Abstract

We aim to build an integrated fixturing model to describe the structural properties and thermal properties of the support frame of glass laser optics. Therefore, (a) a near global optimal set of clamps can be computed to minimize the surface shape error of the glass laser optic based on the proposed model, and (b) a desired surface shape error can be obtained by adjusting the clamping forces under various environmental temperatures based on the model. To construct the model, we develop a new multiple kernel learning method and call it multiple kernel support vector functional regression. The proposed method uses two layer regressions to group and order the data sources by the weights of the kernels and the factors of the layers. Because of that, the influences of the clamps and the temperature can be evaluated by grouping them into different layers.

© 2014 Optical Society of America

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2012

J. X. Yu, S. B. He, X. Xiang, X. D. Yuan, W. G. Zheng, H. B. Lv, and X. T. Zu, “High temperature thermal behaviour modeling of large-scale fused silica optics for laser facility,” Chin. Phys. B 21, 064401 (2012).

P. K. Wong, Q. S. Xu, C. M. Vong, and H. Ch. Wong, “Rate-dependent hysteresis modeling and control of a piezostage using online support vector machine and relevance vector machine,” IEEE Trans. Ind. Electron. 59, 1988–2001 (2012).
[CrossRef]

F. Bellocchio, S. Ferrari, V. Piuri, and N. A. Borghese, “Hierarchical approach for multiscale support vector regression,” IEEE Trans. Neural Netw. Learn. Syst. 23, 1448–1460 (2012).
[CrossRef]

2011

M. Gönen and E. Alpaydim, “Multiple kernel learning algorithms,” J. Mach. Learn. Res. 12, 2211–2268 (2011).

2010

G. J. Michels and V. L. Genberg, “Optomechanical analysis and design tool for adaptive x-ray optics,” Proc. SPIE 7803, 780308 (2010).
[CrossRef]

H. Wang, K. Rong, H. Li, and P. Shaun, “Computer aided fixture design: recent research and trends,” Comput. Aided Des. 42, 1085–1094 (2010).
[CrossRef]

H. Q. Wang, F. C. Sun, Y. N. Cai, N. Cheng, and L. G. Ding, “On multiple kernel learning methods,” Acta Autom. Sinica 36, 1037–1050 (2010).
[CrossRef]

2009

S. B. Qiu and T. Lane, “A framework for multiple kernel support vector regression and its applications to siRNA efficacy prediction,” IEEE/ACM Trans. Comput. Biol. Bioinform. 6, 90–199 (2009).

H. Chang, Z. G. Fan, S. Q. Chen, and Y.-M. Cao, “Impact of the temperature gradient on optical system parameters: modeling and analysis,” Proc. SPIE 7506, 75060G (2009).

Y. Ning, H. Zhou, H. Yu, C. H. Rao, and W. H. Jiang, “Classical areas of phenomenology: thermal stability test and analysis of a 20-actuator bimorph deformable mirror,” Chin. Phys. B 18, 1089–1095 (2009).

2008

M. K. Cho, “Performance prediction of the TMT tertiary mirror support system,” Proc. SPIE 7018, 70184F (2008).
[CrossRef]

2007

L. P. Zhou and D. W. Tang, “A functionally graded structural design of mirrors for reducing their thermal deformations in high-power laser systems by finite element method,” Opt. Laser Technol. 39, 980–986 (2007).
[CrossRef]

Y. H. Liu, H. P. Huang, and C. H. Weng, “Recognition of electromyographic signals using cascaded kernel learning machine,” IEEE/ASME Trans. Mechatron. 12, 253–264 (2007).
[CrossRef]

2006

Y. F. Peng, J. L. Cui, Z. H. Cheng, D. L. Zuo, and Y. N. Zhang, “Characteristics of thermal distortions of the laser mirror substrates filled with phase change materials,” Opt. Laser Technol. 38, 594–598 (2006).
[CrossRef]

M. K. Cho, R. S. Price, and I. K. Moon, “Optimization of the ATST primary mirror support system,” Proc. SPIE 6273, 62731E (2006).
[CrossRef]

2005

V. L. Genberg, G. J. Michels, and K. B. Doyle, “Design optimization of actuator layouts of adaptive optics using a genetic algorithm,” Proc. SPIE 5877, 58770L (2005).

R. Xu and D. Wunsch, “Survey of clustering algorithms,” IEEE Trans. Neural Netw. 16, 645–678 (2005).
[CrossRef]

2004

G. Wang, Y. Li, and D. Bi, “Support vector machine networks for friction modeling,” IEEE/ASME Trans. Mechatron. 9, 601–606 (2004).
[CrossRef]

G. R. G. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui, and M. I. Jordan, “Learning the kernel matrix with semidefinite programming,” J. Mach. Learn. Res. 5, 27–72 (2004).

D. Bi, Y. F. Li, S. K. Tso, and G. L. Wang, “Friction modeling and compensation for haptic display based on support vector machine,” IEEE Trans. Ind. Electron. 51, 491–500 (2004).
[CrossRef]

A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Stat. Comput 14, 199–222 (2004).
[CrossRef]

K. B. Doyle, V. L. Genberg, and G. J. Michels, “Integrated optomechanical analysis of adaptive optical systems,” Proc. SPIE 5178, 20–28 (2004).
[CrossRef]

J. H. Lee, T. K. Uhm, W. S. Lee, and S. K. Youn, “First order analysis of thin plate deformable mirrors,” J. Korean Phys. Soc. 44, 1412–1416 (2004).

2003

Y. Li and D. Bi, “A method for dynamics identification for haptic display of the operating feel in virtual environments,” IEEE/ASME Trans. Mechatron. 8, 476–482 (2003).
[CrossRef]

2002

O. Chapelle, V. Vapnik, O. Bousquet, and S. Mukherjee, “Choosing multiple parameters for support vector machines,” Mach. Learn. 46, 131–159 (2002).
[CrossRef]

1998

L. Daudeville and H. Carre, “Thermal tempering simulation of glass plates: Inner and edge residual stresses,” J. Therm. Stress. 21, 667–689 (1998).
[CrossRef]

H. M. Martin, S. P. Callahan, B. Cuerden, W. B. Davison, S. T. Derigne, L. R. Dettmann, G. Parodi, T. J. Trebisky, S. C. West, and J. T. Williams, “Active supports and force optimization for the MMT primary mirror,” Proc. SPIE 3352, 412–423 (1998).
[CrossRef]

1996

1989

G. L. Herrit and H. E. Reedy, “Advanced figure of merit evaluation for CO2 laser optics using finite element analysis,” Proc. SPIE 1047, 33–42 (1989).
[CrossRef]

Allen, P.

