Spectral Analyses of Nonlinear Interactions

1995 ◽  
Author(s):  
Balakumar Balachandran ◽  
Khalil A. Khan
Keyword(s):  
Coupled Oscillators ◽  
Higher Order ◽  
Nonlinear Interactions ◽  
Phase Coupling ◽  
Spectral Analyses ◽  
Weakly Nonlinear ◽  
Numerical Studies ◽  
Analytical Approximations ◽  
Higher Order Spectra

Abstract Signals pertaining to motions of nonlinearly coupled oscillators are studied using higher-order spectral analyses. The analyses is used to understand the role of phase coupling in nonlinear interactions between two or more Fourier components. For certain motions of weakly nonlinear systems, analytical approximations are obtained for relevant higher-order spectra and coherence functions. Numerical studies are conducted to verify analytical predictions and to illustrate the usefulness of spectral analyses for different cases.

Identification of freeplay and aerodynamic nonlinearities in a 2D aerofoil system with via higher-order spectra

2017 ◽  
Vol 121 (1244) ◽  
pp. 1530-1560 ◽  
Author(s):  
M. Candon ◽  
R. Carrese ◽  
H. Ogawa ◽  
P. Marzocca
Keyword(s):  
Pressure Coefficient ◽  
High Amplitude ◽  
Higher Order ◽  
Limit Cycle Oscillation ◽  
Cubic Phase ◽  
Phase Coupling ◽  
Quadratic Phase ◽  
Power Spectral ◽  
Cycle Oscillation ◽  
Higher Order Spectra

ABSTRACTHigher-Order Spectra (HOS) are used to characterise the nonlinear aeroelastic behaviour of a plunging and pitching 2-degree-of-freedom aerofoil system by diagnosing structural and/or aerodynamic nonlinearities via the nonlinear spectral content of the computed displacement signals. The nonlinear aeroelastic predictions are obtained from high-fidelity viscous fluid-structure interaction simulations. The power spectral, bi-spectral and tri-spectral densities are used to provide insight into the functional form of both freeplay and inviscid/viscous aerodynamic nonlinearities with the system displaying both low- and high-amplitude Limit Cycle Oscillation (LCO). It is shown that in the absence of aerodynamic nonlinearity (low-amplitude LCO) the system is characterised by cubic phase coupling only. Furthermore, when the amplitude of the oscillations becomes large, aerodynamic nonlinearities become prevalent and are characterised by quadratic phase coupling. Physical insights into the nonlinearities are provided in the form of phase-plane diagrams, pressure coefficient distributions and Mach number flowfield contours.

scholarly journals Analysis of EMG Signals in Aggressive and Normal Activities by Using Higher-Order Spectra

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Necmettin Sezgin
Keyword(s):  
Electrical Potential ◽  
Higher Order ◽  
Electrical Potential Difference ◽  
Phase Coupling ◽  
Classification Result ◽  
Learning Machines ◽  
Emg Signal ◽  
Quadratic Phase ◽  
Higher Order Spectra

The analysis and classification of electromyography (EMG) signals are very important in order to detect some symptoms of diseases, prosthetic arm/leg control, and so on. In this study, an EMG signal was analyzed using bispectrum, which belongs to a family of higher-order spectra. An EMG signal is the electrical potential difference of muscle cells. The EMG signals used in the present study are aggressive or normal actions. The EMG dataset was obtained from the machine learning repository. First, the aggressive and normal EMG activities were analyzed using bispectrum and the quadratic phase coupling of each EMG episode was determined. Next, the features of the analyzed EMG signals were fed into learning machines to separate the aggressive and normal actions. The best classification result was 99.75%, which is sufficient to significantly classify the aggressive and normal actions.

Higher-Order Spectral Analysis to Detect Power-Frequency Mechanisms in a Driven Chua's Circuit

1997 ◽  
Vol 07 (06) ◽  
pp. 1431-1440 ◽  
Author(s):  
Domine M. W. Leenaerts
Keyword(s):  
Period Doubling ◽  
Peak Frequency ◽  
Higher Order ◽  
Nonlinear Interactions ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Power Frequency ◽  
Higher Order Spectra ◽  
Doubling Sequence ◽  
Dominant Frequencies

Higher-order spectra have been used to investigate nonlinear interactions between frequency modes in a driven Chua's circuit. The spectra show that an energy transfer takes place to the dominant frequencies in the circuit, i.e. the input frequency, the primary peak frequency and the harmonics of both frequencies. Other frequencies couplings become less important. Obviously, powers are (nonlinearly) related at different frequencies. When the circuit undergoes a period doubling sequence to chaos, the gain is increasing.

