Identification of chaos in a cutting process by the 0–1 test

Litak, Grzegorz; Syta, Arkadiusz; Wiercigroch, Marian

doi:10.1016/j.chaos.2007.09.093

Cited by 76 publications

(48 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…vðiÞ using the characteristic delay time dt equal to one quarter of the excitation period 2p=x. This roughly indicates the vanishing of the mutual information [33,39]. Starting from one of the initial map coordinate v(i), for sampling points i ¼ 1; .…”

Section: The 0-1 Testmentioning

confidence: 87%

See 1 more Smart Citation

Regular and chaotic vibration in a piezoelectric energy harvester

2015

Self Cite

View full text Add to dashboard Cite

We examine regular and chaotic responses of a vibrational energy harvester composed of a vertical beam and a tip mass. The beam is excited horizontally by a harmonic inertial force while mechanical vibrational energy is converted to electrical power through a piezoelectric patch. The mechanical resonator can be described by single or double well potentials depending on the gravity force from the tip mass. By changing the tip mass we examine bifurcations from single well oscillations, to regular and chaotic vibrations between the potential wells. The appearance of chaotic responses in the energy harvesting system is illustrated by the bifurcation diagram, the corresponding Fourier spectra, the phase portraits, and is confirmed by the 0-1 test. The appearance of chaotic vibrations reduces the level of harvested energy.

show abstract

Section: The 0-1 Testmentioning

confidence: 87%

“…However, the Lyapunov exponent can be difficult to estimate in any non-smooth simulated system or measured data [32]. Therefore the 0-1 test can provide a suitable algorithm to identify the chaotic solution [33,[36][37][38].…”

Section: The 0-1 Testmentioning

confidence: 99%

Regular and chaotic vibration in a piezoelectric energy harvester

2015

Self Cite

View full text Add to dashboard Cite

show abstract

“…Also, relative simplicity of the test and the binary nature of the fil result -parameter K ≈1 for chaotic and K ≈0 for regular gnals -made the test an attractive tool in examining signals d systems. Analysis of the properties of the 0/1 test and its teresting applications can also be found in [5]- [9]. While the 1 test for chaos can be applied to discrete and continuous sigls, it appears (based on the literature) that the test is mostly ed to examine discrete signals.…”

Section: The 0/1 Test Fundamentalsmentioning

confidence: 99%

“…The 0/1 test (see [1][2][3][4][5][6][7][8][9][10][11][12][13] for details) is a relatively new tool used to test the presence of chaos in digital sequences when a mathematical model (system of equations) is not available.…”

Section: The 0/1 Test Fundamentalsmentioning

confidence: 99%

On the 0/1 test for chaos in continuous systems

Melosik¹,

Marszałek²

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

View full text Add to dashboard Cite

Abstract. In this paper we discuss in detail the resonance and oversampling features of the 0/1 test for chaos in continuous systems and propose methods to avoid those undesired features. Our method is based on certain frequency properties of the 0/1 test. When reconstructing the phase space, our approach is compared with the first minimum of the mutual information method. Several numerical results for typical chaotic systems (including memristive circuits) are included.Key words: test 0/1 for chaos, oversampling, phase space reconstruction, mutual information, FFT. Abstract. In this paper we discuss in detail the resonance and oversampling features of the 0/1 test for chaos in continuous systems and propose methods to avoid those undesired features. Our method is based on certain frequency properties of the 0/1 test. When reconstructing the phase space, our approach is compared with the first minimum of the mutual information method. Several numerical results for typical chaotic systems (including memristive circuits) are included. On the 0/1 test for chaos in continuous systems

show abstract

“…It has been successfully applied to both numerically obtained [4][5][6][7][8] as well as to simple experimental data [9]. However, in a previous work [10] we have presented evidence that, when applied to time series stemming from nonhomogeneous, i.e dissimilar mass, many-degrees-offreedom systems, the test has serious limitations as an efficient chaos detector for a large system size N .…”

Section: Introductionmentioning

confidence: 99%

Efficient time-series detection of the strong stochasticity threshold in Fermi-Pasta-Ulam oscillator lattices

Romero-Bastida

Reyes-Martínez

2011

Phys. Rev. E

View full text Add to dashboard Cite

In this work we study the possibility of detecting the so-called strong stochasticity threshold, i.e. the transition between weak and strong chaos as the energy density of the system is increased, in anharmonic oscillator chains by means of the 0-1 test for chaos. We compare the result of the aforementioned methodology with the scaling behavior of the largest Lyapunov exponent computed by means of tangent space dynamics, that has so far been the most reliable method available to detect the strong stochasticity threshold. We find that indeed the 0-1 test can perform the detection in the range of energy density values studied. Furthermore, we determined that conventional nonlinear time series analysis methods fail to properly compute the largest Lyapounov exponent even for very large data sets, whereas the computational effort of the 0-1 test remains the same in the whole range of values of the energy density considered with moderate size time series. Therefore, our results show that, for a qualitative probing of phase space, the 0-1 test can be an effective tool if its limitations are properly taken into account.

show abstract

Identification of chaos in a cutting process by the 0–1 test

Cited by 76 publications

References 36 publications

Regular and chaotic vibration in a piezoelectric energy harvester

Regular and chaotic vibration in a piezoelectric energy harvester

On the 0/1 test for chaos in continuous systems

Efficient time-series detection of the strong stochasticity threshold in Fermi-Pasta-Ulam oscillator lattices

Contact Info

Product

Resources

About