scholarly journals Detection of Dynamical Regime Transitions with Lacunarity as a Multiscale Recurrence Quantification Measure

2020 ◽  
Author(s):  
Tobias Braun ◽  
Norbert Marwan ◽  
Vishnu R. Unni ◽  
Raman I. Sujith ◽  
Juergen Kurths
Keyword(s):  
Time Series ◽  
Recurrence Plot ◽  
Dynamical Regime ◽  
Series Length ◽  
Dynamical Complexity ◽  
Recurrence Quantification ◽  
The Rich ◽  
Short Time ◽  
Recurrent Patterns ◽  
Regime Transitions

<p>We propose Lacunarity as a novel recurrence quantification measure and apply it in the context of dynamical regime transitions. Many complex real-world systems exhibit abrupt regime shifts. We carry out a recurrence plot based analysis for different paradigmatic systems and thermoacoustic combustion time series in order to demonstrate the ability of our method to detect dynamical transitions on variable temporal scales. Lacunarity is usually interpreted as a measure of ‘gappiness’ of an arbitrary spatial pattern. In application to recurrence plots, it quantifies the degree of heterogenity in the temporal recurrent patterns. Our method succeeds to distinguish states of varying dynamical complexity in presence of noise and short time series length. In contrast to traditional recurrence quantifiers, no specification of minimal line lengths is required and features beyond the scope of line structures can be accounted for. Applied to acoustic pressure fluctuation time series, it captures both the rich variability in dynamical complexity and detects shifts of characteristic time scales.</p>

scholarly journals Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure

2021 ◽  
Author(s):  
Tobias Braun ◽  
Vishnu R. Unni ◽  
R. I. Sujith ◽  
Juergen Kurths ◽  
Norbert Marwan
Keyword(s):  
Time Series ◽  
Empirical Data ◽  
Acoustic Pressure ◽  
Pressure Fluctuations ◽  
Recurrence Plot ◽  
Dynamical Regime ◽  
Recurrence Plots ◽  
Dynamical Complexity ◽  
Recurrence Quantification ◽  
Regime Transitions

AbstractWe propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot-based analysis for different paradigmatic systems and nonlinear empirical data in order to demonstrate the ability of our method to detect dynamical transitions ranging across different temporal scales. It succeeds to distinguish states of varying dynamical complexity in the presence of noise and non-stationarity, even when the time series is of short length. In contrast to traditional recurrence quantifiers, no specification of minimal line lengths is required and geometric features beyond linear structures in the recurrence plot can be accounted for. This makes lacunarity more broadly applicable as a recurrence quantification measure. Lacunarity is usually interpreted as a measure of heterogeneity or translational invariance of an arbitrary spatial pattern. In application to recurrence plots, it quantifies the degree of heterogeneity in the temporal recurrence patterns at all relevant time scales. We demonstrate the potential of the proposed method when applied to empirical data, namely time series of acoustic pressure fluctuations from a turbulent combustor. Recurrence lacunarity captures both the rich variability in dynamical complexity of acoustic pressure fluctuations and shifting time scales encoded in the recurrence plots. Furthermore, it contributes to a better distinction between stable operation and near blowout states of combustors.

scholarly journals Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 385 ◽  
Author(s):  
David Cuesta-Frau ◽  
Juan Pablo Murillo-Escobar ◽  
Diana Alexandra Orrego ◽  
Edilson Delgado-Trejos
Keyword(s):  
Time Series ◽  
Classification Performance ◽  
Permutation Entropy ◽  
Series Length ◽  
Stability Point ◽  
Long Time ◽  
Model Time Series ◽  
The Stability ◽  
Forbidden Patterns ◽  
Short Time

Permutation Entropy (PE) is a time series complexity measure commonly used in a variety of contexts, with medicine being the prime example. In its general form, it requires three input parameters for its calculation: time series length N, embedded dimension m, and embedded delay τ . Inappropriate choices of these parameters may potentially lead to incorrect interpretations. However, there are no specific guidelines for an optimal selection of N, m, or τ , only general recommendations such as N > > m ! , τ = 1 , or m = 3 , … , 7 . This paper deals specifically with the study of the practical implications of N > > m ! , since long time series are often not available, or non-stationary, and other preliminary results suggest that low N values do not necessarily invalidate PE usefulness. Our study analyses the PE variation as a function of the series length N and embedded dimension m in the context of a diverse experimental set, both synthetic (random, spikes, or logistic model time series) and real–world (climatology, seismic, financial, or biomedical time series), and the classification performance achieved with varying N and m. The results seem to indicate that shorter lengths than those suggested by N > > m ! are sufficient for a stable PE calculation, and even very short time series can be robustly classified based on PE measurements before the stability point is reached. This may be due to the fact that there are forbidden patterns in chaotic time series, not all the patterns are equally informative, and differences among classes are already apparent at very short lengths.

