19
th
International Conference on Production Research
A
N
I
NTELLIGENT
REASONING MODEL
FOR
Y
ARN
MANUFACTURE
J
ian

G
uo
Y
ang
,
Fu Zhou
,
Jing

Zhu Pang, Zhi

Jun Lv
College Of
M
echanical Engineering
,
University of
DongHua,
Ren Min Bei Road 2999, Song Jiang Zone,
Shanghai
,
P
R
China
Abstract
Although many works hav
e been done to construct prediction models on yarn processing quality, the
relation between spinning variables and yarn properties has not been established conclusively so far.
Support vector machines (SVMs), based on statistical learning theory, are gaini
ng applications in the areas
of machine learning and pattern recognition because of the high accuracy and good generalization
capability
. This study briefly introduces the SVM regression
algorithms
, and presents the SVM based
system architecture for
predic
ting
yarn properties. Model selection which amounts to search in
hyper

parameter
space is performed for study of suitable
parameter
s with grid

research method. Experimental
results have been
compar
ed with those of ANN models. The investigation indicates th
at in the small data
sets and real

life production, SVM models are capable of remaining the
stability
of predictive accuracy, and
more suitable for
noisy and
dynamic
spinning process
Keywords
:
Support vector machines
, Structure risk minimization, Predict
ive model, K
ernel function
,
Yarn quality
1
INTRODUCTION
Changing economic and political conditions and the
increasing globalisation of the market mean that the textile
sector faces ever challenges. To stay competitive, there is
an increasing need for co
mpanies to invest in new
products. Along the textile chain, innovative technologies
and solutions are required to continuously
optimize
the
production process. High quality standards and an
extensive technical and trade know

how are thus
prerequisite to ke
ep abreast of the growing dynamics of
the
sector [
1]
.
Although many works have been done to
construct prediction models on yarn processing quality, the
relation between spinning variables and yarn properties
has not been established conclusively so far.. T
he
increasing quality demands from the spinners make clear
the need to explore
innovative
ways of quality prediction
furthermore. The widespread use of artificial intelligence
(AI) has created a revolution in the domain of quality
prediction, for example,
application of artificial
neural
network (ANN)
in textile
engineering [2].
This
study
presents a
support vector machines
based
intelligent
predictive
model
for
yarn
process
quality. The relative
algorithm, model selection and experiments
are presented
in d
etail.
2
SVM
REGRESSION A
LGORITHMS
2.1
Paper title and authors
The main objective of regression is to approximate a
function
g
(x) from a given noisy set of samples
obtained from the function
g
. The
basic idea of support vector machines (S
VM) for
regression is to map the data
x
into a high dimensional
feature space via a nonlinear mapping and to perform a
linear regression in this feature space.
(1)
where
w
denotes the weight vector,
b
is
a constant known
as
“bias
”,
are called
feature
s
. Thus, the
problem of nonlinear regression
in lower

dimensional input
space is transformed into
a linear regression in the high

dimensional feature space.
The unknown parameters
w
and b in Equation (
1
) are est
imated
using the training set,
G
. To avoid over fitting and thereby
improving the
generalization capability, following regularized
functional
involving summation of the empirical risk
and a complexity
term
, is minimized
[3]
(2)
where
λ
is a regularization constant and the cost function
defined by
,
(3)
is called Vapnik
’
s
“
ε

insensitive loss function”
. It can be
shown that the minimizing function has the following fo
rm:
(4)
w
ith
,
and the kernel
function
describes
the
dot
product in the D

dimensional feature space.
(5)
It is important to note that th
e features
Φ
j
need not be
computed; rather what is
needed is the kernel function that
is very simple and has a known analytical form.
The only
condition required is that the kernel function has to satisfy
Mercer’s condition.
Some of the mostly used kernels
include li
near
,
polynomial,
radial basis function
, and
sigmoid. Note also that for Vapnik’s
ε

