Int J Adv Manuf Technol (2012) 62:107121

DOI 10.1007/s00170-011-3797-1

ORIGINAL ARTICLE

Grinding wheel wear monitoring based on wavelet

analysis and support vector machine
Zhensheng Yang & Zhonghua Yu

Received: 20 September 2011 / Accepted: 17 November 2011 / Published online: 4 December 2011
# Springer-Verlag London Limited 2011

Abstract A novel grinding wheel wear monitoring system coef Discrete wavelet decomposition coefficient
based on discrete wavelet decomposition and support vector Mean value of discrete wavelet decomposition
machine is proposed. The grinding signals are collected by coefficient
an acoustic emission (AE) sensor. A preprocessing method
is presented to identify the grinding period signals from raw
AE signals. Root mean square and variance of each decom-
position level are designated as the feature vector using 1 Introduction
discrete wavelet decomposition. Various grinding experi-
ments were performed on a surface grinder to validate the Grinding wheel topography changes during grinding. As a
proposed classification system. The results indicate that the result, the efficiency of grinding process and the quality of
proposed monitoring system could achieve a classification the workpiece are affected negatively most of the time.
accuracy of 99.39% with a cut depth of 10 m, and 100% Wheel wear may induce grinding burn and bad surface
with a cut depth of 20 m. Finally, several factors that may quality, even serious accidents. Unfortunately, current
affect the classification results were discussed as well. approaches dealing with wheel wear are based on human
experience and dressing interval is roughly determined,
Keywords Grinding wheel wear . Acoustic emission (AE) . usually by skilled operators. This induces two adverse
Process monitoring . Contact detection . Discrete wavelet impacts. Firstly, grinding wheel wear might already happen
decomposition . Support vector machine (SVM) before dressing process, which usually causes grinding qual-
ity problems. On the contrary, if dressing process is carried
Nomenclature out ahead of wheel wear, the grinding efficiency is definitely
AERMS Root mean square value of AE signal reduced and the abrasive materials are wasted at the same
a Approximation level of DWT time. Among major machine processes including milling,
d Detail level of DWT drilling and turning, grinding is known as the most compli-
SFRMS RMS value of each decomposition coefficient cated. Grinding wheel wear mechanism is still not fully
SFVAR Variance value of each decomposition coefficient understood today. Grinding wheel wear monitoring is thus
x(k) Original time-series signal necessary in grinding process.
g(k) Low-pass filter The most popular method in grinding wheel condition
h(k) High-pass filter monitoring is called indirect method, which relies on
fn Sampling frequency machining process parameters and sensor signals such as
vibration, forces, current, power, temperature, and acoustic
emission. In contrast, direct methods use vision sensors such
as scanning electron microscope (SEM) to measure grinding
Z. Yang : Z. Yu (*)
wheel surface or its replica directly. Direct methods have
Department of Mechanical Engineering, Zhejiang University,
Hangzhou 310027, Peoples Republic of China good measurement flexibility, high spatial resolution, and
e-mail: caq_221@zju.edu.cn good accuracy. However, they always require interrupting
108 Int J Adv Manuf Technol (2012) 62:107121

