Polynomial chaos representation of spatio-temporal random fields from experimental measurements

Journal of Computational Physics

Volumn 228, Issue 23, 2009, Pages 8726-8751

  Das, Sonjoy ^a   Ghanem, Roger ^a   Finette, Steven ^b  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^b NAVAL RESEARCH LABORATORY   (United States)

Author keywords

Karhunen Lo ve expansion; Non Gaussian random process; Non homogeneous non stationary random process; Polynomial chaos expansion; Probability density function estimation; Rosenblatt transformation; Spearman's rank correlation coefficient

Indexed keywords

GAUSSIAN NOISE (ELECTRONIC); LINEAR TRANSFORMATIONS; MATRIX ALGEBRA; POLYNOMIALS; PROBABILITY DENSITY FUNCTION;

CHAOS EXPANSIONS; KARHUNEN-LOÈVE EXPANSION; NON-GAUSSIAN RANDOM PROCESS; NON-HOMOGENEOUS; NON-HOMOGENEOUS/NON-STATIONARY RANDOM PROCESS; NON-STATIONARY RANDOM PROCESS; POLYNOMIAL CHAOS; POLYNOMIAL CHAOS EXPANSION; PROBABILITY DENSITY FUNCTION ESTIMATIONS; ROSENBLATT TRANSFORMATIONS; SPEARMAN'S RANK CORRELATION COEFFICIENTS;

RANDOM PROCESSES;

EID: 70349750471     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.08.025     Document Type: Article

References (49)

