Characteristic Exponent Extraction of Experimental Nonlinear Time Series

Shu Yong Liu; Xiu Lei Wei

doi:10.4028/www.scientific.net/AMM.556-562.3835

Paper Titles

The Research on the Fusion of Sobel Evaluation Function about Vehicle Contour Clearness Algorithm
p.3818

Spectral Clustering Based on Sparse Representation
p.3822

Research on Efficient Association Analysis Algorithm towards Production Process Data
p.3827

Analyzingand Modeling on Space Environment Effects Equivalence
p.3831

Characteristic Exponent Extraction of Experimental Nonlinear Time Series
p.3835

A Variable Mode QR Decomposition Adaptive Filtering Algorithm for Acoustic Echo Cancellation
p.3839

Bacterial Foraging Optimization Algorithm with Quorum Sensing Mechanism
p.3844

The Application of Computer Simulation Technology in the Queuing System Optimization
p.3849

Improved Artificial Bee Colony Clustering Algorithm Based on K-Means
p.3852

HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 556-562Characteristic Exponent Extraction of Experimental...

Characteristic Exponent Extraction of Experimental Nonlinear Time Series

Abstract:

The experiment of chaotic exponent extraction is carried out on the basis of nonlinear vibration system, and the responses under different conditions are processed with the improved algorithm. Firstly, the weighted wavelet denoise method is applied to filter the contaminated noise. Then, on the basis of fast search technology i.e. space grid hiberarchy inquiry method, the chaos characteristic exponent extraction algorithm is modified and applied to LE and fractal dimension calculation. Finally the piece-wise vibration system is designed, and the nonlinear dynamics under different harmonic frequencies excitation are analyzed. The comprehensive chaos judgment program is developed, in which the time domain diagram, phase space reconstruction attractor, Lyapunov exponent, fractal dimension curve of the measured data are obtained. The interesting phenomena such as AM modulation, limited cycle, and strange attractor are observed.

You might also be interested in these eBooks

View Preview

Info:

Periodical:

Applied Mechanics and Materials (Volumes 556-562)

Pages:

3835-3838

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.556-562.3835

Citation:

Cite this paper

Online since:

May 2014

Authors:

Shu Yong Liu*, Xiu Lei Wei

Keywords:

Chaos Characteristic Exponent, Experimental Analysis, Fast Grid Search, Weighted Wavelet Denoise

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

* - Corresponding Author

References

[1] Mansour Sheikhan, Reza Shahnazi, Sahar Garoncy. Synchronization of general chaotic systems using neural controllers with application to secure communication[J]. Neural computing &applications, 2013, 22(2): 361-373.

DOI: 10.1007/s00521-011-0697-0

Google Scholar

[2] Hu Sheng, yangquan Chen, Tianshuang Qiu. Multifractional property analysis of human sleep EEG signals[J]. International Journal of bifurcation and chaos in applied Sciences and engineering. 2012, 22(4): 1-10.

DOI: 10.1142/s0218127412500800

Google Scholar

[3] Takens F. Dynamical systems and turbulence [A].D. A Rand and L.S. Young, eds. Lecture Notes in Mathematics, Berlin: Springer, 1981, 898: 366-381.

Google Scholar

[4] Jianhua Yang. The maximal Lyapunov exponent for a three-dimensional system driven by white noise, Communications in nonlinear science and numerical simulation. 2010, 15(11): 3498-3499.

DOI: 10.1016/j.cnsns.2009.12.034

Google Scholar

[5] Brunton, SL; Rowley, CW. Fast computation of finite-time Lyapunov exponent fields for unsteady flows, Chaos. 2010, 20(1): 1-12.

DOI: 10.1063/1.3270044

Google Scholar

[6] Grassberger P. Generalized Dimension of Strange Attractors [J]. Physics Letter, 1987, 97: 127-138.

Google Scholar

[7] Xiong Bangshu, He Mingyi, Yu Huajing. Algorithm for Finding K-nearest Neighbors of Scattered Points in Three Dimension[J]. Journal of Computer Aided Design & Computer Graphics, 2004, 16 (7): 909-917.

DOI: 10.1109/icip.2004.1421467

Google Scholar

[8] Shu Zhongling, Wang Linlin, Wang Zuocheng. Improvement of WebGIS Performance Using Multilayer Index[J]. Computer applications, 2004; ( 9): 150-152.

Google Scholar

[9] H. s. kim, R. Eykholt; J.D. Salas,. Nonlinear dynamics, delay times, and embedding windows. Physica D Nonlinear Phenomena, 1999, 127: 48-60.

DOI: 10.1016/s0167-2789(98)00240-1

Google Scholar