machining process and have a strict demand on the environ- model. The best performance index of 83.3% was obtained.
ment. In addition, vision systems are costly. As a result, they In their four papers on grinding wheel condition monitoring,
are more applicable in laboratory at the present stage. Liao et al. [6] kept studying on various signal processing
In this paper, indirect method is used to monitor wheel and classification methodologies. Autoregressive modeling
wear in surface grinding process. A general procedure of and discrete wavelet decomposition were employed as the
indirect grinding conditions monitoring method includes the effective approaches for feature extraction. Hidden Markov
following steps: (1) sensor selection; (2) signal processing; model [6], adaptive genetic clustering algorithm [7], boosted
(3) feature extraction; (4) feature selection; and (5) pattern minimum distance classifiers and four different wrapper
recognition strategies to match the selected features with approach classifiers [8] were introduced respectively to dis-
grinding wheel conditions. A brief review over the past tinguish different states of grinding wheel condition, mainly
decade on this specific issue is given below. sharp and dull. The results were encouraging. For the high
In 2009, Oliveira et al. [1] presented a CIRP keynote material removal rate (MRR) condition, clustering accuracy
paper titled Industrial Challenges in Grinding, in which a of 100% was obtained using Hidden Markov model [6],
similar CIRP keynote paper published by Kegg [2] 26 years while clustering accuracy of an adaptive genetic clustering
ago in 1983 was mentioned. Although almost three decades algorithm was 97% [7]. On the other hand, for the low MRR
passed, some grinding problems are still unsolved in indus- condition, Hidden Markov model could achieve 75% in
try due to their high complexity. Better predictability of clustering accuracy [6], while an adaptive genetic clustering
grinding process is one of those issues. Efforts have been was 86.7% [7]. For the boosted minimum distance classi-
made to attain this target and substantial achievements fiers, the best average classification accuracy of 91.9% was
have been obtained in the past several years. In another obtained using Adaptive Boosting-Minimum distance clas-
keynote paper on grinding process monitoring, Tnshoff sifier (AdaBoost-MDC) [8]. In another report, Liao [9] used
et al. [3] reviewed measuring techniques to monitoring ant colony optimization-based method and the sequential
process quantities as well as output quantities. The micro forward floating selection method to choose the best feature
and macro topography of the active abrasive layer of the subsets. Five classification methods, i.e. the nearest mean
grinding wheel were considered as the dominant features of (NM), k-nearest neighbor (KNN), fuzzy k-nearest neighbor
the process. (FKNN), center-based nearest neighbor (CBNN) and
Lee et al. [4] developed a grinding wheel topographic k-means-based nearest prototype (KMNP), were introduced
mapping system based on AERMS. AE signals were obtained as classifiers. Among all five classifiers, the lowest classifica-
from the contact between diamond tool and grinding wheel tion error of 7.81% was achieved using CBNN for the dataset
and converted into root mean square level. To measure the of wavelet energy feature, while the lowest classification error
contact of the diamond tool with each abrasive grain, a fast was 6.875% using the dataset of AR coefficients. Cakan [10]
time constant was calculated as the average time spent for studied the real-time monitoring of flank wear of an
two consecutive hits between abrasive grains and the alumina-based ceramic cutting tool using a photo electronic
diamond tool. Results showed that the AE mapping sensor and the results were quite encouraging.
system could generate an image similar to the surface Subrahmanya and Shin [11] pointed out that although
topography presented on the grinding wheel surface, various methods had been reported for grinding wheel con-
which was an L mark. Lee et al. [4] provided a new dition monitoring, no widespread applications in industry
approach for grinding wheel topography mapping using had been found as none single method or feature had been
indirect methods. However, it could not be applied in grinding demonstrated to be successful for all setups and wheel
processes due to wheel topography mapping was obtained workpiece combinations. Considering of this circumstance,
during the dressing process. Most of the other indirect meth- Subrahmanya and Shin [11] developed an automated sensor
ods focused on grinding wheel conditions, e.g., wheel wear, selection and fusion combine with parameter-free model
burn or end of wheel life, rather than wheel topography. training approach for monitoring of burn, chatter and wheel
Lezanski [5] developed an intelligent grinding wheel wear. Combination of embedded sensor selection algorithm
condition monitoring system, in which neural network and and an approximate estimate of the leave-one-out (LOO)
fuzzy logic were used to classify the conditions of the error for hyperparameter tuning of least squaressupport
grinding wheel cutting abilities in the external cylindrical vector machines (LS-SVM) were proposed for automated
grinding process. Multiple sensors were used and features feature selection and sensor fusion. Sun et al. [12] provided
were extracted in both time and frequency domain. An 83 a systematic procedure to select training data. The quality of
1 (8 nodes in input layer, 3 nodes in hidden layer, 1 node in the training data was estimated by the performance evalua-
output layer) three layers feed forward back propagation tion through support vector machine. Inasaki [13] developed
neural network was built for feature selection and eight a monitoring and controlling system using the fusion of AE
input features were selected as inputs of the neuro-fuzzy and power sensor to detect and optimize the cylindrical
Int J Adv Manuf Technol (2012) 62:107121 109

grinding process. A summary of viable solutions of tool properties. Support vector machine rather than neural net-
condition monitoring (mainly grinding wheel wear) is works or clustering algorithms is introduced for classifica-
reported in Table 1. tion of sharp and worn wheel states in Section 4. Section 5
Three key conclusions can be drawn from efforts shows the classification results. Different parameters that
mentioned above: may affect the performance of the proposed grinding wheel
wear monitoring system are discussed. Performance of a
1. The prediction accuracy of wheel condition is relatively
backpropagation (BP) neural network is also presented in
low, which limits its application in industry. For exam-
the discussion section and its comparison with the proposed
ple, prediction results reported in the mentioned studies
method is talked. Conclusions are made at the end of the
are generally lower than 95%, except Liaos [6].
paper. The overall structure of this paper is shown in Fig. 1.
2. One of the critical issues of grinding wheel conditions
monitoring is on-line industrial application. Unfortu-
nately, such kind of efforts is rarely seen in papers
2 Experimental setup and procedure
reviewed above.
3. As to signal processing methods using wavelet analysis,
2.1 Experimental setup
the wavelet base is generally selected arbitrarily without
any explanation. Only Jemielniak and Kossakowska
The grinding tests were performed on an ABA Grinding
[14] compared features extracted using 22 wavelets
Technology Z&B Multiline series surface grinder using a
and their sensitivity on tool wear conditions based on
white fused alumina wheel (WA60LmV) to grind carbon steel
AE sensors, and the optimal wavelet was selected
materials (ASTM 1045). The workpiece has a dimension of
because it yielded the best results after comparison
300 mm in length and 50 mm in width. The maximum grind-
with other wavelet bases.
ing wheel speed could reach 30 m/s. An oil-based coolant was
This study focuses on the development of grinding wheel sprayed onto the workpiece during grinding.
wear monitoring system based on discrete wavelet decom- The grinding process was monitored by an acoustic
position and support vector machine, in order to make an emission sensor (SOUNDWEL SR150C) mounted on the
important step towards the on-line industrial applications. In side face of the worktable through magnetic force. Its working
the next section, grinding experiment setup and AE signals frequency was 60400 kHz and the AE signal was collected at
acquisition system are presented. Section 3 introduces the 1 MHz sampling rate using a PC-based data acquisition card
preprocessing methods as well as discrete wavelet decom- (ADLINK DAQ-2010). A schematic diagram of the
position algorithm used to analyze AE signals and extract experimental setup is shown in Fig. 2.
features. In Section 3, a contact detection method is pro-
posed for signal preprocessing to extract signals when 2.2 Experimental procedure
grinding is actually performed, which should be considered
in on-line industrial applications. The optimal wavelet is A white fused alumina-based vitrified bonded grinding
selected to avoid arbitrary selection, after analyzing wavelet wheel with 100 mm in width was used in this study. The

