Generalization of Rayleigh Probability Distribution and its Application

1978 ◽  
Vol 22 (04) ◽  
pp. 259-265
Author(s):  
Michel K. Ochi
Keyword(s):  
Probability Distribution ◽  
Surface Effect ◽  
Ocean Waves ◽  
Random Processes ◽  
Rayleigh Distribution ◽  
Nonlinear Damping ◽  
Statistical Prediction ◽  
Rolling Motion ◽  
Surface Effect Ship ◽  
Non Gaussian

The Rayleigh probability distribution has been used extensively for statistical prediction of ocean waves, responses of ships, and marine structures in a seaway. However, the Rayleigh distribution cannot be used for statistical prediction of non-Gaussian random processes, a typical example of which is ship rolling motion with nonlinear characteristics. To evaluate the statistical properties of the maxima (peak values) of non-Gaussian random processes, this paper discusses generalization of the Rayleigh distribution and its application to practical problems. As examples of application, the problems associated with rolling motion of a vessel stabilized by rudders, responses of a surface effect ship in a seaway, and rolling motion of a ship with nonlinear damping are presented.

Probability Distribution of Peaks for Nonlinear Combination of Vector Gaussian Loads

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Sayan Gupta ◽  
P. H. A. J. M. van Gelder
Keyword(s):  
Probability Distribution ◽  
Gaussian Process ◽  
Joint Probability ◽  
Random Processes ◽  
Von Mises Stress ◽  
Analytical Approximations ◽  
Multidimensional Integration ◽  
Reliability Method ◽  
Non Gaussian ◽  
Von Mises

The problem of approximating the probability distribution of peaks, associated with a special class of non-Gaussian random processes, is considered. The non-Gaussian processes are obtained as nonlinear combinations of a vector of mutually correlated, stationary, Gaussian random processes. The Von Mises stress in a linear vibrating structure under stationary Gaussian loadings is a typical example for such processes. The crux of the formulation lies in developing analytical approximations for the joint probability density function of the non-Gaussian process and its instantaneous first and second time derivatives. Depending on the nature of the problem, this requires the evaluation of a multidimensional integration across a possibly irregular and disjointed domain. A numerical algorithm, based on first order reliability method, is developed to evaluate these integrals. The approximations for the peak distributions have applications in predicting the expected fatigue damage due to combination of stress resultants in a randomly vibrating structure. The proposed method is illustrated through two numerical examples and its accuracy is examined with respect to estimates from full scale Monte Carlo simulations of the non-Gaussian process.

Mathematical modeling of conversion of non-Gaussian random processes, signals and noise in linear and nonlinear systems

2018 ◽  
pp. 66-78
Author(s):  
V. M. Artyushenko ◽  
V. I. Volovach
Keyword(s):  
Mathematical Modeling ◽  
Nonlinear Systems ◽  
Random Processes ◽  
Mathematical Transformation ◽  
Positive And Negative Feedback ◽  
Non Linear Systems ◽  
Linear And Nonlinear ◽  
Non Gaussian ◽  
Linear And Nonlinear Systems ◽  
Inertial Systems

The questions connected with mathematical modeling of transformation of non-Gaussian random processes, signals and noise in linear and nonlinear systems are considered and analyzed. The mathematical transformation of random processes in linear inertial systems consisting of both series and parallel connected links, as well as positive and negative feedback is analyzed. The mathematical transformation of random processes with polygamous density of probability distribution during their passage through such systems is considered. Nonlinear inertial and non-linear systems are analyzed.

Transformation of non-Gaussian random processes, signals and noise in the nonlinear differential systems by the method of cumulative functions

2018 ◽  
Vol 15 (1) ◽  
pp. 84-93
Author(s):  
V. I. Volovach ◽  
V. M. Artyushenko
Keyword(s):  
Spectral Characteristics ◽  
Random Processes ◽  
Spectral Densities ◽  
Differential Systems ◽  
Non Gaussian ◽  
Nonlinear Differential Systems

Reviewed and analyzed the issues linked with the torque and naguszewski cumulant description of random processes. It is shown that if non-Gaussian random processes are given by both instantaneous and cumulative functions, it is assumed that such processes are fully specified. Spectral characteristics of non-Gaussian random processes are considered. It is shown that higher spectral densities exist only for non-Gaussian random processes.

