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Research Papers

Estimating Distributions of Surface Parameters for Classification Purposes

[+] Author and Article Information
Min Zhang

Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109mzhangz@umich.edu

Elizaveta Levina

Department of Statistics, The University of Michigan, Ann Arbor, MI 48109elevina@umich.edu

Dragan Djurdjanovic

Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109ddjurdja@umich.edu

Jun Ni

Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109junni@umich.edu

J. Manuf. Sci. Eng 130(3), 031010 (May 12, 2008) (9 pages) doi:10.1115/1.2844588 History: Received April 27, 2006; Revised December 28, 2007; Published May 12, 2008

The classification of workpiece surface patterns is an essential element in trying to understand how functional performance is influenced by the surface geometry. Filter banks have been investigated in literature for capturing the multiscale characterization of the engineering surfaces. Conventionally, parametric representations of the filter outputs were used for classification. In this paper, the histogram estimators of the filter bank outputs from engineering surfaces in combination with the nearest neighbor method for classification are investigated to improve the classification accuracy, which are accomplished by utilizing distribution dissimilarity measures to compare histograms. Furthermore, for large and complex surfaces, the histogram estimators of local surface flatness parameters are also proposed for the purpose of simple computation. Two case studies have been conducted to demonstrate the proposed methods. Influence of the histogram bins for histograms and the dissimilarity measures on classification performance is studied in detail. Results from the first case study show that the proposed method is less effective in classifying small surfaces with clear surface patterns, because the filtering is influenced by the quality of the surface data collected from the measurement sensor. In comparison, results from the second case study show that the proposed method performs better in classifying large surfaces with mild surface pattern differences. The classification accuracy using the conventional method drops from 100% to around 50% in the second case study. In general, one can achieve misclassification errors below 5% in both case studies with the histogram representations of surface parameters and the appropriate selection of the number of bins for histogram construction.

FIGURES IN THIS ARTICLE
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Copyright © 2008 by American Society of Mechanical Engineers
Topics: Errors , Filters , Filtration
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References

Figures

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Figure 1

The derivatives of Gaussian filter bank

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Figure 2

Four histograms obtained from filtering the measurements of a surface machined under chatter with the first four filters in the DoG filter bank (alpha and beta are the view angles of the 3D surface)

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Figure 3

Four histograms obtained from filtering the measurements of a surface machined under normal conditions with the first four filters in the DoG filter bank (alpha and beta are the view angles of the 3D surface)

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Figure 4

Optical system of the surface measurement device

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Figure 5

(a) Sample surface from Set A and (b) sample surface from Set B

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Figure 6

Misclassification errors for the testing data set (the results are the average of the outputs with k=1,3,5)

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Figure 7

Bin number selection results from fourfold cross validation

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Figure 8

Surface measurement results of two part samples from data sets C and D, respectively

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Figure 9

Markers for local flatness description of the pump surfaces

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Figure 10

Fivefold cross-validated misclassification errors (the results are the average of the outputs with k=1,3,5)

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