Table 1 Summary of grinding wheel condition monitoring and related solutions

Referance Sensor(s) Signal analysis Features Classification Test results

algorithm

Lezanski [5] AE, forces, and Power spectrum 8 features Neuro-fuzzy 83.3%
vibration and time domain
Liao et al.[6] AE Wavelet analysis Wavelet energy HMM-based clustering 100% (high MRR),
methods 75% (low MRR)
Liao et al.[7] AE Wavelet analysis Wavelet energy Adaptive genetic 97% (high MRR),
clustering algorithm 86.7% (low MRR)
Liao et al.[8] AE AR modeling AR order Boosted classifiers 91.9%
Liao [9] AE AR modeling and AR order and NM, KNN, FKNN, 92.19% (wavelet features),
Wavelet analysis wavelet energy CBNN and KMNP 94.125% (AR coefficient)
Subrahmanya and AE, Power and Time domain and AE: 7 features, LOO error, LS-SVM 97.42%
Shin [11] accelerometer frequency domain Accelerometer and
powermeter:
8 features
110 Int J Adv Manuf Technol (2012) 62:107121

Fig. 1 Overall structure of the grinding wheel wear monitoring system

wheel was trued into 500 mm in diameter right before the generated during the spark-in and spark-out stages were
experiment. Then, dressing process was performed using a collected as well. So each signal contains both idle running
table dresser (ABA TAG) magnetically held on the workta- (before wheel/workpiece contact) and grinding period (after
ble. A carbon steel specimen was grinded several times prior wheel/workpiece contact) signals, with duration of about
to the data acquisition to stabilize the grinding wheel. Then 4 s. However, only signal segment during grinding is useful
the monitoring system was turned on to collect signals in the for us. The proposed signal processing and feature
steady state. After that, AE signals were collected when the extraction methodology have the following steps: sig-
grinding wheel reached a worn state. Whether the wheel was nal preprocessing, discrete wavelet decomposition and
worn or not was determined based on the grinding sounds feature extraction. More details are described in the
and sparks with the operators experience. More grinding following subsections.
cycles were performed to make sure the wheel is completely
worn out.
3.1 Preprocessing
Note that the grinding wheel is two times wider than the
workpiece. In order to make full use of the wheel and avoid
There are three purposes in signal preprocessing step: to
localized wheel wear, the grinding process involved having
extract signals during which grinding was actually performed,
a wheel advance along the width direction, while the work-
segment signals into proper length, and filter noise signals
piece moved in the orthogonal direction simultaneously to
generated by coolant and other sources. A novel approach was
make the grinding wheel fully contact with the workpiece
proposed to extract contact signals during grinding period and
during one grinding cycle. Table 2 shows two sets of grind-
eliminate signals in idle running.
ing parameters.
Webster et al. [15] suggested that there were two stages
during wheel and workpiece contact, designated as the grit
contact and wheel contact. Grit contact means that few
3 Signal processing and feature extraction higher grits are engaging the grinding, while wheel contact
indicates that the whole wheel is in contact with the work-
The sampling rate of AE signals was 1 MHz, which was piece continuously rather than intermittently. Traditional
relatively high for continuous collection. In this experiment, methods predominately use AERMS signal as an indicator
in order to capture the full grinding process, signals of wheel and workpiece contact. However, Webster et al.

