### Abstract

Lingua originale | English |
---|---|

pagine (da-a) | 369-384 |

Numero di pagine | 16 |

Rivista | Probabilistic Engineering Mechanics |

Volume | 17 |

Stato di pubblicazione | Published - 2002 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Civil and Structural Engineering
- Nuclear Energy and Engineering
- Condensed Matter Physics
- Aerospace Engineering
- Ocean Engineering
- Mechanical Engineering

### Cita questo

**Approximate solution of the Fokker-Planck-Kolmogorov equation.** / Di Paola, Mario.

Risultato della ricerca: Article

*Probabilistic Engineering Mechanics*, vol. 17, pagg. 369-384.

}

TY - JOUR

T1 - Approximate solution of the Fokker-Planck-Kolmogorov equation

AU - Di Paola, Mario

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10447/196214

M3 - Article

VL - 17

SP - 369

EP - 384

JO - Probabilistic Engineering Mechanics

JF - Probabilistic Engineering Mechanics

SN - 0266-8920

ER -