Errors in the Estimation of Approximate Entropy and Other Recurrence-Plot-Derived Indices Due to the Finite Resolution of RR Time Series

2009 ◽  
Vol 56 (2) ◽  
pp. 345-351 ◽  
Author(s):  
M.A. Garcia-Gonzalez ◽  
M. Fernandez-Chimeno ◽  
J. Ramos-Castro
Keyword(s):  
Time Series ◽  
Approximate Entropy ◽  
Recurrence Plot ◽  
Finite Resolution

scholarly journals Damage detection by recurrence and entropy methods on the basis of time series measured during composite milling

2020 ◽  
Vol 111 (1-2) ◽  
pp. 549-563
Author(s):  
Krzysztof Kecik ◽  
Krzysztof Ciecielag ◽  
Kazimierz Zaleski
Keyword(s):  
Time Series ◽  
Damage Detection ◽  
Approximate Entropy ◽  
Recurrence Plot ◽  
Milling Process ◽  
Fiber Reinforced Polymer ◽  
Reinforced Polymer ◽  
Glass Fiber Reinforced ◽  
Damage Indicators ◽  
Different Diameters

Abstract This paper presents methods for damage detection in machined material on the basis of time series measured during milling of glass-fiber–reinforced polymer (GFRP). Recurrence methods and different types of entropy have emerged as useful tools for detecting subtle non-stationarities and/or changes in nonlinear signals. In this research, a recurrence plot, recurrence quantifications, an approximate entropy, and sample entropy are used. By identifying changes in the cutting force measured during the composite milling process, the damage occurrence has been detected. Firstly, the damage has been modelled as the intentionally introduced hole with different diameters and depths in order to estimate the size detectable damages and to select proper recurrence measures as damage indicators. Next, the experiments with the real damage have been performed and the damage indicators have used.

scholarly journals Multiscale Cross-Approximate Entropy Analysis as a Measure of Complexity among the Aged and Diabetic

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hsien-Tsai Wu ◽  
Cyuan-Cin Liu ◽  
Men-Tzung Lo ◽  
Po-Chun Hsu ◽  
An-Bang Liu ◽  
...  
Keyword(s):  
Type 2 Diabetes ◽  
Time Series ◽  
Pulse Transit Time ◽  
Approximate Entropy ◽  
Physiological Signals ◽  
Diabetes Group ◽  
Group 4 ◽  
Group 2 ◽  
Aged Subjects

Complex fluctuations within physiological signals can be used to evaluate the health of the human body. This study recruited four groups of subjects: young healthy subjects (Group 1,n=32), healthy upper middle-aged subjects (Group 2,n=36), subjects with well-controlled type 2 diabetes (Group 3,n=31), and subjects with poorly controlled type 2 diabetes (Group 4,n=24). Data acquisition for each participant lasted 30 minutes. We obtained data related to consecutive time series with R-R interval (RRI) and pulse transit time (PTT). Using multiscale cross-approximate entropy (MCE), we quantified the complexity between the two series and thereby differentiated the influence of age and diabetes on the complexity of physiological signals. This study used MCE in the quantification of complexity between RRI and PTT time series. We observed changes in the influences of age and disease on the coupling effects between the heart and blood vessels in the cardiovascular system, which reduced the complexity between RRI and PTT series.

scholarly journals Encoding Time Series as Multi-Scale Signed Recurrence Plots for Classification Using Fully Convolutional Networks

Sensors ◽  
2020 ◽  
Vol 20 (14) ◽  
pp. 3818
Author(s):  
Ye Zhang ◽  
Yi Hou ◽  
Shilin Zhou ◽  
Kewei Ouyang
Keyword(s):  
Time Series ◽  
State Of The Art ◽  
Recurrence Plot ◽  
The State ◽  
Recurrence Plots ◽  
Convolutional Networks ◽  
Multi Scale ◽  
Fully Convolutional Networks ◽  
Benchmark Datasets ◽  
Visualization Evaluation

