Confirm
Archive
Special Issues
A New Method Detecting Abrupt Change Base on Moving Cut Data-Permutation Entropy
American Journal of Applied Mathematics
Volume 6, Issue 2, April 2018, Pages: 62-70
Received: Jun. 19, 2018; Published: Jun. 20, 2018
Authors
Luo Wenxiang, School of Mathematics and Information Science, Guangzhou University, Guangzhou, China
Wan Li, School of Mathematics and Information Science, Guangzhou University, Guangzhou, China; Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, China
Lai Simin, School of Mathematics and Information Science, Guangzhou University, Guangzhou, China
Article Tools
Abstract
Permutation entropy is an effective index which can be used to describe the dynamic complexity of a time series, and it can effectively enlarge the small changes of a sequence. In this paper, the moving cut data-permutation entropy, a new method detecting abrupt change is raised by combining the permutation entropy method with the moving cut data technology. Different moving window scales are selected to analyze the mutational detection of linear and nonlinear time series via the new method respectively. The effect of peak noise and white Gaussian noise on this new method in nonlinear time series constructed by Lorenz equation and random sequence was studied. The results show that the moving cut data-permutation entropy method has strong anti-noise ability, which is able to precisely identify the mutational point of both the linear and nonlinear time series, and almost independent the scale of window and the length of sequence.
Keywords
Permutation Entropy, Moving Cut Data, Dynamical Structure, Mutational Detection
Luo Wenxiang, Wan Li, Lai Simin, A New Method Detecting Abrupt Change Base on Moving Cut Data-Permutation Entropy, American Journal of Applied Mathematics. Vol. 6, No. 2, 2018, pp. 62-70. doi: 10.11648/j.ajam.20180602.16
References
[1]
A. B. Lüttger, and T. Feike. “Development of heat and drought related extreme weather events and their effect on winter wheat yields in Germany,” Theor. Appl. Climatol, Vol. 132, No. 1-2, 2017, pp. 1-15.
[2]
T. Yamamoto, and M. Sano, “Theoretical model of chirality-induced helical self-propulsion,” Phys. Rev. E, Vol. 97, No. 1, 2018, pp. 012607.
[3]
C. J. Da, L. Fang, B. L. Shen, P. C. Yan, S. Jian, and D. S. Ma, “Detection of a sudden change of the field time series based on the lorenz system,” Plos One, Vol. 12, No. 1, 2017, pp. e0170720.
[4]
W. P. He, T. He, H. Y. Cheng, W. Zhang, and Q. Wu, “A new method to detect abrupt change based on approximate entropy,” Acta Phys. Sin., Vol. 60, No. 4, 2011, pp. 820-828.
[5]
S. M. Pincus, “Approximate entropy as a measure of system complexity,” Proc. Natl. Acad. Sci. USA, Vol. 88, No. 6, 1991, pp. 2297-2301.
[6]
S. M. Pincus, and R. R. Viscarello, “Approximate entropy: a regularity measure for fetal heart rate analysis,” Obstet. Gynecol., Vol. 79, No. 2, 1992, pp. 249-255.
[7]
A. Singh, B. S. Saini, and D. Singh. “An adaptive technique for multiscale approximate entropy (MAE bin) threshold (r) selection: application to heart rate variability (HRV) and systolic blood pressure variability (SBPV) under postural stress.” Australas. Phys. Eng. Sci. in med., Vol. 39, No. 2, 2016, pp. 557-569.
[8]
C. James, S. Azeem, S. Ric, B. Paul, and M. Chris, “Measurement of cardiac synchrony using approximate entropy applied to nuclear medicine scans,” Biomedical Signal Processing & Control, Vol. 5, No. 1, 2010, pp. 32-36.
[9]
S. M. Pincus, I. M. Gladstone, and R. A. Ehrenkranz, “A regularity statistic for medical data analysis,” Journal of Clinical Monitoring, Vol. 7, No. 4, 1991, pp. 335–345.
[10]
L. Wan, X. Y. Hu, X. C. Deng, “Approximate entrop analysis of metallogenic element content sequences and identification of mineral intensity: A case study of Dayingezhuang gold deposit,” Journal of China University of Mining & Technology, Vol. 43, No. 2, 2014, pp. 345-350.
[11]
D. Y. Sun, Q. Huang, Y. M. Wang, Z. Liu, and L Zhang, “Application of moving approximate entropy to mutation analysis of runoff time series,” Journal of Hydroelectric Engineering, Vol. 33, No. 4, 2014, pp. 1-6.
[12]
J. S. Richman, J. R. Moorman. “Physiological time-series analysis using approximate entropy and sample entropy,” Am. J. Physiol. Heart Circ. Physiol., No. 278, No. 6, 2000, pp. 2039-2049.
[13]
D. E. Lake, J. S. Richman, M. P. Griffin, and J. R. Moorman, “Sample entropy analysis of neonatal heart rate variability,” Am. J. Physiol. Regul. Integr. Comp. Physiol. Vol. 283, No. 3, 2002, pp. R789- R797.
[14]
F. Kaffashi, R. Foglyano, C. G. Wilson, and K. A. Loparo, “The effect of time delay on approximate & sample entropy calculations,” Physica D Nonlinear Phenomena, Vol. 237, No. 23, 2008, pp. 3069-3074.
[15]
C. Bandt, and B. Pompe, “Permutation entropy: A natural complexity measure for time series,” Physical Review Letters, Vol. 88, No. 17, 2002, pp. 174102.