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>

scholarly journals Multiscale Entropy Analysis of Short Signals: The Robustness of Fuzzy Entropy-Based Variants

2021 ◽  
Author(s):  
Airton Monte Serrat Borin ◽  
Anne Humeau-Heurtier ◽  
Luiz Otavio Murta ◽  
Luiz Eduardo Virgilio Silva
Keyword(s):  
Time Series ◽  
Multiscale Entropy ◽  
Entropy Analysis ◽  
Short Term ◽  
Series Length ◽  
Short Time Series ◽  
Fuzzy Algorithms ◽  
Computing Performance ◽  
Similar Accuracy ◽  
Short Time

Abstract Multiscale entropy (MSE) analysis is a fundamental approach to access the complexity of a time series by estimating its information creation over a range of temporal scales. However, MSE may not be accurate or valid for short time series. This is why previous studies applied different kinds of algorithm derivations to short-term time series. However, no study has systematically analyzed and compared their reliabilities. This study compares the MSE algorithm variations adapted to short time series on both human and rat heart rate variability (HRV) time series. The most used variations of MSE are studied: composite MSE (CMSE), refined composite MSE (RCMSE), modified MSE (MMSE), and their fuzzy versions. We also analyze the errors in MSE estimations for a range of incorporated fuzzy exponents. The results show that fuzzy MSE versions-as a function of time series length-present minimal errors compared to the non-fuzzy algorithms. The traditional multiscale entropy algorithm with fuzzy counting (MFE) has similar accuracy to alternative algorithms with better computing performance. For the best accuracy, the findings suggest different fuzzy exponents according to the time series length.

scholarly journals Dynamic Analysis of Blast Furnace Sensor Data using Cross-recurrence Quantification Strategies

2021 ◽  
Vol 2132 (1) ◽  
pp. 012024
Author(s):  
X C Sun ◽  
B Wei ◽  
J h Gao ◽  
J C Fu ◽  
Z G Li
Keyword(s):  
Time Series ◽  
Blast Furnace ◽  
Dimensional Space ◽  
Recurrence Plot ◽  
Analytical Framework ◽  
Gas Production ◽  
Sensor Data ◽  
Blast Furnace Gas ◽  
Recurrence Quantification ◽  
Cross Recurrence Quantification

Abstract This paper investigates impact degree of blast furnace related elements towards blast furnace gas (BFG) production. BFG is a by-product in the steel industry, which is one of the enterprise’s most essential energy resources. While because multiple factors affect BFG production it has characteristics of large fluctuations. Most works focus on finding a satisfactory method or improving the accuracy of existing methods to predict BFG production. There are no special studies on the factors that affect the production of BFG. Finding the elements that affect BFG production is benefit to production of BFG, which has a significance in economy. We propose a novel framework, combining cross recurrence plot (CRP) and cross recurrence quantification analysis (CRQA). Moreover, it supplies a general method to convert time series of BFG related data into high-dimensional space. This is the first analytical framework that attempts to reveal the inherent dynamic similarities of blast furnace gas-related elements. The experimental results demonstrate that this framework can realize the visualization of the time series. In addition, the results also identify the factor that has the greatest impact on blast furnace gas production by quantitative analysis.

scholarly journals Predicting the Health Condition of mHealth App Users with Large Differences in the Number of Recorded Observations - Where to Learn from?

2020 ◽  
pp. 659-673
Author(s):  
Vishnu Unnikrishnan ◽  
Yash Shah ◽  
Miro Schleicher ◽  
Mirela Strandzheva ◽  
Plamen Dimitrov ◽  
...  
Keyword(s):  
Time Series ◽  
Pilot Study ◽  
Predictive Model ◽  
Health Condition ◽  
Diabetic Patients ◽  
User Engagement ◽  
Series Length ◽  
Short Time ◽  
Mhealth Apps ◽  
Over Time

