A probabilistic approach to uncertainty quantification with limited information

Reliability Engineering and System Safety

Volumn 85, Issue 1-3, 2004, Pages 183-190

  Red Horse, J R ^a   Benjamin, A S ^b  

^a SANDIA NATIONAL LABORATORIES   (United States)

^b ARES Corporation   (United States)

Author keywords

Approximate information; Polynomial chaos expansion; Probability; Uncertainty

Indexed keywords

APPROXIMATION THEORY; CHAOS THEORY; MATHEMATICAL TECHNIQUES; MONTE CARLO METHODS; NUMERICAL ANALYSIS; POLYNOMIALS; PROBLEM SOLVING; UNCERTAIN SYSTEMS; WEIBULL DISTRIBUTION;

APPROXIMATE INFORMATION; POLYNOMIAL CHAOS EXPANSION; UNCERTAINTY;

PROBABILITY DISTRIBUTIONS;

EID: 2642532808     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ress.2004.03.011     Document Type: Conference Paper

References (23)

1. Papoulis A. Probability, random variables, and stochastic processes. 1965;McGraw-Hill.
2. Einstein A. Theory of Brownian motion. In: Furth R. (editor). Investigations on the theory of Brownian movement. New York: Dutton.
3. Jazwinski A.H. Stochastic processes and filtering theory. 1970;Academic Press, New York.
4. Soong T.T. Random differential equations in science and engineering. 1973;Academic Press, New York.
5. Ang A.H.-S., Tang W.H. Probability concepts in engineering planning and design: basic principles. vol. 1:1975;Wiley, New York.
6. Ang A.H.-S., Tang W.H. Probability concepts in engineering planning and design: decision, risk and reliability. vol. 2:1975;Wiley, New York.
7. Kalos M., Whitlock P. Monte Carlo methods, volume 1: basics. 1986;Wiley, New York.
8. Friedman A. Foundations of modern analysis. 1982;Dover Publications, Inc. New York.
9. Kolmogorov A.N., Fomin S.V. Elements of the theory of functions and functional analysis. 1957;Dover Publications, Mineola, NY.
10. Young N. An introduction to Hilbert space. 1997;Cambridge University Press, Cambridge.
11. Wiener N. The homogeneous chaos. Am J Math. 60:1938;897-936.
12. Ghanem R., Spanos P.D. Stochastic finite elements: a spectral approach. 1991;Springer, Berlin.
13. Field R. Jr, Red-Horse J.R., Paez T.L. A nondeterministic shock and vibration application using polynomial chaos expansions. In: Proceedings of the Eighth ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability. 2000.
14. Abramowitz M., Stegun I.A. Handbook of mathematical functions, Nineth Printing. 1970;Dover Publications, New York.
15. Cameron R.H., Martin W.T. The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals. Ann. Math. 1947;385-392.
16. Wiener N. Nonlinear problems in random theory. 1958;Technology Press of the Massachussets Institute of Technology/Wiley, New York.
17. Loève M. Probability theory. 1960;D. Van Nostrand, Princeton.
18. Rosenblatt M. Remarks on a multivariate transformation. Ann Math Stat. 23:(3):1952;470-472.
19. Erickson G.J., Smith C.R. Maximum-entropy and Bayesian methods in science and engineering. 1988;Kluwer, Dordrecht.
20. Joslyn C, Ferson S. Convolutions of representations of random intervals. Int J Approx Reason.
21. McKay M.D., Conover W.J., Beckman R.J. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics. 21:1979;239-245.
22. Oberkampf W.L., Helton J.C., Joslyn C.A., Wojtkiewicz S.F., Ferson S. Challenge problems: uncertainty in system response given uncertain parameters. Reliab Engng Syst Safety. 2004;. this issue.
23. Clough R., Penzien J. Dynamics of structures. 1993;McGraw-Hill, New York.