TOOL WEAR PREDICTION BASED ON WAVELET
TRANSFORM AND SUPPORT VECTOR MACHINES
Dongfeng Shi
1
and Nabil N. Gindy
2
1
Optimized Systems and Solutions, Rolls-Royce Group, Derby, U.K.
2
School of Mechanical, Materials and Manufacturing Engineering
The University of Nottingham, NG7 2RD Nottingham, U.K.
Keywords: Support Vector Machine, Wavelet Transform, Machining Process Monitoring.
Abstract: The machining quality and efficiency may be improved significantly by using appropriate tool wear
prediction techniques. A new approach based on wavelet transform and support vector machine is proposed
to improve the accuracy of tool wear prediction in this paper. Firstly, the wavelet transform is introduced to
decompose sensory signals into different scales to reduce the dimensionality of original signals and extract
features associated with different tool wear condition. Secondly, the least square support vector machine is
further presented to construct predictive model due to its high convergence rate and powerful generalization
ability. Thirdly, the possibility to employ power sensor rather than delicate dynamometer for the tool wear
monitoring is explored. Finally, the effectiveness of proposed tool wear prediction approach is demonstrated
by extensive experimental turning trials.
1 INTRODUCTION
Tool wear will progress with the proceeding of the
machining process due to the involvement of
fracturing, abrasion, plastic deformation, diffusion
and grain-pullout. The dimensional accuracy and
surface quality of machined component may be
deteriorated by excessive worn tool. Consequently,
the online tool wear monitoring is required within
aero-engine manufacturing industry to improve the
machining quality of critical components made of
Titanium or Nickel alloys. Due to high corrosion
resistance associated with those super alloys, the
wear of machining tool deteriorates rapidly. Through
the utilization of tool wear prediction technique, the
worn tool can be detected and replaced in time to
avoid scrapping critical components. Moreover,
common industrial practice by replacing or
regrinding tools according to a conservative
schedule is not cost-effective. By implementation of
tool wear prediction technique, the tooling cost may
be reduced and tool life may be prolonged
significantly.
Several indirect tool wear predictive approaches
have been investigated by modelling the correlation
between tool wear and sensory signals, namely
force, vibration and acoustic emission, acquired in
machining processes (Sick, 2002). However, further
efforts are still required in the following aspects
despite the fact that several achievements have been
made in tool wear prediction so far. Firstly, although
several different types of sensor, e.g. accelerometer,
dynamometer, acoustic emission and motor current
sensor have been employed to measure the responses
in machining processes, the overall performance of
these sensors in terms of accuracy, robustness and
cost-effectiveness is still not satisfaction. In general,
the cutting force acquired from dynamometers is
regarded as one of significant variables in the
machining processes due to its direct relation with
tool wear. However, the implementation of
dynamometers in shop floor is restricted due to high
cost, negative impact on machining system rigidity,
the requirement for a wiring harness and extra space
for installation (Shi et al., 2006). Recently, indirect
sensing cutting force through the feed or spindle
motor current of a machining tool has been
investigated extensively due to the ease of
installation and low cost (Stein and Wang, 1990,
Altintas, 1992, Lee et al., 1995). However, this
indirect approach has been reported not sensitive and
accurate enough to measure the cutting force in
machining process due to limited frequency range
479
Shi D. and N. Gindy N..
TOOL WEAR PREDICTION BASED ON WAVELET TRANSFORM AND SUPPORT VECTOR MACHINES.
DOI: 10.5220/0003647304790485
In Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics (MSIE-2011), pages 479-485
ISBN: 978-989-8425-75-1
Copyright
c
 2011 SCITEPRESS (Science and Technology Publications, Lda.)

(Altintas, 1992). As a result, for the purpose of
implementation of tool wear monitoring system in
industrial environment, alternative sensing solutions
have to be investigated to strike the balance between
effectiveness and cost. Secondly, feature extraction
plays crucial role in the improvement of accuracy
and robustness of tool wear predictive model since
the original sensory signals usually are interfered
with noise, disturbance and redundant information.