Abstract Some mHealth apps record user activity continuously and unobtrusively, while other apps rely by nature on user engagement and self-discipline: users are asked to enter data that cannot be assessed otherwise, e.g., on how they feel and what non-measurable symptoms they have. Over time, this leads to substantial differences in the length of the time series of recordings for the different users. In this study, we propose two algorithms for wellbeing-prediction from such time series, and we compare their performance on the users of a pilot study on diabetic patients - with time series length varying between 8 and 87 recordings. Our first approach learns a model from the few users, on which many recordings are available, and applies this model to predict the 2nd, 3rd, and so forth recording of users newly joining the mHealth platform. Our second approach rather exploits the similarity among the first few recordings of newly arriving users. Our results for the first approach indicate that the target variable for users who use the app for long are not predictive for users who use the app only for a short time. Our results for the second approach indicate that few initial recordings suffice to inform the predictive model and improve performance considerably.

Multiscale Cross-Recurrence Plot and Recurrence Quantification Analysis Based on Coarse-Grained

2021 ◽  
pp. 2150037
Author(s):  
A. Jingjing Huang ◽  
B. Danlei Gu ◽  
C. Qian He
Keyword(s):  
Time Series ◽  
Time Scales ◽  
Real World ◽  
Recurrence Plot ◽  
Recurrence Quantification Analysis ◽  
Coarse Grained ◽  
Internal Dynamic ◽  
Recurrence Quantification ◽  
Quantification Analysis ◽  
Different Time Scales

In this paper, we proposed multiscale cross-recurrence quantification analysis (MSCRQA) method to analyze the dynamic states of two time series at different time scales. We apply this method to model system (two coupled van der Pol oscillators) and real-world system (SSEC and SZSE). It demonstrates that the MSCRQA can show richer and more recognizable information compared with single time scale. The state of dynamics is different under different time scales. MSCRQA method shows another multiscale perspective to fully mine more hidden internal dynamic information of a time series. This method may provide another method reference for practical application to better explore the laws of the real world.

Recurrence quantification analysis for detecting dynamical changes in earthquake magnitude time series

2015 ◽  
Vol 26 (07) ◽  
pp. 1550077 ◽  
Author(s):  
Min Lin ◽  
Gang Zhao ◽  
Gang Wang
Keyword(s):  
Time Series ◽  
Main Shock ◽  
Recurrence Plot ◽  
Recurrence Quantification Analysis ◽  
Confidence Levels ◽  
Aftershock Sequences ◽  
Recurrence Quantification ◽  
Before And After ◽  
Quantification Analysis ◽  
Simultaneous Change

In this study, recurrence plot (RP) and recurrence quantification analysis (RQA) techniques are applied to a magnitude time series composed of seismic events occurred in California region. Using bootstrapping techniques, we give the statistical test of the RQA for detecting dynamical transitions. From our results, we find the different patterns of RPs for magnitude time series before and after the M6.1 Joshua Tree Earthquake. RQA measurements of determinism (DET) and laminarity (LAM) quantifying the order with confidence levels also show peculiar behaviors. It is found that DET and LAM values of the recurrence-based complexity measure significantly increase to a large value at the main shock, and then gradually recovers to a small values after it. The main shock and its aftershock sequences trigger a temporary growth in order and complexity of the deterministic structure in the RP of seismic activity. It implies that the onset of the strong earthquake event is reflected in a sharp and great simultaneous change in RQA measures.

scholarly journals Application of Recurrence Quantification Analysis for Non-Linear Dynamical Systems

2019 ◽  
Vol 9 (1S5) ◽  
pp. 92-94
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Dynamical Systems ◽  
Recurrence Plot ◽  
Recurrence Quantification Analysis ◽  
Recurrence Plots ◽  
Space Trajectories ◽  
Recurrence Quantification ◽  
Quantification Analysis ◽  
Phase Space Trajectories

The Recurrence plots (RPs) have been introduced in several different scientific and medical disciplines. The main purpose of recurrence plot is used to of identify the higher dimensional phase space trajectories. RPs are purely graphically representation which have been designed for the detection of hidden dynamical patterns and non-linearity present in the data, the evaluation of error which is caused by observational noise can be done by Recurrence Quantification Analysis (RQA). RQA method is initially used to minimize the error present in the given signals. RQA method is a basically a technique for the analysis of nonlinear data to quantify the number and duration of a dynamical systems. The recurrence plot is used for time series domain for multidimensional signal also. Recurrence is the property of non-stationary and dynamical system to characteristics the time series analysis in phase space trajectories. Recurrence Quantification Analysis is used to derive from recurrence plots, which are based upon distances matrices of time series.

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