scholarly journals The Methodology of Distinguish Between Random and Chaotic Machine Tool Oscillations

2021 ◽  
Vol 1208 (1) ◽  
pp. 012009
Author(s):  
Sanel Gredelj
Keyword(s):  
Nonlinear Dynamics ◽  
Machine Tool ◽  
Time Domain ◽  
Correlation Dimension ◽  
Multidisciplinary Approach ◽  
Kolmogorov Entropy ◽  
Chaotic Oscillations ◽  
Nonparametric Hypothesis ◽  
The Time Domain

Abstract Machine tool oscillations are irregular or aperiodic. Most often, these oscillations are chaotic but, in some cases, they can be quasi-periodic or random. The methodology for characterizing oscillations in the first of two steps uses the nonparametric hypothesis tests which the observed oscillations confirmed as irregular. The methodology for the final characterization of oscillations is based on chaos quantifiers. A time series defined as the measured values of oscillations in the time domain is the basis for calculating the quantifiers of chaos. There are four quantifiers of chaos: the Lyapunov exponent, Kolmogorov entropy, fractal dimension and correlation dimension. The correlation dimension and Kolmogorov entropy are important for distinguishing between random and chaotic oscillations. Other quantifiers of chaos are not used for this purpose. The methodology requires a multidisciplinary approach based on combining Nonlinear Dynamics and Probability Theory and Statistics. The methodology can be applied to many oscillating phenomena. Therefore, the paper mainly used the term oscillations, not vibrations, chatter, etc.

scholarly journals Application of nonlinear dynamics methods for quantitative and qualitative evaluation of properties of 2D models of S-chaos

2021 ◽  
Vol 16 (91) ◽  
pp. 125-143
Author(s):  
Aleksei A. Gavrishev ◽  
Keyword(s):  
Nonlinear Dynamics ◽  
Lower Bound ◽  
Time Domain ◽  
Initial Conditions ◽  
Qualitative Evaluation ◽  
Recurrence Analysis ◽  
Combined Application ◽  
Student Version ◽  
The Time Domain ◽  
Property Characteristic

In this article, based on the mathematical, numerical and computer modeling carried out by the combined application of E&F Chaos, Past, Fractan, Visual Recurrence Analysis, Eviews Student Version Lite programs, some of the well-known 2D models of S-chaos are modeled, the data obtained are studied using nonlinear dynamics methods and the fact of their relation or non-relation to chaotic (quasi-chaotic) processes is established. As a result, it was found that the time diagrams obtained for the studied 2D models of S-chaos have a complex noise-like appearance and are continuous in the time domain. The resulting spectral diagrams have both a complex noise-like and regular appearance and are continuous in the spectral regions. The obtained values of BDS-statistics show that some of the time implementations can be attributed to chaotic (quasi-chaotic) processes. Also, the obtained values of BDS-statistics show that the studied 2D models of S-chaos have a property characteristic of classical chaotic (quasi-chaotic) processes: the slightest change in the initial conditions leads to the generation of a new set of signals. The obtained values of the lower bound of the KS-entropy show that the studied models also have the properties of chaotic (quasi-chaotic). Taking into account the conducted research and data from known works [1–5], it is possible to conclude that 2D models of S-chaos can relate to chaotic (quasi-chaotic) processes.

Exploring the discrimination power of the time domain for segmentation and characterization of active lesions in serial MR data

2000 ◽  
Vol 4 (1) ◽  
pp. 31-42 ◽  
Author(s):  
Guido Gerig ◽  
Daniel Welti ◽  
Charles R.G. Guttmann ◽  
Alan C.F. Colchester ◽  
Gábor Székely
Keyword(s):  
Time Domain ◽  
Discrimination Power ◽  
The Time Domain

Coherent electric field characterization of molecular chirality in the time domain

