Correlation Dimension

2018 ◽  
pp. 39-44
Author(s):  
Eric Rosenberg
Keyword(s):  
Correlation Dimension

EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

Relevance of Correlation Dimension and Kolmogorov Entropy in the State Discriminant of Gearbox

2014 ◽  
Vol 644-650 ◽  
pp. 858-862
Author(s):  
Xiang Dong Mao ◽  
Hui Qun Yuan ◽  
Hua Gang Sun
Keyword(s):  
Correlation Dimension ◽  
Kolmogorov Entropy ◽  
Calculation Methods ◽  
Characteristic Parameters ◽  
State Monitoring ◽  
Basic Principles ◽  
Parameters Selection ◽  
Good Consistency ◽  
Chaotic Characteristic ◽  
Working Status

This paper introduces the basic principles and calculation methods for the correlation dimension and Kolmogorov entropy. By calculating the correlation dimension and Kolmogorov entropy when the gear is under different working conditions, we can analyze the inherent relationship between the two in depicting of the running condition of the gearbox. The result shows that,the correlation dimension and Kolmogorov entropy have a good consistency in the description of working status of gearbox. This conclusion not only provides a good basis for the gearbox running condition judgment and fault diagnosing, but can also provide the experimental basis for the chaotic characteristic parameters selection in state monitoring and fault diagnosing.

On some problems encountered in the estimation of the correlation dimension of the EEG

1986 ◽  
Vol 118 (2) ◽  
pp. 63-66 ◽  
Author(s):  
Ivan Dvorak ◽  
Jaromir Siska
Keyword(s):  
Correlation Dimension

Effect of Ethanol on Human Sleep EEG Using Correlation Dimension Analysis

2002 ◽  
Vol 46 (2) ◽  
pp. 104-110 ◽  
Author(s):  
Toshio Kobayashi ◽  
Shigeki Madokoro ◽  
Yuji Wada ◽  
Kiwamu Misaki ◽  
Hiroki Nakagawa
Keyword(s):  
Correlation Dimension ◽  
Sleep Eeg ◽  
Human Sleep ◽  
Dimension Analysis

APPLICATION OF CORRELATION DIMENSION IN LEAK IDENTIFICATION OF TRANSPORT PIPELINES

2006 ◽  
Vol 39 (13) ◽  
pp. 998-1002
Author(s):  
Hongying Yang ◽  
Hao Ye ◽  
Guizeng Wang ◽  
Guolin Hu
Keyword(s):  
Correlation Dimension

Improved correlation dimension estimates through change of variable

1992 ◽  
Vol 163 (4) ◽  
pp. 269-274 ◽  
Author(s):  
M. Lefranc ◽  
D. Hennequin ◽  
P. Glorieux
Keyword(s):  
Correlation Dimension ◽  
Change Of Variable
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