal produced only 2 SFs. The mostproductive type of SF was the kurtosis (7 SFs), whilethe skewness did not give any useful SF. All of theseobservations are summarized in Table 1.

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Application of wavelet transform of acoustic emission and cutting force signals 127

Fig. 5 Used-up portion of the tool life evaluated by theTCM system (�Tev) versus actual one (�T ) aftertraining on all signals from the first three tool livesand testing on the remaining four

5 TOOL CONDITION ESTIMATION

The automatically selected signal features were fedto the decision-making algorithm of the TCM sys-tem, which evaluated the used-up portion of tool life(�T ). The hierarchical TCM algorithm, described inreference [7], was applied here. In the first step of thisalgorithm, �T was calculated using the current signalfeature value and the direct relationship between thesignal feature and �T , SFTfav(�T ), for each SF sepa-rately [21]. In the second step, all of the�T values wereaveraged into a final tool condition evaluation. Asthree tool lives were used for the TCM system training,the remaining four were used for the system testing.Examples of this estimation are presented in Fig. 5as the used-up part of a tool’s life evaluated by thesystem (�Tev) versus actual �T . Errorless estimationis shown by the straight, dashed line and deviationsfrom this line are presented as the root mean squareerror (RMSE = 6.22).

As there were three signals measured, it is interest-ing to consider what would have happened if not all ofthem were available. First, the system was fed with thecutting forces signals only (Fig. 6(a)). It appeared thatresults were not much worse, which is not surprising,as AE provided only two signal features (see Table 1).When only one cutting force signal was used, the accu-racy of the tool condition evaluation was significantlyworse (RMSE = 10.81 for Fx only and RMSE = 9.82 forFz only) but still reasonably good. Rather surprising isthe relatively good result achieved when only the AEsignal was available (Fig. 6(d)), despite the fact thatonly two SFs were then selected. Nevertheless, all ofthe results prove that WPT provides a powerful tool forsignal feature extraction, which is very useful for toolcondition monitoring. It was also again shown that thehierarchical algorithm applied here is very effective in

Fig. 6 Used-up portion of the tool life evaluated by theTCM system (�Tev) versus actual one (�T ) aftertraining on selected signals from the first three toollives and testing on the remaining four: (a) Fx + Fz ,(b) Fx only, (c) Fz only, and (d) AE only

this monitoring, as it was in two other applications[18–20].

6 CONCLUSIONS

This paper presented an application of the waveletpacket transform of AE and cutting force signals intool condition monitoring during the rough turningof Inconel 625. Several signal features (SFs) wereextracted from wavelet coefficients. New, improvedmethods of SF relevancy evaluation were proposedbased on determination and correlation coefficients.The coefficient of determination was used for select-ing SFs that changed regularly and smoothly withthe used-up portion of tool life, which was consid-ered to be a measure of the correlation between theSF and �T . The same coefficient was also used forselecting repeatable SFs. The coefficient of correla-tion was applied to eliminate SFs that were similar(correlated) to better ones. Finally, the selected signalfeatures were used in a hierarchical algorithm for toolcondition evaluation.

The results of this research can be summarized asfollows:

1. The proposed method of automatic signal featureextraction and selection provided informative SFs,which were successfully used in tool conditionmonitoring.

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128 K Jemielniak, J Kossakowska, and T Urbanski

2. The most effective type of wavelet coefficient fea-ture appeared to be kurtosis, while skewness didnot produce any useful SF.

3. Most of the informative SFs were obtained fromcutting force signals, while the AE signal providedonly two SFs.

4. Tool condition monitoring based on the selectedSFs appeared to be most successful when all threesignals were available; however, even single signalsappeared to be acceptable in this application.

ACKNOWLEDGEMENT

Financial support of Structural Funds in the Oper-ational Programme – Innovative Economy (IE OP),financed from the European Regional Develop-ment Fund (Project ‘Modern material technologiesin aerospace industry’, POIG.0101.02-00-015/08), isgratefully acknowledged.

© Authors 2011

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APPENDIX

Notation

ap depth of cutA approximation (DWT coefficient)A1 approximation (DWT coefficient) at

level 1A2 approximation (DWT coefficient) at

level 2AE acoustic emissionAEAAA,Sk skew of coefficient AAA of AE signalAEDD,Ku kurtosis of coefficient DD of AE signalAEDDA,E energy of coefficient DDA of AE signalD detail (DWT coefficient)D1 detail (DWT coefficient) at level 1D2 detail (DWT coefficient) at level 2DWT discrete wavelet transformE logarithmic energyf feed rate

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Application of wavelet transform of acoustic emission and cutting force signals 129

Fz cutting force signal measured in thecutting speed direction

Fx cutting force signal measured in the feeddirection

Fx/ADA,Ku kurtosis of coefficient ADA of Fx signalFx/ADD,Ku kurtosis of coefficient ADD of Fx signalFx/DAA,rms r.m.s. of coefficient DAA of Fx signalFx/DAA,Ku kurtosis of coefficient DAA of Fx signalFx/DDD,E energy of coefficient DDD of Fx signalFx/DDD,rms r.m.s. of coefficient DDD of Fx signalFz/AD,Ku kurtosis of coefficient AD of Fz signalFz/AAD,Ku kurtosis of coefficient AAD of Fz signalFz/AD,Pw pulse width of coefficient AD of Fz signalFz/D,Ku kurtosis of coefficient D of Fz signalFz/DA,E energy of coefficient DA of Fz signalFz/DA,Rd ring-down count of coefficient DA of Fz

signalFz/DAA,Ku kurtosis of coefficient DAA of Fz signalFz/DAA,Rd ring-down count of coefficient DAA of Fz

signalFz/DDD,rms r.m.s. of coefficient DDD of Fz signalg impulse response of the highpass filterh impulse response of the lowpass filterKu fourth statistical moment of a distribu-

tion (kurtosis)Pw percentage of time during which the

signal remains above threshold (pulsewidth)

r2 correlation coefficientRd number of times the signal crosses the

threshold level (ring-down count)

R2r coefficient of determination (repeatabil-

ity)R2

s coefficient of determination (smooth-ness)

r.m.s. effective value (root mean square)RMSE root mean squared errorSFT signal features normalized in timeSFTav average value of SFTSFTi single value of SFTSFTf signal features normalized in time and

lowpass filteredSFTfavi average of SFTf in ith pointSFTf i single value of SFTfSFTf ji value of SFTf in ith point (i = 0, . . . , 100)

and jth tool life (j = 1, . . . , 3)SF3Tfav average of all SFTf values in three tool

livesSk third statistical moment of a distribution

(skewness)t performed cutting timeT overall tool life spanTCM tool condition monitoringWPT wavelet packet transformvc cutting speedxi single wavelet coefficient value

�T used-up portion of the tool life�Tev used-up part of the tool life evaluated by

the TCM systemµ meanσ standard deviation

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