Correlation and Distribution Analyses of Estimated Fractal Dimensions and Hurstas Exponent from Waveforms of Excited Nonlinear Pendulum
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 R2 = 0.68 and R2 = 0.66. A higher correlation coefficient ( R2 = 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.
