Estimating a non-Gaussian probability density of the rolling motion in irregular beam seas

2018 ◽  
Vol 24 (4) ◽  
pp. 1071-1077 ◽  
Author(s):  
Atsuo Maki ◽  
Masahiro Sakai ◽  
Naoya Umeda
Keyword(s):  
Probability Density ◽  
Rolling Motion ◽  
Beam Seas ◽  
Non Gaussian ◽  
Irregular Beam Seas

Governing equations for probability densities of Marcus stochastic differential equations with Lévy noise

2016 ◽  
Vol 17 (05) ◽  
pp. 1750033 ◽  
Author(s):  
Xu Sun ◽  
Xiaofan Li ◽  
Yayun Zheng
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Probability Density ◽  
Lévy Processes ◽  
Planck Equation ◽  
Levy Processes ◽  
Stochastic Dynamical Systems ◽  
Non Gaussian ◽  
Fokker Planck Equations ◽  
Fokker Planck

Marcus stochastic differential equations (SDEs) often are appropriate models for stochastic dynamical systems driven by non-Gaussian Lévy processes and have wide applications in engineering and physical sciences. The probability density of the solution to an SDE offers complete statistical information on the underlying stochastic process. Explicit formula for the Fokker–Planck equation, the governing equation for the probability density, is well-known when the SDE is driven by a Brownian motion. In this paper, we address the open question of finding the Fokker–Planck equations for Marcus SDEs in arbitrary dimensions driven by non-Gaussian Lévy processes. The equations are given in a simple form that facilitates theoretical analysis and numerical computation. Several examples are presented to illustrate how the theoretical results can be applied to obtain Fokker–Planck equations for Marcus SDEs driven by Lévy processes.

Non-Gaussian clutter characterization applied to OTHR using a mixture of two Rayleigh probability density functions

2009 ◽  
Vol 44 (6) ◽  
pp. 663-666
Author(s):  
Steven C. Gustafson ◽  
Evan A. James ◽  
Andrew J. Terzuoli ◽  
Lindsay N. Weidenhammer ◽  
Rod I. Barnes
Keyword(s):  
Probability Density ◽  
Probability Density Functions ◽  
Density Functions ◽  
Non Gaussian

Vehicle Risk Level Estimation by Using Experimental Trajectories in Bend

2011 ◽  
Author(s):  
Abdourahmane Koita ◽  
Dimitri Daucher ◽  
Michel Fogli
Keyword(s):  
Probability Density ◽  
Reliability Analysis ◽  
Probabilistic Models ◽  
Hermite Polynomials ◽  
Probabilistic Methods ◽  
Risk Level ◽  
General Context ◽  
Risk Levels ◽  
Modelling Uncertainties ◽  
Non Gaussian

This paper tackles the general context of road safety, focussing on the light vehicles safety in bends. It consists to use a reliability analysis in order to estimate the failure probability of vehicle trajectories. Firstly, we build probabilistic models able to describe measured trajectories in a given bend. The models are transforms of scalar normalized second order stochastic processes which are stationary, ergodic and non-Gaussian. The process is characterized by its probability density function and its power spectral density estimated starting from the experimental trajectories. The probability density is approximated by a development on the Hermite polynomials basis. The second part is devoted to apply a reliability strategy intended to associate a risk level to each class of trajectories. Based on the joint use of probabilistic methods for modelling uncertainties, reliability analysis for assessing risk levels and statistics for classifying the trajectories, this approach provides a realistic answer to the tackled problem.

scholarly journals EMD OF GAUSSIAN WHITE NOISE: EFFECTS OF SIGNAL LENGTH AND SIFTING NUMBER ON THE STATISTICAL PROPERTIES OF INTRINSIC MODE FUNCTIONS

2009 ◽  
Vol 01 (04) ◽  
pp. 517-527 ◽  
Author(s):  
GASTÓN SCHLOTTHAUER ◽  
MARÍA EUGENIA TORRES ◽  
HUGO L. RUFINER ◽  
PATRICK FLANDRIN
Keyword(s):  
White Noise ◽  
Probability Density ◽  
Kernel Smoothing ◽  
Gaussian White Noise ◽  
Large Data ◽  
Intrinsic Mode Functions ◽  
Mode Decomposition ◽  
Non Gaussian ◽  
Data Length ◽  
Number Of Iterations

This work presents a discussion on the probability density function of Intrinsic Mode Functions (IMFs) provided by the Empirical Mode Decomposition of Gaussian white noise, based on experimental simulations. The influence on the probability density functions of the data length and of the maximum allowed number of iterations is analyzed by means of kernel smoothing density estimations. The obtained results are confirmed by statistical normality tests indicating that the IMFs have non-Gaussian distributions. Our study also indicates that large data length and high number of iterations produce multimodal distributions in all modes.

Sign in / Sign up

Export Citation Format

Share Document