Capability of high intrinsic quality Space Filling Design for global sensitivity analysis and metamodelling of interference optical systems

Chemometrics and Intelligent Laboratory Systems

Volumn 113, Issue , 2012, Pages 10-18

  Vasseur, O ^a   Azarian, A ^a   Jolivet, V ^a   Bourdon, P ^a  

^a ONERA   (France)

Author keywords

Complex systems; Computer experiments; Minimal Spanning Tree; Minimum Spanning Tree; Optical filter; Sensitivity analysis; Space Filling Designs; Thin film coatings

Indexed keywords

ACCURACY; ARTICLE; COMPUTER MODEL; COMPUTER SIMULATION; CONTROLLED STUDY; CORRELATION ANALYSIS; EMPIRICAL RESEARCH; EXPERIMENTAL DESIGN; METHODOLOGY; MINIMUM SPANNING TREE; MONITORING; PRIORITY JOURNAL; QUALITY CONTROL PROCEDURES; SENSITIVITY ANALYSIS; SPACE; SPACE FILLING DESIGN;

EID: 80455145861     PISSN: 01697439     EISSN: 18733239     Source Type: Journal    
DOI: 10.1016/j.chemolab.2011.05.008     Document Type: Article

References (40)

1. Atanassov E., Karaivanova A., Ivanovska S. Tuning the generation of Sobol sequence with Owen scrambling. Large-Scale Scientific Computing - Lecture Notes in Computer Science 2010, Springer Berlin.
2. Azarian A., Vasseur O., Bennaï B., Lombard L., Canat G., Jolivet V., Jaouën Y., Bourdon P. Global sensitivity analyses of coherent beam combining of fiber amplifier arrays by the use of numerical Space Filling Designs. Proc. of SPIE 2011, Photonics West, San Francisco, paper 7914-52.
3. Badoil B., Lemarchand F., Cathelinaud M., Lequime M. Interest of broadband optical monitoring for thin-film filter manufacturing. Appl. Opt. 2007, 46:4294-4303.
4. Beardwood J., Halton J.H., Hammersley J.M. The shortest path through many points. Camb. Philos. Soc. Proc. 1959, 55:299-327.
5. Chun B.J., Hwangbo C.K., Kim J.S. Optical monitoring of nonquarterwave layers of dielectric multilayer filters using optical admittance. Opt. Express 2006, 14:2473-2480.
6. Dussert C., Rasigni G., Rasigni M., Palmari J. Minimal spanning tree: a new approach for studying order and disorder. Phys. Rev. B 1986, 34:3528-3531.
7. Fan T.Y. Laser beam combining for high-power, high-radiance sources. IEEE J. Sel. Topics Quantum Electron. 2005, 11:567-577.
8. Faure H. Discrépance de suites associées à un système de numération (en dimensions). Acta Arith. 1982, 41:337-351.
9. Franco J., Vasseur O., Corre B., Sergent M. Minimum Spanning Tree: a new approach to assess the quality of the design of computer experiments. Chemom. Intell. Lab. Syst. 2009, 97:164-169.
10. Greenwood M. The statistical study of infectious diseases. J. R. Stat. Soc. 1946, 109:85-110.
11. Halton J.H. On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numer. Math. 1960, 2:84-90.
12. Hoffman R., Jain A. A test of randomness based on the minimal spanning tree. Pattern Recogn. Lett. 1983, 1:175-180.
13. http://cran.r-project.org/.
14. http://www.dice-consortium.fr/.
15. Jaouën Y., Canat G., Grot S., Bordais S. Power limitation induced by nonlinear effects in pulsed high-power fiber amplifiers. C. R. Phys. 2006, 7:163-169.
16. Jolivet V., Bourdon P., Bennaï B., Lombard L., Goular G., Pourtal E., Canat G., Jaouën Y., Moreau B., Vasseur O. Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence. IEEE J. Sel. Topics Quantum Electron. 2009, 15:257-268.
17. Kruskal J.B. On the shortest spanning subtree of a graph and travelling salesman problem. Proc. Am. Math. Soc. 1956, 7:48-50.
