An efficient computational solution scheme of the random eigenvalue problem

Chowdhury, R. and Adhikari, S.
50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Palm Springs, California, USA, May 2009.

This paper presents a practical solution for probabilistic characterization of real valued eigenvalues of positive semi-definite random matrices. The present method is founded on the concept of high dimensional model representation (HDMR) technique. The method involves HDMR that facilitates lower dimensional approximation of the eigenvalues, response surface generation of HDMR component functions, and efficient Monte Carlo simulation for probability density functions. HDMR is a general set of quantitative model assessment and analysis tools for capturing the high-dimensional relationships between sets of input and output model variables. It is a very efficient formulation of the system response, if higher-order variable correlations are weak, allowing the physical model to be captured by the first few lower-order terms. Results of two numerical examples indicate that the proposed method provides accurate and computationally efficiency. Compared with commonly-used perturbation and recently-developed asymptotic methods, no derivatives of eigenvalues are required in the present method.
BiBTeX Entry
@INPROCEEDINGS{cp58,
    AUTHOR={R. Chowdhury and S. Adhikari},
    TITLE={An efficient computational solution scheme of the random eigenvalue problem},
    BOOKTITLE={Proceedings of the 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics \& Materials Conference},
    YEAR={2009},
    Address={Palm Springs, California, USA},
    Month={May}
}
by Sondipon Adhikari