Estudo de características da entropia aproximada utilizando sinais simulados e experimentais

Abstract

Approximate Entropy ApEn (m,r,N) has been used to investigate the regularity / complexity of signals with several lengths (N) and tolerance (r) between 0.1 sd and 0.25 sd. However, the punctual estimate ApEn (m,r,N) can provide questionable results for radius values "r" chosen empirically and small signs stretches. This paper investigates some technical characteristics of the Approximate Entropy aiming to clarify aspects related to the number of samples, the radius value "r" and the delay used. Furthermore a method is proposed for standardization of results. For this research simulated signals were used as: senoid with 10 Hz, 50 Hz and 100 Hz (sampling frequencies of 1.000, 10.000 and 100.000 Hz), Logistic Mapping attractor, Henon attractor, Rossler attractor, Lorenz attractor, random signals of White Gaussian Noise (WGN) and White Uniform Noise (WUN) and experimental signals as newborn EEG, adult EEG and adult heart rate variability (HRV). Stretches of different length and radius "r" value or tolerance between zero and 5.0 times the standard deviation ("SD") were used. The results show great variability and overlap of several estimates ApEn for small stretches, making it difficult to interpret. The stretch length increment reduces the variability of estimates and highlights the existence of waveforms related to the phase portraits of the structures. The maximum values of estimates of ApEn curves, for random and chaotic signals, show a seemingly linear relationship with the logarithm of the number of samples and a specific order of level of regularity / complexity of signals. The highest level of regularity (less complexity) was found to senoid, followed by Rossler attractor, Logistic Mapping attractor, Henon attractor, Lorenz attractor and then to the noise signals: RBG and RBU. Among the experimental signals the adult EEG signals showed more complex values (less regularity). The method of standardization of maximum values of ApEn curves facilitates the comparison of results in percentage form. The use of the maximum values of the ApEn curves and the normalization procedure allows the proposal of a statistic that does not depend on the radius "r" and the number of samples "N" of the signal (for high "N"), and can be described as : NApEn ( m ).