Correlation and Distribution Analyses of Estimated Fractal Dimensions and Hurstas Exponent from Waveforms of Excited Nonlinear Pendulum

Ajide O.O.; Salau T. A.O.

Correlation and Distribution Analyses of Estimated Fractal Dimensions and Hurstas Exponent from Waveforms of Excited Nonlinear Pendulum

Ajide O.O. * §

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Salau T. A.O.

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UNIVERSITY OF IBADAN,IBADAN,NIGERIA

Correlation and Distribution Analyses of Estimated Fractal Dimensions and Hurstas Exponent from Waveforms of Excited Nonlinear Pendulum

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Abstract

This study utilised correlation and distribution analyses to investigate the acceptability of application of two fractal dimension estimators to characterise the waveforms originating from excited nonlinear pendulum. Parameters selection sensitive simulation of the excited nonlinear pendulum waveforms was performed with the constant time step fourth order Runge-Kutta algorithm with codes developed in FORTRAN90. However, the waveforms validated by Gregory and Jerry (1990) and treated as time series were characterized using developed codes of Carlos (1998) and Hurst fractal dimension estimation procedures. The validation results compare qualitatively well and the correlation coefficients between Carlos (1998)-based and Hurst’s exponent based dimension estimate for the angular displacement and velocity are respectively R 2 = 0.68 and R 2 = 0.66. A higher correlation coefficient (R 2 = 0.84) existed between the estimated Hurst’s exponent of the angular displacement and velocity. The Hurst distribution exhibited both full spectrum and peak values range 0.04 to 1.00 and percentage probability range 2 to 12. The sum of this study results is the interchange possibility and utility of the two fractal dimension estimators as waveforms characterising tool.

References

17 Cites in Article

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

Ajide O.O., Salau A.O.. 2013. "Correlation and Distribution Analyses of Estimated Fractal Dimensions and Hurstas Exponent from Waveforms of Excited Nonlinear Pendulum". Global Journal of Research in Engineering, Global Journal of Research in Engineering - A : Mechanical & Mechanics GJRE-A Volume 13 (GJRE Volume 13 Issue A7).

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GJRE Volume 13 Issue A7

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Journal Specifications

Crossref Journal DOI 10.17406/gjre

Print ISSN 0975-5861

e-ISSN 2249-4596

Keywords

excited nonlinear pendulum fractal dimension hurst’s exponent waveforms and runge-kutta

Classification

GJRE-A Classification FOR Code: 850508

091399

Submission ReceivedDecember 6, 2012
Peer Review Double Blind
Handling Editor
Accepted December 31, 2012
Published January 15, 2013

Version of record

v1.2

Issue date

August 19, 2013

Language

English

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Article Matrices

Total Score: 102

Country: Nigeria

Subject: Global Journal of Research in Engineering

Authors: Salau T. A.O., Ajide O.O. (PhD/Dr. count: 0)

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