For a system with the parameters modeled as uncertain, polynomial approximations such as polynomial chaos expansion provide an effective way to estimate the statistical behavior of the eigenvalues and eigenvectors, provided the eigenvalues are widely spaced. For a system with a set of clustered eigenvalues, the corresponding eigenvalues and eigenvectors are very sensitive to perturbation of the system parameters. An enrichment scheme to the polynomial chaos expansion is proposed here in order to capture the behavior of such eigenvalues and eigenvectors. It is observed that for judiciously chosen enrichment functions, the enriched expansion provides better estimate of the statistical behavior of the eigenvalues and eigenvectors.
- Design Engineering Division and Computers and Information in Engineering Division
An Enrichment Scheme for Polynomial Chaos Expansion Applied to Random Eigenvalue Problem
Ghanem, R, & Ghosh, D. "An Enrichment Scheme for Polynomial Chaos Expansion Applied to Random Eigenvalue Problem." Proceedings of the ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C. Long Beach, California, USA. September 24–28, 2005. pp. 1449-1456. ASME. https://doi.org/10.1115/DETC2005-85450
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