insensitive loss
function, the Lagrange
multipliers
are sparse, i.e.
they result in nonzero values after the optimization
(2) only
if they are on the
boundary, which means that they satisfy
the Karush
–
Kuhn
–
Tucker conditions. The
coefficients
are obtained by maximizing the
following form
:
(6)
(7)
Only a n
umber of coefficients
will be different from
zero, and the data
points associated to them are called
support vectors. Parameters
C
and
ε
are free
and have to
be decided by the user. Computing b requires a more
direct use of the
Karush
–
Kuhn
–
Tucker conditions that lead
to the quadratic programming problems
stated above. The
key idea is to pick those values for a point
on the
margin, i.e.
or
in the open interval (0, C). One
would be sufficient but for
stability purposes it is
recommended that one take the average over all points on
the margin. More det
ailed description of SVM for
regression can be found in
Ref. [3~6]
3
SVM BASED YARN PREDI
CTIVE MODEL
3.1
Model Architecture
Considering some salient features of SVM such as
the
absence
of local minima, the sparseness of the solution
and the
improved generalizati
on, there was
proposed
SVM

based yarn
quality
prediction system (shown as
Fig.1). The system architecture mainly consists
of three
module
s, i.e. data acquisition, reasoning machine, and
user
interface. Among
them, the user interface provides
friendly inter
active operation with the
model, including
data
cleaning, model training, parameter selection, and so on.
The data acquisition collects and transforms the various
data from yarn production process into engineering
database. The reasoning machines are a SVM

based yarn
process simulator in nature, which are used to train the
predictive models, and then make some real

world
process decision in term of the different raw materials
inputs
3.2
Model
Selections
In
the yarn
predictive learning task,
the
appropriate mode
l
and parameter estimation method should be selected to
obtain a high level of performance of the learning machine.
Lacking a priori information about the accuracy of the y

values, it can be difficult to come up with a reasonable
value of
ε
a prior. Instead, one would rather specify the
degree of sparseness and let the algorithms
automatically
compute
ε
from the data. This is the idea of
ν

SVM, a
modification of the original
ε

SVM introduced by
Sch
ő
lkopf, Smola, Williamson et al [6], which w
ere used to
construct the yarn predictive model in our study.
Under the
approach, the usually parameters to be
chosen are the
following:
the penalty term C which determines the tradeoff
between the complexity of the decision function and
the number of trai
ning examples misclassified;
the sparsity parameter
ν
in accordance with the noise
that is in the output values in order to get the highest
generalization accuracy.
the kernel function such that
According to the reference [7], the sparsity parameter
ν
usually may be choose in the inte
rval [0.3, 0.6], here
ν
=0.583. And radial basis function (RBF)
kernel
, given by
Equitation 8 is used:
(8)
where
σ
is the width of the RBF
kernel
parameter.
The RBF kernel nonlinearly maps samples into a higher
dimensional space,
so it, unlike the linear kernel,
can
handle the case when the relation between
inputs
and
outputs
is nonlinear.
In addition, the sigmoid kernel
behaves
like RBF for certain parameters.
The reason
using RBF kernels
is the number of hyper

parameters
Reasoning Machines
User Interface
Fig.
1
Yarn Quality Predictive Model Architecture
Yarn Production Process
Data Acquisition
SVM

based Process Simulator
Yarn Quality Prediction
Raw
Material
Yarn
Properties
Textile Engineering Database
19
th
International Conference on Production Research
which in
fluences the complexity
of model selection. The
polynomial kernel has more hyper

parameters than
the
RBF kernel. Finally,
for
the RBF kernel
, it
has less
numerical difficulties
;
and a
key point is
in
contrast to polynomial kernels of
which kernel values may
go to infinity or zero while the degree is large. Moreover,
it
is
note
d
that the sigmoid kernel is not valid (i.e. not the
inner product of two vectors)
under some parameters
[4].
3.3
Optimization of Model Parameter
Obviously, in the S
VM model t
here are
still
two
key
parameters
need choosing
: C and
σ.
U
nfortunately
, i
t is
difficult to
know
beforehand which C and
σ
are the best for
one problem.
Our
goal is
just about
to identify good
(C, σ)
so that the
model
can accurately predict unknown data
(i.e., testing data).
Therefore,
a common way is to
separa
te training data to two parts of which one is
considered
unknown in training the
model
. Then the
prediction accuracy on
data
set
s
can more
precisely reflect
the performance on
predict
ing unknown data.
The
procedure
for improved model
is
called as
cross