Random filters which preserve the stability of random inputs

1988 ◽  
Vol 20 (2) ◽  
pp. 275-294 ◽  
Author(s):  
Stamatis Cambanis
Keyword(s):  
Transfer Function ◽  
Moving Average ◽  
Random Processes ◽  
Time Shift ◽  
Linear Filter ◽  
Random Inputs ◽  
The Stability ◽  
Non Gaussian ◽  
Random Gain

A stationary stable random processes goes through an independently distributed random linear filter. It is shown that when the input is Gaussian or harmonizable stable, then the output is also stable provided the filter&s transfer function has non-random gain. In contrast, when the input is a non-Gaussian stable moving average, then the output is stable provided the filter&s randomness is due only to a random global sign and time shift.

scholarly journals Stochastic Inverse Identification of Nonlinear Roll Damping Moment of a Ship Moving at Nonzero-Forward Speeds

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
S. L. Han ◽  
Takeshi Kinoshita
Keyword(s):  
Nonlinear Damping ◽  
Rolling Motion ◽  
Forward Speed ◽  
Roll Damping ◽  
Nonparametric Approach ◽  
Nonlinear Responses ◽  
Different Types ◽  
Experimental Trials ◽  
And Control ◽  
Ship Rolling

The nonlinear responses of ship rolling motion characterized by a roll damping moment are of great interest to naval architects and ocean engineers. Modeling and identification of the nonlinear damping moment are essential to incorporate the inherent nonlinearity in design, analysis, and control of a ship. A stochastic nonparametric approach for identification of nonlinear damping in the general mechanical system has been presented in the literature (Han and Kinoshits 2012). The method has been also applied to identification of the nonlinear damping moment of a ship at zero-forward speed (Han and Kinoshits 2013). In the presence of forward speed, however, the characteristic of roll damping moment of a ship is significantly changed due to the lift effect. In this paper, the stochastic inverse method is applied to identification of the nonlinear damping moment of a ship moving at nonzero-forward speed. The workability and validity of the method are verified with laboratory tests under controlled conditions. In experimental trials, two different types of ship rolling motion are considered: time-dependent transient motion and frequency-dependent periodic motion. It is shown that this method enables the inherent nonlinearity in damping moment to be estimated, including its reliability analysis.

scholarly journals Electromagnetic Waves Through Disordered Systems: Comparison of Intensity, Transmission and Conductance

2001 ◽  
Vol 694 ◽  
Author(s):  
Fredy R Zypman ◽  
Gabriel Cwilich
Keyword(s):  
Probability Distribution ◽  
Disordered Systems ◽  
Electromagnetic Waves ◽  
Delta Function ◽  
Rayleigh Distribution ◽  
Dirac Delta Function ◽  
Universal Form ◽  
Dirac Delta ◽  
Diffusive Regime ◽  
Analytical Expressions

AbstractWe obtain the statistics of the intensity, transmission and conductance for scalar electromagnetic waves propagating through a disordered collection of scatterers. Our results show that the probability distribution for these quantities x, follow a universal form, YU(x) = xne−xμ. This family of functions includes the Rayleigh distribution (when α=0, μ=1) and the Dirac delta function (α →+ ∞), which are the expressions for intensity and transmission in the diffusive regime neglecting correlations. Finally, we find simple analytical expressions for the nth moment of the distributions and for to the ratio of the moments of the intensity and transmission, which generalizes the n! result valid in the previous case.

Large Surface Effect Ship Size Limits

2013 ◽  
Vol 29 (02) ◽  
pp. 84-91
Author(s):  
Stefanos Koullias ◽  
Santiago Balestrini Robinson ◽  
Dimitri N. Mavris
Keyword(s):  
Historical Data ◽  
Surface Effect ◽  
Advanced Materials ◽  
Complex Structures ◽  
First Principle ◽  
Simplified Models ◽  
Surface Effect Ship ◽  
Size Limits ◽  
Technology Level ◽  
Insight Into

The purpose of this study is to obtain insight into surface effect ship (SES) endurance without reliance on historical data as a function of geometry, displacement, and technology level. First-principle models of the resistance, structures, and propulsion system are developed and integrated to predict large SES endurance and to suggest the directions that future large SESs will take. It is found that large SESs are dominated by structural weight, which indicates the need for advanced materials and complex structures, and that advanced propulsion cycles can increase endurance by up to 33%. SES endurance is shown to be a nonlinear discontinuous function of geometry, displacement, and technology level that cannot be predicted by simplified models or assumptions.

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