Fig. 2 Experimental setup

Int J Adv Manuf Technol (2012) 62:107121 111

Table 2 Grinding parameters forecast chatter in boring operation. Chatter and wheel/
Level Depth of Grinding Feed velocity Workpiece workpiece contact are similar to some extent because both
cut (m) velocity (m/s) (mm/min) Material of them generate a sudden change when the two phenomena
took place. In this study, after wavelet transform of raw AE
1 10 20 24 ASTM 1045 signals, the energy of decomposition level 2 was calculated
2 20 20 24 ASTM 1045 using time constant of 0.5 ms.
It was found that the energy signals of the idle running
period were close to zero, while the grinding period signals
[15] pointed out that AERMS signals in grit contact stage increased significantly. Therefore, energy signals were
were too weak and the burst AE signals generated by grit selected as the criterion to extract grinding period signals.
cutting could be easily confused with other noises. In this Results are shown in Fig. 5.
paper, a wheel and workpiece contact detection method Three conclusions could be drawn from the Fig. 5: (1)
through discrete wavelet decomposition of AE raw signals energy of the idle running period signals was close to zero;
was proposed to extract signals when grinding was actually (2) energy increased significantly after the wheel engaging
performed. The process of discrete wavelet decomposition the workpiece and (3) there was a time advantage of energy
is described in Section 3.2. Raw AE signals containing idle signal compared with raw AE signal. Thus, energy
running signal segment and grinding signal segment are value prior to contact was selected as reference datum,
shown in Fig. 3. which could be obtained when the wheel and workpiece
It is noticed that AE signal amplitude rises notably as were not in contact. A threshold was set as 10 dB of
soon as the wheel and workpiece make contact. However, the reference datum. Signals lower than the threshold
there are distinguished fluctuations prior to the contact, was set as zero and discarded. Signals obtained using this
which could be generated by coolants sprayed onto the method were believed to be generated in grinding period,
workpiece during grinding. Misjudgment might occur if which are shown in Fig. 6.
contaminated signals were used directly to forecast wheel After extracting grinding signals from the raw data, it was
and workpiece contact. Therefore, a denoising method found that the data length of each grinding period was still
based on discrete wavelet decomposition was used to very large (nearly 500,000 samples). Redundant amount of
eliminate the fluctuations. information could increase the processing time and it was
Daubechies wavelet family is compactly supported and not necessarily needed. In order to shorten the calculation
orthogonal with maximum regularity, which is preferable to time and retain adequate amount of information, AE signal
detect abrupt signals. After four-level decomposition and was segmented into ten adjacent parts so there were 50,000
single-level reconstruction using wavelet db5, the original data points in each segment.
signal and the decomposition levels 1, 2, 3 and 4 are shown The raw AE signals contain grinding information as well
in Fig. 4. It was observed that fluctuations during idle as noises. Most of the proposed wheel wear monitoring
running period declined dramatically in decomposition level systems were performed without coolant. It was not quite
2. Therefore, the decomposition level 2 was then extracted in accord with actual conditions. Coolant brings more noises
for further analysis. and uncertainties than dry grinding. In this paper, it was
Yao et al. [16] suggested that the standard deviation and found that useful grinding AE signals for wear detection
energy of proper wavelet decomposition could be used to were contaminated at lower frequencies when the grinding

Fig. 3 Raw AE signal

112 Int J Adv Manuf Technol (2012) 62:107121

Fig. 4 Discrete wavelet decomposition results of raw AE signals

was accompanied with coolants. Fast Fourier Transform was relatively weak. Besides, the amplitude is smaller than
performed on signals during idle running and grinding grinding signals. On the contrary, frequency spectrums of
period. The results are shown in Fig. 7. It is noticed that grinding period signals higher than 90 kHz are distinct and
the frequency spectrums of idle running period signals visible. Meanwhile, frequency at 30 kHz increases signifi-
mainly concentrate at frequency domains lower than cantly compared with idle running signals. Therefore, an
90 kHz. Frequency spectrums higher than 90 kHz are infinite impulse response (IIR) Butterworth high-pass filter
Int J Adv Manuf Technol (2012) 62:107121 113

Fig. 5 Energy of decomposition level 2 and raw AE signal in time domain: a a full view; b a zoom view of the non-grinding section; c a zoom view
of the onset section; and d a zoom view of the ending section

with cut-off frequency of 30 kHz was designed. Considering wheel condition monitoring researches. Features commonly
that AE signals contain more valuable information in higher used in time domain were signal amplitude, root mean
frequency domain, 90 kHz was finally used as cut-off square, mean value, standard deviation [5], skewness and
frequency and it performed better than 30 kHz in the kurtosis [11], etc. For AE signals in particular, Jemielniak
subsequent classification process. and Kossakowska [14] used features such as AE event, ring-
Details of the performance using different cut-off frequen- down count and AE signal duration in AE-based monitoring
cies, i.e. signals high-pass filtered at cut-off frequency of system. Although time domain approaches have advantages
30 kHz and signals high-pass filtered at cut-off frequencies of time-saving and convenience in calculation, lots of valuable
of 90 kHz were presented in Section 6.1. information is omitted. As a matter of fact, time domain
So far, the preprocessing procedure was accomplished methods are mostly used in real-time circumstances.
and the each filtered AE signal was processed in the subse- Among various approaches that have been taken to ana-
quent section for further analysis. lyze acoustic emission signals, Fourier transform method
has been considered as an effective approach for grinding
3.2 Feature extraction based on wavelet wheel wear monitoring. In the traditional Fourier transform,
the frequency is defined for the sine or cosine function
Conventional signal processing methodologies are generally spanning the whole data length. Therefore, the disadvantage
carried out in time domain, frequency domain or both. Time of Fourier transform is that it is impossible to have a good
domain approaches have been employed in earlier grinding resolution both in time domain and in frequency domain.
114 Int J Adv Manuf Technol (2012) 62:107121

