摘要:

The geometry of homoclinic orbits is known to be closely related to the chaotic behavior of a system. A homoclinic orbit is the intersection between a stable and unstable manifold of the same point, or orbit. Four different manifestations of an unstable manifold, and attendant homoclinic orbits, playing a role in chaos are discussed. © 1994 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.45290

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

We give results of a few simple applications of a statistical test for ‘‘smoothness’’ of embedded time series recently introduced by the authors. The method, which is applicable to both map and flow data, exploits an arbitrariness in the choice of vector field for computation of a statistic forming the basis of the test. The statistic we choose is a natural extension to the general vector field setting of Kaplan and Glass’s &Lgr;‐statistic, although that specific choice is not essential to the method. Unavoidable uncertainties in &Lgr; due to finite numerics are mitigated by the device of employing maximum and minimum values of &Lgr; over a set of many randomly chosen vector fields. We examine properties under the test of examples chosen to illustrate the variety of effects that can occur in implementation of the test. Although we have focussed our investigations on low values of embedding trial dimension, the method seems likely to be generally reliable if appropriate data requirements are met. © 1994 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.45296

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

In this paper a model is posited for deterministic, random‐like noise in machines with sliding rigid parts impacting linear continuous machine structures. Such problems occur in gear transmission systems. A mathematical model is proposed to explain the random‐like structure‐borne and air‐borne noise from such systems when the input is a periodic deterministic excitation of the quasi‐rigid impacting parts. An experimental study is presented which supports the model. A thin circular plate is impacted by a chaotically vibrating mass excited by a sinusoidal moving base. The results suggest that the plate vibrations might be predicted by replacing the chaotic vibrating mass with a probabilistic forcing function. Prechaotic vibrations of the impacting mass show classical period doubling phenomena. © 1994 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.45288

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

We use the methods reviewed by Professor Abarbanel to show that accelerometer data from a gearbox are chaotic. These data have broad‐band Fourier components and a natural question arises as to whether these data are chaotic. The requirements for chaos are that:      The Fourier spectrum is broad‐band,    There is a non‐integer fractal dimension,    There is at least one positive Lyapunov exponent.   These analysis are a prelude to fault prediction and analysis. In this paper we present the results of our studies on a good high‐speed gearbox data. That is, the gearbox was known to contain no faults. © 1994 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.45291

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

Data from experiments on the turbulent boundary layer around an axisymmetric vehicle rising under its own buoyancy are described in detail and analyzed using tools developed in nonlinear dynamics. Arguments are given that in this experiment the size of the wall mounted pressure sensors would make the data sensitive to the dynamics of about ten or so coherent structures in the turbulent boundary layer. Analysis of a substantial number of large, well sampled data sets indicates that the (integer) dimension of the embedding space required to capture the dynamics of the observed flows in the laminar regime is very large. This is consistent with there being no pressure fluctuations expected here and the signal being dominated by instrumental ‘noise’. In a consistency check we find that data from the ambient state of the vehicle before buoyant rise occurs and data from an accelerometer mounted in the prow are also consistent with this large dimension. The time scales in those data are also unrelated to fluid dynamic phenomena.In thetransitionandturbulentregions of the flow we find the pressure fluctuation time scales to be consistent with those of the fluid flow (about 240 to 250 &mgr;sec) and determine the dimension required for embedding the data to be about 7–8 for the transitional region and about 8–9 for the turbulent regime. These results are examined in detail using both global and local false nearest neighbor methods as well as mutual information aspects of the data. The results indicate that the pressure fluctuations are determined in these regimes by the coherent structures in the turbulent boundary layer. Applications and further investigations suggested by these results are discussed. © 1994 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.45292

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

Under the assumption of statistical independence of velocity increments across scales of the order of the Kolmogorov scale, it is shown that a modified version of Kolmogorov’s refined similarity hypotheses follows purely from probabilistic arguments. The connection of this result to three‐dimensional fluid turbulence is discussed briefly. © 1994 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.45305

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

This analysis investigated experimentally the chaotic and spectral dynamics of an open boundary layer in the direction of flow to acquire a better understanding of the noise generating mechanisms. If the mechanisms are low dimensional chaotic processes, a variety of chaotic noise reduction techniques would be available. The specific data parameters investigated were: time series of wall pressure disturbance, temporal spectra, autocorrelation, embedding dimension, lyapunov exponent, correlation dimension, and phase space trajectories. Evidence of low dimension dynamics was found in the impingement wall pressure time series data. The major system test parameters were: vehicle velocity, 41 knots; sampling rate, 65536 Hz; and filter bandwidth, low pass@xa6400 Hz. The data conditioning was performed in the Naval Undersea Warfare Center, Test and Evaluation Signal Processing Facility. © 1994 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.45293

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

Recent work using chaotic signals to drive nonlinear systems shows that chaotic dynamics is rich in new application possibilities. The approach of using nonlinear dynamics concepts to guide synthesis of new nonlinear systems leads to the concept of synchronization of chaotic systems. We demonstrate this concept here in computer models and in circuits. We also show how these ideas might be used for communications. © 1994 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.45294

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The concepts of chaos and its control are reviewed. Both are discussed from an experimental as well as a theoretical viewpoint. Examples are then given of the control of chaos in a diverse set of experimentsl systems. Current and future applications are discussed. © 1994 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.45295

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

Adaptive, or time‐varying, modeling approaches to signal processing have typically been employed when non‐stationarity is presumed to exist. In a nonlinear dynamics framework, the adaptive paradigm has an additional application in modeling which simultaneously addresses some of the limitations of local linear and static global methods, even for stationary situations. These new methods therefore have the ability to account for non‐stationarity as well as nonlinear signal properties. We discuss the implementation of two continuous model update schemes, as well as applications to system characterization, parameter tracking, and transient detection in noise. © 1994 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.45297

出版商:AIP    

年代:1994

数据来源: AIP