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


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

                                    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:                                 E-Mail:

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
                                                                  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

                                                                                              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

                                                                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 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:

                                                                                            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
      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

                 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.

                                                                                            ISSN 1947-5500
                                              (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
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.

1. Read each Image
2. Remove noise
3. Enhance image
4. Decompose by discrete wavelet (DWT) of type
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

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

Optics & Laser Technology, Volume 33, Issue 6,
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