Original title: Probability density determination by means of Gibbs entropy probability density
Authors: Náprstek, Jiří ; Fischer, Cyril
Document type: Papers
Conference/Event: DYMAMESI 2019 - Dynamics of Machines and Mechanical Systems with Interactions, Cracow (PL), 20190305
Year: 2019
Language: eng
Abstract: A method of random response investigation of a nonlinear dynam-ical system is discussed. In particular, the solution of the probability density of a single/multi-degree of freedom (SDOF/MDOF) system response is investigated. Multiple stable equilibrium states with possible jumps of the snap-through type among them are considered. The system is Hamiltonian with weak damping excited by a set of non-stationary Gaussian white noises. The solution, which is based on the Gibbs principle of the maximum entropy of probability, can be employed 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 di_erential equations for the stochastic moments of the response derived from the relevant FPE
Keywords: Fokker-Planck equation; Gibbs entropy functional; maximum entropy; probability density principle
Project no.: GA19-21817S (CEP)
Funding provider: GA ČR
Host item entry: The international colloquium Dynamics of machines and mechanical systems with interactions. DYMAMESI 2019 Proceedings, ISBN 978-80-87012-70-3

Institution: Institute of Theoretical and Applied Mechanics AS ČR (web)
Document availability information: Fulltext is available at the institute of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0294422

Permalink: http://www.nusl.cz/ntk/nusl-394143


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