[16]
M. Zanin, L. Zunino, O. A. Rosso, and D. Papo, “Permutation entropy and its main biomedical and econophysics applications: a review,” Entropy, No. 14, No. 8, 2012, pp. 1553-1577.
[17]
M. Riedl, A. Müller, and N. Wessel. “Practical considerations of permutation entropy,” Eur. Phys. J. Special Topics, Vol. 222, No. 2, 2013, pp. 249-262.
[18]
H. Azami, and J. Escudero. “Improved multiscale permutation entropy for biomedical signal analysis: Interpretation and application to electroencephalogram recordings,” Biomedical Signal Processing & Control, Vol. 23, No. 1, 2015, pp. 28-41.
[19]
Y. J. Li, W. H. Zhang, Q. Xiong, D. B. Luo, G. M. Mei, and T. Zhang, “A rolling bearing fault diagnosis strategy based on improved multiscale permutation entropy and least squares SVM,” Journal of Mechanical Science & Technology, Vol. 31, No. 6, 2017, pp. 2711-2722.
[20]
C. Bandt, “A new kind of permutation entropy used to classify sleep stages from invisible EEG microstructure,” Entropy, Vol. 19, No. 5, 2017, pp. 197.
[21]
Y. Hou, F. Liu, J. Gao, C. Cheng, and C. Song, “Characterizing complexity changes in chinese stock markets by permutation entropy,” Entropy, Vol. 19, No. 10, 2017, pp. 514.
[22]
Y. S. Choi, “Improved multiscale permutation entropy measure for analysis of brain waves,” International Journal of Fuzzy Logic & Intelligent Systems, Vol. 17, No. 3, 2017, pp. 194-201.
[23]
O. Dostál, O. Vysata, L. Pazdera, A. Procházka, J. Kopal, J. Kuchyňka, and M. Vališ, “Permutation entropy and signal energy increase the accuracy of neuropathic change detection in needle EMG,” Computational Intelligence & Neuroscience, Vol. 2018, No. 6, 2018, pp. 1-5.
[24]
M. Kuai, G. Cheng, Y. Pang, and Y. Li, “Research of planetary gear fault diagnosis based on permutation entropy of CEEMDAN and ANFIS,” Sensors, Vol. 18, No. 3, 2018, pp. 782.
[25]
Y. Gao, F. Villecco, M. Li, and W. Song, “Multi-scale permutation entropy based on improved LMD and HMM for rolling bearing diagnosis,” Entropy, Vol. 19, No. 4, 2017, pp. 176.
[26]
K. Keller, T. Mangold, I. Stolz, and J. Werner, “Permutation entropy: New ideas and challenges,” Entropy, Vol. 19, No. 3, 2017, pp. 134.
[27]
Q. G. Wang, Z. P. Zhang, “The research of detecting abrupt climate change with approximate entropy,” Acta Phys. Sin., Vol. 57, No. 3, 2008, pp. 1976-1983.
[28]
J. Guckenheimer, and R. F. Williams. “Structural stability of Lorenz attractors.” Publications Mathématiques De Linstitut Des Hautes Études Scientifiques, Vol. 50, No. 1, 1979, pp. 59-72.
[29]
I. Grigorenko, and E. Grigorenko, “Chaotic dynamics of the fractional Lorenz system,” Physical Review Letters, Vol. 91, No. 3, 2003, pp. 034101.
[30]
N. C. Kakwani, “Applications of Lorenz curves in economic analysis,” Econometrica, Vol. 45, No. 3, 1977, pp. 719-727.
[31]
P. G. Baines, “Lorenz, EN 1963: Deterministic nonperiodic flow. Journal of the Atmospheric Sciences 20, 130-41,” Physical Geography, Vol. 32, No. 4, 2008, pp. 475-480.
[32]
H. M. Jin, W. P. He, W. Zhang, A. X. Feng, and W. Hou, “Effect of noises on moving cut data-approximate entropy,” Acta Phys. Sin., Vol. 61, No. 12, 2012, pp. 069201-160.
[33]
I. Castillo, and R. Nickl. “Nonparametric Bernstein-von Mises theorems in Gaussian white noise,” Annals of Statistics, Vol. 41, No. 4, 2013, pp. 1999-2028.
[34]
A. Hariri, and M. Babaie-Zadeh, “Compressive detection of sparse signals in additive white Gaussian noise without signal reconstruction,” Signal Processing, Vol. 131, 2016, pp. 376-385.
[35]
S. S. Dasgupta, V. Rajamohan, and A. K. Jha, “Dynamic characterization of a bistable energy harvester under Gaussian white noise for larger time constant,” Arabian Journal for Science & Engineering, 2018, pp. 1-10.
[36]
A. Dechant, A. Baule, and S. I. Sasa, “Gaussian white noise as a resource for work extraction,” Physical Review E, Vol. 95, 2017, pp. 032132.
[37]
S. Benkrinah, and M. Benslama “Acquisition of PN sequences using multilayer perceptron neural network adaptive processor for multiuser detection in spread-spectrum communication systems,” International Journal of Numerical Modelling Electronic Networks Devices & Fields, Vol. 31, No. 1, 2018, pp. e2265.
[38]
S. Stevanovic, and B. Pervan, “A GPS phase-locked loop performance metric based on the phase discriminator output,” Sensors, Vol. 18, No. 1, 2018, pp. 296.
PUBLICATION SERVICES