Recurrence-plot-based measures of complexity and their application to heart-rate-variability data

Marwan, Norbert; Wessel, Niels; Meyerfeldt, Udo; Schirdewan, Alexander; Kurths, Jürgen

doi:10.1103/physreve.66.026702

Cited by 846 publications

(658 citation statements)

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“…One of the main advantages of the RP is that they allow the E-dimensional phase-space trajectory to be investigated through a binary two-dimensional representation of the recurrences of the states. Additionally, the quantification of the number and duration of the recurrences allows us to study the degree of predictability [16] as well as some other characteristics of the underlying dynamic systems: laminar phases [17], unstable periodic orbits [18], etc.…”

Section: Recurrence Plotsmentioning

confidence: 99%

Measuring predictability in ultrasonic signals: An application to scattering material characterization

2014

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In this paper, we present a novel and completely di↵erent approach to the problem of scattering material characterization: measuring the degree of predictability of the time series. Measuring predictability can provide information of the signal strength of the deterministic component of the time series in relation to the whole time series acquired. This relationship can provide information about coherent reflections in material grains with respect to the rest of incoherent noises that typically appear in non-destructive testing using ultrasonics. This is a non-parametric technique commonly used in chaos theory that does not require making any kind of assumptions about attenuation profiles. In highly scattering media (low SNR), it has been shown theoretically that the degree of predictability allows material characterization. The experimental results obtained in this work with 32 cement probes of 4 di↵erent porosities demonstrate the ability of this technique to do classification. It has also been shown that, in this particular application, the measurement of predictability can be used as an indicator of the percentages of porosity of the test samples with great accuracy.Keywords: Ultrasonic Signal Modality, Ultrasonic NDT, Multiple scattering, Noise, Determinism, Chaos Theory, Higher order statistics IntroductionWhen scattering materials are subject to ultrasonic non-destructive testing (NDT), the ultrasonic pulse undergoes some variations that are related to the internal grain microstructure of the specimen. Each grain behaves like a scattering center, producing an echo that when superimposed on other echoes coming from other grains can even hide the echoes produced by a possible defect. Similar situations are found in other related fields such as ultrasound B-mode scans (where the grain noise is called speckle) and in radar with clutter [1].In the literature, a wide range of solutions has been proposed to enhance the detection of small cracks or defects and to reduce (or even eliminate) the e↵ect discussed in each of the above situations. Some of these solutions are signal averaging, auto-and cross-correlation, matched filtering, frequency spectrum analysis [2], spectral correlation [3], and wavelet transformations [4]. The aforementioned analyses discard the information encoded in the grain noise; however, this information can be used to recognize potential di↵erences among materials, tissues, or surfaces. This approach has been employed to characterize materials by extracting temporal signal statistics [1], the resonance frequency [5], and even the penetration depth [6]. Our work continues with this line of thought and proposes a new approach that attempts to extract information about the nature of the signal, thereby characterizing the signal modality. Signal modality characterization is a key concept of a multidisciplinary research topic that includes di↵erent concepts such as signal linearity, stationarity, and stochasticity [7]. The applications of signal modality characterization are becoming mo...

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Section: Recurrence Plotsmentioning

confidence: 99%

Measuring predictability in ultrasonic signals: An application to scattering material characterization

2014

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“…It looks like the state is trapped for some time, which is a typical behaviour of laminar states [4]. Because RPs are symmetric about the LOI by definition (1), each vertical line has a corresponding horizontal line.…”

Section: Recurrence Plotsmentioning

confidence: 99%

“…The method of recurrence plots (RPs) was introduced by Eckmann et al [2]. Together with different RP quantification approaches [3,4], this method has attracted growing interest for both theory and applications [5].…”

Section: Introductionmentioning

confidence: 99%

Generalised recurrence plot analysis for spatial data

2007

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“…Presently at least 8 different statistical RQA characteristics are known (Zbilut and Weber, 1992;Ivanski and Bradley, 1998;Marwan, 2003), though their practical meaning is not always quite clear. Computation of these measures in small windows moving along the main diagonal of the RP reveal the time dependent behavior of these variables, making possible the identification of unknown dynamical patterns in time series (Zbilut and Weber, 1992;Marwan and Kurths, 2002). Here we briefly touch only on main RQA statistical values.…”

Section: Phase Space Structures As Image Of Dynamicsmentioning

confidence: 99%

“…The cut-off distance defines a sphere centered at → x i . Recurrence of the phase space trajectory to a certain state is a fundamental property of deterministic dynamical systems (Argyris and Haase, 1994;Marwan and Kurths, 2002). If the trajectory in the reconstructed phase space returns at time i into the -neighborhood of its location at time j (i.e.…”

Section: Phase Space Structures As Image Of Dynamicsmentioning

confidence: 99%

Identification of Complex Processes Based on Analysis of Phase Space Structures

Matcharashvili

Chélidzé

Janiashvili³

Imaging for Detection and Identification

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Abstract. The problem of investigation of temporal and/or spatial behavior of highly nonlinear or complex natural systems has long been of fundamental scientific interest. At the same time it is presently well understood that identification of dynamics of processes in complex natural systems, through their qualitative description and quantitative evaluation, is far from a purely academic question and has an essential practical importance. This is quite understandable as systems with complex dynamics abound in nature and examples can be found in very different areas such as medicine and biology (rhythms, physiological cycles, epidemics), atmosphere (climate and weather change), geophysics (tides, earthquakes, volcanoes, magnetic field variations), economy (financial markets behavior, exchange rates), engineering (friction, fracturing), communication (electronic networks, internet packet dynamics) etc. The past two decades of research on qualitative and especially quantitative investigations of dynamics of real processes of different origin brought significant progress in the understanding of behavior of natural processes. At the same time serious drawbacks have also been revealed. This is why exhaustive investigation of dynamical properties of complex processes for scientific, engineering or practical purposes is now recognized as one of the main scientific challenges. Much attention is paid to elaboration of appropriate methods aiming to measuring the complexity of both global and local dynamical behaviors from the observed data sets -time series. This chapter presents a short overview of modern methods of qualitative and quantitative evaluation of dynamics of complex natural processes such as calculation of Lyapunov exponents and fractal dimensions, recurrence plots and recurrence quantification analysis. Other related methods are also described. The traditional approach to studying dynamical behavior of complex nonlinear systems is to reconstruct from observation scalar time series state or phase space plot. This graph indicates how the systems behavior changes over the time. We focus on the methods of identification and quantitative evaluation of complex dynamics that are based on the testing of evolutionary and geometric properties of phase space graphs as images of investigated complex dynamics. For practical examples of the application c 2006 Springer. Printed in the Netherlands.of nonlinear methods for identification of complex natural processes, our results on medical, geophysical, hydrological, and stick-slip time series analysis are presented.

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Recurrence-plot-based measures of complexity and their application to heart-rate-variability data

Cited by 846 publications

References 30 publications

Measuring predictability in ultrasonic signals: An application to scattering material characterization

Measuring predictability in ultrasonic signals: An application to scattering material characterization

Generalised recurrence plot analysis for spatial data

Identification of Complex Processes Based on Analysis of Phase Space Structures

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