R. Pelossof, A. Miller, P. Allen, and T. Jebara, “A SVM learning approach to robotic grasping,” in IEEE International Conference on Robotics and Automation (2004), Vol. 4, pp. 3512–3518.

Alpaydim, E.

M. Gönen and E. Alpaydim, “Multiple kernel learning algorithms,” J. Mach. Learn. Res. 12, 2211–2268 (2011).

Alpaydin, E.

M. Gönen and E. Alpaydin, “Localized multiple kernel learning,” in Proceedings 25th International Conference on Machine Learning (2008), pp. 352–359.

M. Gönen and E. Alpaydin, “Localized multiple kernel regression,” in Proceedings 20th IAPR International Conference on Pattern Recognition (2010), pp. 1425–1428.

Bartlett, P.

G. R. G. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui, and M. I. Jordan, “Learning the kernel matrix with semidefinite programming,” J. Mach. Learn. Res. 5, 27–72 (2004).

Bellocchio, F.

F. Bellocchio, S. Ferrari, V. Piuri, and N. A. Borghese, “Hierarchical approach for multiscale support vector regression,” IEEE Trans. Neural Netw. Learn. Syst. 23, 1448–1460 (2012).
[CrossRef]

Bi, D.

D. Bi, Y. F. Li, S. K. Tso, and G. L. Wang, “Friction modeling and compensation for haptic display based on support vector machine,” IEEE Trans. Ind. Electron. 51, 491–500 (2004).
[CrossRef]

G. Wang, Y. Li, and D. Bi, “Support vector machine networks for friction modeling,” IEEE/ASME Trans. Mechatron. 9, 601–606 (2004).
[CrossRef]

Y. Li and D. Bi, “A method for dynamics identification for haptic display of the operating feel in virtual environments,” IEEE/ASME Trans. Mechatron. 8, 476–482 (2003).
[CrossRef]

Borghese, N. A.

F. Bellocchio, S. Ferrari, V. Piuri, and N. A. Borghese, “Hierarchical approach for multiscale support vector regression,” IEEE Trans. Neural Netw. Learn. Syst. 23, 1448–1460 (2012).
[CrossRef]

Bousquet, O.

O. Chapelle, V. Vapnik, O. Bousquet, and S. Mukherjee, “Choosing multiple parameters for support vector machines,” Mach. Learn. 46, 131–159 (2002).
[CrossRef]

Cai, Y. N.

H. Q. Wang, F. C. Sun, Y. N. Cai, N. Cheng, and L. G. Ding, “On multiple kernel learning methods,” Acta Autom. Sinica 36, 1037–1050 (2010).
[CrossRef]

Callahan, S. P.

H. M. Martin, S. P. Callahan, B. Cuerden, W. B. Davison, S. T. Derigne, L. R. Dettmann, G. Parodi, T. J. Trebisky, S. C. West, and J. T. Williams, “Active supports and force optimization for the MMT primary mirror,” Proc. SPIE 3352, 412–423 (1998).
[CrossRef]

Cao, Y.-M.

H. Chang, Z. G. Fan, S. Q. Chen, and Y.-M. Cao, “Impact of the temperature gradient on optical system parameters: modeling and analysis,” Proc. SPIE 7506, 75060G (2009).

Carre, H.

L. Daudeville and H. Carre, “Thermal tempering simulation of glass plates: Inner and edge residual stresses,” J. Therm. Stress. 21, 667–689 (1998).
[CrossRef]

Chang, H.

H. Chang, Z. G. Fan, S. Q. Chen, and Y.-M. Cao, “Impact of the temperature gradient on optical system parameters: modeling and analysis,” Proc. SPIE 7506, 75060G (2009).

Chapelle, O.

O. Chapelle, V. Vapnik, O. Bousquet, and S. Mukherjee, “Choosing multiple parameters for support vector machines,” Mach. Learn. 46, 131–159 (2002).
[CrossRef]

Chen, S. Q.

H. Chang, Z. G. Fan, S. Q. Chen, and Y.-M. Cao, “Impact of the temperature gradient on optical system parameters: modeling and analysis,” Proc. SPIE 7506, 75060G (2009).

Cheng, N.

H. Q. Wang, F. C. Sun, Y. N. Cai, N. Cheng, and L. G. Ding, “On multiple kernel learning methods,” Acta Autom. Sinica 36, 1037–1050 (2010).
[CrossRef]

Cheng, Z. H.

Y. F. Peng, J. L. Cui, Z. H. Cheng, D. L. Zuo, and Y. N. Zhang, “Characteristics of thermal distortions of the laser mirror substrates filled with phase change materials,” Opt. Laser Technol. 38, 594–598 (2006).
[CrossRef]

Cho, M. K.

M. K. Cho, “Performance prediction of the TMT tertiary mirror support system,” Proc. SPIE 7018, 70184F (2008).
[CrossRef]

M. K. Cho, R. S. Price, and I. K. Moon, “Optimization of the ATST primary mirror support system,” Proc. SPIE 6273, 62731E (2006).
[CrossRef]

Clausen, J.

J. Clausen, “Branch and bound algorithms-principles and examples,” in Parallel Computing in Optimization (Applied Optimization) (Springer, 1997), pp. 239–267.

Creath, K.

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. R. Shannon and J. C. Wyant, eds. (Academic, 1992), Vol. 11, pp. 38–39.

Cristianini, N.

G. R. G. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui, and M. I. Jordan, “Learning the kernel matrix with semidefinite programming,” J. Mach. Learn. Res. 5, 27–72 (2004).

Cuerden, B.

