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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