Stochastic model of the gearbox pair vibration

2021 ◽  
Vol 2021 (49) ◽  
pp. 26-31
Author(s):  
І. M. Javorskyj ◽  
◽  
R. M. Yuzefovych ◽  
O. V. Lychak ◽  
G. R. Trokhym ◽  
...  
Keyword(s):  
Stochastic Model ◽  
Random Process ◽  
Covariance Function ◽  
Vibration Signal ◽  
Least Square ◽  
Stationary Random Process ◽  
Process Mean ◽  
Hidden Periodicities

The model of vibration signal of gearbox pair in the form of periodically correlated non-stationary random process is considered. It is shown that hidden periodicities in biperiodic correlated random process mean and covariance function, characterizing the vibrations of gearbox pair can be detected using the component and least square methods. Seven particular cases of the bi-rhythmic hidden periodicity for different modulation modes are analyzed.

A note on the estimation of the mean of a homogeneous random field

1971 ◽  
Vol 8 (3) ◽  
pp. 626-629
Author(s):  
Michael Skalsky
Keyword(s):  
Finite Number ◽  
Random Field ◽  
Random Process ◽  
Mathematical Expectation ◽  
Covariance Function ◽  
Arithmetic Mean ◽  
Stationary Random Process ◽  
Homogeneous Random Field ◽  
The Mean

An important problem, arising in connection with the estimation of mathematical expectation of a homogeneous random field X(x1, ···, xn) in Rn by means of the arithmetic mean of observed values, is to determine the number of observations for which the variance of the estimate attains its minimum. Vilenkin [2] has shown, that in the case of a stationary random process X(x) such a finite number exists, provided that the covariance function satisfies certain conditions.

A note on the estimation of the mean of a homogeneous random field

1971 ◽  
Vol 8 (03) ◽  
pp. 626-629
Author(s):  
Michael Skalsky
Keyword(s):  
Finite Number ◽  
Random Field ◽  
Random Process ◽  
Mathematical Expectation ◽  
Covariance Function ◽  
Arithmetic Mean ◽  
Stationary Random Process ◽  
Homogeneous Random Field ◽  
The Mean

An important problem, arising in connection with the estimation of mathematical expectation of a homogeneous random field X(x 1, ···, xn ) in Rn by means of the arithmetic mean of observed values, is to determine the number of observations for which the variance of the estimate attains its minimum. Vilenkin [2] has shown, that in the case of a stationary random process X(x) such a finite number exists, provided that the covariance function satisfies certain conditions.

A Stochastic Model for the Inheritance of the Cancer Proneness Phenotype

1987 ◽  
Vol 26 (03) ◽  
pp. 117-123
Author(s):  
P. Tautu ◽  
G. Wagner
Keyword(s):  
Stochastic Model ◽  
Gaussian Process ◽  
Covariance Function ◽  
Neoplastic Disease ◽  
Disease Phenotype ◽  
Probabilistic Representation ◽  
Temporal Behaviour ◽  
Continuous Trait ◽  
Continuous Parameter ◽  
Level Zero

SummaryA continuous parameter, stationary Gaussian process is introduced as a first approach to the probabilistic representation of the phenotype inheritance process. With some specific assumptions about the components of the covariance function, it may describe the temporal behaviour of the “cancer-proneness phenotype” (CPF) as a quantitative continuous trait. Upcrossing a fixed level (“threshold”) u and reaching level zero are the extremes of the Gaussian process considered; it is assumed that they might be interpreted as the transformation of CPF into a “neoplastic disease phenotype” or as the non-proneness to cancer, respectively.

Induced transformations of recurrent a.m.s. dynamical systems

2015 ◽  
Vol 15 (02) ◽  
pp. 1550010
Author(s):  
Sheng Huang ◽  
Mikael Skoglund
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Random Process ◽  
Ergodic Theorem ◽  
Finite Measure ◽  
Stationary Random Process ◽  
Finite State ◽  
Ratio Ergodic Theorem

This note proves that an induced transformation with respect to a finite measure set of a recurrent asymptotically mean stationary dynamical system with a sigma-finite measure is asymptotically mean stationary. Consequently, the Shannon–McMillan–Breiman theorem, as well as the Shannon–McMillan theorem, holds for all reduced processes of any finite-state recurrent asymptotically mean stationary random process. As a by-product, a ratio ergodic theorem for asymptotically mean stationary dynamical systems is presented.

Parameters Identification for Nonlinear Duffing System Based on Wavelet Transformation

2013 ◽  
Vol 357-360 ◽  
pp. 1524-1530
Author(s):  
Shi Zhou ◽  
Dong Mei Huang ◽  
Wei Xin Ren ◽  
Qiong Li Wang
Keyword(s):  
Forced Vibration ◽  
Wavelet Transformation ◽  
Recognition Accuracy ◽  
Vibration Signal ◽  
Least Square Method ◽  
Least Square ◽  
Instantaneous Amplitude ◽  
Approximate Analytical Expression ◽  
Duffing System ◽  
The Relationship

Continuous wavelet transformation is made to identify the parameters of damped harmonic forced vibration Duffing system. With the aid of conversion relationship between the scale and frequency, the solution of nonlinear Duffing equation is adopted by average method, which gained approximate analytical expression for instantaneous amplitude and instantaneous frequency of the system. The nonlinear stiffness coefficient and natural frequency can be gained by least square method and the relationship between recognition accuracy and parameter selection are summarized in the article. Parameter identification method of harmonic forced vibration system is proposed in this paper. Studying the wavelet ridge and corresponding scale by segments to filter out the affects of the simple harmonic motion, to extract systems free vibration signal and to achieve the goal of identifying system parameters.

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