H. M. Martin, S. P. Callahan, B. Cuerden, W. B. Davison, S. T. Derigne, L. R. Dettmann, G. Parodi, T. J. Trebisky, S. C. West, and J. T. Williams, “Active supports and force optimization for the MMT primary mirror,” Proc. SPIE 3352, 412–423 (1998).
[CrossRef]

Cui, J. L.

Y. F. Peng, J. L. Cui, Z. H. Cheng, D. L. Zuo, and Y. N. Zhang, “Characteristics of thermal distortions of the laser mirror substrates filled with phase change materials,” Opt. Laser Technol. 38, 594–598 (2006).
[CrossRef]

Dai, G. M.

Daudeville, L.

L. Daudeville and H. Carre, “Thermal tempering simulation of glass plates: Inner and edge residual stresses,” J. Therm. Stress. 21, 667–689 (1998).
[CrossRef]

Davison, W. B.

H. M. Martin, S. P. Callahan, B. Cuerden, W. B. Davison, S. T. Derigne, L. R. Dettmann, G. Parodi, T. J. Trebisky, S. C. West, and J. T. Williams, “Active supports and force optimization for the MMT primary mirror,” Proc. SPIE 3352, 412–423 (1998).
[CrossRef]

de Diego, I. M.

J. M. Moguerza, A. Muñoz, and I. M. de Diego, “Improving support vector classification via the combination of multiple sources of information,” in Proceedings of the Structural, Syntactic, and Statistical Pattern Recognition, Joint IAPR International Workshops (2004).

Derigne, S. T.

H. M. Martin, S. P. Callahan, B. Cuerden, W. B. Davison, S. T. Derigne, L. R. Dettmann, G. Parodi, T. J. Trebisky, S. C. West, and J. T. Williams, “Active supports and force optimization for the MMT primary mirror,” Proc. SPIE 3352, 412–423 (1998).
[CrossRef]

Dettmann, L. R.

H. M. Martin, S. P. Callahan, B. Cuerden, W. B. Davison, S. T. Derigne, L. R. Dettmann, G. Parodi, T. J. Trebisky, S. C. West, and J. T. Williams, “Active supports and force optimization for the MMT primary mirror,” Proc. SPIE 3352, 412–423 (1998).
[CrossRef]

Ding, L. G.

H. Q. Wang, F. C. Sun, Y. N. Cai, N. Cheng, and L. G. Ding, “On multiple kernel learning methods,” Acta Autom. Sinica 36, 1037–1050 (2010).
[CrossRef]

Doyle, K. B.

V. L. Genberg, G. J. Michels, and K. B. Doyle, “Design optimization of actuator layouts of adaptive optics using a genetic algorithm,” Proc. SPIE 5877, 58770L (2005).

K. B. Doyle, V. L. Genberg, and G. J. Michels, “Integrated optomechanical analysis of adaptive optical systems,” Proc. SPIE 5178, 20–28 (2004).
[CrossRef]

Duan, L. Y.

J. J. Yang, Y. N. Li, Y. H. Tian, L. Y. Duan, and W. Gao, “Group-sensitive multiple kernel learning for object categorization,” in Proceedings of the 12th IEEE International Conference on Computer Vision (2009), pp. 436–443.

Fan, Z. G.

H. Chang, Z. G. Fan, S. Q. Chen, and Y.-M. Cao, “Impact of the temperature gradient on optical system parameters: modeling and analysis,” Proc. SPIE 7506, 75060G (2009).

Ferrari, S.

F. Bellocchio, S. Ferrari, V. Piuri, and N. A. Borghese, “Hierarchical approach for multiscale support vector regression,” IEEE Trans. Neural Netw. Learn. Syst. 23, 1448–1460 (2012).
[CrossRef]

Ford, R. G.

Y. Miyamoto, W. A. Kaysser, B. H. Rabin, A. Kawasaki, and R. G. Ford, Functionally Graded Materials: Design, Processing and Applications (Kluwer, 1999).

Gao, W.

J. J. Yang, Y. N. Li, Y. H. Tian, L. Y. Duan, and W. Gao, “Group-sensitive multiple kernel learning for object categorization,” in Proceedings of the 12th IEEE International Conference on Computer Vision (2009), pp. 436–443.

Genberg, V. L.

G. J. Michels and V. L. Genberg, “Optomechanical analysis and design tool for adaptive x-ray optics,” Proc. SPIE 7803, 780308 (2010).
[CrossRef]

V. L. Genberg, G. J. Michels, and K. B. Doyle, “Design optimization of actuator layouts of adaptive optics using a genetic algorithm,” Proc. SPIE 5877, 58770L (2005).

K. B. Doyle, V. L. Genberg, and G. J. Michels, “Integrated optomechanical analysis of adaptive optical systems,” Proc. SPIE 5178, 20–28 (2004).
[CrossRef]

G. J. Michels and V. L. Genberg, “Advances in the analysis and design of adaptive optics,” in Imaging and Applied Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper AMC2.

Ghaoui, L. E.

G. R. G. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui, and M. I. Jordan, “Learning the kernel matrix with semidefinite programming,” J. Mach. Learn. Res. 5, 27–72 (2004).

Gönen, M.

M. Gönen and E. Alpaydim, “Multiple kernel learning algorithms,” J. Mach. Learn. Res. 12, 2211–2268 (2011).

M. Gönen and E. Alpaydin, “Localized multiple kernel learning,” in Proceedings 25th International Conference on Machine Learning (2008), pp. 352–359.

M. Gönen and E. Alpaydin, “Localized multiple kernel regression,” in Proceedings 20th IAPR International Conference on Pattern Recognition (2010), pp. 1425–1428.

He, S. B.

J. X. Yu, S. B. He, X. Xiang, X. D. Yuan, W. G. Zheng, H. B. Lv, and X. T. Zu, “High temperature thermal behaviour modeling of large-scale fused silica optics for laser facility,” Chin. Phys. B 21, 064401 (2012).

Herrit, G. L.

G. L. Herrit and H. E. Reedy, “Advanced figure of merit evaluation for CO2 laser optics using finite element analysis,” Proc. SPIE 1047, 33–42 (1989).
[CrossRef]

Huang, H. P.

