Abstract

The surface roughness prediction model based on a support vector machine was proposed and the multi-wavelength fiber optic sensor was established. The specimens with different surface roughness selected as the test samples were analyzed by using the prediction model when the incident wavelengths were 650 nm and 1310 nm, respectively. The working distance of 2.5 mm ~3.5 mm was chosen as the optimum measurement distance. The experimental results indicate that the error range of surface roughness is 0.74% ~7.56% at 650 nm, and the error range of surface roughness is 1.03% ~5.92% at 1310 nm. The average relative error is about 2.669% at 650 nm, while it is about 2.431% at 1310 nm. The error of roughness measurement is less than 3% by using the model, which is acceptable. The error of surface roughness based on the prediction model is smaller than that by using the characteristic curves between surface roughness and the scattering intensity ratio.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2016 (1)

N. N. Zhu and J. Zhang, “Surface roughness measurement based on fiber optic sensor,” Measurement 86, 239–245 (2016).
[Crossref]

2013 (1)

H. Zhao and D. X. Hua, “Modifications to Beckmann-Kirchhoff model for random rough surfaces with non-paraxial angles,” J. Xi’an University Technol. 29(3), 285–289 (2013).

2011 (1)

2010 (1)

A. K. Gupta, “Predictive modeling of turning operations using response surface methodology, artificial neural networks and support vector regression,” Int. J. Prod. Res. 48(3), 763–778 (2010).
[Crossref]

2009 (2)

D. R. Salgado, F. J. Alonso, I. Cambero, and A. Marcelo, “In-process surface roughness prediction system using cutting vibrations in turning,” Int. J. Adv. Manuf. Technol. 43(1-2), 40–51 (2009).
[Crossref]

R. P. Guo and Z. S. Tao, “The modified Beckmann–Kirchhoff scattering theory for surface characteristics in-process measurement,” Opt. Lasers Eng. 47(11), 1205–1211 (2009).
[Crossref]

2007 (1)

M. F. Ruiz Gale, E. N. Hogert, and N. G. Gaggioli, “Apparent and real roughness,” Opt. Lasers Eng. 45(9), 947–952 (2007).
[Crossref]

2006 (2)

J. E. Harvey, A. Krywonos, and D. Bogunovic, “Nonparaxial scalar treatment of sinusoidal phase gratings,” J. Opt. Soc. Am. A 23(4), 858–865 (2006).
[Crossref] [PubMed]

H. Dong, D. H. Wu, and H. T. Su, “Use of least square support vector machine in surface roughness prediction model,” Proc. SPIE 6280, 628022 (2006).
[Crossref]

2003 (1)

S. S. Keerthi and C. J. Lin, “Asymptotic behaviors of support vector machines with Gaussian kernel,” Neural Comput. 15(7), 1667–1689 (2003).
[Crossref] [PubMed]

1999 (1)

1995 (1)

1992 (1)

A. W. Domanski and T. R. Wolinski, “Surface roughness measurement with optical fibers,” IEEE Trans. Instrum. Meas. 41(6), 1057–1061 (1992).
[Crossref]

1990 (1)

K. E. Peiponen and T. Tsuboi, “Metal surface roughness and optical reflectance,” Opt. Laser Technol. 22(2), 127–130 (1990).
[Crossref]

1984 (1)

J. C. Stover, S. A. Serati, and C. H. Cillespie, “Calculation of surface statistics from light scatter,” Opt. Eng. 23(4), 406–412 (1984).
[Crossref]

Alonso, F. J.

D. R. Salgado, F. J. Alonso, I. Cambero, and A. Marcelo, “In-process surface roughness prediction system using cutting vibrations in turning,” Int. J. Adv. Manuf. Technol. 43(1-2), 40–51 (2009).
[Crossref]

Basano, L.

Bogunovic, D.

Cambero, I.

D. R. Salgado, F. J. Alonso, I. Cambero, and A. Marcelo, “In-process surface roughness prediction system using cutting vibrations in turning,” Int. J. Adv. Manuf. Technol. 43(1-2), 40–51 (2009).
[Crossref]

Cao, G. H.

L. J. Li, H. Yu, G. H. Cao, and W. G. Cao, “Non-contacted optical instrument for the simultaneous measurement of the surface roughness,” in 5th International Symposium on Test and Measurement6, 4911~4914 (2003).

Cao, W. G.

L. J. Li, H. Yu, G. H. Cao, and W. G. Cao, “Non-contacted optical instrument for the simultaneous measurement of the surface roughness,” in 5th International Symposium on Test and Measurement6, 4911~4914 (2003).

