Characterization of an experimental strange attractor by periodic orbits

Lathrop, Daniel P.; Kostelich, Eric J.

doi:10.1103/physreva.40.4028

Cited by 318 publications

(137 citation statements)

References 17 publications

Supporting

Mentioning

132

Contrasting

Unclassified

Order By: Relevance

“…(51) can usually be extracted directly from the measurement [9]. The location of the periodic orbits are obtained by looking at recurrences in the embedded space [46,47]. The matrix A in Eq.…”

Section: Use Of Delay Coordinatesmentioning

confidence: 99%

The control of chaos: theory and applications

et al. 2000

View full text Add to dashboard Cite

Section: Use Of Delay Coordinatesmentioning

confidence: 99%

The control of chaos: theory and applications

et al. 2000

View full text Add to dashboard Cite

“…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%

“…The simulated signals were obtained using the model presented in [1] and reproduced in Equation (18). This equation simulates a backscattered ultrasonic signal at time t for a given transducer position z.…”

Section: Application To the Ultrasound Modelmentioning

confidence: 99%

“…Before using the proposed DAKDS parameter, the variance of the estimator should be analyzed. This analysis was conducted for the ultrasonic backscattered signal of Equation (18). The parameters employed in the simulation were: w 0 = 2·⇡·10 MHz, attenuation 10 dB/cm, percentage of scatterers 40%, and K-Type amplitude distributed reflections.…”

Section: Application To the Ultrasound Modelmentioning

confidence: 99%

See 1 more Smart Citation

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

2014

View full text Add to dashboard Cite

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...

show abstract

“…First we sought recurrences used for extracting unstable periodic orbits (UPOs) [26][27][28][29][30][31]. Recurrences are defined as instances for which |y n −y n+k | < ǫ, where y m is the reconstructed vector, and ǫ is a tolerance chosen by prescription.…”

Section: Characterization Of the Datamentioning

confidence: 99%

Fractional derivative reconstruction of forced oscillators

2008

View full text Add to dashboard Cite

Fractional derivatives are applied in the reconstruction, from a single observable, of the dynamics of a Duffing oscillator and a two-well experiment. The fractional derivatives of time series data are obtained in the frequency domain. The derivative fraction is evaluated using the average mutual information between the observable and its fractional derivative. The ability of this reconstruction method to unfold the data is assessed by the method of global false nearest neighbors. The reconstructed data is used to compute recurrences and fractal dimensions. The reconstruction is compared to the true phase space and the delay reconstruction in order to assess the reconstruction parameters and the quality of results.

show abstract

Characterization of an experimental strange attractor by periodic orbits

Cited by 318 publications

References 17 publications

The control of chaos: theory and applications

The control of chaos: theory and applications

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

Fractional derivative reconstruction of forced oscillators

Contact Info

Product

Resources

About