Y. H. Liu, H. P. Huang, and C. H. Weng, “Recognition of electromyographic signals using cascaded kernel learning machine,” IEEE/ASME Trans. Mechatron. 12, 253–264 (2007).
[CrossRef]

Jebara, T.

R. Pelossof, A. Miller, P. Allen, and T. Jebara, “A SVM learning approach to robotic grasping,” in IEEE International Conference on Robotics and Automation (2004), Vol. 4, pp. 3512–3518.

Jiang, W. H.

Y. Ning, H. Zhou, H. Yu, C. H. Rao, and W. H. Jiang, “Classical areas of phenomenology: thermal stability test and analysis of a 20-actuator bimorph deformable mirror,” Chin. Phys. B 18, 1089–1095 (2009).

Jordan, M. I.

G. R. G. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui, and M. I. Jordan, “Learning the kernel matrix with semidefinite programming,” J. Mach. Learn. Res. 5, 27–72 (2004).

Kawasaki, A.

Y. Miyamoto, W. A. Kaysser, B. H. Rabin, A. Kawasaki, and R. G. Ford, Functionally Graded Materials: Design, Processing and Applications (Kluwer, 1999).

Kaysser, W. A.

Y. Miyamoto, W. A. Kaysser, B. H. Rabin, A. Kawasaki, and R. G. Ford, Functionally Graded Materials: Design, Processing and Applications (Kluwer, 1999).

Kingsbury, N.

N. Kingsbury, D. B. H. Tay, and M. Palaniswami, “Multi-scale kernel methods for classification,” in Proceedings of the IEEE Workshop on Machine Learning for Signal Processing (2005), pp. 43–48.

Lanckriet, G. R. G.

G. R. G. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui, and M. I. Jordan, “Learning the kernel matrix with semidefinite programming,” J. Mach. Learn. Res. 5, 27–72 (2004).

Lane, T.

S. B. Qiu and T. Lane, “A framework for multiple kernel support vector regression and its applications to siRNA efficacy prediction,” IEEE/ACM Trans. Comput. Biol. Bioinform. 6, 90–199 (2009).

Lee, J. H.

J. H. Lee, T. K. Uhm, W. S. Lee, and S. K. Youn, “First order analysis of thin plate deformable mirrors,” J. Korean Phys. Soc. 44, 1412–1416 (2004).

Lee, W. S.

J. H. Lee, T. K. Uhm, W. S. Lee, and S. K. Youn, “First order analysis of thin plate deformable mirrors,” J. Korean Phys. Soc. 44, 1412–1416 (2004).

Li, H.

H. Wang, K. Rong, H. Li, and P. Shaun, “Computer aided fixture design: recent research and trends,” Comput. Aided Des. 42, 1085–1094 (2010).
[CrossRef]

Li, Y.

G. Wang, Y. Li, and D. Bi, “Support vector machine networks for friction modeling,” IEEE/ASME Trans. Mechatron. 9, 601–606 (2004).
[CrossRef]

Y. Li and D. Bi, “A method for dynamics identification for haptic display of the operating feel in virtual environments,” IEEE/ASME Trans. Mechatron. 8, 476–482 (2003).
[CrossRef]

Li, Y. F.

D. Bi, Y. F. Li, S. K. Tso, and G. L. Wang, “Friction modeling and compensation for haptic display based on support vector machine,” IEEE Trans. Ind. Electron. 51, 491–500 (2004).
[CrossRef]

Li, Y. N.

J. J. Yang, Y. N. Li, Y. H. Tian, L. Y. Duan, and W. Gao, “Group-sensitive multiple kernel learning for object categorization,” in Proceedings of the 12th IEEE International Conference on Computer Vision (2009), pp. 436–443.

Liu, Y. H.

Y. H. Liu, H. P. Huang, and C. H. Weng, “Recognition of electromyographic signals using cascaded kernel learning machine,” IEEE/ASME Trans. Mechatron. 12, 253–264 (2007).
[CrossRef]

Lv, H. B.

J. X. Yu, S. B. He, X. Xiang, X. D. Yuan, W. G. Zheng, H. B. Lv, and X. T. Zu, “High temperature thermal behaviour modeling of large-scale fused silica optics for laser facility,” Chin. Phys. B 21, 064401 (2012).

Martin, H. M.

H. M. Martin, S. P. Callahan, B. Cuerden, W. B. Davison, S. T. Derigne, L. R. Dettmann, G. Parodi, T. J. Trebisky, S. C. West, and J. T. Williams, “Active supports and force optimization for the MMT primary mirror,” Proc. SPIE 3352, 412–423 (1998).
[CrossRef]

Michels, G. J.

G. J. Michels and V. L. Genberg, “Optomechanical analysis and design tool for adaptive x-ray optics,” Proc. SPIE 7803, 780308 (2010).
[CrossRef]

V. L. Genberg, G. J. Michels, and K. B. Doyle, “Design optimization of actuator layouts of adaptive optics using a genetic algorithm,” Proc. SPIE 5877, 58770L (2005).

K. B. Doyle, V. L. Genberg, and G. J. Michels, “Integrated optomechanical analysis of adaptive optical systems,” Proc. SPIE 5178, 20–28 (2004).
[CrossRef]

G. J. Michels and V. L. Genberg, “Advances in the analysis and design of adaptive optics,” in Imaging and Applied Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper AMC2.

Miller, A.

R. Pelossof, A. Miller, P. Allen, and T. Jebara, “A SVM learning approach to robotic grasping,” in IEEE International Conference on Robotics and Automation (2004), Vol. 4, pp. 3512–3518.

Miyamoto, Y.

Y. Miyamoto, W. A. Kaysser, B. H. Rabin, A. Kawasaki, and R. G. Ford, Functionally Graded Materials: Design, Processing and Applications (Kluwer, 1999).

Moguerza, J. M.

J. M. Moguerza, A. Muñoz, and I. M. de Diego, “Improving support vector classification via the combination of multiple sources of information,” in Proceedings of the Structural, Syntactic, and Statistical Pattern Recognition, Joint IAPR International Workshops (2004).

Moon, I. K.

M. K. Cho, R. S. Price, and I. K. Moon, “Optimization of the ATST primary mirror support system,” Proc. SPIE 6273, 62731E (2006).
[CrossRef]

Mukherjee, S.