Cillespie, C. H.

J. C. Stover, S. A. Serati, and C. H. Cillespie, “Calculation of surface statistics from light scatter,” Opt. Eng. 23(4), 406–412 (1984).
[Crossref]

Coriand, L.

Domanski, A. W.

A. W. Domanski and T. R. Wolinski, “Surface roughness measurement with optical fibers,” IEEE Trans. Instrum. Meas. 41(6), 1057–1061 (1992).
[Crossref]

Dong, H.

H. Dong, D. H. Wu, and H. T. Su, “Use of least square support vector machine in surface roughness prediction model,” Proc. SPIE 6280, 628022 (2006).
[Crossref]

Duparré, A.

Gaggioli, N. G.

M. F. Ruiz Gale, E. N. Hogert, and N. G. Gaggioli, “Apparent and real roughness,” Opt. Lasers Eng. 45(9), 947–952 (2007).
[Crossref]

Guo, R. P.

R. P. Guo and Z. S. Tao, “The modified Beckmann–Kirchhoff scattering theory for surface characteristics in-process measurement,” Opt. Lasers Eng. 47(11), 1205–1211 (2009).
[Crossref]

Gupta, A. K.

A. K. Gupta, “Predictive modeling of turning operations using response surface methodology, artificial neural networks and support vector regression,” Int. J. Prod. Res. 48(3), 763–778 (2010).
[Crossref]

Harvey, J. E.

Hogert, E. N.

M. F. Ruiz Gale, E. N. Hogert, and N. G. Gaggioli, “Apparent and real roughness,” Opt. Lasers Eng. 45(9), 947–952 (2007).
[Crossref]

Hu, H.

X. M. Xu and H. Hu, “Development of non-contact surface roughness measurement in last decades,” in 2009 International Conference on Measuring Technology and Mechatronics Automation (2009), pp. 210–213.
[Crossref]

Hua, D. X.

H. Zhao and D. X. Hua, “Modifications to Beckmann-Kirchhoff model for random rough surfaces with non-paraxial angles,” J. Xi’an University Technol. 29(3), 285–289 (2013).

Keerthi, S. S.

S. S. Keerthi and C. J. Lin, “Asymptotic behaviors of support vector machines with Gaussian kernel,” Neural Comput. 15(7), 1667–1689 (2003).
[Crossref] [PubMed]

Krywonos, A.

Lehmann, P.

Leporatti, S.

Li, L. J.

L. J. Li, H. Yu, G. H. Cao, and W. G. Cao, “Non-contacted optical instrument for the simultaneous measurement of the surface roughness,” in 5th International Symposium on Test and Measurement6, 4911~4914 (2003).

Lin, C. J.

S. S. Keerthi and C. J. Lin, “Asymptotic behaviors of support vector machines with Gaussian kernel,” Neural Comput. 15(7), 1667–1689 (2003).
[Crossref] [PubMed]

Marcelo, A.

D. R. Salgado, F. J. Alonso, I. Cambero, and A. Marcelo, “In-process surface roughness prediction system using cutting vibrations in turning,” Int. J. Adv. Manuf. Technol. 43(1-2), 40–51 (2009).
[Crossref]

Ottonello, P.

Palestini, V.

Peiponen, K. E.

K. E. Peiponen and T. Tsuboi, “Metal surface roughness and optical reflectance,” Opt. Laser Technol. 22(2), 127–130 (1990).
[Crossref]

Penalver, D. H.

Rolandi, R.

Ruiz Gale, M. F.

M. F. Ruiz Gale, E. N. Hogert, and N. G. Gaggioli, “Apparent and real roughness,” Opt. Lasers Eng. 45(9), 947–952 (2007).
[Crossref]

Salgado, D. R.

D. R. Salgado, F. J. Alonso, I. Cambero, and A. Marcelo, “In-process surface roughness prediction system using cutting vibrations in turning,” Int. J. Adv. Manuf. Technol. 43(1-2), 40–51 (2009).
[Crossref]

Schröder, S.

Serati, S. A.

J. C. Stover, S. A. Serati, and C. H. Cillespie, “Calculation of surface statistics from light scatter,” Opt. Eng. 23(4), 406–412 (1984).
[Crossref]

Stover, J. C.

J. C. Stover, S. A. Serati, and C. H. Cillespie, “Calculation of surface statistics from light scatter,” Opt. Eng. 23(4), 406–412 (1984).
[Crossref]

Su, H. T.

H. Dong, D. H. Wu, and H. T. Su, “Use of least square support vector machine in surface roughness prediction model,” Proc. SPIE 6280, 628022 (2006).
[Crossref]

Tao, Z. S.