1. Apel J.R., Badiey B., Chiu C.S., Finette S., Headrick J., Kemp J.N., Lynch J.F., Newhall A., Orr M.H., Pasewark B.H., Tielbuerger D., Turgut A., von der Heydt K., and Wolf S. An overview of the 1995 SWARM shallow-water internal wave acoustic scattering experiment. IEEE Journal of Oceanic Engineering 22 3 (1997) 465-500
2. M. Cario, B. Nelson, Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix, Tech. rep., Department of Industrial Engineering and 35 Management Sciences, Northwestern University, Evanston, Illinois, 1997. URL: .
3. Deodatis G., and Micaletti R.C. Simulation of highly skewed non-Gaussian stochastic processes. Journal of Engineering Mechanics - ASCE 127 12 (2001) 1284-1295
4. Rosenblatt M. Remarks on multivariate transformation. The Annals of Mathematical Statistics 23 3 (1952) 470-472
5. Izenman A. Recent developments in nonparametric density estimation. Journal of the American Statistical Association 86 413 (1991) 205-224
6. Scott D. Multivariate Density Estimation: Theory, Practice and Visualization (1992), Wiley-Interscience
7. Ghosh S., and Henderson S. Chessboard distributions and random vectors with specified marginals and covariance matrix. Operations Research 50 5 (2002) 820-834
8. Embrechts P., McNeil A., and Straumann D. Correlation and dependence in risk management: properties and pitfalls. In: Dempster M. (Ed). Risk Management: Value at Risk and Beyond (2001), Cambridge University Press 176-223
9. Lehmann E. Nonparametrics: Statistical Methods Based on Ranks (1975), McGraw-Hill International Book Company, New York
10. Hörmann W., Leydold J., and Derflinger G. Automatic Nonuniform Random Variate Generation (2004), Springer
11. Ghosh S., and Henderson S. Behavior of the NORTA method for correlated random vector generation as the dimension increases. ACM Transactions on Modeling and Computer Simulation 13 3 (2003) 276-294. http://www.informs-cs.org/wsc02papers/034.pdf also see http://www.informs-cs.org/wsc02papers/034.pdf
12. Kouskoulas Y., Pierce L., and Ulaby F. A computationally efficient multivariate maximum-entropy density estimation (MEDE) technique. IEEE Transactions on Geoscience and Remote Sensing 42 2 (2004) 457-468
13. van der Geest P. An algorithm to generate samples of multi-variate distributions with correlated marginals. Computational Statistics and Data Analysis 27 3 (1998) 271-289
14. Sakamoto S., and Ghanem R. Simulation of multi-dimensional non-Gaussian non-stationary random fields. Probabilistic Engineering Mechanics 17 2 (2002) 167-176
15. Ghanem R., and Spanos P. Stochastic Finite Elements: A Spectral Approach (1991), Springer-Verlag, New York, USA (revised edition published by Dover in 2003)
16. Lancaster H. Some properties of the bivariate normal distribution considered in the form of a contingency table. Biometrika 44 1-2 (1957) 289-292
17. Ghanem R. Ingredients for a general purpose stochastic finite elements implementation. Computer Methods in Applied Mechanics and Engineering 168 1-4 (1999) 19-34
18. Xiu D., and Karniadakis G. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM Journal on Scientific Computing 24 2 (2002) 619-644
19. Soize C., and Ghanem R. Physical systems with random uncertainties: Chaos representations with arbitrary probability measure. SIAM Journal on Scientific Computing 26 2 (2004) 395-410
20. Wan X., and Karniadakis G.E. An adaptive multi-element generalized polynomial chaos method for stochastic differential equations. Journal of Computational Physics 209 2 (2005) 617-642
21. Pellissetti M., and Ghanem R. Iterative solution of systems of linear equations arising in the context of stochastic finite elements. Advances in Engineering Software 31 (2000) 607-616
22. Reagan M., Najm H., Ghanem R., and Knio O. Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection. Combustion and Flame 132 3 (2003) 545-555
23. Ghosh D., Ghanem R., and Red-Horse J. Analysis of eigenvalues and modal interaction of stochastic systems. AIAA Journal 43 10 (2005) 2196-2201
24. Witteveen J., Sarkar S., and Bijl H. Modeling physical uncertainties in dynamic stall induced fluid structure interaction of turbine blades using arbitrary polynomial chaos. Computers and Structures 85 11-14 (2007) 866-878
25. Ghanem R., and Doostan A. On the construction and analysis of stochastic models: Characterization and propagation of the errors associated with limited data. Journal of Computational Physics 217 1 (2006) 63-81
26. Priestley M.B. Spectral Analysis and Time Series vols. I and II (1981), Academic Press, New York
27. Billingsley P. Probability and Measure (1995), John Wiley & Sons, New York
28. Desceliers C., Ghanem R., and Soize C. Maximum likelihood estimation of stochastic chaos representation from experimental data. International Journal for Numerical Methods in Engineering 66 6 (2006) 978-1001
29. Lindsay B. Composite likelihood methods. Contemporary Mathematics 80 (1988) 221-239
30. S. Das, R. Ghanem, J.C. Spall, Asymptotic sampling distribution for polynomial chaos representation from data: a maximum entropy and Fisher information approach, SIAM Journal on Scientific Computing 30(5) (2008) 2207-2234. doi:10.1137/060652105.
31. Cameron R., and Martin W. The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals. The Annals of Mathematics, Second Series 48 2 (1947) 385-392
32. Wiener N. The homogeneous chaos. American Journal of Mathematics 60 4 (1938) 897-936
33. Le Maître O., Najm H., Ghanem R., and Knio O. Multi-resolution analysis of Wiener-type uncertainty propagation schemes. Journal of Computational Physics 197 2 (2004) 502-531
34. S. Das, Model, identification and analysis of complex stochastic systems: applications in stochastic partial differential equations and multiscale mechanics, Ph.D. Thesis, Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, USA, 2008. .
35. Tolstov G. Fourier Series (1962), Prentice-Hall
36. Lebedev N. Special Functions and Their Applications (1972), Dover, New York
37. Kurowicka D., and Cooke R. Uncertainty Analysis with High Dimensional Dependence Modelling (2006), John Wiley & Sons Ltd.
38. V. Schmitz, Copulas and stochastic processes, Ph.D. Thesis, Rheinisch-Westfälische Technische Hochschule Aachen, Fakultät für Mathematik, Informatik und Naturwissenschaften, 2003. .
39. Nelsen R. An Introduction to Copulas (2006), Springer
40. Fishman G. Monte Carlo: Concepts, Algorithms and Applications (1996), Springer, New York
41. Vandenberghe L., and Boyd S. Semidefinite programming. SIAM Review 38 1 (1996) 49-95
42. J. Löfberg, YALMIPA toolbox for modeling and optimization in MATLAB, in: Proceedings of the IEEE Conference on Computer Aided Control Systems Design (CACSD), Taipei, Taiwan, 2004. .
43. Finette S., Orr M., Turgut A., Apel J., Badiey C., Chiu B., Headrick J., Kemp J., Lynch J., Newhall A., Heydt K.D., Pasewark B., Wolf S., and Tielbuerger D. Acoustic field variability induced by time evolving internal wave fields. Journal of the Acoustical Society of America 108 3 (2000) 957-972
44. Pellissetti M., and Ghanem R. A method for validation of the predictive computations using a stochastic approach. Journal of Offshore Mechanics and Arctic Engineering 126 (2004) 227-234
45. S. Das, R. Ghanem, Uncertainty analysis for surface ship subjected to underwater detonation, in: Proceedings of the IMAC-XXII Conference and Exposition on Structural Dynamics, Dearborn, Michigan, USA, 2004.
46. Loève M. Probability Theory II (1978), Springer-Verlag, New York
47. Hwang J., and Ding A. Convergence study of the truncated Karhunen-Loève expansion for simulation of stochastic processes. International Journal for Numerical Methods in Engineering 52 (2001) 1029-1043
48. Schwab C., and Todor R.A. Karhunen-Loève approximation of random fields by generalized fast multipole methods. Journal of Computational Physics 217 (2006) 100-122
49. Phillips G. Interpolation and Approximation by Polynomials (2003), Springer