O. Chapelle, V. Vapnik, O. Bousquet, and S. Mukherjee, “Choosing multiple parameters for support vector machines,” Mach. Learn. 46, 131–159 (2002).
[CrossRef]

Muñoz, A.

J. M. Moguerza, A. Muñoz, and I. M. de Diego, “Improving support vector classification via the combination of multiple sources of information,” in Proceedings of the Structural, Syntactic, and Statistical Pattern Recognition, Joint IAPR International Workshops (2004).

Ning, Y.

Y. Ning, H. Zhou, H. Yu, C. H. Rao, and W. H. Jiang, “Classical areas of phenomenology: thermal stability test and analysis of a 20-actuator bimorph deformable mirror,” Chin. Phys. B 18, 1089–1095 (2009).

Osten, W.

T. Ruppel, O. Sawodny, and W. Osten, “Actuator placement for minimum force modal control of continuous faceplate deformable mirrors,” in IEEE International Conference on Control Applications (2010), pp. 867–872.

Palaniswami, M.

N. Kingsbury, D. B. H. Tay, and M. Palaniswami, “Multi-scale kernel methods for classification,” in Proceedings of the IEEE Workshop on Machine Learning for Signal Processing (2005), pp. 43–48.

Parodi, G.

H. M. Martin, S. P. Callahan, B. Cuerden, W. B. Davison, S. T. Derigne, L. R. Dettmann, G. Parodi, T. J. Trebisky, S. C. West, and J. T. Williams, “Active supports and force optimization for the MMT primary mirror,” Proc. SPIE 3352, 412–423 (1998).
[CrossRef]

Pelossof, R.

R. Pelossof, A. Miller, P. Allen, and T. Jebara, “A SVM learning approach to robotic grasping,” in IEEE International Conference on Robotics and Automation (2004), Vol. 4, pp. 3512–3518.

Peng, Y. F.

Y. F. Peng, J. L. Cui, Z. H. Cheng, D. L. Zuo, and Y. N. Zhang, “Characteristics of thermal distortions of the laser mirror substrates filled with phase change materials,” Opt. Laser Technol. 38, 594–598 (2006).
[CrossRef]

Piuri, V.

F. Bellocchio, S. Ferrari, V. Piuri, and N. A. Borghese, “Hierarchical approach for multiscale support vector regression,” IEEE Trans. Neural Netw. Learn. Syst. 23, 1448–1460 (2012).
[CrossRef]

Price, R. S.

M. K. Cho, R. S. Price, and I. K. Moon, “Optimization of the ATST primary mirror support system,” Proc. SPIE 6273, 62731E (2006).
[CrossRef]

Qiu, S. B.

S. B. Qiu and T. Lane, “A framework for multiple kernel support vector regression and its applications to siRNA efficacy prediction,” IEEE/ACM Trans. Comput. Biol. Bioinform. 6, 90–199 (2009).

Rabin, B. H.

Y. Miyamoto, W. A. Kaysser, B. H. Rabin, A. Kawasaki, and R. G. Ford, Functionally Graded Materials: Design, Processing and Applications (Kluwer, 1999).

Rao, C. H.

Y. Ning, H. Zhou, H. Yu, C. H. Rao, and W. H. Jiang, “Classical areas of phenomenology: thermal stability test and analysis of a 20-actuator bimorph deformable mirror,” Chin. Phys. B 18, 1089–1095 (2009).

Reedy, H. E.

G. L. Herrit and H. E. Reedy, “Advanced figure of merit evaluation for CO2 laser optics using finite element analysis,” Proc. SPIE 1047, 33–42 (1989).
[CrossRef]

Rong, K.

H. Wang, K. Rong, H. Li, and P. Shaun, “Computer aided fixture design: recent research and trends,” Comput. Aided Des. 42, 1085–1094 (2010).
[CrossRef]

Ruppel, T.

T. Ruppel, O. Sawodny, and W. Osten, “Actuator placement for minimum force modal control of continuous faceplate deformable mirrors,” in IEEE International Conference on Control Applications (2010), pp. 867–872.

Sawodny, O.

T. Ruppel, O. Sawodny, and W. Osten, “Actuator placement for minimum force modal control of continuous faceplate deformable mirrors,” in IEEE International Conference on Control Applications (2010), pp. 867–872.

Schölkopf, B.

A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Stat. Comput 14, 199–222 (2004).
[CrossRef]

Shaun, P.

H. Wang, K. Rong, H. Li, and P. Shaun, “Computer aided fixture design: recent research and trends,” Comput. Aided Des. 42, 1085–1094 (2010).
[CrossRef]

Smola, A. J.

A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Stat. Comput 14, 199–222 (2004).
[CrossRef]

Sun, F. C.

H. Q. Wang, F. C. Sun, Y. N. Cai, N. Cheng, and L. G. Ding, “On multiple kernel learning methods,” Acta Autom. Sinica 36, 1037–1050 (2010).
[CrossRef]

Tang, D. W.

L. P. Zhou and D. W. Tang, “A functionally graded structural design of mirrors for reducing their thermal deformations in high-power laser systems by finite element method,” Opt. Laser Technol. 39, 980–986 (2007).
[CrossRef]

Tay, D. B. H.

N. Kingsbury, D. B. H. Tay, and M. Palaniswami, “Multi-scale kernel methods for classification,” in Proceedings of the IEEE Workshop on Machine Learning for Signal Processing (2005), pp. 43–48.

Tian, Y. H.

J. J. Yang, Y. N. Li, Y. H. Tian, L. Y. Duan, and W. Gao, “Group-sensitive multiple kernel learning for object categorization,” in Proceedings of the 12th IEEE International Conference on Computer Vision (2009), pp. 436–443.

Trebisky, T. J.

H. M. Martin, S. P. Callahan, B. Cuerden, W. B. Davison, S. T. Derigne, L. R. Dettmann, G. Parodi, T. J. Trebisky, S. C. West, and J. T. Williams, “Active supports and force optimization for the MMT primary mirror,” Proc. SPIE 3352, 412–423 (1998).
[CrossRef]

Tso, S. K.

