The average number of trajectory overshoots of a non-gaussian random process above a given level

1978 ◽  
Vol 21 (8) ◽  
pp. 819-823
Author(s):  
V. I. Khimenko
Keyword(s):  
Random Process ◽  
Gaussian Random Process ◽  
Non Gaussian

Identification of Non-Gaussian Stochastic System

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Sung-man Park ◽  
O-shin Kwon ◽  
Jin-sung Kim ◽  
Jong-bok Lee ◽  
Hoon Heo
Keyword(s):  
Random Process ◽  
Random Noise ◽  
Stochastic Simulations ◽  
Kolmogorov Equation ◽  
Gaussian Random Process ◽  
System Parameters ◽  
Analysis Technique ◽  
Gaussian Analysis ◽  
Gaussian System ◽  
Non Gaussian

This paper proposes a method to identify non-Gaussian random noise in an unknown system through the use of a modified system identification (ID) technique in the stochastic domain, which is based on a recently developed Gaussian system ID. The non-Gaussian random process is approximated via an equivalent Gaussian approach. A modified Fokker–Planck–Kolmogorov equation based on a non-Gaussian analysis technique is adopted to utilize an effective Gaussian random process that represents an implied non-Gaussian random process. When a system under non-Gaussian random noise reveals stationary moment output, the system parameters can be extracted via symbolic computation. Monte Carlo stochastic simulations are conducted to reveal some approximate results, which are close to the actual values of the system parameters.

scholarly journals Duration Distribution and Up-crossings Rate of Generalized Hyperbolic Processes

2016 ◽  
Vol 36 (3) ◽  
Author(s):  
Moh’d T. Alodat ◽  
Khalid M. Aludaat
Keyword(s):  
Gaussian Process ◽  
Random Process ◽  
Alternative Model ◽  
Sea Surface ◽  
Surface Elevation ◽  
Gaussian Random Process ◽  
Duration Distribution ◽  
Non Gaussian

A Gaussian process is usually used to model the sea surface elevation in the oceanography. As the depth of the water decreases or the sea severity increases, the sea surface elevation departs from symmetry and Gaussianity. In this paper, a stationary non-Gaussian random process called the generalized hyperbolic process is used as an alternative model. The process generates a family of processes. We derive the rate of up-crossings for this process and the distribution of the height of the process. We also derive the duration distribution of an excursion for the generalized hyperbolic process.

Numerical Generation of Compound Random Processes with an Arbitrary Autocorrelation Function

2018 ◽  
Vol 17 (01) ◽  
pp. 1850001 ◽  
Author(s):  
Dima Bykhovsky ◽  
Tom Trigano
Keyword(s):  
Random Process ◽  
Autocorrelation Function ◽  
Analytical Study ◽  
Random Processes ◽  
The Other ◽  
Gaussian Random Process ◽  
Numerical Examples ◽  
Compound Process ◽  
Numerical Generation ◽  
Non Gaussian

The generation of non-Gaussian random processes with a given autocorrelation function (ACF) is addressed. The generation is based on a compound process with two components. Both components are solutions of appropriate stochastic differential equations (SDEs). One of the components is a Gaussian process and the other one is non-Gaussian with an exponential ACF. The analytical study shows that a compound combination of these processes may be used for the generation of a non-Gaussian random process with a required ACF. The results are verified by two numerical examples.

scholarly journals On Spectrum Estimation of a Clipped Gaussian Random Process

1972 ◽  
Vol 12 (2) ◽  
pp. 11-15
Author(s):  
V. G. Alekseyev
Keyword(s):  
Random Process ◽  
Spectrum Estimation ◽  
Gaussian Random Process

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: В. Алексеев. Об оценке спектра квантованного по уровню гауссовского случайного процесса V. Aleksejevas. Apie atsitiktinio Gauso proceso spektro, kvantuoto pagal lygmenį, įvertinimą H

A Mathematical Basis for the Random Decrement Vibration Signature Analysis Technique

1982 ◽  
Vol 104 (2) ◽  
pp. 307-313 ◽  
Author(s):  
J. K. Vandiver ◽  
A. B. Dunwoody ◽  
R. B. Campbell ◽  
M. F. Cook
Keyword(s):  
Random Process ◽  
Linear Time ◽  
Signature Analysis ◽  
Gaussian Random Process ◽  
Mathematical Basis ◽  
Linear Time Invariant ◽  
Random Decrement Technique ◽  
Random Decrement ◽  
Vibration Signature ◽  
Linear Time Invariant System

The mathematical basis for the Random Decrement Technique of vibration signature analysis is established. The general relationship between the autocorrelation function of a random process and the Randomdec signature is derived. For the particular case of a linear time invariant system excited by a zero-mean, stationary, Gaussian random process, a Randomdec signature of the output is shown to be proportional to the auto-correlation of the output. Example Randomdec signatures are computed from acceleration response time histories from an offshore platform.

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