Normally, statistical moments based features, i.e.
mean value, standard deviation, extracted from
sensory signal have been always employed to predict
tool wear. However, this feature extraction
technique is not effective enough to explore the
instinct features associated with tool wear.
Consequently, a more advanced feature extraction
technique is required to filter out the noise
component and reduce the dimensionality of the
original data to improve prediction accuracy.
Finally, neural network has been extensively used to
model the correlation between sensory signals and
tool wear. However, the prediction results were not
satisfied due to some disadvantages, i.e. low
convergence rate, obvious ‘over-fitting’ and
especially poor generalization when few samples are
available. Support Vector Machines (SVM) based on
statistical learning theory is a new achievement in
the field of data-driven modelling and implemented
successfully in classification, regression and
function estimation (Kwok, 1999, Cao and Tay,
2003, Goethals and Pelckmans, 2005). SVM has
been proved less vulnerable to overfitting problem
and higher generalization ability since SVM is
designed to minimize structural risk whereas
previous neural networks techniques, i.e. MLP, are
usually based on minimization of empirical risk
(Kwok, 1999). Consequently, the applicability of
SVM in the tool wear modeling will be explored in
this paper.
The objective of this paper is to develop a new
monitoring approach to predict tool wear using
sensory signals acquired in machining processes.
The organization of the work is as follows. In
Section 2, wavelet transform is explored to extract
features from sensory signals. The SVM is further
introduced to model the correlation between tool
wear and extracted features in Section 3. The
performance of proposed approach is demonstrated
by experimental data acquired from turning
processes in Section 4. The conclusions are given in
last Section.
2 WAVELET TRANSFORM
BASED FEATURE
EXTRACTION
The sensory signals acquired in machining process
are typical non-stationary multi-componential
signals caused by uneven material removing process.
Different tool malfunctions, i.e. tool wear, tool
chipping and tool breakage, may possess different
frequency characteristics in sensory signals. For
instance, the cutting force will increase gradually
with the increase of tool wear and will be obviously
reflected in the lower frequency band or so-called
static component of sensory signals. On the contrary,
tool chipping or breakage will cause cutting force
changed suddenly and may be observed in higher
frequency band or so-called dynamic component of
sensory signals. As a result, the features associated
with different tool malfunctions may be extracted
from either static or dynamic component of sensory
signals. Several techniques, i.e. band-pass filtering,
resample and wavelet transform, may be employed
to decompose sensory signals. From the point of
view of filter design, wavelet transform is a typical
cascade band-pass filter with a varying bandwidth.
The sensory signals can be decomposed into
different frequency bands or scales to capture
localized features i.e. abrupt or gradual changes
within the sensory signals by analysis corresponding
wavelet coefficients. Wavelet transform provides an
efficient way to identify the location and possible
root cause of the malfunction within the machining
processes because of powerful decomposition
ability. Additionally, by implementation wavelet
transform at specified scale, the sensory signal can
be descried as few wavelet coefficients and the
dimensionality of sensory signals can be
dramatically reduced. Hence, in comparison with
other two decomposition techniques, wavelet
transform is more powerful and flexible due to its
multi-resolution capability and hence explored to
obtain static component for feature extractions. The
wavelet transform of signal s(t) is defined as the
inner product in the Hilbert space of L2 norm as
follows (Mallat, 1997):
1/2
*
,
(,) () ()
ab
Cab a st tdt ψ
+∞
−
−∞
=
∫
(1)
where
)(
*
,
t
ba
ψ
is the complex conjugate of
)(
,
t
ba
ψ
generated by scaling and shifting from so-called a
‘mother wavelet’ function expressed as
1/ 2
,
() ( )
ab
tb
ta
a
ψψ
−
−
=
(2)
ICINCO 2011 - 8th International Conference on Informatics in Control, Automation and Robotics
480

where a is a scale factor and b is a translation or
time shift parameter. The factor
2/1−
a
is used to
ensure energy preservation. A family of scaled and
shifted wavelets can be produced through varying
the parameters a and b. Therefore, the time-scale
characteristics of the signal s(t) can be analyzed by
the inner product to the series of scaled and shifted
wavelets. In order to obtain the numerical result of
wavelet transform, the parameter of scale a and shift
b must be discretized. Discrete wavelet transform
normally is conducted by dyadic discretization,
a=2
j
, b=k2
j
, (i, j)
∈
Z
2
. Additionally, regarding the
possibility of time-frequency localization, the
mother wavelet must be compactly supported and
satisfied with the admissibility condition:
2
() /Cd ωωω
+∞
Ψ
−∞
=Ψ <∞
∫
(3)
where
)(
ω
Ψ
is the Fourier transform of
)(t
ψ
.