D. Bi, Y. F. Li, S. K. Tso, and G. L. Wang, “Friction modeling and compensation for haptic display based on support vector machine,” IEEE Trans. Ind. Electron. 51, 491–500 (2004).
[CrossRef]

Uhm, T. K.

J. H. Lee, T. K. Uhm, W. S. Lee, and S. K. Youn, “First order analysis of thin plate deformable mirrors,” J. Korean Phys. Soc. 44, 1412–1416 (2004).

Vapnik, V.

O. Chapelle, V. Vapnik, O. Bousquet, and S. Mukherjee, “Choosing multiple parameters for support vector machines,” Mach. Learn. 46, 131–159 (2002).
[CrossRef]

Vong, C. M.

P. K. Wong, Q. S. Xu, C. M. Vong, and H. Ch. Wong, “Rate-dependent hysteresis modeling and control of a piezostage using online support vector machine and relevance vector machine,” IEEE Trans. Ind. Electron. 59, 1988–2001 (2012).
[CrossRef]

Wang, G.

G. Wang, Y. Li, and D. Bi, “Support vector machine networks for friction modeling,” IEEE/ASME Trans. Mechatron. 9, 601–606 (2004).
[CrossRef]

Wang, G. L.

D. Bi, Y. F. Li, S. K. Tso, and G. L. Wang, “Friction modeling and compensation for haptic display based on support vector machine,” IEEE Trans. Ind. Electron. 51, 491–500 (2004).
[CrossRef]

Wang, H.

H. Wang, K. Rong, H. Li, and P. Shaun, “Computer aided fixture design: recent research and trends,” Comput. Aided Des. 42, 1085–1094 (2010).
[CrossRef]

Wang, H. Q.

H. Q. Wang, F. C. Sun, Y. N. Cai, N. Cheng, and L. G. Ding, “On multiple kernel learning methods,” Acta Autom. Sinica 36, 1037–1050 (2010).
[CrossRef]

Weng, C. H.

Y. H. Liu, H. P. Huang, and C. H. Weng, “Recognition of electromyographic signals using cascaded kernel learning machine,” IEEE/ASME Trans. Mechatron. 12, 253–264 (2007).
[CrossRef]

West, S. C.

H. M. Martin, S. P. Callahan, B. Cuerden, W. B. Davison, S. T. Derigne, L. R. Dettmann, G. Parodi, T. J. Trebisky, S. C. West, and J. T. Williams, “Active supports and force optimization for the MMT primary mirror,” Proc. SPIE 3352, 412–423 (1998).
[CrossRef]

Williams, J. T.

H. M. Martin, S. P. Callahan, B. Cuerden, W. B. Davison, S. T. Derigne, L. R. Dettmann, G. Parodi, T. J. Trebisky, S. C. West, and J. T. Williams, “Active supports and force optimization for the MMT primary mirror,” Proc. SPIE 3352, 412–423 (1998).
[CrossRef]

Wong, H. Ch.

P. K. Wong, Q. S. Xu, C. M. Vong, and H. Ch. Wong, “Rate-dependent hysteresis modeling and control of a piezostage using online support vector machine and relevance vector machine,” IEEE Trans. Ind. Electron. 59, 1988–2001 (2012).
[CrossRef]

Wong, P. K.

P. K. Wong, Q. S. Xu, C. M. Vong, and H. Ch. Wong, “Rate-dependent hysteresis modeling and control of a piezostage using online support vector machine and relevance vector machine,” IEEE Trans. Ind. Electron. 59, 1988–2001 (2012).
[CrossRef]

Wunsch, D.

R. Xu and D. Wunsch, “Survey of clustering algorithms,” IEEE Trans. Neural Netw. 16, 645–678 (2005).
[CrossRef]

Wyant, J. C.

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. R. Shannon and J. C. Wyant, eds. (Academic, 1992), Vol. 11, pp. 38–39.

Xiang, X.

J. X. Yu, S. B. He, X. Xiang, X. D. Yuan, W. G. Zheng, H. B. Lv, and X. T. Zu, “High temperature thermal behaviour modeling of large-scale fused silica optics for laser facility,” Chin. Phys. B 21, 064401 (2012).

Xu, Q. S.

P. K. Wong, Q. S. Xu, C. M. Vong, and H. Ch. Wong, “Rate-dependent hysteresis modeling and control of a piezostage using online support vector machine and relevance vector machine,” IEEE Trans. Ind. Electron. 59, 1988–2001 (2012).
[CrossRef]

Xu, R.

R. Xu and D. Wunsch, “Survey of clustering algorithms,” IEEE Trans. Neural Netw. 16, 645–678 (2005).
[CrossRef]

Yang, J. J.

J. J. Yang, Y. N. Li, Y. H. Tian, L. Y. Duan, and W. Gao, “Group-sensitive multiple kernel learning for object categorization,” in Proceedings of the 12th IEEE International Conference on Computer Vision (2009), pp. 436–443.

Youn, S. K.

J. H. Lee, T. K. Uhm, W. S. Lee, and S. K. Youn, “First order analysis of thin plate deformable mirrors,” J. Korean Phys. Soc. 44, 1412–1416 (2004).

Yu, H.

Y. Ning, H. Zhou, H. Yu, C. H. Rao, and W. H. Jiang, “Classical areas of phenomenology: thermal stability test and analysis of a 20-actuator bimorph deformable mirror,” Chin. Phys. B 18, 1089–1095 (2009).

Yu, J. X.

J. X. Yu, S. B. He, X. Xiang, X. D. Yuan, W. G. Zheng, H. B. Lv, and X. T. Zu, “High temperature thermal behaviour modeling of large-scale fused silica optics for laser facility,” Chin. Phys. B 21, 064401 (2012).

Yuan, X. D.

J. X. Yu, S. B. He, X. Xiang, X. D. Yuan, W. G. Zheng, H. B. Lv, and X. T. Zu, “High temperature thermal behaviour modeling of large-scale fused silica optics for laser facility,” Chin. Phys. B 21, 064401 (2012).

Zhang, Y. N.

