Details
| Original language | English |
|---|---|
| Pages (from-to) | 773-779 |
| Number of pages | 7 |
| Journal | Journal of engineering mechanics |
| Volume | 133 |
| Issue number | 7 |
| Early online date | 10 Jul 2007 |
| Publication status | Published - Jul 2007 |
| Externally published | Yes |
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.
Keywords
- Computer aided simulation, Monte Carlo method, Numerical analysis, Spectral analysis, Stochastic processes
ASJC Scopus subject areas
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
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In: Journal of engineering mechanics, Vol. 133, No. 7, 07.2007, p. 773-779.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Karhunen-Loéve expansion of stochastic processes with a modified exponential covariance kernel
AU - Spanos, Pol D.
AU - Beer, Michael
AU - Red-Horse, John
PY - 2007/7
Y1 - 2007/7
N2 - 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.
AB - 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.
KW - Computer aided simulation
KW - Monte Carlo method
KW - Numerical analysis
KW - Spectral analysis
KW - Stochastic processes
UR - http://www.scopus.com/inward/record.url?scp=34347253251&partnerID=8YFLogxK
U2 - 10.1061/(ASCE)0733-9399(2007)133:7(773)
DO - 10.1061/(ASCE)0733-9399(2007)133:7(773)
M3 - Article
AN - SCOPUS:34347253251
VL - 133
SP - 773
EP - 779
JO - Journal of engineering mechanics
JF - Journal of engineering mechanics
SN - 0733-9399
IS - 7
ER -