Extrema Prediction and Fatigue Assessment of Highly Non-Gaussian Random Processes Using a Homogenous Reproduction Method

2020 ◽  
Vol 146 (4) ◽  
pp. 04020018 ◽  
Author(s):  
X. Y. Zheng ◽  
S. Gao ◽  
Y. Huang
Keyword(s):  
Random Processes ◽  
Fatigue Assessment ◽  
Non Gaussian ◽  
Reproduction Method

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.

Analysis and Simulation of Radar Clutter Using Spherically Invariant Random Processe

2013 ◽  
Vol 765-767 ◽  
pp. 431-435
Author(s):  
Hong Sen Xie ◽  
Jin Bo Shi ◽  
Bao Kuan Luan ◽  
Hua Ming Tian ◽  
Peng Zhou
Keyword(s):  
Correlation Function ◽  
Probability Function ◽  
Temporal Correlation ◽  
Random Processes ◽  
Spatial Correlation Function ◽  
Radar Clutter ◽  
Gaussian Probability Distribution ◽  
Non Gaussian ◽  
Simulation And Validation ◽  
Temporal Correlation Function

Non-Gaussian probability distribution radar clutter not only is temporal correlated between different pulses, but also is spatial correlated between different range bins. In this paper, the method of simulation and validation of radar clutter is proposed using spherically invariant random processes (SIRP). The amplitude probability function and temporal correlation function of radar clutter can be controlled respectively, and the spatial correlation function can be also specified. The computer simulation of K-distribution and CHI-distribution radar clutter is used to validate the method, and is to validate the amplitude probability function, temporal-spatial 2D correlation function.

Reliability Analysis and Random Vibration of Nonlinear Systems Using the Adjoint Method and Projected Differentiation

2020 ◽  
Vol 143 (6) ◽  
Author(s):  
Dimitrios Papadimitriou ◽  
Zissimos P. Mourelatos ◽  
Zhen Hu
Keyword(s):  
Reliability Analysis ◽  
Equations Of Motion ◽  
Random Variables ◽  
Random Processes ◽  
Time Dependent ◽  
Vibratory System ◽  
Standard Normal ◽  
Non Gaussian ◽  
Nonlinear Equations Of Motion ◽  
Adjoint Approach

Abstract This paper proposes a new methodology for time-dependent reliability and random vibrations of nonlinear vibratory systems using a combination of a time-dependent adjoint variable (AV) method and a projected differentiation (PD) method. The proposed approach is called AV-PD. The vibratory system is excited by stationary Gaussian or non-Gaussian input random processes. A Karhunen–Loeve (KL) expansion expresses each input random process in terms of standard normal random variables. The nonlinear equations of motion (EOM) are linearized using a Taylor expansion using the first-order derivatives of the output with respect to the input KL random variables. An adjoint approach obtains the output derivatives accurately and efficiently requiring the solution of as many sets of EOM as the number of outputs of interest, independently of the number of KL random variables. The proposed PD method then computes the autocorrelation function of each output process at an additional cost of solving as many sets of EOM as the number of outputs of interest, independently of the time horizon (simulation time). A time-dependent reliability analysis is finally performed using a KL expansion of the output processes and Monte Carlo simulation (MCS). The number of solutions of the EOM scales only with the number of output random processes which is commonly much smaller than the number of input KL random variables. The efficiency and accuracy of the proposed approach is demonstrated using a four degree-of-freedom (DOF) half-car vibratory problem.

Formation of non-Gaussian random processes, signals and interference, on the basis of stochastic differential equations

2018 ◽  
pp. 45-58
Author(s):  
V. M. Artyushenko ◽  
V. I. Volovach
Keyword(s):  
Differential Equations ◽  
Poisson Process ◽  
Stochastic Differential Equations ◽  
Gaussian Processes ◽  
Random Processes ◽  
Parametric Noise ◽  
Non Gaussian

Reviewed and analyzed issues associated with the formation of naguszewski random processes using stochastic differential equations. Algorithms of formation of scalar, vector and n –connected continuous Markov non-Gaussian sequences are considered. Forming filters with parametric noise and with disturbing influences, which are not Gaussian processes, are analyzed. The analysis of formation of non Gaussian sequences by means of Poisson process and stochastic filters is carried out.

Stable Non-Gaussian Random Processes

2017 ◽  
Author(s):  
Gennady Samorodnitsky ◽  
Murad S. Taqqu
Keyword(s):  
Random Processes ◽  
Non Gaussian
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