Then, the discrete synthesis of wavelet transform is
expressed as
,
() ( , ) ()
jk
jZkZ
s
tCjkt ψ
∈∈
=
∑∑
(4)
At specified scale J, the discrete synthesis can be
further rewritten as
() () ()
Jj
jJ
s
tAt Dt
≤
=+
∑
(5)
where D
j
(t) is called the detail of the signal s(t) at
scale j and expressed as
()
,
() , ()
jjk
kZ
Dt Cjk t ψ
∈
=
∑
(6)
and A
J
(t) is called an approximation of the signal s(t)
at scale J and expressed as
() ()
Jj
jJ
A
tDt
>
=
∑
(7)
S
cD
1
cA
1
cD
2
cA
2
cD
3
cA
3
.......
Figure 1: Illustration of decomposition tree of wavelet
transform.
As a result, a decomposition tree is formed where
the signal is decomposed to a number of details and
one approximation as shown in Figure 1. The
approximation captures the low frequency content
which corresponds to static component of the signal
and details reflect the high frequency contents which
correspond to dynamic components of the signal. As
described earlier, wavelet transform is a typical set
of cascade band-pass filters with varying bandwidth.
The central frequency and bandwidth of the wavelet-
based cascade filter depends on the choice of scale.
If Daubechies-wavelet, i.e. db5, is selected as a
mother wavelet, the wavelet-based band-pass filter
at scale J will be centred at the quotient between
sampling frequency and 2
J
. In this paper, the
decomposition scale of sensory signals is specified
as J=8 since the highest frequency of static
component of sensory signal (sampled at 1000Hz) is
found less than 4Hz. Additionally, the
dimensionality of sensory signal can be reduced
significantly since the length of the static component
is only 1/2
J
times of the length of original sensory
signal. Hence, the corresponding wavelet
coefficients at specified scale J can be formed as
feature vectors to feed into SVM-based tool wear
predictive model as introduced in Section 3.
3 LS-SVM BASED TOOL WEAR
PREDICTIVE MODEL
SVM is a novel machine-learning tool and especially
useful for the classification and prediction with
small-sample cases (Vapnik, 1999). This novel
approach motivated by statistical learning theory led
to a class of algorithms characterized by the use of
nonlinear kernels, high generalization ability and the
sparseness of the solution. Unlike the classical
neural networks approach the SVM formulation of
the learning problem leads to quadratic
programming (QP) with linear constraint. However,
the size of matrix involved in the QP problem is
directly proportional to the number of training
points. Hence, to reduce the complexity of
optimization processes, a modified version, called
LS-SVM is proposed by taking with equality instead
of inequality constraints to obtain a linear set of
equations instead of a QP problem in the dual space
(Suykens et al., 2002, Suykens and Vandewalle,
1999). Instead of solving a quadratic programming
problem as in SVM, LS-SVM can obtain the
solutions of a set of linear equations. The
formulation of LS-SVM is introduced as follows.
