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.

Stationary Response of Multidegree-of-Freedom Strongly Nonlinear Systems to Fractional Gaussian Noise

2017 ◽  
Vol 84 (10) ◽  
Author(s):  
Qiang Feng Lü ◽  
Mao Lin Deng ◽  
Wei Qiu Zhu
Keyword(s):  
Hamiltonian System ◽  
Gaussian Noise ◽  
Hurst Index ◽  
Fractional Gaussian Noise ◽  
Stationary Response ◽  
Completely Integrable ◽  
Strongly Nonlinear ◽  
Fractional Stochastic Differential Equations ◽  
Strongly Nonlinear System ◽  
Probability Densities

The stationary response of multidegree-of-freedom (MDOF) strongly nonlinear system to fractional Gaussian noise (FGN) with Hurst index 1/2 < H < 1 is studied. First, the system is modeled as FGN-excited and -dissipated Hamiltonian system. Based on the integrability and resonance of the associated Hamiltonian system, the system is divided into five classes: partially integrable and resonant, partially integrable and nonresonant, completely integrable and resonant, completely integrable and nonresonant, and nonintegrable. Then, the averaged fractional stochastic differential equations (SDEs) for five classes of quasi-Hamiltonian systems with lower dimension and involving only slowly varying processes are derived. Finally, the approximate stationary probability densities and other statistics of two example systems are obtained by numerical simulation of the averaged fractional SDEs to illustrate the application and compared with those from original systems to show the advantages of the proposed procedure.

Human-Induced Loads on Grandstands as Non-Stationary Gaussian Processes

2016 ◽  
Vol 837 ◽  
pp. 191-197 ◽  
Author(s):  
Ondrej Rokos ◽  
Jiří Maca
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Gaussian Processes ◽  
Gaussian Noise ◽  
Mean Value ◽  
Moment Equations ◽  
Overall Performance ◽  
Stationary Gaussian Processes ◽  
Stationary Approximation ◽  
Transition Stages

In this contribution, we employ non-stationary filtered Gaussian processes as an enrichment of a periodic mean value in order to approximate crowd loads on grandstands. Our work generalizes previous considerations where the superposition of a mean value and a stationary filtered Gaussian noise was used, and helps therefore to better predict the response of a structure mainly in the transition stages. We specify general theory of stochastic differential equations within the context of grandstands by recalling particular moment equations, and demonstrate its benefits or drawbacks on two simple examples. Overall performance is measured in terms of the second moment evolutions in time and in terms of the total up-crossings of the system's response compared to previously developed stationary approximation and Monte Carlo simulation. Throughout, only an active part of a crowd is considered.

Interval estimation of operational availability of tree harvesting machines

1987 ◽  
Vol 17 (11) ◽  
pp. 1451-1454
Author(s):  
C. H. Meng ◽  
S. Z. Tang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Analytical Solutions ◽  
Analytical Approach ◽  
Interval Estimation ◽  
Pulp And Paper ◽  
Point Estimation ◽  
Interval Estimate ◽  
Point Estimates ◽  
The Mean

The Canadian Pulp and Paper Association has defined the operational availability of a piece of logging equipment as A = (T − M − D)/T, where T denotes total scheduled machine hours per day, M denotes maintenance hours per day, and D denotes machine downtime per day. The existing literature on logging machines contains only point estimates of the mean operational availability. This paper propounds interval estimation as a preferable alternative since, unlike point estimation, it provides an indication of the uncertainty involved. Two methods of interval estimation are developed: (i) an analytical approach derived from basic theories and (ii) a Monte Carlo simulation. A detailed example is given to demonstrate the application of both methods to the same logging machine. For situations in which theoretical distributions for downtimes and repair times can be assumed, analytical solutions provide general and exact answers for the interval estimate of machine operational availability. However, if theoretical distributions cannot be reasonably assumed and if the integration involved is difficult, the analytical procedures become difficult. In such cases, operational availability can be approximated by the method of Monte Carlo simulation.

Random distribution active site model for ice nucleation in water droplets

CrystEngComm ◽  
2019 ◽  
Vol 21 (25) ◽  
pp. 3810-3821 ◽  
Author(s):  
Noriaki Kubota
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Analytical Solutions ◽  
Active Site ◽  
Random Distribution ◽  
Ice Nucleation ◽  
Water Droplets ◽  
Site Model ◽  
Temperature Distributions ◽  
Active Site Model

Analytical solutions and Monte Carlo simulation agree well with experimental ice nucleation temperature distributions for water droplets.

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