Fig. 6 Contact signals: a a full view; b a zoom view of the onset section; and c a zoom view of the ending section

That is why Fourier transform is unsuitable for identifying time-frequency resolution of the continuous wavelet
non-stationary transient information. Time-frequency anal- transform (CWT) depends on the frequency of the sig-
ysis is the most popular method for non-stationary signals, nal. The quality factor of CWT is constant in the time-
such as the short-time Fourier transform (STFT). The STFT frequency plane. CWT is an effective tool for signal
could provide time-frequency representations for the signal analysis. However, it involves much redundant informa-
by successively sliding the window along the time axis. tion and is computationally slow. In discrete wavelet
However, since the STFT relies on the traditional Fourier transform (DWT), the wavelets are discretely sampled,
analysis, the signals should be piecewise stationary. On the and signals can be separated into several approximation
other hand, the problem with STFT is that the window for the signals and detail signals. It is less time-consuming
analysis of the entire signal could not change. Therefore, compared with the CWT. Three levels DWT decomposi-
STFT provides a constant resolution for all frequencies. It is tion tree of a signal with frequency range 0 to fn is shown in
still impossible to have good resolutions in time as well as Fig. 8.
frequency at the same time. Wavelet transform was proposed
to overcome these drawbacks. Wavelet transform allows long
time intervals with more precise low frequency information 3.2.2 Extraction of wavelet coefficient features
and shorter regions with high frequency information. Due to
this advantage, wavelet transform was widely used in signal There are various wavelet base functions available. Teti
processing in the past decade and it is still a stimulating et al. [17] pointed out that in most process monitoring
approach nowadays. The basics of discrete wavelet transforms studies, the type of wavelet was arbitrarily selected without
are briefly presented and the use of discrete wavelet transform any explanation. Different base functions have different
to extract feature is described in the next subsection. properties, such as order of approximation, vanishing
moments, orthogonality, and compact support. The result
3.2.1 Discrete wavelet transform of wavelet transform strongly depends on the type of the
wavelet base, which makes it critical to choose a proper
Wavelet transform allows one to unfold a signal into wavelet base to match the signal to be analyzed for wavelet
both space and scale. Compared with the STFT, the transform applications. There are several factors which
Int J Adv Manuf Technol (2012) 62:107121 115

Fig. 7 The frequency spectrum of: a idle running and b grinding period

should be considered in choosing the wavelet basic (3) Shape. The wavelet base should reflect the type of
function. features present in the time series. To analyze an im-
pulse signal, base wavelet with similar shape should be
(1) Orthogonality. In orthogonal wavelet analysis, the
employed to perfectly extract the components of the
number of convolutions at each scale is proportional
signal. For example, Singh and Tiwari [19] selected the
to the width of the wavelet base at that scale [18].
optimal wavelet to analyze electrocardiogram (ECG)
Orthogonal wavelet could reduce the redundant infor-
signal by choosing the maximum cross correlation
mation and improve calculation speed.
coefficient between ECG signal and the wavelet filter.
(2) Compact support. Most compactly supported wavelets
are designed to have a rapid fall-off so that they can be Other properties such as symmetry, regularity and van-
considered as band-limited. Compactly supported ishing moments are also important while choosing wavelet
wavelet could reduce computation complexity and bases. In this study, the coif2 wavelet with level of 5 was
have better time resolution. chosen for its orthogonality, compactly supported and its