val
idation.
The cross

validation procedure can
also
prevent the over

fitting problem
furthermore
.
In
this
study,
the regression function was built with a given set of
parameters {C,
σ}
.
The performance of the parameter set
is
measured by the
computational
risk, here mean squared
error (
MSE
, see Equation 9)
on the last subset. The above
procedure is repeated
p
times, so that each subset is used
once
for testing. Averaging the MSE over t
he
p
trials gives
an
estimate of the expected generalization error for
training on
sets of size
,
l
is the number of
training data.
(9)
where
q
is the sample number of tested subset in the
training set;
and
are the
observed value and
predicted value under
tested subset, respectively. In
order to capture the better pairs of (C,
σ
), a
“
grid

search
”
[8] on C and
σ
is employed in this work. Firstly, in term of
possible range of the two parameters, C and
σ
were
divided r pairs; t
hen
each pair of the parameters was tried
using cross

validation and the one with the best cross

validatio
n accuracy was picked up as optimal parameters
of the model.
4
T
HE EXPERIMENTS STUDY
In this work, a small
population
(a total of twenty

six
different data samples) from real worsted spinning was
acquired. To
demonstrate
the generalization performance
of SVM
model, different experiments were
completed
and
comparisons
with ANN models.To make problem more
simply, like most ANN models[2, 9], some
fibre
properties
and processing information were selected as the SVM
model
’
s inputs, which were mean
fibre
diameter (
MFD,
μ
m), diameter distribute (CVD, %), hauteur (HT, mm), fiber
length distribution (CVH, %), short fiber content (SFC, %),
yarn count (CT, tex), twist (TW, t.p.m), draft ratio (DR),
spinning speed (SS, r.p.m),
traveler
number (TN). Four
yarn properties, n
amely
unevenness
(CV %), elongation at
break (EB, %), break force (BF, cN) and end

down per
1000 spindle hour (ED), served as the SVM model
’
s
outputs.
One of the primary aspects of developing a SVM
regression model is the selection of the
penalty term
C
an
d
the width of the RBF
kernel
parameter
σ
. To optimize
the two parameters, the
“
grid

search
”
method above was
applied in the present work. In fact, optimizing the model
parameters need an
iterative
process which can
continuously
shrink
the searching area and as a result,
obtain a satisfying solu
tion. Table
1
lists the final searching
area and optimal values of the four SVM models,
respectively.
After the completion of model development or training, all
the models based on SVM (and ANN) were subjected to
the unseen testing data set. Statistical par
ameters such as
the correlation coefficient between the actual and
predicted values (R), mean squared error, and mean
error%, were used to compare the predictive power of the
SVM

based and ANN

based models. Results are shown in
Table
2
. It has observed that
for ANN models, the mean
error (%)
of three models
is more than
10% except that the
CV% remains about
5%
, and the correlation coefficient
(R)
of the CV% and EB models is very low, shown as 0.76 and
0.67 respectively. However, for SVM models, the mean
erro
r (%)
is
less
than
10% except that the ED is still high,
and the correlation coefficient
(R)
of all models is improved
to more than 0.80. On the other hand, the cases with over
10% error also decrease from 5 and 6 in ANN models to 2
and 3 in SVM models. In
fact, among all four yarn
properties considered in our work, end

down per 1000
spindle hours could be affected by different operators and
observers [10]
,
which data often
result
in undermining the
prediction accuracy of various regression models. Even
so,
for ED, almost all
statistical
parameters using SVM
model seem to be much better than using ANN model
5
CONCLUSIONS
Support vector machines are a new learning

by

example paradigm with many potential applications in
science and engineering. The salient featu
res of SVM
include
the absence
of local minima, the sparseness of the
solution and the
improved generalization
.
SVMs being a
relatively new technique, their application on textile
production have
hitherto
been quite limited. However, the
elegance of the fo
rmalism
involved
and their successful
use in diverse science and engineering applications
confirm the expectations raised in this appealing learning
from examples
approach
. In this study, we presented the
SVM model for predicting the yarn properties and
compared with the BP neural network model. We have
found that like ANN model, the SVM model is able to
predict to a reasonably good accuracy in most of cases.
And a more
interest
ed
phenomenon
is that in smal
l data
set and real

