Karhunen-Loéve expansion of stochastic processes with a modified exponential covariance kernel

authored by: Pol D. Spanos, Michael Beer, John Red-Horse
Abstract: The spectral representation of stationary stochastic processes via the Karhunen-Loéve (KL) expansion is examined from a numerical efficiency perspective. Attention is focused on processes which have commonly been characterized by covariance kernels decaying exponentially versus the position/time delay variable. By introducing a slight modification in the mathematical description of this covariance kernel, the nondifferentiability at its peak is eliminated, whereas most of its advantageous properties are retained. It is shown that compared to the common exponential model, the requisite number of terms for representing the process in context with the modified kernel is significantly smaller. The effect is demonstrated by means of a specific numerical example. This is done by first determining the eigenfunctions/ eigenvalues associated with the KL expansion for the modified kernel model, and by afterwards estimating the approximation errors corresponding to the two kernels considered for specific numerical values. Clearly, the enhanced computational efficiency of the KL expansion associated with the modified kernel can significantly expedite its incorporation in stochastic finite elements and other areas of stochastic mechanics.
External Organisation(s): Rice University
National University of Singapore
Sandia National Laboratories NM
Type: Article
Journal: Journal of engineering mechanics
Volume: 133
Pages: 773-779
No. of pages: 7
ISSN: 0733-9399
Publication date: 07.2007
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Mechanics of Materials, Mechanical Engineering
Electronic version(s): https://doi.org/10.1061/(ASCE)0733-9399(2007)133:7(773) (Access: Closed)