R. P. Guo and Z. S. Tao, “The modified Beckmann–Kirchhoff scattering theory for surface characteristics in-process measurement,” Opt. Lasers Eng. 47(11), 1205–1211 (2009).
[Crossref]

Tsuboi, T.

K. E. Peiponen and T. Tsuboi, “Metal surface roughness and optical reflectance,” Opt. Laser Technol. 22(2), 127–130 (1990).
[Crossref]

Tünnermann, A.

Wolinski, T. R.

A. W. Domanski and T. R. Wolinski, “Surface roughness measurement with optical fibers,” IEEE Trans. Instrum. Meas. 41(6), 1057–1061 (1992).
[Crossref]

Wu, D. H.

H. Dong, D. H. Wu, and H. T. Su, “Use of least square support vector machine in surface roughness prediction model,” Proc. SPIE 6280, 628022 (2006).
[Crossref]

Xu, X. M.

X. M. Xu and H. Hu, “Development of non-contact surface roughness measurement in last decades,” in 2009 International Conference on Measuring Technology and Mechatronics Automation (2009), pp. 210–213.
[Crossref]

Yu, H.

L. J. Li, H. Yu, G. H. Cao, and W. G. Cao, “Non-contacted optical instrument for the simultaneous measurement of the surface roughness,” in 5th International Symposium on Test and Measurement6, 4911~4914 (2003).

Zhang, J.

N. N. Zhu and J. Zhang, “Surface roughness measurement based on fiber optic sensor,” Measurement 86, 239–245 (2016).
[Crossref]

Zhao, H.

H. Zhao and D. X. Hua, “Modifications to Beckmann-Kirchhoff model for random rough surfaces with non-paraxial angles,” J. Xi’an University Technol. 29(3), 285–289 (2013).

Zhu, N. N.

N. N. Zhu and J. Zhang, “Surface roughness measurement based on fiber optic sensor,” Measurement 86, 239–245 (2016).
[Crossref]

Appl. Opt. (2)

IEEE Trans. Instrum. Meas. (1)

A. W. Domanski and T. R. Wolinski, “Surface roughness measurement with optical fibers,” IEEE Trans. Instrum. Meas. 41(6), 1057–1061 (1992).
[Crossref]

Int. J. Adv. Manuf. Technol. (1)

D. R. Salgado, F. J. Alonso, I. Cambero, and A. Marcelo, “In-process surface roughness prediction system using cutting vibrations in turning,” Int. J. Adv. Manuf. Technol. 43(1-2), 40–51 (2009).
[Crossref]

Int. J. Prod. Res. (1)

A. K. Gupta, “Predictive modeling of turning operations using response surface methodology, artificial neural networks and support vector regression,” Int. J. Prod. Res. 48(3), 763–778 (2010).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Xi’an University Technol. (1)

H. Zhao and D. X. Hua, “Modifications to Beckmann-Kirchhoff model for random rough surfaces with non-paraxial angles,” J. Xi’an University Technol. 29(3), 285–289 (2013).

Measurement (1)

N. N. Zhu and J. Zhang, “Surface roughness measurement based on fiber optic sensor,” Measurement 86, 239–245 (2016).
[Crossref]

Neural Comput. (1)

S. S. Keerthi and C. J. Lin, “Asymptotic behaviors of support vector machines with Gaussian kernel,” Neural Comput. 15(7), 1667–1689 (2003).
[Crossref] [PubMed]

Opt. Eng. (1)

J. C. Stover, S. A. Serati, and C. H. Cillespie, “Calculation of surface statistics from light scatter,” Opt. Eng. 23(4), 406–412 (1984).
[Crossref]

Opt. Express (1)

Opt. Laser Technol. (1)

K. E. Peiponen and T. Tsuboi, “Metal surface roughness and optical reflectance,” Opt. Laser Technol. 22(2), 127–130 (1990).
[Crossref]

Opt. Lasers Eng. (2)

M. F. Ruiz Gale, E. N. Hogert, and N. G. Gaggioli, “Apparent and real roughness,” Opt. Lasers Eng. 45(9), 947–952 (2007).
[Crossref]

R. P. Guo and Z. S. Tao, “The modified Beckmann–Kirchhoff scattering theory for surface characteristics in-process measurement,” Opt. Lasers Eng. 47(11), 1205–1211 (2009).
[Crossref]

Proc. SPIE (1)

H. Dong, D. H. Wu, and H. T. Su, “Use of least square support vector machine in surface roughness prediction model,” Proc. SPIE 6280, 628022 (2006).
[Crossref]

Other (6)

C. C. Chang and C. J. Lin, “LIBSVM: a library for support vector machines,” 2001. http://www.csie.ntu.edu.tw/ ~cjlin/libsvm.