Recent advances in time series classification (TSC) have exploited deep neural networks (DNN) to improve the performance. One promising approach encodes time series as recurrence plot (RP) images for the sake of leveraging the state-of-the-art DNN to achieve accuracy. Such an approach has been shown to achieve impressive results, raising the interest of the community in it. However, it remains unsolved how to handle not only the variability in the distinctive region scale and the length of sequences but also the tendency confusion problem. In this paper, we tackle the problem using Multi-scale Signed Recurrence Plots (MS-RP), an improvement of RP, and propose a novel method based on MS-RP images and Fully Convolutional Networks (FCN) for TSC. This method first introduces phase space dimension and time delay embedding of RP to produce multi-scale RP images; then, with the use of asymmetrical structure, constructed RP images can represent very long sequences (>700 points). Next, MS-RP images are obtained by multiplying designed sign masks in order to remove the tendency confusion. Finally, FCN is trained with MS-RP images to perform classification. Experimental results on 45 benchmark datasets demonstrate that our method improves the state-of-the-art in terms of classification accuracy and visualization evaluation.

Recurrence Plot based entropies and their ability to detect transitions

2020 ◽  
Author(s):  
K. Hauke Kraemer ◽  
Norbert Marwan ◽  
Karoline Wiesner ◽  
Jürgen Kurths
Keyword(s):  
Time Series ◽  
Shannon Entropy ◽  
Recurrence Plot ◽  
Climate Dynamics ◽  
Value Distribution ◽  
Tipping Points ◽  
Recurrence Plots ◽  
The Past ◽  
Entropy Measures ◽  
Regime Transitions

<p>Many dynamical processes in Earth Sciences are the product of many interacting components and have often limited predictability, not least because they can exhibit regime transitions (e.g. tipping points).To quantify complexity, entropy measures such as the Shannon entropy of the value distribution are widely used. Amongst other more sophisticated ideas, a number of entropy measures based on recurrence plots have been suggested. Because different structures, e.g. diagonal lines, of the recurrence plot are used for the estimation of probabilities, these entropy measures represent different aspects of the analyzed system and, thus, behave differently. In the past, this fact has led to difficulties in interpreting and understanding those measures. We review the definitions, the motivation and interpretation of these entropy measures, compare their differences and discuss some of the pitfalls when using them.</p><p>Finally, we illustrate their potential in an application on paleoclimate time series. Using the presented entropy measures, changes and transitions in the climate dynamics in the past can be identified and interpreted.</p>

Measuring body temperature time series regularity using approximate entropy and sample entropy

2009 ◽  
Author(s):  
D. Cuesta-Frau ◽  
P. Miro-Martinez ◽  
S. Oltra-Crespo ◽  
M. Varela-Entrecanales ◽  
M. Aboy ◽  
...  
Keyword(s):  
Time Series ◽  
Body Temperature ◽  
Approximate Entropy ◽  
Sample Entropy ◽  
Temperature Time Series ◽  
Temperature Time

scholarly journals A Review on the Nonlinear Dynamical System Analysis of Electrocardiogram Signal

2018 ◽  
Vol 2018 ◽  
pp. 1-19 ◽  
Author(s):  
Suraj K. Nayak ◽  
Arindam Bit ◽  
Anilesh Dey ◽  
Biswajit Mohapatra ◽  
Kunal Pal
Keyword(s):  
Signal Analysis ◽  
System Analysis ◽  
Nonlinear Dynamical System ◽  
Approximate Entropy ◽  
Recurrence Plot ◽  
Fluctuation Analysis ◽  
Ecg Signal ◽  
Poincaré Plot ◽  
Nonlinear Methods ◽  
Nonlinear Dynamical

Electrocardiogram (ECG) signal analysis has received special attention of the researchers in the recent past because of its ability to divulge crucial information about the electrophysiology of the heart and the autonomic nervous system activity in a noninvasive manner. Analysis of the ECG signals has been explored using both linear and nonlinear methods. However, the nonlinear methods of ECG signal analysis are gaining popularity because of their robustness in feature extraction and classification. The current study presents a review of the nonlinear signal analysis methods, namely, reconstructed phase space analysis, Lyapunov exponents, correlation dimension, detrended fluctuation analysis (DFA), recurrence plot, Poincaré plot, approximate entropy, and sample entropy along with their recent applications in the ECG signal analysis.

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