HIGHER-ORDER SPECTRAL ANALYSIS TO DETECT NONLINEAR INTERACTIONS IN MEASURED TIME SERIES AND AN APPLICATION TO CHUA’S CIRCUIT

1993 ◽  
Vol 03 (01) ◽  
pp. 19-34 ◽  
Author(s):  
STEVE ELGAR ◽  
VINOD CHANDRAN
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Higher Order ◽  
Nonlinear Interactions ◽  
Chua’S Circuit ◽  
Phase Coupling ◽  
Chua's Circuit ◽  
Nonlinear Phase ◽  
Wide Range ◽  
Measured Time

Higher-order spectra have been used to investigate nonlinear interactions between the Fourier components of measured time series in a remarkably wide range of random processes. The basic techniques of detecting and isolating nonlinear phase coupling in observed data using higher-order spectral analysis are reviewed here. These techniques are then used to investigate nonlinear interactions in time series of voltages measured from a realization of Chua’s circuit. For period-doubled limit cycles, quadratic and cubic nonlinear interactions result in phase coupling and energy exchange between increasing numbers of triads and quartets of Fourier components as the nonlinearity of the system is increased. For circuit parameters that result in a chaotic, Rössler-type attractor, bicoherence and tricoherence spectra indicate that both quadratic and cubic nonlinear interactions are important to the dynamics. For parameters that lead to the double-scroll chaotic attractor the bispectrum is zero, but the tricoherences are high, consistent with the importance of higher-than-second order nonlinear interactions during chaos associated with the double scroll.

scholarly journals BISPECTRAL AND TRISPECTRAL CHARACTERIZATION OF TRANSITION TO CHAOS IN THE DUFFING OSCILLATOR

1993 ◽  
Vol 03 (03) ◽  
pp. 551-557 ◽  
Author(s):  
VINOD CHANDRAN ◽  
STEVE ELGAR ◽  
CHARLES PEZESHKI
Keyword(s):  
Numerical Solutions ◽  
Duffing Oscillator ◽  
Broad Band ◽  
Power Spectra ◽  
Period Doubling ◽  
Higher Order ◽  
Nonlinear Interactions ◽  
Route To Chaos ◽  
Higher Order Spectra

Higher-order spectral (bispectral and trispectral) analyses of numerical solutions of the Duffing equation with a cubic stiffness are used to isolate the coupling between the triads and quartets, respectively, of nonlinearly interacting Fourier components of the system. The Duffing oscillator follows a period-doubling intermittency catastrophic route to chaos. For period-doubled limit cycles, higher-order spectra indicate that both quadratic and cubic nonlinear interactions are important to the dynamics. However, when the Duffing oscillator becomes chaotic, global behavior of the cubic nonlinearity becomes dominant and quadratic nonlinear interactions are weak, while cubic interactions remain strong. As the nonlinearity of the system is increased, the number of excited Fourier components increases, eventually leading to broad-band power spectra for chaos. The corresponding higher-order spectra indicate that although some individual nonlinear interactions weaken as nonlinearity increases, the number of nonlinearly interacting Fourier modes increases. Trispectra indicate that the cubic interactions gradually evolve from encompassing a few quartets of Fourier components for period-1 motion to encompassing many quartets for chaos. For chaos, all the components within the energetic part of the power spectrum are cubically (but not quadratically) coupled to each other.

scholarly journals Higher-Order Spectra of Nonlinear Polynomial Models for Chua's Circuit

1998 ◽  
Vol 08 (12) ◽  
pp. 2425-2431 ◽  
Author(s):  
Steve Elgar ◽  
Barry Vanhoff ◽  
Luis A. Aguirrre ◽  
Ubiratan S. Freitas ◽  
Vinod Chandran
Keyword(s):  
Time Series ◽  
Higher Order ◽  
Nonlinear Interactions ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Process Dynamics ◽  
Measured Time ◽  
Polynomial Models ◽  
The Individual ◽  
Higher Order Spectra

Polynomial models are shown to simulate accurately the quadratic and cubic nonlinear interactions (e.g. higher-order spectra) of time series of voltages measured in Chua's circuit. For circuit parameters resulting in a spiral attractor, bispectra and trispectra of the polynomial model are similar to those from the measured time series, suggesting that the individual interactions between triads and quartets of Fourier components that govern the process dynamics are modeled accurately. For parameters that produce the double-scroll attractor, both measured and modeled time series have small bispectra, but nonzero trispectra, consistent with higher-than-second order nonlinearities dominating the chaos.

Sign in / Sign up

Export Citation Format

Share Document