life production, the predictive power of ANN
models appears to decrease, while SVM models are still
capable of remaining the
stability
of predictive accuracy to
some extent. The experimental results indicate that the
SVM models are more
suitable for
noisy and
dynamic
spinning process. Of course, like other
emerging
industrial
techniques,
applied
issues on SVM reaffirm the due
commitment to their further development and investigation,
such as the problems how to design the kernel function
and how to set the SVM hyper

parameters (to make the
industrial
model development more easily). Our research
thus far
demonstrates
that SVMs are able to provide an
alternative solution for the spinners to predict yarn
properties more
correctly
and
reliabl
y
6
ACKNOWLEDGMENT
This research was supported by
national science
foundation and
technology
support
plan
of the People
Republic of China, under contract number
70371040
and
2006BAF01A44
respectively.
7
REFERENCES
[1]
Renate Esswein,
“
Knowledge assures qualit
y
”
,
International Textile Bulletin,
2004
,
Vol15, no2,
17~21,
[2]
R. Chattonpadhyay and A. Guha,
“
Artificial Neural
Networks: Applications to Textiles
”
, Textile Progress,
2004
,
Vol35, no1, 1~42,
[3]
V. David Sanchez A,
“
Advanced Support Vector
Machines a
nd Kernel Methods
”
,
Neurocomputing
,
2003
,
Vol55, no3, 5

20 ,
[4]
V. N. Vapnik,
1999
,
The Nature of Statistical Learning
Theory, 2nd ed., Berlin: Springer,
31

188,
[5]
B. Scholkopf, C. Burges, and A. Smola,
1999
,
Advances in Kernel
Methods
—
Support Vect
or
Learning. Cambridge, MA: MIT Press,
5

73,
[6]
B. Scholkopf, Smola A. and Williamson. R.C.,
et al
,
“
New support vector algorithms
”
, Neural
Computation,
2000
,
Vol12, no4, 1207

1245,
[7]
Athanassia Chalimourda, B. Scholkopt, A. Smola,
“Experimentally
O
ptimal
ν
in
S
upport
V
ector
R
egression for
D
ifferent
N
oise
M
odels and
P
arameter
S
ettings”
,
IEEE
trans. on Neural Netw.,
2004
,
Vol17, no2,
127

141
[8]
Chih

Wei Hsu, Chih

Chung Chang, and Chih

Jen Lin,
A practical guide to support vector classification,
available at http://www.csie.ntu.edu.tw/~cjlin/paper
[9]
Refael B., Lijing W., Xungai W.,
“
P
redicting
worsted
spinning performance with an artificial neural network
model
”
, Textile Res. J. ,
2004
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763,
[10]
Peter R. Lord,
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Handbook
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(Technology, Science and Economics), Abinhton
England: Woodhead publishing Limited, 95

212
Table1 The optimal values of
σ
and C
Output parameter
Optimal value
CV %
Elongation at break
Breaking force
Ends

down
Table
2
Comparison of the predictive power of t
he SVM

based and ANN

based models
Sample No.
Predicted value using ANN model
Predicted value using SVM model
CV%
EB
BF
ED
CV%
EB
BF
ED
W21
19.32
13.81
113.89
70.41
19.66
12.85
116.24
72.06
W22
20.52
16.55
61.91
75.78
20.88
12.25
76.87
72.40
W23
15.62
12.32
153.46
39.40
16.84
15.59
156.57
42.22
W24
20.66
16.55
61.91
75.78
20.75
12.25
76.87
72.40
W25
22.60
19.77
47.00
69.84
19.66
12.76
76.86
59.31
W26
20.70
11.87
66.76
79.22
21.20
12.59
66.62
81.27
Correlation
coefficient. R
0.76
0.67
0.96
0.88
0.88
0.80
0.99
0.91
Mean squared error
0.01
0.12
0.07
0.03
0.003
0.05
0.01
0.03
Mean error%
5.73
24.35
13.67
19.99
2.85
9.23
5.52
17.29
Cases with
over 10% error
1
6
5
6
0
2
2
3
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