Y. F. Peng, J. L. Cui, Z. H. Cheng, D. L. Zuo, and Y. N. Zhang, “Characteristics of thermal distortions of the laser mirror substrates filled with phase change materials,” Opt. Laser Technol. 38, 594–598 (2006).
[CrossRef]

Zheng, W. G.

J. X. Yu, S. B. He, X. Xiang, X. D. Yuan, W. G. Zheng, H. B. Lv, and X. T. Zu, “High temperature thermal behaviour modeling of large-scale fused silica optics for laser facility,” Chin. Phys. B 21, 064401 (2012).

Zhou, H.

Y. Ning, H. Zhou, H. Yu, C. H. Rao, and W. H. Jiang, “Classical areas of phenomenology: thermal stability test and analysis of a 20-actuator bimorph deformable mirror,” Chin. Phys. B 18, 1089–1095 (2009).

Zhou, L. P.

L. P. Zhou and D. W. Tang, “A functionally graded structural design of mirrors for reducing their thermal deformations in high-power laser systems by finite element method,” Opt. Laser Technol. 39, 980–986 (2007).
[CrossRef]

Zu, X. T.

J. X. Yu, S. B. He, X. Xiang, X. D. Yuan, W. G. Zheng, H. B. Lv, and X. T. Zu, “High temperature thermal behaviour modeling of large-scale fused silica optics for laser facility,” Chin. Phys. B 21, 064401 (2012).

Zuo, D. L.

Y. F. Peng, J. L. Cui, Z. H. Cheng, D. L. Zuo, and Y. N. Zhang, “Characteristics of thermal distortions of the laser mirror substrates filled with phase change materials,” Opt. Laser Technol. 38, 594–598 (2006).
[CrossRef]

Acta Autom. Sinica

H. Q. Wang, F. C. Sun, Y. N. Cai, N. Cheng, and L. G. Ding, “On multiple kernel learning methods,” Acta Autom. Sinica 36, 1037–1050 (2010).
[CrossRef]

Chin. Phys. B

J. X. Yu, S. B. He, X. Xiang, X. D. Yuan, W. G. Zheng, H. B. Lv, and X. T. Zu, “High temperature thermal behaviour modeling of large-scale fused silica optics for laser facility,” Chin. Phys. B 21, 064401 (2012).

Y. Ning, H. Zhou, H. Yu, C. H. Rao, and W. H. Jiang, “Classical areas of phenomenology: thermal stability test and analysis of a 20-actuator bimorph deformable mirror,” Chin. Phys. B 18, 1089–1095 (2009).

Comput. Aided Des.

H. Wang, K. Rong, H. Li, and P. Shaun, “Computer aided fixture design: recent research and trends,” Comput. Aided Des. 42, 1085–1094 (2010).
[CrossRef]

IEEE Trans. Ind. Electron.

D. Bi, Y. F. Li, S. K. Tso, and G. L. Wang, “Friction modeling and compensation for haptic display based on support vector machine,” IEEE Trans. Ind. Electron. 51, 491–500 (2004).
[CrossRef]

P. K. Wong, Q. S. Xu, C. M. Vong, and H. Ch. Wong, “Rate-dependent hysteresis modeling and control of a piezostage using online support vector machine and relevance vector machine,” IEEE Trans. Ind. Electron. 59, 1988–2001 (2012).
[CrossRef]

IEEE Trans. Neural Netw.

R. Xu and D. Wunsch, “Survey of clustering algorithms,” IEEE Trans. Neural Netw. 16, 645–678 (2005).
[CrossRef]

IEEE Trans. Neural Netw. Learn. Syst.

F. Bellocchio, S. Ferrari, V. Piuri, and N. A. Borghese, “Hierarchical approach for multiscale support vector regression,” IEEE Trans. Neural Netw. Learn. Syst. 23, 1448–1460 (2012).
[CrossRef]

IEEE/ACM Trans. Comput. Biol. Bioinform.

S. B. Qiu and T. Lane, “A framework for multiple kernel support vector regression and its applications to siRNA efficacy prediction,” IEEE/ACM Trans. Comput. Biol. Bioinform. 6, 90–199 (2009).

IEEE/ASME Trans. Mechatron.

Y. H. Liu, H. P. Huang, and C. H. Weng, “Recognition of electromyographic signals using cascaded kernel learning machine,” IEEE/ASME Trans. Mechatron. 12, 253–264 (2007).
[CrossRef]

G. Wang, Y. Li, and D. Bi, “Support vector machine networks for friction modeling,” IEEE/ASME Trans. Mechatron. 9, 601–606 (2004).
[CrossRef]

Y. Li and D. Bi, “A method for dynamics identification for haptic display of the operating feel in virtual environments,” IEEE/ASME Trans. Mechatron. 8, 476–482 (2003).
[CrossRef]

J. Korean Phys. Soc.

J. H. Lee, T. K. Uhm, W. S. Lee, and S. K. Youn, “First order analysis of thin plate deformable mirrors,” J. Korean Phys. Soc. 44, 1412–1416 (2004).

J. Mach. Learn. Res.

M. Gönen and E. Alpaydim, “Multiple kernel learning algorithms,” J. Mach. Learn. Res. 12, 2211–2268 (2011).

G. R. G. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui, and M. I. Jordan, “Learning the kernel matrix with semidefinite programming,” J. Mach. Learn. Res. 5, 27–72 (2004).

J. Opt. Soc. Am. A

J. Therm. Stress.

L. Daudeville and H. Carre, “Thermal tempering simulation of glass plates: Inner and edge residual stresses,” J. Therm. Stress. 21, 667–689 (1998).
[CrossRef]

Mach. Learn.

O. Chapelle, V. Vapnik, O. Bousquet, and S. Mukherjee, “Choosing multiple parameters for support vector machines,” Mach. Learn. 46, 131–159 (2002).
[CrossRef]

Opt. Laser Technol.

