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.

scholarly journals Description of the macroscopic dynamics of populations of phase elements with white non-Gaussian noise based on the circular cumulant approach

2021 ◽  
pp. 05-12
Author(s):  
A. V. Dolmatova ◽  
◽  
I. V. Tiulkina ◽  
D. S. Goldobin ◽  
◽  
...  
Keyword(s):  
White Noise ◽  
Probability Density ◽  
Gaussian Noise ◽  
Gaussian White Noise ◽  
Macroscopic Description ◽  
Reduced Equations ◽  
Non Gaussian ◽  
Dynamics Of Populations ◽  
Stable Noise ◽  
Good Agreement

We use the method of circular cumulants, which allows us to construct a low-mode macroscopic description of the dynamics of populations of phase elements subject to non-Gaussian white noise. In this work, we have obtained two-cumulant reduced equations for alpha-stable noise. The application of the approach is demonstrated for the case of the Kuramoto ensemble with non-Gaussian noise. The results of numerical calculations for the ensemble of N = 1500 elements, the numericalsimulation of the chain of equations for the Kuramoto–Daido order parameters (Fourier modes of the probability density) with 200 terms (in the thermodynamic limit of an infinitely large ensemble) and the theoretical solution on the basis of the two-cumulant approximation are in good agreement with each other.

scholarly journals Filtering with a limiter

1998 ◽  
Vol 11 (3) ◽  
pp. 289-300 ◽  
Author(s):  
R. Liptser ◽  
P. Muzhikanov
Keyword(s):  
Weak Convergence ◽  
Diffusion Process ◽  
White Noise ◽  
Discrete Time ◽  
Diffusion Approximation ◽  
Conditional Expectation ◽  
Gaussian White Noise ◽  
Sampling Step ◽  
Non Gaussian ◽  
Filtering Problem

We consider a filtering problem for a Gaussian diffusion process observed via discrete-time samples corrupted by a non-Gaussian white noise. Combining the Goggin's result [2] on weak convergence for conditional expectation with diffusion approximation when a sampling step goes to zero we construct an asymptotic optimal filter. Our filter uses centered observations passed through a limiter. Being asymptotically equivalent to a similar filter without centering, it yields a better filtering accuracy in a prelimit case.

scholarly journals A Cautionary Note on the Reproduction of Dependencies through Linear Stochastic Models with Non-Gaussian White Noise

Water ◽  
2018 ◽  
Vol 10 (6) ◽  
pp. 771 ◽  
Author(s):  
Ioannis Tsoukalas ◽  
Simon Papalexiou ◽  
Andreas Efstratiadis ◽  
Christos Makropoulos
Keyword(s):  
White Noise ◽  
Stochastic Models ◽  
Gaussian White Noise ◽  
Cautionary Note ◽  
Non Gaussian

scholarly journals The Measurement and Elimination of Mode Splitting: From the Perspective of the Partly Ensemble Empirical Mode Decomposition

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Bin Liu ◽  
Peng Zheng ◽  
Qilin Dai ◽  
Zhongli Zhou
Keyword(s):  
Spectral Analysis ◽  
White Noise ◽  
Empirical Mode Decomposition ◽  
Ensemble Empirical Mode Decomposition ◽  
Permutation Entropy ◽  
Intrinsic Mode Functions ◽  
Mode Splitting ◽  
Mode Decomposition ◽  
Microseismic Signal ◽  
Mode Mixing

The problems of mode mixing, mode splitting, and pseudocomponents caused by intermittence or white noise signals during empirical mode decomposition (EMD) are difficult to resolve. The partly ensemble EMD (PEEMD) method is introduced first. The PEEMD method can eliminate mode mixing via the permutation entropy (PE) of the intrinsic mode functions (IMFs). Then, bilateral permutation entropy (BPE) of the IMFs is proposed as a means to detect and eliminate mode splitting by means of the reconstructed signals in the PEEMD. Moreover, known ingredient component signals are comparatively designed to verify that the PEEMD method can effectively detect and progressively address the problem of mode splitting to some degree and generate IMFs with better performance. The microseismic signal is applied to prove, by means of spectral analysis, that this method is effective.

Response Statistics and Reliability Analysis of a Mistuned and Frictionally Damped Bladed Disk Assembly Subjected to White Noise Excitation

2010 ◽  
Author(s):  
Pankaj Kumar ◽  
S. Narayanan
Keyword(s):  
White Noise ◽  
Probability Density ◽  
Gaussian White Noise ◽  
Random Excitation ◽  
Forced Response ◽  
Computationally Efficient ◽  
Bladed Disk ◽  
White Noise Excitation ◽  
Bladed Disk Assembly ◽  
Mean Square Response

In the design of gas turbine engines, the analysis of nonlinear vibrations of mistuned and frictionally damped blade-disk assembly subjected to random excitation is highly complex. The transitional probability density function (PDF) for the random response of nonlinear systems under white or coloured noise excitation (delta-correlated) is governed by both the forward Fokker-Planck (FP) and backward Kolmogorov equations. This paper presents important improvement and extensions to a computationally efficient higher order, finite difference (FD) technique for the solution of higher dimensional FP equation corresponding to a two degree of freedom nonlinear system representative of vibration of tip shrouded frictionally damped bladed disk assembly subjected to Gaussian white noise excitation. Effects of friction damping on the mean square response of a blade are investigated. The friction coefficient of the damper is assumed to be a function of the sliding velocity of the contact surface. The effects of stiffness and damping mistuning on the forced response of frictionally damped bladed disk are investigated. Numerical studies are presented for a pair of mistuned blades of cyclic assemblies. The response and reliability of a blade subjected to random excitation is also obtained. With time averaged probability density as an invariant measure, the probability of large excursion in case of damping mistuning is also presented. The results of the FD method are validated by comparing with Monte Carlo Simulation (MCS) results.

Extension of Nonlinear Stochastic Solution to Include Sinusoidal Excitation—Illustrated by Duffing Oscillator

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
R. J. Chang
Keyword(s):  
White Noise ◽  
Correction Factor ◽  
Duffing Oscillator ◽  
Gaussian White Noise ◽  
Noise Spectrum ◽  
Linearization Method ◽  
Algebraic Equations ◽  
Stochastic Solution ◽  
Non Gaussian ◽  
Sinusoidal Excitation

A new non-Gaussian linearization method is developed for extending the analysis of Gaussian white-noise excited nonlinear oscillator to incorporate sinusoidal excitation. The non-Gaussian linearization method is developed through introducing a modulated correction factor on the linearization coefficient which is obtained by Gaussian linearization. The time average of cyclostationary response of variance and noise spectrum is analyzed through the correction factor. The validity of the present non-Gaussian approach in predicting the statistical response is supported by utilizing Monte Carlo simulations. The present non-Gaussian analysis, without imposing restrictive analytical conditions, can be obtained by solving nonlinear algebraic equations. The non-Gaussian solution effectively predicts accurate sinusoidal and noise response when the nonlinear system is subjected to both sinusoidal and white-noise excitations.

Sign in / Sign up

Export Citation Format

Share Document