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

verfasst von

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.

Externe Organisation(en)

Rice University
National University of Singapore
Sandia National Laboratories NM

Typ

Artikel

Journal

Journal of engineering mechanics

Band

133

Seiten

773-779

Anzahl der Seiten

7

ISSN

0733-9399

Publikationsdatum

07.2007

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Werkstoffmechanik, Maschinenbau

Elektronische Version(en)

https://doi.org/10.1061/(ASCE)0733-9399(2007)133:7(773) (Zugang: Geschlossen)