Fig. 8 Three level DWT

decomposition
116 Int J Adv Manuf Technol (2012) 62:107121

similarity to the shape of acoustic emission signals. Consid- cutting depths and set as inputs for the SVM classification
ering that coif2 is not the only wavelet base which possesses system in the next section.
these properties, performance comparisons of different
wavelet bases were presented in the Section 6.2. Teti et al.
[17] showed that wavelet transform coefficients were 4 Support vector machine for classification
usually treated as separate signals, each characterized
by features used for time domain signals. In this paper, SVM is based on statistical learning theory. Conventional
after five-level decomposition on each AE signal seg- classification method and artificial neural network (ANN)
ment, features of the root mean square and variance of are studied that the sufficient samples are available, which is
each separate coefficient were calculated as they repre- difficult to obtain in practice. SVM based on statistical
sented signals effective value and fluctuations. As a learning theory has better generalization than ANN for a
result, for each decomposition coefficient, feature vector smaller number of samples. The VapnikChervonenkis
of SFRMS is obtained and defined as theory (VC theory) and structural risk minimization
s guarantee the local and global optimal solution are
1 X nd
exactly the same, and disadvantages like over-fitting
SFRMS ns ; nc coef 2 i; nc 1
nd i1 problem and poor generalization in small samples which
are commonly seen in neural network and other machine
in which ns is the specimen size, and nd indicates the length
learning theories have been overcome in SVM approach.
of each decomposition coefficient, while coef is the decom-
Besides, SVM is good at two-class tasks. It is proved to be
position coefficient matrix of ns rows and nc columns. nc is
an effective tool for classification, regression and function
given by
estimation and it is widely used in the field of data-driven
nc n 1 2 modeling. In fact, Burges [20] showed that SVM performed
well when finite samples were available and it had been
successfully implemented in many fields including hand-
where n is the decomposition level. Feature vector of SFVAR
written digit recognition, object recognition, speaker identi-
is defined as
fication, text categorization and other pattern recognition
1 X nd cases as well as regression estimation cases.
SFVAR ns ; nc coef i; nc  nc 2 3 In this study, due to the fact that sufficient grinding wheel
nd i1
wear samples are not always available in practice, as well as
in which is the mean value matrix of nc columns. Table 3, it has high accuracy and good generalization for a smaller
4, 5, and 6 show SF1 and SF2 values of a specified segment number of samples, SVM algorithm was used to predict
with cut depths of 10 and 20 m. grinding wheel wear. A radial basis function (RBF) kernel
It can be observed that except several outliers at decom- was selected for its good performance, which was necessary
position level d1, d2, d3, and d4, SFRMS and SFVAR values to map the original finite-dimensional space into a much
of worn wheel conditions are generally higher than sharp higher-dimensional space. In standard SVM, the penalty
conditions in each decomposition coefficient. Therefore, parameter and kernel function parameter of RBF kernel
feature vector is constructed by [SFRMS, SFVAR] under two were arbitrarily selected, or selected by trial-and-error

Table 3 SFRMS values extracted

by five-level coif2 wavelet, No. States d1 d2 d3 d4 d5 a5
depth of cut010 m
1 Sharp 0.0306 0.1402 0.1668 0.0485 0.0178 0.0561
2 Sharp 0.0366 0.1611 0.1676 0.0445 0.0163 0.0098
3 Sharp 0.0285 0.1251 0.1378 0.0373 0.0138 0.0166
4 Sharp 0.0361 0.1450 0.1503 0.0416 0.0149 0.0104
5 Worn 0.0588 0.2728 0.3008 0.0871 0.0310 0.0686
6 Worn 0.0384 0.1932 0.2334 0.0676 0.0250 0.0294
7 Worn 0.0532 0.2392 0.2549 0.0746 0.0259 0.0287
8 Worn 0.0476 0.2126 0.2348 0.0575 0.0253 0.0500
9 Worn 0.0568 0.2215 0.2247 0.0591 0.0227 0.0293
10 Worn 0.0396 0.1868 0.2054 0.0512 0.0206 0.0104
11 Worn 0.0467 0.2049 0.2051 0.0504 0.0194 0.0162
Int J Adv Manuf Technol (2012) 62:107121 117

Table 4 SFVAR values extracted

by five-level coif2 wavelet, No. States d1(104) d2(102) d3(102) d4(103) d5(104) a5(105)
depth of cut010 m
1 Sharp 9.3396 1.9664 2.7812 2.3490 3.1738 312.91
2 Sharp 1.3362 2.5963 2.8089 1.9796 2.6583 9.5469
3 Sharp 8.1455 1.5662 1.9001 1.3927 1.8974 27.436
4 Sharp 13.057 2.1019 2.2591 1.7345 2.2259 10.810
5 Worn 34.565 7.4449 9.0466 7.5922 9.6167 469.13
6 Worn 14.763 3.7338 5.4451 4.5674 6.2529 85.612
7 Worn 28.337 5.7229 6.4990 5.5699 6.6841 82.162
8 Worn 22.684 4.5200 5.5120 3.3066 6.3783 250.17
9 Worn 32.219 4.9047 5.0480 3.4945 5.1704 85.249
10 Worn 15.667 3.4909 4.2174 2.6207 4.2316 10.910
11 Worn 21.848 4.1986 4.2065 2.5404 3.7603 26.073

