Reliability of quasi integrable and non-resonant Hamiltonian systems under fractional Gaussian noise excitation

2020 ◽  
Vol 36 (4) ◽  
pp. 902-909 ◽  
Author(s):  
Q. F. Lü ◽  
W. Q. Zhu ◽  
M. L. Deng
Keyword(s):  
Hamiltonian Systems ◽  
Gaussian Noise ◽  
Fractional Gaussian Noise

Response of Quasi-Integrable and Resonant Hamiltonian Systems to Fractional Gaussian Noise

2021 ◽  
Vol 144 (1) ◽  
Author(s):  
Q. F. Lü ◽  
W. Q. Zhu ◽  
M. L. Deng
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Analytical Solutions ◽  
Gaussian Noise ◽  
Nonlinear Dynamical Systems ◽  
Original System ◽  
System Response ◽  
Fractional Gaussian Noise

Abstract The major difficulty in studying the response of multi-degrees-of-freedom (MDOF) nonlinear dynamical systems driven by fractional Gaussian noise (fGn) is that the system response is not Markov process diffusion and thus the diffusion process theory cannot be applied. Although the stochastic averaging method (SAM) for quasi Hamiltonian systems driven by fGn has been developed, the response of the averaged systems still needs to be predicted by using Monte Carlo simulation. Later, noticing that fGn has rather flat power spectral density (PSD) in certain frequency band, the SAM for MDOF quasi-integrable and nonresonant Hamiltonian system driven by wideband random process has been applied to investigate the response of quasi-integrable and nonresonant Hamiltonian systems driven by fGn. The analytical solution for the response of an example was obtained and well agrees with Monte Carlo simulation. In the present paper, the SAM for quasi-integrable and resonant Hamiltonian systems is applied to investigate the response of quasi-integrable and resonant Hamiltonian system driven by fGn. Due to the resonance, the theoretical procedure and calculation will be more complicated than the nonresonant case. For an example, some analytical solutions for stationary probability density function (PDF) and stationary statistics are obtained. The Monte Carlo simulation results of original system confirmed the effectiveness of the analytical solutions under certain condition.

scholarly journals Generalized Wavelet Fisher’s Information of1/fαSignals

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Julio Ramírez-Pacheco ◽  
Homero Toral-Cruz ◽  
Luis Rizo-Domínguez ◽  
Joaquin Cortez-Gonzalez
Keyword(s):  
Fisher Information ◽  
Gaussian Noise ◽  
Structural Breaks ◽  
Wavelet Domain ◽  
Fractional Gaussian Noise ◽  
Domain Definition ◽  
Potential Applications ◽  
Definition Of ◽  
The Time Domain ◽  
Fisher's Information

This paper defines the generalized wavelet Fisher information of parameterq. This information measure is obtained by generalizing the time-domain definition of Fisher’s information of Furuichi to the wavelet domain and allows to quantify smoothness and correlation, among other signals characteristics. Closed-form expressions of generalized wavelet Fisher information for1/fαsignals are determined and a detailed discussion of their properties, characteristics and their relationship with waveletq-Fisher information are given. Information planes of1/fsignals Fisher information are obtained and, based on these, potential applications are highlighted. Finally, generalized wavelet Fisher information is applied to the problem of detecting and locating weak structural breaks in stationary1/fsignals, particularly for fractional Gaussian noise series. It is shown that by using a joint Fisher/F-Statistic procedure, significant improvements in time and accuracy are achieved in comparison with the sole application of theF-statistic.

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