Approximate solution of the Fokker-Planck-Kolmogorov equation

被引：69

作者：

Di Paola, M ^{[1
]}

Sofi, A ^{[1
]}

机构：

[1] Univ Palermo, Dipartimento Ingn Strutturale & Geotecn, I-90128 Palermo, Italy

来源：

PROBABILISTIC ENGINEERING MECHANICS | 2002年 / 17卷 / 04期

关键词：

probability density function; Fokker-Planck-Kolmogorov equation; weighted residuals method;

D O I：

10.1016/S0266-8920(02)00034-6

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

The aim of this paper is to present a thorough investigation of approximate techniques for estimating the stationary and non-stationary probability density function (PDF) of the response of nonlinear systems subjected to (additive and/or multiplicative) Gaussian white noise excitations. Attention is focused on the general scheme of weighted residuals for the approximate solution of the Fokker-Planck-Kolmogorov (FPK) equation. It is shown that the main drawbacks of closure schemes, such as negative values of the PDF in some regions, may be overcome by rewriting the FPK equation in terms of log-probability density function (log-PDF). The criteria for selecting the set of weighting functions in order to obtain improved estimates of the response PDF are discussed in detail. Finally, a simple and very effective iterative solution procedure is proposed. (C) 2002 Published by Elsevier Science Ltd.

引用

页码：369 / 384

页数：16

共 42 条

[21] SOLUTION OF THE MULTIVARIATE FOKKER-PLANCK EQUATION BY USING A MAXIMUM PATH ENTROPY PRINCIPLE [J].