V. N. Vapnik, The Nature of Statistical Learning Theory (Springer-Verlag, 2000).

L. J. Li, H. Yu, G. H. Cao, and W. G. Cao, “Non-contacted optical instrument for the simultaneous measurement of the surface roughness,” in 5th International Symposium on Test and Measurement6, 4911~4914 (2003).

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).

X. M. Xu and H. Hu, “Development of non-contact surface roughness measurement in last decades,” in 2009 International Conference on Measuring Technology and Mechatronics Automation (2009), pp. 210–213.
[Crossref]

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic Press, 1969).

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Figures (3)

Fig. 1
Fig. 1 Experimental-setup for measuring surface roughness by multi-wavelength fiber sensor.
Fig. 2
Fig. 2 (a) Schematic diagram of the fiber bundle end face 2(b) Intensity of transmitting fiber under Gaussian distribution.
Fig. 3
Fig. 3 The reflected intensity of grinding specimens ( R a = 0.012μm, 0.025μm, 0.05μm, and 0.10μm) varying as the working distance under the different wavelengths. (a) λ 1 = 650 nm; (b) λ 2 = 1310 nm.

Tables (2)

Tables Icon

Table 1 The surface roughness obtained by using the prediction model at 650 nm.

Tables Icon

Table 2 The surface roughness obtained by using the prediction model at 1310 nm.

Equations (19)

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min ω,b, ξ ( ) 1 2 ω 2 +C i=1 l ( ξ i + ξ i ) s.t. y i ( ( ω x i )+b )ε+ ξ i ,i=1,,l ( ( ω x i )+b ) y i ε+ ξ i ,i=1,,l ξ i ( ) 0,i=1,,l
L( ω,b, ξ ( ) , α ( ) , η ( ) )= 1 2 ω 2 +C i=1 l ( ξ i + ξ i ) i=1 l ( η i ξ i + η i ξ i ) i=1 l α i ( ε+ ξ i + y i ( ω x i )b ) i=1 l α i ( ε+ ξ i y i +( ω x i )+b )
ω L=0, b L=0, ξ i ( ) L=0
ω= i=1 l ( α i α i ) x i
i=1 l ( α i α i ) =0
C α i ( ) η i ( ) =0,i=1,,l
max α ( ) , η ( ) R 2l 1 2 i,j=1 l ( α i α i )( α j α j )( x i x j )ε i=1 l ( α i + α i )+ i=1 l y i ( α i α i ) s.t. i=1 l ( α i α i )=0 C α i ( ) η i ( ) =0,i=1,,l α i ( ) 0, η i ( ) 0,i=1,,l
φ: R n H xX=φ( x )
max α ( ) , η ( ) R 2l 1 2 i,j=1 l ( α i α i )( α j α j )( φ( x i )φ( x j ) )ε i=1 l ( α i + α i )+ i=1 l y i ( α i α i ) s.t. i=1 l ( α i α i )=0 C α i ( ) η i ( ) =0,i=1,,l α i ( ) 0, η i ( ) 0,i=1,,l
min α ( ) R 2l 1 2 i,j=1 l ( α i α i )( α j α j )( φ( x i )φ( x j ) )+ε i=1 l ( α i + α i ) i=1 l y i ( α i α i ) s.t. i=1 l ( α i α i )=0 0 α i ( ) C,i=1,,l
ω ¯ = i=1 l ( α i ¯ α i ¯ )φ( x i )
b ¯ = y j i=1 l ( α i ¯ α i ¯ )( φ( x i )φ( x j ) )+ε
b ¯ = y k i=1 l ( α i ¯ α i ¯ )( φ( x i )φ( x k ) )ε
c( x,y,g( x ) )= | yg( x ) | ε
| yg( x ) | ε ={ 0 | yg( x ) |ε | yg( x ) |ε other
y=g( x )=( ω ¯ ϕ( x ) )+ b ¯ = i=1 l ( α i ¯ α i ¯ )( ϕ( x i )ϕ( x ) )+ b ¯
I= I 0 M S exp[ 2 ( 4πσ λ ) 2 ]
σ 2 = 1 2 1 ( 4π ) 2 λ 1 2 λ 2 2 ( λ 1 2 λ 2 2 ) ln[ I λ 1 I λ 2 I 0 λ 2 I 0 λ 1 ]
R a = 4 5 σ

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