scholarly journals Permutation entropy based time series analysis: Equalities in the input signal can lead to false conclusions

2017 ◽  
Vol 381 (22) ◽  
pp. 1883-1892 ◽  
Author(s):  
Luciano Zunino ◽  
Felipe Olivares ◽  
Felix Scholkmann ◽  
Osvaldo A. Rosso
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Input Signal ◽  
Permutation Entropy ◽  
Series Analysis

scholarly journals Evaluating Temporal Correlations in Time Series Using Permutation Entropy, Ordinal Probabilities and Machine Learning

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1025
Author(s):  
Bruno R. R. Boaretto ◽  
Roberto C. Budzinski ◽  
Kalel L. Rossi ◽  
Thiago L. Prado ◽  
Sergio R. Lopes ◽  
...  
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Time Series Analysis ◽  
Flicker Noise ◽  
Learning Algorithm ◽  
Temporal Correlation ◽  
Permutation Entropy ◽  
Series Analysis ◽  
Temporal Correlations ◽  
The Difference

Time series analysis comprises a wide repertoire of methods for extracting information from data sets. Despite great advances in time series analysis, identifying and quantifying the strength of nonlinear temporal correlations remain a challenge. We have recently proposed a new method based on training a machine learning algorithm to predict the temporal correlation parameter, α, of flicker noise (FN) time series. The algorithm is trained using as input features the probabilities of ordinal patterns computed from FN time series, xαFN(t), generated with different values of α. Then, the ordinal probabilities computed from the time series of interest, x(t), are used as input features to the trained algorithm and that returns a value, αe, that contains meaningful information about the temporal correlations present in x(t). We have also shown that the difference, Ω, of the permutation entropy (PE) of the time series of interest, x(t), and the PE of a FN time series generated with α=αe, xαeFN(t), allows the identification of the underlying determinism in x(t). Here, we apply our methodology to different datasets and analyze how αe and Ω correlate with well-known quantifiers of chaos and complexity. We also discuss the limitations for identifying determinism in highly chaotic time series and in periodic time series contaminated by noise. The open source algorithm is available on Github.

A Nonlinear Time Series Analysis Method for Health Monitoring of Rolling Bearings

2010 ◽  
Author(s):  
Yongbin Liu ◽  
Ruqiang Yan ◽  
Robert X. Gao
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Health Monitoring ◽  
Nonlinear Time Series ◽  
Permutation Entropy ◽  
Nonlinear Time Series Analysis ◽  
Analysis Method ◽  
Series Analysis ◽  
Rotating Machine ◽  
Linear Behavior

This paper presents a nonlinear time series analysis method for rotating machine damage detection and diagnostics. Specifically, the permutation entropy is investigated as a statistical measure for signal characterization. Through space reconstruction, the permutation entropy describes the complexity of the time series measured on a physical system, and takes its non-linear behavior into account. By identifying changes in the vibration signals measured on rotating machines, which are typical precursors of defect occurrence, permutation entropy can serve as a diagnostic tool. Experiments on a custom-designed gearbox system have confirmed its effectiveness for machine structural health monitoring applications.

Dynamical Peculiarities of Concatenational Changes in Functional Cardiovascular Parameters

2018 ◽  
Vol 3 (82) ◽  
Author(s):  
Eurelija Venskaitytė ◽  
Jonas Poderys ◽  
Tadas Česnaitis
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Functional State ◽  
The Body ◽  
Functional Changes ◽  
High Intensity Training ◽  
Series Analysis ◽  
Greco Roman ◽  
St Segment ◽  
Standard Lead

Research  background  and  hypothesis.  Traditional  time  series  analysis  techniques,  which  are  also  used  for the analysis of cardiovascular signals, do not reveal the relationship between the  changes in the indices recorded associated with the multiscale and chaotic structure of the tested object, which allows establishing short-and long-term structural and functional changes.Research aim was to reveal the dynamical peculiarities of interactions of cardiovascular system indices while evaluating the functional state of track-and-field athletes and Greco-Roman wrestlers.Research methods. Twenty two subjects participated in the study, their average age of 23.5 ± 1.7 years. During the study standard 12 lead electrocardiograms (ECG) were recorded. The following ECG parameters were used in the study: duration of RR interval taken from the II standard lead, duration of QRS complex, duration of JT interval and amplitude of ST segment taken from the V standard lead.Research  results.  Significant  differences  were  found  between  inter-parametric  connections  of  ST  segment amplitude and JT interval duration at the pre and post-training testing. Observed changes at different hierarchical levels of the body systems revealed inadequate cardiac metabolic processes, leading to changes in the metabolic rate of the myocardium and reflected in the dynamics of all investigated interactions.Discussion and conclusions. It has been found that peculiarities of the interactions of ECG indices interactions show the exposure of the  functional changes in the body at the onset of the workload. The alterations of the functional state of the body and the signs of fatigue, after athletes performed two high intensity training sessions per day, can be assessed using the approach of the evaluation of interactions between functional variables. Therefore the evaluation of the interactions of physiological signals by using time series analysis methods is suitable for the observation of these processes and the functional state of the body.Keywords: electrocardiogram, time series, functional state.

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