Uncertainty quantification using multi-dimensional hermite polynomials

Geotechnical Special Publication

Volumn , Issue 170, 2007, Pages 12-

  Phoon, K K ^a   Huang, S P ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL CODES; RANDOM OUTPUT VECTORS; STOCHASTIC PROBLEMS;

NUMBER THEORY; NUMERICAL METHODS; PROBLEM SOLVING; RANDOM PROCESSES; VECTORS;

POLYNOMIALS;

EID: 34548617618     PISSN: 08950563     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1061/40914(233)12     Document Type: Conference Paper

References (22)

1. Au, S. K. (2001). On the solution of first excursion problems by simulation with applications to probabilistic seismic performance assessment. PhD Thesis, California Institute of Technology, Pasadena, California.
2. Box, G. P. & Draper, N. R. (1987). Empirical model-building and response surface. Wiley, New York.
3. Debusschere, B. J., Najm, H. N., Pebay, P. P., Knio, O., Ghanem, R. G. & Le Matre, P. P. (2004). "Numerical challenges in using polynomial chaos." SIAM Journal of Scientific Computing, Special Issue on Uncertainty Quantification, 26(2), 698-719.
4. Fenton, G. A. & Griffiths, D. V. (1997). "Extreme hydraulic gradient statistics in a stochastic earth dam." Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 123(11), 995-1000.
5. Fenton, G. A. & Griffiths, D. V. (2002). "Probabilistic foundation settlement on spatially random soil." Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 128(5), 381-390.
6. Fenton, G. A. & Griffiths, D. V. (2003). "Bearing capacity prediction of spatially random c-φ soils." Canadian Geotechnical Journal, 40(1), 54-65.
7. Field, R. V. & Grigoriu, M. (2004). "On accuracy of the polynomial chaos approximation." Probabilistic Engineering Mechanics, 19(1-2), 65-80.
8. Ghanem R. & Spanos P. D. (1991). Stochastic Finite Element: A Spectral Approach. Springer-Verlag.
9. Goh, A. T. C. and Kulhawy, F. H. (2005). "Reliability assessment of serviceability performance of braced retaining walls using a neural network approach." International Journal of Numerical and Analytical Methods in Geomechanics, 29, 627-642.
10. Griffiths, D. V. & Fenton, G. A. (1993). "Seepage beneath water retaining structures founded on spatially random soil." Geotechnique, 43(6), 577-587.
11. Griffiths, D. V. & Fenton, G. A. (1997). "Three dimensional seepage through spatially random soil." Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 123(2), 153-160.
12. Griffiths, D. V. and Fenton, G. A. (2001). "Bearing capacity of spatially random soil: the undrained clay Prandtl problem revisited." Geotechnique, 54(4), 351-359.
13. Isukapalli, S. S. (1999). UncertaintyAn alysis of Transport- Transformation Models, PhD Thesis, The State University of New Jersey, New Brunswick, New Jersey.
14. Phoon, K. K., Huang S. P. & Quek, S. T. (2002). "Implementation of Karhunen-Loeve expansion for simulation using a wavelet-Galerkin scheme." Probabilistic Engineering Mechanics, 17(3), 293-303.
15. Phoon, K.K. (2003). "Representation of random variables using orthogonal polynomials." Proc. Ninth International Conference on Applications of Statistics and Probability in Civil Engineering, San Francisco, 1, 97-104.
16. Phoon, K. K. (2004). General Non-Gaussian Probability Models for First-Order Reliability Method (FORM): A State-of-the-Art Report, ICG Report 2004-2-4 (NGI Report 20031091-4), International Centre for Geohazards, Oslo.
17. Phoon, K. K., Huang H. W. & Quek, S. T. (2004). "Comparison Between Karhunen-Loeve and Wavelet Expansions for Simulation of Gaussian Processes." Computers and Structures, 82(13-14), 985-991.
18. Phoon, K. K. and Honjo, Y. (2005). "Geotechnical reliability analyses: towards development of some user-friendly tools." Proc. Sixteenth International Conference on Soil Mechanics and Geotechnical Engineering, Osaka, Japan, CDROM.
19. Robinson, D.G., Atcitty A. 1999. "Comparison of quasi-Monte Carlo and Latin hypercube sampling for reliability and uncertainty analysis". Proc. AIAA Structures, Structural Dynamics and Materials Conference, St. Louis, MO, 12-15 April, 1999. AIAA 99-1589: American Institute of Aeronautics and Astronautics.
20. Sudret, B. & Der Kiureghian, A. (2000). Stochastic finite elements and reliability: A state-of-the-art report. Report UCB/SEMM-2000/08, University of California, Berkeley.
21. M. A. Tatang (1995). Direct incorporation of uncertainty in chemical and environmental engineering systems. PhD Thesis, Massachusetts Institute of Technology.
22. Wong, F. S. (1985). "Slope reliability and response surface method." Journal of Geotechnical Engineering, ASCE, 111(1), 32-53.