method, which made it hard to get the satisfied classification Chang and Lin [21]. Result of the GA-SVM classification
results. Therefore, we introduced genetic algorithm (GA) to is presented in the next section. The comparison between
select the optimal parameters automatically. The classifica- GA-SVM and BP neural network was discussed in
tion accuracy was designated as fitness function in GA, and Section 6.3.
then the optimal penalty parameter and kernel function
parameter would be obtained when they yielded the best
classification accuracy. The population size was set as 100 5 Results
and the maximum number of generations was set as 25.
The states of grinding wheel are classified into two Two sets of feature vectors extracted from AE signals using
categories: sharp and worn, which were designated as the the previous methods were input in the SVM classification
output of our pattern recognition system. The output result system. The first feature vector had 40 records of sharp
of 1 represents that the wheel is sharp and 1 means the conditions and 70 records of worn conditions with the cut
wheel is worn. Feature vector [SFRMS, SFVAR] of each depth of 10 m, while the other set had 80 records of sharp
signal segments under two cutting depths was scaled to the conditions and 20 records of worn conditions with the cut
range of [0, 1] using equation: depth of 20 m. Half records of each feature vector were
x  xmin taken out for training and the other half for testing.
x!y 2 0; 1 4 Each classification was repeated for five times and the
xmax  xmin
mean value was obtained. Table 7 shows the classification
where x is the original value, and xmin, xmax are the mini- results under the two cutting conditions. The classification
mum and maximum values in the feature vector. The scaled accuracy was 100% under the cutting depth of 20 m. With
feature vector was then input into the SVM classification the cutting depth of 10 m, the accuracy is a little lower,
system using a Matlab SVM toolbox modified based on which was 99.39%. The classification results indicate that

Table 5 SFRMS values extracted

by five-level coif2 wavelet, No. States d1 d2 d3 d4 d5 a5
depth of cut020 m
1 Sharp 0.0450 0.2081 0.2597 0.0760 0.0279 0.0666
2 Sharp 0.0529 0.2266 0.2600 0.0681 0.0260 0.0066
3 Sharp 0.0520 0.2486 0.3050 0.0887 0.0289 0.0445
4 Sharp 0.0753 0.3139 0.3564 0.0950 0.0356 0.0681
5 Sharp 0.0495 0.2388 0.2782 0.0758 0.0283 0.0280
6 Sharp 0.0698 0.3021 0.3333 0.0955 0.0341 0.0324
7 Sharp 0.0564 0.2463 0.2599 0.0649 0.0250 0.0248
8 Sharp 0.0764 0.3157 0.2921 0.0748 0.0274 0.0248
9 Worn 0.0959 0.4252 0.4937 0.1435 0.0519 0.1148
10 Worn 0.1123 0.4829 0.5583 0.1447 0.0536 0.0598
118 Int J Adv Manuf Technol (2012) 62:107121

Table 6 SFVAR values extracted

by five-level coif2 wavelet, No. States d1(103) d2(102) d3(102) d4(103) d5(104) a5(105)
depth of cut020 m
1 Sharp 2.0270 4.3297 6.7423 5.7708 7.7765 443.59
2 Sharp 2.8030 5.1340 6.7606 4.6391 6.7662 4.3223
3 Sharp 2.7039 6.1811 9.3026 7.8762 8.2666 197.38
4 Sharp 5.6678 9.8526 12.701 9.0347 12.663 463.03
5 Worn 2.4495 5.7044 7.7383 5.7524 8.0022 78.228
6 Worn 4.8713 9.1244 11.107 9.1254 11.661 103.98
7 Worn 3.1834 6.0691 6.7573 4.2186 6.2564 61.345
8 Worn 5.8368 9.9652 8.5284 5.5959 7.5272 60.979
9 Worn 9.2066 18.079 24.372 20.612 26.854 1311.7
10 Worn 12.617 23.318 31.159 20.949 28.697 356.16

the grinding wheel wear monitoring system performs quite Apparently, both cutting conditions reveal better classifica-
well on wheel wear prediction. tion results with cut-off frequency of 90 kHz.
The results show that the signals filtered out in higher
frequency should contain more information about the wheel
6 Discussion wear. As can be seen in Fig. 7, power in both the idle
running and grinding period signals is mainly concentrated
There are several parameters that could affect the per- at lower frequencies, which could submerge the useful
formance of the proposed grinding wheel wear monitor- wheel wear information at higher frequencies. If, therefore,
ing system. Related to high-pass filter in preprocessing the AE signals are high-pass filtered out at cut-off frequency
procedure is the cut-off frequency. Butterworth high- of 30 kHz, the results are poorer, since the part of the wheel
pass filter with cut-off frequency of 90 kHz was used. wear information stored in the high frequencies are sub-
With respect to the discrete wavelet decomposition pro- merged by lower frequencies.
cedure are the wavelet base and decomposition level. It has to be mentioned that cut-off frequency of 90 kHz is
Coif2 wavelet with decomposition level of 5 was select- not always the best for all wheel wear monitoring. As can be
ed. Performance of BP neural network and its compar- seen in Fig. 7, there is no apparent change at 90 kHz. The
ison with the proposed method were also discussed. cut-off frequency was employed since it performed much
better than lower frequencies. Moreover, the optimal cut-off
6.1 Performance under different cut-off frequencies frequency should be different at various cutting conditions.
The results indicate that it is better to extract wheel wear
As mentioned in Section 3.1, frequencies of idle running information from the high frequencies than the low frequen-
signals are generally lower than 90 kHz. Meanwhile, it is cies since useful information seemed to be submerged by
noticed that grinding signals frequency at 30 kHz increases noises at low frequencies.
significantly compared with idle running. An IIR Butter-
worth high-pass filter with cut-off frequency of 30 kHz was 6.2 Influence using different base wavelets
designed. Butterworth rather than Chebyshev filter was
employed as it yielded better results in further classification. The coif2 wavelet with level of 5 was employed in Section 3
Performance using different cut-off frequencies, i.e., signals for its orthogonality, compactly supported and its similarity
high-pass filtered at cut-off frequency of 30 kHz and signals to the shape of acoustic emission signals. However, as noted
high-pass filtered at cut-off frequencies of 90 kHz was earlier, coif2 is not the only wavelet compliant with the
compared and the classification result is shown in Table 8. above mentioned requirements. To evaluate the influence

