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Maximum entropy probability density principle in probabilistic investigations of dynamic systems
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SYSNO ASEP 0494588 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Maximum entropy probability density principle in probabilistic investigations of dynamic systems Tvůrce(i) Náprstek, Jiří (UTAM-F) RID, ORCID, SAI
Fischer, Cyril (UTAM-F) RID, SAI, ORCIDCelkový počet autorů 2 Číslo článku 790 Zdroj.dok. Entropy. - : MDPI
Roč. 20, č. 10 (2018)Poč.str. 23 s. Forma vydání Tištěná - P Jazyk dok. eng - angličtina Země vyd. CH - Švýcarsko Klíč. slova Boltzmann solution ; Fokker–Planck equation ; Gibbs entropy functional ; maximum entropy probability density principle ; random earthquake process ; stochastically proportional system Vědní obor RIV JM - Inženýrské stavitelství Obor OECD Civil engineering CEP GC17-26353J GA ČR - Grantová agentura ČR Institucionální podpora UTAM-F - RVO:68378297 UT WOS 000448545700071 EID SCOPUS 85055711351 DOI 10.3390/e20100790 Anotace 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. Pracoviště Ústav teoretické a aplikované mechaniky Kontakt Kulawiecová Kateřina, kulawiecova@itam.cas.cz, Tel.: 225 443 285 Rok sběru 2019 Elektronická adresa https://doi.org/10.3390/e20100790
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