6533b831fe1ef96bd1299134

RESEARCH PRODUCT

Approximate solution of the Fokker-Planck-Kolmogorov equation

M. Di PaolaAlba Sofi

subject

Mechanical EngineeringMultiplicative functionAerospace EngineeringOcean EngineeringStatistical and Nonlinear PhysicsProbability density functionWhite noiseCondensed Matter PhysicsMultiplicative noiseWeightingNonlinear systemsymbols.namesakeNuclear Energy and EngineeringGaussian noiseProbability density functionsymbolsApplied mathematicsFokker–Planck equationWeighted residuals methodSafety Risk Reliability and QualityCivil and Structural EngineeringMathematical physicsMathematicsFokker-Planck-Kolmogorov equation

description

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. © 2002 Published by Elsevier Science Ltd.

yearjournalcountryeditionlanguage
2002-10-01
10.1016/s0266-8920(02)00034-6http://hdl.handle.net/10447/196214