L. P. Zhou and D. W. Tang, “A functionally graded structural design of mirrors for reducing their thermal deformations in high-power laser systems by finite element method,” Opt. Laser Technol. 39, 980–986 (2007).
[CrossRef]

Y. F. Peng, J. L. Cui, Z. H. Cheng, D. L. Zuo, and Y. N. Zhang, “Characteristics of thermal distortions of the laser mirror substrates filled with phase change materials,” Opt. Laser Technol. 38, 594–598 (2006).
[CrossRef]

Proc. SPIE

G. L. Herrit and H. E. Reedy, “Advanced figure of merit evaluation for CO2 laser optics using finite element analysis,” Proc. SPIE 1047, 33–42 (1989).
[CrossRef]

K. B. Doyle, V. L. Genberg, and G. J. Michels, “Integrated optomechanical analysis of adaptive optical systems,” Proc. SPIE 5178, 20–28 (2004).
[CrossRef]

H. Chang, Z. G. Fan, S. Q. Chen, and Y.-M. Cao, “Impact of the temperature gradient on optical system parameters: modeling and analysis,” Proc. SPIE 7506, 75060G (2009).

V. L. Genberg, G. J. Michels, and K. B. Doyle, “Design optimization of actuator layouts of adaptive optics using a genetic algorithm,” Proc. SPIE 5877, 58770L (2005).

G. J. Michels and V. L. Genberg, “Optomechanical analysis and design tool for adaptive x-ray optics,” Proc. SPIE 7803, 780308 (2010).
[CrossRef]

M. K. Cho, “Performance prediction of the TMT tertiary mirror support system,” Proc. SPIE 7018, 70184F (2008).
[CrossRef]

H. M. Martin, S. P. Callahan, B. Cuerden, W. B. Davison, S. T. Derigne, L. R. Dettmann, G. Parodi, T. J. Trebisky, S. C. West, and J. T. Williams, “Active supports and force optimization for the MMT primary mirror,” Proc. SPIE 3352, 412–423 (1998).
[CrossRef]

M. K. Cho, R. S. Price, and I. K. Moon, “Optimization of the ATST primary mirror support system,” Proc. SPIE 6273, 62731E (2006).
[CrossRef]

Stat. Comput

A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Stat. Comput 14, 199–222 (2004).
[CrossRef]

Other

M. Gönen and E. Alpaydin, “Localized multiple kernel regression,” in Proceedings 20th IAPR International Conference on Pattern Recognition (2010), pp. 1425–1428.

M. Gönen and E. Alpaydin, “Localized multiple kernel learning,” in Proceedings 25th International Conference on Machine Learning (2008), pp. 352–359.

R. Pelossof, A. Miller, P. Allen, and T. Jebara, “A SVM learning approach to robotic grasping,” in IEEE International Conference on Robotics and Automation (2004), Vol. 4, pp. 3512–3518.

J. M. Moguerza, A. Muñoz, and I. M. de Diego, “Improving support vector classification via the combination of multiple sources of information,” in Proceedings of the Structural, Syntactic, and Statistical Pattern Recognition, Joint IAPR International Workshops (2004).

N. Kingsbury, D. B. H. Tay, and M. Palaniswami, “Multi-scale kernel methods for classification,” in Proceedings of the IEEE Workshop on Machine Learning for Signal Processing (2005), pp. 43–48.

J. J. Yang, Y. N. Li, Y. H. Tian, L. Y. Duan, and W. Gao, “Group-sensitive multiple kernel learning for object categorization,” in Proceedings of the 12th IEEE International Conference on Computer Vision (2009), pp. 436–443.

J. Clausen, “Branch and bound algorithms-principles and examples,” in Parallel Computing in Optimization (Applied Optimization) (Springer, 1997), pp. 239–267.

G. J. Michels and V. L. Genberg, “Advances in the analysis and design of adaptive optics,” in Imaging and Applied Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper AMC2.

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. R. Shannon and J. C. Wyant, eds. (Academic, 1992), Vol. 11, pp. 38–39.

T. Ruppel, O. Sawodny, and W. Osten, “Actuator placement for minimum force modal control of continuous faceplate deformable mirrors,” in IEEE International Conference on Control Applications (2010), pp. 867–872.

Y. Miyamoto, W. A. Kaysser, B. H. Rabin, A. Kawasaki, and R. G. Ford, Functionally Graded Materials: Design, Processing and Applications (Kluwer, 1999).

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Figures (8)

Fig. 1.
Fig. 1.

Structure of the support frame.

Fig. 2.
Fig. 2.

Block diagram of the optimization process.

Fig. 3.
Fig. 3.

ANSYS software environment to created datasets.

Fig. 4.
Fig. 4.

(a) RMSEs. (b) MAPEs.

Fig. 5.
Fig. 5.

Deformation of the optic under a given temperature.

Fig. 6.
Fig. 6.

Deformation of the optic.

Fig. 7.
Fig. 7.

Layout of the clamps.

Fig. 8.
Fig. 8.

Deformation of the optic.

Tables (9)

Tables Icon

Algorithm 1. Branch-and-Bound Algorithm

Tables Icon

Table 1. Optic and Support Element Properties

Tables Icon

Table 2. Input Vector and the Output

Tables Icon

Table 3. Comparison of the MKSVFR and Other Methods

Tables Icon

Table 4. Minimal Deformation and the Related Clamping Forces

Tables Icon

Table 5. Minimal Deformation and the Related Clamping Forces

Tables Icon

Table 6. Properties of the Optic

Tables Icon

Table 7. Input Vector and the Output

Tables Icon

Table 8. Minimal Deformation and the Related Clamping Forces

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

f(x)=F(f1(x1),,fn(xn)),
fi(x)=k=1makiKMi(xi,xki)+bi,
KMi(xi,xki)=mi=1Miμmiikmii(xi,mi,xki,mi),
fi(xi)=mi=1Miμmiiωmii,Φmii(xi)+bi.
F(X)=F(fi(xi),Ti).
X={(aki,bi,Ti)}i=1n.
A(X)=i=1nβik(X,Xi)+ν,
B(X)=i=1nγik(X,Xi)+λ,
F(X)=i=1nAi(X)KM(X,Xi)+B(X),
F(X)=i=1nϖi(Ti)·fi(xi)+θ(xi),
ϖi(Ti)=g(TTi2),
g()=κ*exp(TTi22σ2)+λ,
i=1nϖi=0.
Dmin=min(maxXΩF(X)),
Xopt=argmin(maxXΩF(X)).
km(x,xim)=exp(xxi22σ2).

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