Multiresolution Wavelet And Locally Weighted Projection Regression Method For Surface Roughness Measurements
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 IJCSIS invites authors to submit their original and unpublished work that communicates current research on information assurance and security regarding both the theoretical and methodological aspects, as well as various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.
(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: firstname.lastname@example.org E-Mail: email@example.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 . 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 . 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 . 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 . 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 . 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 . 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. . 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. . 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 . 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. . 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. . 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. . 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.  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.  Bruno Josso, David R. Burton, Michael J. Lalor, Frequency normalised wavelet transform for surface roughness analysis and characterization,Wear, Wear 252 (2002) 491–500.  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. 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