TOOL WEAR PREDICTION BASED ON WAVELET TRANSFORM AND SUPPORT VECTOR MACHINES
481

Consider a given training set
{}
Nk
kk
yx
",1
,
=
with
input data
n
k
x ℜ∈
and output data
ℜ
∈
k
y
. The
following regression model can be constructed by
using nonlinear mapping function
)(⋅
ϕ
bxwxy
T
+= )()( ϕ
(8)
where w is the weight vector and b is the bias term.
By mapping the original input data into a high-
dimensional space, the nonlinear separable problem
becomes linearly separable in space. Then, the
following cost function is formulated in the
framework of empirical risk minimization.
2
1
11
min ( , )
22
N
T
k
k
J
we w w e γ
=
=+
∑
; (9)
subject to equality constraints
() 1,,
T
kkk
y
wx be k N φ =++="
(10)
where e
k
is the random errors and γ is a
regularization parameter in determining the trade-off
between minimizing the training errors and
minimizing the model complexity. To solve this
optimization problem, Lagrange function is
constructed as
1
(,,;) (,) { ( ) }
N
T
kk kk
k
L
wbe J we w x b e y ααφ
=
=− ++−
∑
(11)
where a
k
are Lagrange multipliers. The solution of
Equation (11) can be obtained by partially
differentiating with respect to w, b, e
k
and a
k
1
0()
N
kk
k
L
wx
w
αφ
=
∂
=→ =
∂
∑
(12)
1
00
N
k
k
L
b
α
=
∂
=→ =
∂
∑
(13)
01,
kk
k
L
ek N
e
αγ
∂
=→ = =
∂
"
(14)
0() 0,1,
T
kkk
k
L
wx bey k N
φ
α
∂
=→ ++ − = =
∂
"
(15)
The Equations (12)-(15) can be rewritten as
1
01 0
1
T
b
y
I
α
γ
−
⎡⎤
⎡⎤ ⎡⎤
=
⎢⎥
⎢⎥ ⎢⎥
⎢⎥
⎣⎦ ⎣⎦
Ω+
⎣⎦
G
G
(16)
Where
1
[]
N
y
yy= "
1[11]=
G
"
1
[]
N
α
αα = "
() () , 1
T
kl k l
x
xkl N φφ Ω= =""
Finally, b and a
k
can be obtained by the solution to
the linear system
11
11
1( )
ˆ
1( ) 1
T
n
T
n
Iy
b
I
γ
γ
−−
−−
Ω+
=
Ω+
G
G
G
(17)
11
ˆ
ˆ
()(1)Iyb
αγ
−−
=Ω+ −
G
(18)
According to Mercer’s theorem, the resulting LS-
SVM model can be expressed as:
()
1
() ,
N
kk
k
yx Kxx b α
=
=
+
∑
(19)
where
),(
k
xxK
is the nonlinear kernel function. In
comparison with some other feasible kernel
functions, the RBF function is a more compact
supported kernel and able to reduce computational
complexity of the training process and improve
generalization performance of LS-SVM. As a result,
RBF kernel was selected as kernel function as
2
2
2
( , ) exp( )
kk
Kxx x x σ
−
=−⋅
, (20)
where σ is the scale factor for tuning.
To achieve a high level of performance with LS-
SVM models, some parameters have to be tuned,
including the regularization parameter γ and the
kernel parameter corresponding to the kernel type,
i.e. σ. Finally, the features extracted in Section 2 and
actual tool wear measured by optical scan
microscope can be employed to construct input-
output pairs to train LS-SVM. In the training stage,
the correlation between sensory signals and tool
wear is learned by LS-SVM. Once the training stage
is accomplished, the trained LS-SVM is used to
predict tool wear by using the features extracted
from wavelet transform.