18. Loeppky J., Sacks J., Welch W. Choosing the sample size of a computer experiment: a practical guide. Technometrics 2009, 51:366-376.
19. Macleod H.A. Turning value monitoring of narrow-band all dielectric thin film optical filters. Opt. Acta 1972, 19:1-28.
20. Macleod H.A. Thin film optical filters 1986, Adam Hilger ltd, Bristol.
21. Macleod H.A., Pelletier E. Error compensation mechanisms in some thin-film monitoring systems. Opt. Acta 1977, 24:907-930.
22. Mc Kay M.D., Beckman R.J., Conover W.J. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 1979, 21:239-245.
23. A. Marrel, Mise en œuvre et utilisation du métamodèle processus gaussien pour l'analyse de sensibilité de modèles numériques, PhD. Thesis, INSA, 2008.
24. Neyman J., Scott E.L. Statistical approach to problems of cosmology. J. R. Stat. Soc. B 1958, 20:1-43.
25. Owen O. Scrambling Sobol' and Niederreiter-Xing Points. J. Complex. 1998, 14:466-489.
26. Prim R.C. Shortest connection networks and some generalizations. Bell Syst. Tech. J. 1957, 36:1389-1401.
27. Roustant O., Franco J., Carraro L., Jourdan A. A radial scanning statistic for selecting space-filling designs in computer experiments, in mODa 9 - advances in model-oriented design and analysis. Proceedings of the 9th International Workshop in Model-Oriented Design and Analysis held in Bertinoro, Italy, June 14-18 2010, 189-196. Springer, Heildeberg.
28. Saltelli A., Chan K., Scott E.M. Sensitivity Analysis 2000, Wiley, New-York.
29. Scholl M. Measured spatial properties of the cw Nd:YAG laser beam. Appl. Opt. 1980, 19:3655-3659.
30. Sergent M., Phan-Tan-Luu R., Elguero J. Statistical Analysis of Solvent Scales. Part 1. Anal. Quimica Int. Ed. 1997, 93:3-6.
31. Shay T.M., Benham V., Baker J.T., Sanchez A.D., Pilkington D., Lu C.A. Self-synchronous and self-referenced coherent beam combination for large optical arrays. IEEE J. Sel. Topics Quantum Electron. 2007, 13:480-486.
32. Sobol' I.M. On the distribution of points in a cube and the approximate evaluation of integrals. USSR Comput. Math. Math. Phys. 1967, 7:86-112.
33. Sullivan B.T., Clarke G.A., Akiyama T., Osborne N., Ranger M., Dobrowolski J.A., Howe L., Matsumoto A., Song Y., Kikuchi K. High-rate automated deposition system for the manufacture of complex multilayer coatings. Appl. Opt. 2000, 39:157-167.
34. Tan K.S., Boyle P.P. Applications of scrambled low discrepancy sequences to exotic options. International AFIR Colloquium Proceedings 1997.
35. Tikhonravov A., Trubetskov M., Amotchkina T. Computational experiments on optical coating production using monochromatic monitoring strategy aimed at eliminating a cumulative effect of thickness errors. Appl. Opt. 2007, 46:6936-6944.
36. Vassallo C. Reflectivity of multidielectric coatings deposited on the end facet of a weakly guiding dielectric slab waveguide. J. Opt. Soc. Am. A 1988, 5:1918-1928.
37. Vasseur O. Reflectivity of dielectric coatings deposited on the end facet of a weakly guiding fiber. J. Opt. Soc. Am. A 1998, 12:77-83.
38. Vasseur O., Cathelinaud M., Claeys-Bruno M., Sergent M. Global sensitivity analysis of bandpass and antireflection coatings manufacturing by numerical Space Filling Designs. Appl. Opt. 2011, 50:C117-C123.
39. Wallet F., Dussert C. Comparison of spatial point patterns and processes characterization methods. Europhys. Lett. 1998, 42:493-498.
40. Zhan C. Graph-theoretical methods for detecting and describing gestalt clusters. IEEE T. Comput. 1971, C-20:68-86.