Table 7 Classification results

Depth of cut is 10 m Depth of cut is 20 m

States Prediction Target amount Result States Prediction Target amount Result
amount amount
Sharp 19 20 99.39% Sharp 40 40 100%
Worn 35 35 Worn 10 10
Int J Adv Manuf Technol (2012) 62:107121 119

Table 8 Classification results using different cut-off frequencies

Depth of cut is 10 m Depth of cut is 20 m

States Prediction amount Target amount Result States Prediction amount Target amount Result
30 kHz 90 kHz 30 kHz 90 kHz
Sharp 19 20 92.73% 99.39% Sharp 40 40 98% 100%
Worn 35 35 Worn 10 10

of different base wavelets and decomposition levels, we e.g., the standard SVM, BP neural network. It is noticed that
compared the classification results using db1, db2, db3, Lezanski [5] and Salgado et al. [22] used neural network
coif1, coif2, coif3, sym2, sym3, and sym4. The decompo- related methods for grinding wheel wear monitoring, and
sition levels are varied from 2 to 12. Each classification the results are quite encouraging. Hence, in this study, we
process was repeated three times and the mean value was constructed a wheel monitoring system using the popular
computed. Fig. 9 shows the results with the cut depth of BP neural network, as a comparison with the proposed GA
10 m. It indicates that the classification accuracy is affect- based SVM method.
ed to some extent, but not very seriously. Coif3 at level 6, The same input data sets as for the support vector
coif1 at level 6, db3 at level 7 and sym3 at level 7 perform machine system has been used in the neural network system.
not as well as others, but still higher than 90%. coif2, db1, The input data was scaled to the range of [0, 1] using Eq. 4
db2, sym1, and sym2 maintain high classification accuracy and divided into two setsa training set and a testing set.
at different levels, which could be used as the optimal The goal of training is to optimize the network connection
wavelet bases. There are no obvious changes with the cut weights and minimize the difference between the outputs
depth of 20 m. Classification accuracy of 100% can be generated by the trained network and the outputs from the
obtained using different base wavelets, except coif2 at level testing set. The inputs and outputs of the network have been
4, coif3 at levels higher than 6 and db1 at levels higher than determined yet, so the number of hidden layers and the
8. The worst result of coif3 and db1 is 96%. number of nodes in hidden layers have to be selected and
Although several reports showed that the result of wavelet optimized. It has been proved that the three-layer network
transform strongly depends on the type of the wavelet bases, with sufficient number of nodes is able to model any math-
results presented in our study indicate that the relationship is ematical function [23], and it was also found out that there
to some extent, not very serious. We attribute this to the signal was no improvement given by having two hidden layers in
preprocessing, to be more precise, the high-pass filtering the network [22], so the hidden layer is limited to one.
process, in which noises were eliminated and useful informa- The number of nodes in the hidden layer is decided using
tion concerning wheel wear was extracted. weight pruning method [5]. The initial weights and the
number of nodes are determined randomly and training is
6.3 Comparison with BP neural network continued until a satisfied level of the RMS error is reached.
Then, the number of nodes can be optimized by elimination
Before we employ support vector machine for classification, of nodes whose absolute value of output weight is smaller
several other popular classification methods were considered, than a certain percent of weights with the smallest value.

Fig. 9 Classification accuracy at different decomposition levels using: a coif1, coif2, coif3, b db1, db2, db3, c sym1, sym2 and sym3 with the cut
depth of 10 m
120 Int J Adv Manuf Technol (2012) 62:107121

The initial network structure was set as 12202. After only under the specific conditions. Since industrial applica-
pruning, the number of nodes in the hidden layer was tions are much more complicated, further improvement
reduced to 4 and the classification results under the two should be carried out in more complicated grinding condi-
cutting conditions were obtained. The classification accura- tions. Developing a more robust and universal on-line wheel
cy was 96% under the cutting depth of 20 m, while wear monitoring system will be part of our future effort.
however, the accuracy is a much lower at the cutting depth
of 10 m, which drops to 90.91%.
Acknowledgments This study has been made possible with the sup-
There might be two reasons to explain the results. First, ports from National Natural Science Foundation of China (Grant Nos.
as discussed by Silva [24], the cutting condition interval is 71071138 and No. 50835008).
too narrow, and the neural network could hardly classify
tool wear under such condition. On the other hand, the
training samples are not sufficient enough to obtain the
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