Maximum entropy probability density principle in probabilistic investigations of dynamic systems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68378297%3A_____%2F18%3A00494588" target="_blank" >RIV/68378297:_____/18:00494588 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.3390/e20100790" target="_blank" >https://doi.org/10.3390/e20100790</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/e20100790" target="_blank" >10.3390/e20100790</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Maximum entropy probability density principle in probabilistic investigations of dynamic systems

Popis výsledku v původním jazyce

In this study, we consider a method for investigating the stochastic response of a nonlinear dynamical system affected by a random seismic process. We present the solution of the probability density of a single/multiple-degree of freedom (SDOF/MDOF) system with several statically stable equilibrium states and with possible jumps of the snap-through type. The system is a Hamiltonian system with weak damping excited by a system of non-stationary Gaussian white noise. The solution based on the Gibbs principle of the maximum entropy of probability could potentially be implemented in various branches of engineering. The search for the extreme of the Gibbs entropy functional is formulated as a constrained optimization problem. The secondary constraints follow from the Fokker–Planck equation (FPE) for the system considered or from the system of ordinary differential equations for the stochastic moments of the response derived from the relevant FPE. In terms of the application type, this strategy is most suitable for SDOF/MDOF systems containing polynomial type nonlinearities. Thus, the solution links up with the customary formulation of the finite elements discretization for strongly nonlinear continuous systems.

Název v anglickém jazyce

Maximum entropy probability density principle in probabilistic investigations of dynamic systems

Popis výsledku anglicky

In this study, we consider a method for investigating the stochastic response of a nonlinear dynamical system affected by a random seismic process. We present the solution of the probability density of a single/multiple-degree of freedom (SDOF/MDOF) system with several statically stable equilibrium states and with possible jumps of the snap-through type. The system is a Hamiltonian system with weak damping excited by a system of non-stationary Gaussian white noise. The solution based on the Gibbs principle of the maximum entropy of probability could potentially be implemented in various branches of engineering. The search for the extreme of the Gibbs entropy functional is formulated as a constrained optimization problem. The secondary constraints follow from the Fokker–Planck equation (FPE) for the system considered or from the system of ordinary differential equations for the stochastic moments of the response derived from the relevant FPE. In terms of the application type, this strategy is most suitable for SDOF/MDOF systems containing polynomial type nonlinearities. Thus, the solution links up with the customary formulation of the finite elements discretization for strongly nonlinear continuous systems.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20102 - Construction engineering, Municipal and structural engineering

Projekt

<a href="/cs/project/GC17-26353J" target="_blank" >GC17-26353J: Teoretické prediktivní modely interakce proměnného a pohyblivého zatížení využitelné v monitoringu mostních konstrukcí</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Entropy

ISSN

1099-4300

e-ISSN

—

Svazek periodika

20

Číslo periodika v rámci svazku

10

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

23

Strana od-do

—

Kód UT WoS článku

000448545700071

EID výsledku v databázi Scopus

2-s2.0-85055711351