Multiresolution Wavelet And Locally Weighted Projection Regression Method For Surface Roughness Measurements

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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 2, February 2011

MULTIRESOLUTION WAVELET AND
LOCALLY WEIGHTED PROJECTION
REGRESSION METHOD FOR SURFACE
ROUGHNESS MEASUREMENTS
1
Chandra Rao Madane and 2Dr..S.Purushothaman

1 2
Chandra Rao Madane, Dr.S.Purushothaman, Principal ,
Research Scholar, Sun College of Engineering and Technology,
Department of Mechanical Engineering, Sun Nagar, Erachakulum,
Vinayaka Missions University, Salem, Tamilnadu, Kanyakumari district-629902, India
India, E-Mail: madane61@yahoo.com E-Mail: dr.s.purushothaman@gmail.com

Abstract--This paper presents the benefits of using single technique that can be used to entirely
coiflet wavelet for feature extraction from the surface characterize a texture. Image is analyzed at one
roughness image. The features extracted are learnt by single-scale; a limitation that can be removed by
the Locally weighted projection regression network employing a multiscale representation of the textures
(LWPR) method. The image captured through Charge similar to wavelet transform. Wavelets have already
coupled device (CCD) camera undergoes preprocessing been applied successfully as a tool for characterizing
to remove noise and enhance the quality of image to engineered surfaces with one-dimensional (1D)
make the details of the pixels more clear. The image is
profiles but also in 2D for characterizing some
decomposed by using coiflet wavelet. Four level of
decomposition is done to obtain detailed information, particular engineering applications. Industrial
Entropy measure is applied and subsequently Locally inspection is a very popular field for using wavelets.
weighted projection regression network method They are well suited to detect the defects like
(LWPR) is used for training the entropy calculated. The scratches on a uniform texture. It should be
target values labeled are with surface roughness within mentioned that for special monitoring tasks, images
the limits or not. The values are trained using LWPR to be processed often come from a CCD camera.
and a set of final weights are obtained. Using this final
weight values, different portion of the image is analyzed
to verify, if the roughness is within the limit or not Surface finish is an apparent witness of tool
marks or - lack of same - on the machined surface of
a work piece. Surface finish is a characteristic of any
machined surface [1-5]. It is sometimes called
Keywords- Locally weighted projection surface texture or roughness. The design engineer is
regression network method (LWPR), discrete wavelet
usually the person who decides what the surface
(DWT)
finish of a work piece should be. They base their
1. INTRODUCTION reasoning on what the work piece is supposed to do.
Here are a few examples that the engineer considers
when applying a surface finish specification:
Measuring a rough surface is based on grey
levels corresponding to the surface texture. Deeper a • Good surface finishes increase the wear
valley, the darker the corresponding pixel, the higher resistance of two work pieces in an assembly
a peak, the brighter the corresponding area in the • Good surface finishes reduce the friction
image. Modern instruments can give a three- between two work pieces in an assembly
dimensional (3D) measure of a surface. There is no

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ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 2, February 2011

Surface finishes are usually specified with a "check
mark" on the blueprint as shown in the Figure 1.
Surface finishes are specified in micro inches and are
located on the left side of the symbol above the check
mark "V” shown Figure 1. The waviness requirement
(if specified) is usually given in thousands of an inch
and is located on the top right of the symbol. In the
example it is the value ".0015". The roughness width
requirement (if specified) is usually given in
thousands of an inch and is located on the bottom
right of the symbol. In the example it is the value
".002". The lay direction requirement (if specified) is Fig.2 Wavelet
usually represented by a symbol [6-10] and is located
right below the roughness width requirement. In the
The continuous wavelet transform (CWT) (Figure 3)
example it is the symbol for perpendicularity. The
is defined as the sum over all time of the signal
graphic below show the rest of the symbols [11].
multiplied by scaled, shifted versions of the wavelet
function:

(2)
The result of the CWT is many wavelet coefficients
C, which are a function of scale and position.
Multiplying each coefficient by the appropriately
scaled and shifted wavelet yields the constituent
wavelets of the original signal:

