scholarly journals A comparative study of the stochastic averaging method and the path integration method for nonlinear ship roll motion in random beam seas

2017 ◽  
Vol 23 (4) ◽  
pp. 854-865 ◽  
Author(s):  
Wei Chai ◽  
Leo Dostal ◽  
Arvid Naess ◽  
Bernt J. Leira
Keyword(s):  
Path Integration ◽  
Averaging Method ◽  
Integration Method ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Roll Motion ◽  
Beam Seas ◽  
Path Integration Method ◽  
Ship Roll ◽  
Ship Roll Motion

scholarly journals Ship roll motion prediction based on ℓ1 regularized extreme learning machine

PLoS ONE ◽  
2018 ◽  
Vol 13 (10) ◽  
pp. e0206476 ◽  
Author(s):  
Binglei Guan ◽  
Wei Yang ◽  
Zhibin Wang ◽  
Yinggan Tang
Keyword(s):  
Extreme Learning Machine ◽  
Motion Prediction ◽  
Roll Motion ◽  
Ship Roll ◽  
Learning Machine ◽  
Ship Roll Motion

An improved energy envelope stochastic averaging method and its application to a nonlinear oscillator

2016 ◽  
Vol 23 (1) ◽  
pp. 119-130 ◽  
Author(s):  
Yaping Zhao
Keyword(s):  
Steady State ◽  
Probability Density Function ◽  
Probability Density ◽  
Averaging Method ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
System Response ◽  
Mean Square ◽  
Fpk Equation ◽  
The Mean

An improved stochastic averaging method of the energy envelope is proposed, whose application sphere is extensive and whose implementation is convenient. An oscillating system with both nonlinear damping and stiffness is taken into account. Its averaged Fokker-Planck-Kolmogorov (FPK) equation in respect of the transition probability density function of the energy envelope is deduced by virtue of the method mentioned above. Under the initial and boundary conditions, the joint probability density function as to the displacement and velocity of the system is worked out in closed form after solving the averaged FPK equation by right of a technique based on the integral transformation. With the aid of the special functions, the transient solutions of the probabilistic characteristics of the system response are further derived analytically, including the probability density functions and the mean square values. A simple approach to generate the ideal white noise is drastically ameliorated in order to produce the stationary wide-band stochastic external excitation for the Monte Carlo simulating investigation of the nonlinear system. Both the theoretical solution and the numerical solution of the probabilistic properties of the system response are obtained, which are extremely coincident with each other. The numerical simulation and the theoretical computation all show that the time factor has a certain influence on the probability characteristics of the response. For example, the probabilistic distribution of the displacement tends to be scattered and the mean square displacement trends toward its steady-state value as time goes by. Of course the transient process to reach the steady-state value will obviously be shorter if the damping of the system is greater.

The Effects of Correlated Noise on Bifurcation in Birhythmicity Driven by Delay

2018 ◽  
Vol 28 (10) ◽  
pp. 1850127 ◽  
Author(s):  
Lijuan Ning ◽  
Zhidan Ma
Keyword(s):  
Averaging Method ◽  
Harmonic Approximation ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Self Control ◽  
Correlated Noise ◽  
State Variables ◽  
Stationary Probability Density Function ◽  
Fpk Equation ◽  
Control Feedback

We consider bifurcation regulations under the effects of correlated noise and delay self-control feedback excitation in a birhythmic model. Firstly, the term of delay self-control feedback is transferred into state variables without delay by harmonic approximation. Secondly, FPK equation and stationary probability density function (SPDF) for amplitude can be theoretically mapped with stochastic averaging method. Thirdly, the intriguing effects on bifurcation regulations in a birhythmic model induced by delay and correlated noise are observed, which suggest the violent dependence of bifurcation in this model on delay and correlated noise. Particularly, the inner limit cycle (LC) is always standing due to noise. Lastly, the validity of analytical results was confirmed by Monte Carlo simulation for the dynamics.

Stochastic dynamics of a nonlinear time-varying spur gear model using an adaptive time-stepping path integration method

2019 ◽  
Vol 447 ◽  
pp. 170-185
Author(s):  
Saeed Gheisari Hasnijeh ◽  
Mehrdad Poursina ◽  
Bernt Johan Leira ◽  
Hossein Karimpour ◽  
Wei Chai
Keyword(s):  
Path Integration ◽  
Stochastic Dynamics ◽  
Integration Method ◽  
Spur Gear ◽  
Time Varying ◽  
Time Stepping ◽  
Path Integration Method ◽  
Adaptive Time ◽  
Adaptive Time Stepping
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