Initial application and evaluation of a promising new sampling method for response surface generation: Centroidal Voronoi Tessellation

44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

Volumn , Issue , 2003, Pages

  Romero, V ^a   Burkardt, J ^b   Gunzburger, M ^b   Peterson, J ^b   Krishnamurthy, T ^c  

^a SANDIA NATIONAL LABORATORIES   (United States)

^b FLORIDA STATE UNIVERSITY   (United States)

^c NASA LANGLEY RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CENTROIDAL VORONOI TESSELLATION; CORRELATION EFFECT; HIGHER DIMENSIONS; LATIN HYPERCUBE SAMPLING; MOVING LEAST SQUARES; PARAMETER SPACES; RESPONSE SURFACE; SAMPLING DENSITIES;

MONTE CARLO METHODS; STRUCTURAL DYNAMICS; SURFACE PROPERTIES;

VARIABLE SPEED TRANSMISSIONS;

EID: 84896693256     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (23)

1. Atluri, S.N., and T. Zhu, "A New Meshless Local Petrov-Galerkin Approach in Computational Mechanics, " Computational Mechanics, Vol. 22, 1998.
2. Beachkofski, B.K., and R.V. Grandhi, "Improved Distributed Hypercube Sampling, " paper AIAA-2002-1274, 43rd Structures, Structural Dynamics, and Materials Conference, April 22-25, Denver, CO.
3. Burkardt, J.S., M.D. Gunzburger, J.S. Peterson, R. Brannon, "User Manual and Supporting Information for Library of Codes for Centroidal Voronoi Point Placement and Associated Zeroth, First, and Second Moment Determination, " Sandia National Laboratories report SAND2002-0099, printed Feb. 2002.
4. Conover, W.M., "On a Better Method for Selecting Input Variables, " 1975 unpublished Los Alamos National Laboratories manuscript, reproduced as Appendix A of "Latin Hypercube Sampling and the Propagation of Uncertainty in Analyses of Complex Systems" by J.C. Helton and F.J. Davis, Sandia National Laboratories report SAND2001-0417 printed Novermber 2002.
5. Du, Q., V. Faber, M. Gunzburger, "Centroidal Voronoi tessellations: applications and algorithms, " SIAM Review. Vol. 41, 1999, pp. 637-676.
6. Franke, R., and G.M. Nielson, "Scattered Data Interpolation and Applications: A Tutorial and Survey, " in Geometric Modeling: Methods and Applications, 1990, Springer, Berlin
7. Burkardt, J.V., M.D. Gunzburger, J.S. Peterson, V.J. Romero, "Comparison of Sampling Methods for Achieving a Uniform Point Distribution in a Hypercube, " to be submitted for the 4th International Symposium on Uncertainty Modeling and Simulation (ISUMA'03), Sept. 21-24 2003, College Park, MD.
8. Hanson, K.M., "Quasi-Monte Carlo: halftoning in high dimensions, " to appear in Proceedings of SPIE 5016 (2003), Computational Imaging, C.A. Bouman and R.L. Stevenson, eds.
9. Iman, R.L., and Shortencarier, M.J., "A FORTRAN77 Program and User's Guide for the Generation of Latin Hypercube and Random Samples to Use with Computer Models, " Sandia National Laboratories report SAND83-2365 (RG), printed March 1984.
10. Iman, R.L., and W.J. Conover, "A Distribution-Free Approach to Inducing Rank Correlation Among Input Variables, " Communications in Statistics, B11(3) 1982a, pp. 311-334.
11. Kalagnanam, J.R., and Diwekar, U.M., "An Efficient Sampling Technique for Off-line Quality Control, " Technometrics, August 1997, Vol.39, No.3.
12. Ju, L., Q. Du., M. Gunzburger, "Probabilistic algorithms for centroidal Voronoi tessellations and their parallel implementation, " Parallel Computing, Vol. 28, 2002, pp. 1477-1500.
13. Krishnamurthy, T., "Response Surface Approximation with Augmented and Compact Support Radial Basis Functions, " paper AIAA-2003-7561, 44th Structures, Structural Dynamics, and Materials Conference, April 7-10, Norfolk, VA.
14. Krishnamurthy, T., and V.J. Romero, "Construction of Response Surfaces with Higher Order Continuity and its Application to Reliability Engineering, " paper AIAA-2002-1466, 43rd Structures, Structural Dynamics, and Materials Conference, April 22-25, Denver, CO.
15. Lloyd, S., "Least squares quantization in PCM, " IEEE Transactions in Information Theory, Vol. 28, 1982, pp. 129-137.
16. MacQueen, J., "Some methods for classification and analysis of multivariate observations, " Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. I, Ed. by L. Le Cam and J. Neyman, University of California, Berkeley, 1967, pp. 281-297.
17. Manteufel, R.D., "Distributed Hypercube Sampling Algorithm, " paper AIAA-2001-1673, 42nd Structures, Structural Dynamics, and Materials Conference, April 16-19, Seattle, WA.
18. Okabe, A., B. Boots, K. Sugihara, S. Chui, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, 2nd Edition, Wiley, Chichester, 2000.
19. Press, W.H., S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd Edition, Cambridge University Press, 1992.
20. Robinson, D., and Atcitty, D., "Comparison of Quasi-and Pseudo-Monte Carlo Sampling for Reliability and Uncertainty Analysis, " paper AIAA-1999-1589, 40th Structures, Structural Dynamics, and Materials Conference, April 12-15, St. Louis, MO.
21. Romero, V.J., and S.D. Bankston, "Progressive-Lattice-Sampling Methodology and Application to Benchmark Probability Quantification Problems, " Sandia National Laboratories report SAND98-0567, printed March 1998.
22. Romero, V.J., L.P. Swiler, A.A. Giunta, "Application of Finite Element, Global Polynomial, and Kriging Response Surfaces in Progressive Lattice Sampling Designs, " paper PMC2000-175, 8th ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability, July 24-26, 2000, University of Notre Dame, IN.
23. Romero, V.J., J.S. Burkardt, M.D. Gunzburger, J.S. Peterson, "Initial Evaluation of Centroidal Voronoi Tessellation Sampling Method for Integration and Statistical Sampling" to be submitted for the 4th International Symposium on Uncertainty Modeling and Simulation (ISUMA'03), Sept. 21-24 2003, College Park, MD.