Maximum entropy probability density principle in probabilistic investigations of dynamic systems

0494588 - ÚTAM 2019 RIV CH eng J - Journal Article
Náprstek, Jiří - Fischer, Cyril
Maximum entropy probability density principle in probabilistic investigations of dynamic systems.
Entropy. Roč. 20, č. 10 (2018), č. článku 790. E-ISSN 1099-4300
R&D Projects: GA ČR(CZ) GC17-26353J
Institutional support: RVO:68378297
Keywords : Boltzmann solution * Fokker–Planck equation * Gibbs entropy functional * maximum entropy probability density principle * random earthquake process * stochastically proportional system
OECD category: Civil engineering
Impact factor: 2.419, year: 2018
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.
Permanent Link: http://hdl.handle.net/11104/0287697