4 EXPERIMENTAL RESULTS
AND DISCUSSIONS
4.1 Experimental Configuration
Two types of sensors, namely, dynamometers
(Kistler 9257B) and power sensor (Load control LC-
PH-3A-10V) are employed to conduct experiments
in turning processes. The possibility of the
utilization of power sensor rather than delicate
dynamometer will be investigated based on critical
analysis of experimental results. The power sensor
was installed with spindle motor to measure the
machining power. The power is estimated by vector
multiplications between current and voltage samples
sensed by Hall-effect sensors. In comparison with
well-known motor current sensor, the power sensor
is more accurate and appropriate to measure power
consuming
in machining process due to the con-
ICINCO 2011 - 8th International Conference on Informatics in Control, Automation and Robotics
482

Figure 2: Schematic diagram of the online turning
monitoring system.
sideration of power factor variation with the
changing load.
National Instruments PXI modules, namely, NI PXI-
1031 chassis, 3.0GHz Pentium 4 Rack-mount PXI
controller and 16-Bit NI PXI-6251 with 16 analog
inputs and 24 digital I/Os, have been specified as the
hardware platform to construct DAQ package.
LabVIEW has been selected as software platform to
develop the whole package due to its powerful
performance in data acquisition, graphical user
interface (GUI) design, and hardware connectivity.
The developed process monitoring software is
capable to acquire, analyze and present the data
simultaneously due to the utilization of multithread
programming techniques i.e. queue technique. For
the purpose of the reduction the manual interference,
data can be automatically stored in specified file and
the name of file can be stamped according to the
starting time of sampling. Moreover, the power
sensory signal has been selected as the triggering
source to conduct self-triggering by using the
impulse generated by the starting of spindle motor.
The corresponding software has been developed to
run in re-triggerable manner to acquire signals
successively without manual interferences. By the
implementation of self-triggering
technique, the acquired signals are started at exact
same moment without the requirement for further
alignment. The whole online machining process
monitoring system is shown schematically in Figure
2.
4.2 Tool Wear Prediction in Turning
Process
A Swedturn 4-axes CNC twin lathe was employed to
manufacture Inconel 718 disc. Ceramic tools were
used in the experimental trials due to the
performance in terms of high melting point,
excellent hardness and wear resistance for the
machining of hard materials. Ceramic insert RCGX
35T-0320 with constant tool edge preparation
(clearance angle 1° and rake angle 13°) and different
tooling conditions were employed to conduct turning
trials. To meet industrial requirements, the Inconel
718 disc with complicated profile as shown in
Figure 3 was specified to manufacture.
40
250 240
75
Figure 3: Geometrical parameter of Inconel 718 disc for
turning.
Additionally, the dynamometer Kistler 9257B and
power sensor Load control LC-PH-3A-10V were
installed to acquire force and power signals
respectively. To demonstrate the effectiveness of
proposed prediction approach based on wavelet
transform and SVM, several turning trials have been
performed to acquire sensory signals under different
tool wear conditions. The tool wear in terms of VB
was measured by optical scan microscope after each
cutting as shown in Figure 4.
Figure 4: Photo of turning tool wear taken by optical scan
microscope.
The original force and power signals acquired from
initial fresh tool toward to excessive tool wear are
shown in Figure 5 and 6 respectively. It can be seen
that the power signals have the same pattern as force
signals acquired from dynamometer. Both signals
TOOL WEAR PREDICTION BASED ON WAVELET TRANSFORM AND SUPPORT VECTOR MACHINES
483

Figure 5: Original force acquired from dynamometer with
different wear.
Figure 6: Original power signals with different tool wear.
possess different characteristics at different segment
of the profile caused by the variation of effective
cutting length between insert and workpiece. The
power sensor is recognized as an appropriate
alternative sensor for machining process monitoring
due to the ease of installation and low cost.
However, it seems that the power signal is less
sensitive than force signal in the detection of tool
wear due to the interference from dynamic
components. Hence, the wavelet transform is further
employed to decompose power signals into static
and dynamic components. It can be seen that
amplitude of static components of power signals
increased with the proceeding of tool wear as shown
in Figure 7.