Fig.1 Surface finish representation

2. WAVELETS (WT)
The WT was developed as an alternative to
the short time Fourier transform (STFT). A wavelet is
a waveform with limited duration that has an average
Fig.3 Continuous wavelet
value of zero. Comparing wavelets with sine waves,
sinusoids do not have limited duration, they extend Scaling
from minus to plus infinity and where sinusoids are
smooth and predictable [12]. Wavelet analysis is the Scaling a wavelet simply means stretching (or
breaking up of a signal into shifted and scaled compressing) it. The scale factor works exactly the
versions of the original (or mother) wavelet. same with wavelets. The smaller the scale factor, the
Mathematically, the process of Fourier analysis is more “compressed” the wavelet.
represented by the Fourier transform:
Shifting
Shifting a wavelet simply means delaying (or
hastening) its onset. Mathematically, delaying a
(1) function by k
which is the sum over all time of the signal f(t) Coiflet wavelet
multiplied by a complex exponential. The results of
the transform are the Fourier coefficients, which Inspite of existing different wavelets, coiflet wavelet
when multiplied by a sinusoid of frequency, yield the whose function has 2N moments equal to 0 and the
constituent sinusoidal components of the original scaling function has 2N-1 moments equal to 0 has
signal. Graphically, the process looks like:

42 http://sites.google.com/site/ijcsis/
ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 2, February 2011

been considered. The two functions have a support of 8. Check if new random field has to be added.
length 6N-1.
9. Find mean square errors between target and
The features are obtained from the Approximation the estimated values.
and Details of the 4th level by using the following
equations 10. Repeat steps 5 to 9 until all the patterns are
presented.
V1=1/d ∑ (Approximation details) (3)
Where d = Samples in a frame and
4 SCHEMATIC DIAGRAM
V1 = Mean value of approximation
V2=1/d ∑ (Approximation or details –V1)) (4)
Where V2=Standard Deviation of approximation
V3=maximum (Approximation or details) (5)
V4=minimum (Approximation or details) (6)
V5=norm (Approximation or Details)2 (7)
Where V5 = Energy value of frequency

3. .LOCALLY WEIGHTED PROJECTION
REGRESSION (LWPR)

LWPR achieves better results in nonlinear function
approximation in high dimensional spaces. It is
insensitive to redundant data. It uses linear models
locally [13, 14]. Univariate regressions in selected
directions are used in the input space. The
nonparametric local learning system learns rapidly. It
uses second order learning methods based on
incremental training. Weight adjustments are done
based on local information only. Training LWPR is
done as follows,
The 5 features obtained are used as inputs for the
LWPR and the target values for training each surface
roughness type is based on labeling.
1. Input extracted features from wavelet.
2. Initialize LWPR using diagonal distance
matrix α, norm, meta rate and initial_λ. Many
other variables can be initialized or made
constants depending upon the requirements.
3. Create random numbers.
4. Choose input and target output of a pattern
Fig.4 Training and testing
5. Find global mean and variance of the patterns.
6. Normalize input and output.
7. Compute the weight.

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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 2, February 2011

5 IMPLEMENTATION M3,F150,S1000,.5DOC,49DIA CUTTER
Training M4,F150,S1000,.8DOC,49DIA CUTTER
1. Read each Image M5,F200,S800,..5DOC,49DIA CUTTER
2. Remove noise M6,F200,S800,.8DOC,49DIA CUTTER
3. Enhance image M7,F200,S1000,.5DOC,49DIA CUTTER
4. Decompose by discrete wavelet (DWT) of type M8,F200,S1000,.8DOC,49DIA CUTTER
coiflet
5. Decompose by 4 levels
7. RESULTS
6. Find feature from the approximation matrix at the
4th level decomposition Sample images

7. Label the features based on the type of surface
roughness measured for the machined work piece
using profilometer
8. Repeat step 1 to step 7 for different types of
acceptable and unacceptable roughness values
9. Train the LWPR using input and corresponding
labels obtained in previous steps.
11. Store the Final Weights in a File.

Testing
1. Read each Image
2. Remove noise
3. Enhance image
4. Decompose by discrete wavelet (DWT) of type
coiflet
5. Decompose by 4 levels
6. Find feature from the approximation matrix at the
4th level decomposition
7 process with final weights of LWPR
8. Classify the roughness.
6 . EXPERIMENT DETAILS
Milling machine has been used to machine flat
specimen under the following condition
M1,F150,S800,.5DOC,49DIA CUTTER
M2,F150,S800,1DOC,49DIA CUTTER Fig. 5 Images used for training and testing LWPR

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Vol. 9, No. 2, February 2011

8. CONCLUSION
This work has been focused in estimating
the surface roughness values from the image of
machined surface in milling. Coiflet wavelet is used
for image decomposition and radial basis function
network for learning the training patterns to obtain
final weights for finding roughness from new images.
The performance of this work is only 95%. The
performance has to be improved by changing the
topology of the LWPR
9. References
Fig.6 Surface roughness under magnification
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Vol. 9, No. 2, February 2011

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