Počet záznamů: 1  

Maximum entropy probability density principle in probabilistic investigations of dynamic systems

  1. 1.
    0494588 - UTAM-F 2019 RIV CH eng J - Článek v odborném periodiku
    Náprstek, Jiří - Fischer, Cyril
    Maximum entropy probability density principle in probabilistic investigations of dynamic systems.
    Entropy. Roč. 20, č. 10 (2018), č. článku 790. ISSN 1099-4300
    Grant CEP: GA ČR(CZ) GC17-26353J
    Institucionální podpora: RVO:68378297
    Klíčová slova: Boltzmann solution * Fokker–Planck equation * Gibbs entropy functional * maximum entropy probability density principle * random earthquake process * stochastically proportional system
    Kód oboru RIV: JM - Inženýrské stavitelství
    Obor OECD: Construction engineering, Municipal and structural engineering
    Impakt faktor: 2.305, rok: 2017
    https://doi.org/10.3390/e20100790

    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.
    Trvalý link: http://hdl.handle.net/11104/0287697