Additionally, for the purpose of feature extraction,
the dimensionality or length of sensory signal can be
reduced significantly by the utilization of wavelet
transform. Finally, the data sets composed features
extracted by wavelet transform and corresponding
tool wear measured by optical scan microscope were
obtained. The desired output of the LS-SVM
represents wear states of the cutting tool in terms of
VB. Then all features were normalized against their
respective standard deviations. The whole data sets
can be further divide into two sub-sets, i.e. training
sets and validation sets. Then, the SVM-based tool
wear model was trained by training sets and two
turning parameters γ and σ was selected as 10 and
0.3 respectively. By application of training
algorithm for training sets, the b and a
k
can be
obtained and stored to construct predictive model.
Once the training stage is accomplished, the SVM-
based tool wear model was validated by validation
sets. The predicted tool wear by using SVM model
and actual tool wear measured by optical scan
microscope is compared in the Figure 8. A good
agreement between them can be found at each level
of tool wear. The experimental results show that
SVM-based model is effective to predict tool wear
by using features extracted from wavelet transform.
Figure 7: Static components of power signals extracted by
wavelet transform.
Figure 8: Comparisons between predicted and actual tool
wear measured by optical scan microscope.
0 5 10 15 20 25 30 35 40 45 50
-0.5
0
0.5
1
1.5
2
2.5
tims/s
cutting force/kN
VB=0.00
VB=0.11
VB=0.15
VB=0.19
VB=0.22
VB=0.27
0 5 10 15 20 25 30 35 40 45 50
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
tims/s
power/kW
VB=0.00
VB=0.11
VB=0.15
VB=0.19
VB=0.22
VB=0.27
0 5 10 15 20 25 30 35 40 45 50
-1.5
-1
-0.5
0
0.5
1
tims/s
Power/kW
VB=0.00
VB=0.11
VB=0.15
VB=0.19
VB=0.22
VB=0.27
1 2 3 4 5 6 7 8 9 10 11 12 13
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
serial number of samples
VB (mm)
Estimated tool wear
Measured tool wear
ICINCO 2011 - 8th International Conference on Informatics in Control, Automation and Robotics
484

5 CONCLUSIONS
A new tool wear prediction approach based on
wavelet transform and LS-SVM has been developed
and demonstrated in turning trials. The major
contributions of this work can be summarized as
follows:
1. Wavelet transform has been implemented in
dimensionally reduction and feature extraction for
sensory signals acquired in machining processes. In
comparison with conventional feature extraction
approaches, wavelet transform technique is capable
of exploring the instinct correlation between the
sensory signals and tool wear due to its powerful
multi-scale decomposition capability.
2. LS-SVM technique has been developed to predict
tool wear by using extracted features from wavelet
transform. Due to the utilization of statistical
learning theory, LS-SVM can overcome several
disadvantages with traditional machine learning
techniques, e.g. local optimal solution, low
convergence rate and poor generalization ability
when few samples are available.
3. It has been proved that the sensory signal
measured by alternative sensors, i.e. power sensor,
correlate with dynamometer signal very well and is
sensitive enough to detect tool wear. As a result, the
power signals have been selected to conduct feature
extraction due to the cost-effectiveness and the ease
of installation.
4. The effectiveness of proposed prediction approach
has been demonstrated in experimental turning trials.
A good agreement can be found between predicted
tool wear obtained by LS-SVM and actual tool wear
measured by optical scan microscope.
ACKNOWLEDGEMENTS
The financial sponsorship from EPSRC and
technical supports from industrial partners, namely,
Rolls-Royce (Colin Sage, Jamie McGourlay and
John Burkinshaw), Siemens (Julian Timothy and
Gordon Lanes), Kistler (Eddie Jackson) and TBG
Solution (Paul Rawlinson) are gratefully acknowl-
edged.
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