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On the characterization and analysis...

Ghosh, Debraj.

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On the characterization and analysis of the random eigenvalue problem.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	On the characterization and analysis of the random eigenvalue problem./
作者:	Ghosh, Debraj.
面頁冊數:	112 p.
附註:	Source: Dissertation Abstracts International, Volume: 66-11, Section: B, page: 6131.
Contained By:	Dissertation Abstracts International66-11B.
標題:	Engineering, Civil. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3197152
ISBN:	9780542429644

On the characterization and analysis of the random eigenvalue problem.
Ghosh, Debraj.

On the characterization and analysis of the random eigenvalue problem. - 112 p.

Source: Dissertation Abstracts International, Volume: 66-11, Section: B, page: 6131.

Thesis (Ph.D.)--The Johns Hopkins University, 2006.

Observed behavior of most physical systems differs from the behavior of their deterministic predictive models. Probabilistic methods offer a way to model and analyze a system such that the discrepancy in behavior of the predictive model and of the actual system is minimal in some sense. Certain parameters in these predictive models are represented as random quantities. Random eigenvalue problem arises naturally in common procedures for analyzing the behavior of such models.

ISBN: 9780542429644Subjects--Topical Terms:

783781
Engineering, Civil.

On the characterization and analysis of the random eigenvalue problem.
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245 1 0 $a On the characterization and analysis of the random eigenvalue problem.
300 $a 112 p.
500 $a Source: Dissertation Abstracts International, Volume: 66-11, Section: B, page: 6131.
500 $a Adviser: Roger Ghanem.
502 $a Thesis (Ph.D.)--The Johns Hopkins University, 2006.
520 $a Observed behavior of most physical systems differs from the behavior of their deterministic predictive models. Probabilistic methods offer a way to model and analyze a system such that the discrepancy in behavior of the predictive model and of the actual system is minimal in some sense. Certain parameters in these predictive models are represented as random quantities. Random eigenvalue problem arises naturally in common procedures for analyzing the behavior of such models.
520 $a Main contribution of this thesis is to present a new insight and method for the analysis of random eigenvalue problem. Three methods are used here to characterize the solution of the random eigenvalue problem, namely, the Taylor series based perturbation expansion, the polynomial chaos expansion coupled with Galerkin projection, and Monte Carlo simulation. It is observed that the polynomial chaos based method gives more accurate estimates of the statistical moments than the perturbation method, especially for the higher modes. The difference of accuracy in these two methods are more pronounced as the system variability increases. Moreover, the chaos expansion gives more detailed probabilistic description of the eigenvalues and the eigenvectors. However, currently available statistical simulation based method of estimating the chaos coefficients is computationally intensive, and accuracy of the estimated coefficients is influenced by the problems associated with random number generation. To circumvent these problems an efficient method for estimating the coefficients is proposed. This method uses a Galerkin based approach by orthogonalizing the residual in the eigenvalue-eigenvector equation to the subspace spanned by the basis functions used for approximation.
520 $a A new representation of the statistics of the random eigenvectors is proposed to capture the modal interaction. This representation offers a more detailed description and clearer prediction model of the behavior of the mode shapes of an uncertain system. This representation can also be used in efficient and accurate system reduction. An enriched version of the chaos expansion is proposed that will be helpful in capturing the behavior of the eigenvalues and eigenvectors for the systems with repeated or closely spaced eigenvalues.
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