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

Document Sample
Multiresolution Wavelet And Locally Weighted Projection Regression Method For Surface Roughness Measurements Powered By Docstoc
					                                                   (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



                                                            41                                http://sites.google.com/site/ijcsis/
                                                                                              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.



                                                          43                                http://sites.google.com/site/ijcsis/
                                                                                            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
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




                                                       44                                 http://sites.google.com/site/ijcsis/
                                                                                          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
                                                                [1]. Kaye, J. E.; Yaan, D. H.; Popplewell, N.;
                                                                Balakrishnan, S. Thomson, D. J., Electronic system
                                                                for surface roughness measurements in turning
                                                                International Journal of Electronics. 1993 May,
                                                                Precision Engineering, Volume 16, Issue 1, January
                                                                1994, Page 71


                                                                [2]. Yves Beauchamp, Marc Thomas, Youssef A.
                                                                Youssef and Jacques Masounave, Investigation of
                                                                cutting parameter effects on surface roughness in
                                                                lathe boring operation by use of a full factorial
                                                                design, Computers & Industrial Engineering, Volume
                                                                31, Issues 3-4, December 1996, Pages 645-651
                                                                [3]. M. Thomas, Y. Beauchamp, A. Y. Youssef and J.
Fig.7 Histogram of an image with surface roughness              Masounave, Effect of tool vibrations on surface
                                                                roughness during lathe dry turning process,
                                                                Computers & Industrial Engineering, Volume 31,
                                                                Issues 3-4, December 1996, Pages 637-644
                                                                [4]. Z. Yilbas and M. S. J. Hashmi, An optical
                                                                method and neural network for surface roughness
                                                                measurement, Optics and Lasers in Engineering,
                                                                Volume 29, Issue 1, 1 January 1998, Pages 1-15.
                                                                 [5]. M. A. Younis, On line surface roughness
                                                                measurements using image processing towards an
                                                                adaptive   control,  Computers     &    Industrial
                                                                Engineering, Volume 35, Issues 1-2, October 1998,
                                                                Pages 49-52.
                                                                [6]. P. L. Wong and K. Y. Li, In-process roughness
Fig 8 Surface roughness pattern                                 measurement on moving surfaces, Optics & Laser
                                                                Technology, Volume 31, Issue 8, November 1999,
                                                                Pages 543-548.
Feature patterns are developed from the surface                 [7]. C. J. Luis Perez, J. Vivancos and M. A.
roughness images obtained after machining. The                  Sebastián, Surface roughness analysis in layered
patters are separated as training and testing patterns.         forming processes, Precision Engineering, Volume
The patterns are labeled with range of surface                  25, Issue 1, January 2001, Pages 1-12.
roughness values.
                                                                [8]. S. L. Toh, C. Quan, K. C. Woo, C. J. Tay and H.
                                                                M. Shang, Whole field surface roughness
                                                                measurement by laser speckle correlation technique,



                                                          45                                http://sites.google.com/site/ijcsis/
                                                                                            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,
September 2001, Pages 427-434.
[9]. A. J. Baker and W. J. Giardini, Developments in
Australia's surface roughness measurement system,
International Journal of Machine Tools and
Manufacture, Volume 41, Issues 13-14, October
2001, Pages 2087-2093.
[10]. R. I. Campbell, M. Martorelli and H. S. Lee,
Surface roughness visualisation for rapid prototyping
models, Computer-Aided Design, Volume 34, Issue
10, 1 September 2002, Pages 717-725.
[11] Mr. John Cooper and Dr. Bruce DeRuntz, The
relation between the workpiece extension
length/diameter ratio and surface roughness in
turning application, Journal of industrial technology,
Volume 23, Number 2 - April 2007 through June
2007.
[12] Bruno Josso, David R. Burton, Michael J. Lalor,
Frequency normalised wavelet transform for surface
roughness analysis and characterization,Wear, Wear
252 (2002) 491–500.
[13] Sethu Vijayakumar, Stefan Schaal, Locally
Weighted Projection Regression : An O(n) Algorithm
for Incremental Real Time Learning in High
Dimensional    Space,    Proc.    of   Seventeenth
International Conference on Machine Learning
(ICML2000), 2000, pp. 1079-1086.
[14]Stefan Klanke, Sethu Vijayakumar,      Stefan
Schaal, A Library for Locally Weighted Projection
Regression, Journal of Machine Learning Research
9, 2008, pp. 623-626.




                                                         46                                http://sites.google.com/site/ijcsis/
                                                                                           ISSN 1947-5500

				
DOCUMENT INFO
Description: The International Journal of Computer Science and Information Security (IJCSIS Vol. 9 No. 2) is a reputable venue for publishing novel ideas, state-of-the-art research results and fundamental advances in all aspects of computer science and information & communication security. IJCSIS is a peer reviewed international journal with a key objective to provide the academic and industrial community a medium for presenting original research and applications related to Computer Science and Information Security. . The core vision of IJCSIS is to disseminate new knowledge and technology for the benefit of everyone ranging from the academic and professional research communities to industry practitioners in a range of topics in computer science & engineering in general and information & communication security, mobile & wireless networking, and wireless communication systems. It also provides a venue for high-calibre researchers, PhD students and professionals to submit on-going research and developments in these areas. . IJCSIS invites authors to submit their original and unpublished work that communicates current research on information assurance and security regarding both the theoretical and methodological aspects, as well as various applications in solving real world information security problems.