Polynomial Chaos - References

References

• Wiener N. (October 1938). "The Homogeneous Chaos". American Journal of Mathematics (American Journal of Mathematics, Vol. 60, No. 4) 60 (4): 897–936. doi:10.2307/2371268. JSTOR 2371268. (original paper)

• D. Xiu, Numerical Methods for Stochastic Computations: A Spectral Method Approach Princeton University Press, 2010. ISBN 978-0-691-14212-8

• Ghanem, R., and Spanos, P., Stochastic Finite Elements: A Spectral Approach, Springer Verlag, 1991. (reissued by Dover Publications, 2004.)

• Bin Wu, Jianwen Zhu, Farid N. Najm. "A Non-parametric Approach for Dynamic Range Estimation of Nonlinear Systems". In Proceedings of Design Automation Conference(841-844) 2005

• Bin Wu, Jianwen Zhu, Farid N. Najm "Dynamic Range Estimation". IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 25 Issue:9 (1618-1636) 2006

• Bin Wu, “A Statistically Optimal Macromodeling Framework with Application in Process Variation Analysis of MEMS Devices” IEEE 10th International New Circuits and Systems Conference (NEWCAS-12) June 2012

• K. Sepahvand, S. Marburg and H.-J. Hardtke, Uncertainty quantification in stochastic systems using polynomial chaos expansion, International Journal of Applied Mechanics, vol. 2, No. 2,p. 305-353, 2010.

• Nonlinear Estimation of Hypersonic State Trajectories in Bayesian Framework with Polynomial Chaos – P. Dutta, R. Bhattacharya, Journal of Guidance, Control, and Dynamics, vol.33 no.6 (1765–1778).

• Optimal Trajectory Generation with Probabilistic System Uncertainty Using Polynomial Chaos – J. Fisher, R. Bhattacharya, Journal of Dynamic Systems, Measurement and Control, volume 133, Issue 1.

• Linear Quadratic Regulation of Systems with Stochastic Parameter Uncertainties – J. Fisher, R. Bhattacharya, Automatica, 2009.

• E. Blanchard, A. Sandu, and C. Sandu: "Polynomial Chaos Based Parameter Estimation Methods for Vehicle Systems". Journal of Multi-body dynamics, in print, 2009.

• H. Cheng and A. Sandu: "Efficient Uncertainty Quantification with the Polynomial Chaos Method for Stiff Systems". Computers and Mathematics with Applications, VOl. 79, Issue 11, p. 3278-3295, 2009.

• Peccati, G. and Taqqu, M.S., 2011, Wiener Chaos: Moments, Cumulants and Diagrams: A Survey with Computer Implementation. Springer Verlag.

• Stochastic Processes and Orthogonal Polynomials Series: Lecture Notes in Statistics, Vol. 146 by Schoutens, Wim, 2000, XIII, 184 p., Softcover ISBN 978-0-387-95015-0
• Oladyshkin, S. and W. Nowak. Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion. Reliability Engineering & System Safety, Elsevier, V. 106, P. 179–190, 2012. DOI: 10.1016/j.ress.2012.05.002.