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Karhunen–loéve expansion of stochastic processes with a modified exponential covariance kernel / Pol D. Spanos in Journal of engineering mechanics, Vol. 133 N°7 (Juillet 2007) 

Public ISBD [article]  in Journal of engineering mechanics > Vol. 133 N°7 (Juillet 2007) . - pp.773–779. Titre : Karhunen–loéve expansion of stochastic processes with a modified exponential covariance kernel Type de document : texte imprimé Auteurs : Pol D. Spanos, Auteur ; Michael Beer, Auteur ; John Red-Horse, Auteur Année de publication : 2007 Article en page(s) : pp.773–779. Note générale : Applied mechanics Langues : Anglais (eng) Mots-clés : Stochastic  processes  Spectral  analysis  Monte  Carlo  method  Computer  aided  simulation  Numerical  analysis Résumé : 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. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%290733-9399%282007%29133%3A7%2877 [...] [article] Karhunen–loéve expansion of stochastic processes with a modified exponential covariance kernel [texte imprimé] / Pol D. Spanos, Auteur ; Michael Beer, Auteur ; John Red-Horse, Auteur . - 2007 . - pp.773–779. Applied mechanics Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 133 N°7 (Juillet 2007) . - pp.773–779. Mots-clés : Stochastic  processes  Spectral  analysis  Monte  Carlo  method  Computer  aided  simulation  Numerical  analysis Résumé : 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. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%290733-9399%282007%29133%3A7%2877 [...]