2012 ◽  
Vol 41 (12) ◽  
pp. 4457 ◽  
Author(s):  
Hanju Rhee ◽  
Intae Eom ◽  
Sung-Hyun Ahn ◽  
Minhaeng Cho
Keyword(s):  
Electric Field ◽  
Time Domain ◽  
Molecular Chirality ◽  
The Time Domain

scholarly journals Models of dielectric relaxation based on completely monotone functions

2016 ◽  
Vol 19 (5) ◽  
Author(s):  
Roberto Garrappa ◽  
Francesco Mainardi ◽  
Maione Guido
Keyword(s):  
Time Domain ◽  
Differential Operators ◽  
Dielectric Materials ◽  
Monotone Functions ◽  
Mathematical Functions ◽  
Completely Monotone Functions ◽  
Wing Model ◽  
Completely Monotone ◽  
The Time Domain

AbstractThe relaxation properties of dielectric materials are described, in the frequency domain, according to one of the several models proposed over the years: Kohlrausch-Williams-Watts, Cole-Cole, Cole-Davidson, Havriliak-Negami (with its modified version) and Excess wing model are among the most famous. Their description in the time domain involves some mathematical functions whose knowledge is of fundamental importance for a full understanding of the models. In this work, we survey the main dielectric models and we illustrate the corresponding time-domain functions. In particular, we stress the attention on the completely monotone character of the relaxation and response functions. We also provide a characterization of the models in terms of differential operators of fractional order.

scholarly journals The Future of the Time Domain with LSST

2011 ◽  
Vol 7 (S285) ◽  
pp. 158-158
Author(s):  
Lucianne M. Walkowicz
Keyword(s):  
Time Domain ◽  
Survey Design ◽  
Ancillary Data ◽  
Event Identification ◽  
Scientific Investigations ◽  
The Time Domain ◽  
First Time

SummaryIn the coming decade LSST's combination of all-sky coverage, consistent long-term monitoring and flexible criteria for event identification will revolutionize studies of a wide variety of astrophysical phenomena. Time-domain science with LSST encompasses objects both familiar and exotic, from classical variables within our Galaxy to explosive cosmological events. Increased sample sizes of known-but-rare observational phenomena will quantify their distributions for the first time, thus challenging existing theories. Perhaps most excitingly, LSST will provide the opportunity to sample previously untouched regions of parameter space. LSST will generate ‘alerts’ within 60 seconds of detecting a new transient, permitting the community to follow up unusual events in greater detail. However, follow-up will remain a challenge as the volume of transients will easily saturate available spectroscopic resources. Characterization of events and access to appropriate ancillary data (e.g. from prior observations, either in the optical or in other passbands) will be of the utmost importance in prioritizing follow-up observations. The incredible scientific opportunities and unique challenges afforded by LSST demand organization, forethought and creativity from the astronomical community. To learn more about the telescope specifics and survey design, as well as obtaining a overview of the variety of the scientific investigations that LSST will enable, readers are encouraged to look at the LSST Science Book: http://www.lsst.org/lsst/scibook. Organizational details of the LSST science collaborations and management may be found at http://www.lsstcorp.org.

Approximate Structural Response Characterization Using Parametric and Envelope Models for Multimodal Systems

1986 ◽  
Vol 108 (1) ◽  
pp. 39-43
Author(s):  
P. Davies ◽  
J. K. Hammond
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Structural Response ◽  
Parametric Models ◽  
Response Signal ◽  
Response Characteristics ◽  
Multimodal Systems ◽  
Time Domain Response ◽  
The Time Domain

In the study of the response of systems to an excitation there are circumstances when it is desirable to obtain some overall or average characterization of the system and its response rather than a detailed description. In this paper two methods are used to describe the overall features of the system: one appropriate for the frequency domain and one for the time domain. For modally dense systems the main features of the frequency response function are described in terms of low-order parametric models. While these models may be adequate for the frequency domain representation, they may not produce a good approximation to the response of the system in the time domain. The second approach relates the envelope of the input signal to the envelope of the response signal, in order to describe the overall time domain response characteristics.

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