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Fractional empirical mode decomposition energy entropy based on segmentation and its application to the electrocardiograph signal

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Abstract

The generalized fractional entropy is a powerful tool for allowing an high sensitivity to the signal evolution, which is available to depict the dynamics of complex systems. Besides, empirical mode decomposition (EMD) energy entropy has received largely extensive attention, such as the field of roller bearing fault diagnosis. In this paper, we change the perspective of research and propose an improved EMD energy entropy built on the theory of the generalized fractional entropy, that is, fractional EMD energy entropy. Furthermore, we also combine the proposed method with new multi-scale algorithm based on the segmentation ideas. In order to show the advantages of this particular method for detecting the complexity of systems, several simulated time series and electrocardiograph (ECG) signal experiments are chosen to examine the performance of them. Through experiments, we find that the new fractional EMD energy entropy shows a better characteristic in the complexity analysis of dynamical systems compared with the classical EMD energy entropy. Moreover, the results reveal that tuning the fractional order allows a higher sensitivity to the series fluctuation. In addition, when the experiment bonds with the multi-scale algorithm based on segmentation, we can obtain more abundant complexity properties of time series through fractional EMD energy entropy. Also, it can effectively discriminate the differences in the complexity of different time series, whereas the original method does not have such good advantages. Especially when applied to ECG signals, this new method can be more effective to distinguish between healthy people and patients with heart disease, which is a valuable advantage. Beyond all that, results of the test on surrogate data generated by randomizing series also further strengthen our summing-up.

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Acknowledgements

The financial supports from the funds of the Fundamental Research Funds for the Central Universities (2018JBZ104, 2018YJS174), the China National Science (61771035) and the Beijing National Science (4162047) are gratefully acknowledged.

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  1. Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, 100044, China

    Lei Rong & Pengjian Shang

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  1. Lei Rong
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Rong, L., Shang, P. Fractional empirical mode decomposition energy entropy based on segmentation and its application to the electrocardiograph signal. Nonlinear Dyn 94, 1669–1687 (2018). https://doi.org/10.1007/s11071-018-4448-y

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