Quadratic phase coupling detection using higher order statistics

Fackrell, Justin; McLaughlin, Steve

doi:10.1049/ic:19950736

Cited by 16 publications

(7 citation statements)

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“…A clear concentration of spectral density can be observed at the forcing reduced frequency K ≈ 0.63 (corresponding to V r =10). As the phased-filtered bispectrum is presented (Kavrakov et al, 2020), it means that there is zero phase between the main and second-order harmonic, which is a nessesary condition for nonlinearity (Fackrell and McLaughlin, 1995). Similar indications were noted bispectra of the other cases of combined effects due to gust and motion (omitted for the sake of brevity).…”

Section: Aerodynamic Forces Due To Combined Effects Of Gust and Motionsupporting

confidence: 59%

Numerical investigation of the nonlinear interaction between the sinusoidal motion-induced and gust-induced forces acting on bridge decks

Tesfaye,

Kavrakov,

Morgenthal

2021

Preprint

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With the increasing spans and complex deck shapes, aerodynamic nonlinearity becomes a crucial concern in the design of long-span bridges. This paper investigates the nonlinear interaction between the gust-induced and motion-induced forces acting on bridge decks using the Vortex Particle Method (VPM) as a Computational Fluid Dynamics (CFD) method. This nonlinear interaction is complex and intractable by the conventional linear semi-analytical models that employ the superposition principle. To excite such interaction, a sinusoidally oscillating bridge deck is subjected to sinusoidal vertical gusts. Two distinct aspects are studied: The influence of large-scale sinusoidal vertical gusts on the shear layer of a moving body and the nonlinear dependence of the aerodynamic forces on the effective angle of attack. For the latter, the resultant aerodynamic forces based on a linear semi-analytical and a CFD model are compared for the same effective angle of attack due to sinusoidal gust and motion. The methodology is first employed to verify the linear behavior of a flat plate and then study the nonlinear behavior of two bridge decks. The results show that the linear superposition principle holds for streamlined bridge decks with minimal shear layer instability. However, this principle may not be valid for bluff bridge decks due to strong separation vortices that dictate the shear layer, which induces nonlinearity in the aerodynamic forces manifested through amplitude difference in the first harmonic and emergence of higher-order harmonics. The outcome of this study aims to provide a deeper understanding of the complex nonlinear fluid-structure interaction occurring for bluff bodies subjected to motion and free-stream gusts.

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Section: Aerodynamic Forces Due To Combined Effects Of Gust and Motionsupporting

confidence: 59%

Numerical investigation of the nonlinear interaction between the sinusoidal motion-induced and gust-induced forces acting on bridge decks

Tesfaye,

Kavrakov,

Morgenthal

2021

Preprint

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“…Nonlinear interactions of frequencies and their phases (e.g., quadratic phase coupling) cannot be detected by a power spectrum—the Fourier transform of the autocorrelation function (second-order cumulant)—since phase relationships and frequency couplings of signals are lost. Such couplings are usually detected by bispectral analysis (Tukey, 1953; Kolmogorov & Rozanov, 1960;Leonov & Shiryeav, 1959; Rosenblatt & Van Ness, 1965; Brillinger & Rosenblatt, 1967; Swami, 2003; Mendel, 1991; Fackrell & McLaughlin, 1995). The bispectrum or bispectral density is the Fourier transform of the third-order cumulant (bicorrelation function).…”

Section: Functional Embedding As a Connection Between Nonlinear Dynmentioning

confidence: 99%

Delay Differential Analysis of Time Series

Lainscsek

Sejnowski

2015

Neural Computation

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Nonlinear dynamical system analysis based on embedding theory has been used for modeling and prediction, but it also has applications to signal detection and classification of time series. An embedding creates a multidimensional geometrical object from a single time series. Traditionally either delay or derivative embeddings have been used. The delay embedding is composed of delayed versions of the signal, and the derivative embedding is composed of successive derivatives of the signal. The delay embedding has been extended to nonuniform embeddings to take multiple timescales into account. Both embeddings provide information on the underlying dynamical system without having direct access to all the system variables. Delay differential analysis is based on functional embeddings, a combination of the derivative embedding with nonuniform delay embeddings. Small delay differential equation (DDE) models that best represent relevant dynamic features of time series data are selected from a pool of candidate models for detection or classification. We show that the properties of DDEs support spectral analysis in the time domain where nonlinear correlation functions are used to detect frequencies, frequency and phase couplings, and bispectra. These can be efficiently computed with short time windows and are robust to noise. For frequency analysis, this framework is a multivariate extension of discrete Fourier transform (DFT), and for higher-order spectra, it is a linear and multivariate alternative to multidimensional fast Fourier transform of multidimensional correlations. This method can be applied to short or sparse time series and can be extended to cross-trial and cross-channel spectra if multiple short data segments of the same experiment are available. Together, this time-domain toolbox provides higher temporal resolution, increased frequency and phase coupling information, and it allows an easy and straightforward implementation of higher-order spectra across time compared with frequency-based methods such as the DFT and cross-spectral analysis.

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“…Several approaches for practical estimation of the bispectrum terms in bispectral analysis have been developed, as can be found in the literature. [30][31][32] Implementing similar approaches in the higher-order Volterra approach will be considered as future work, since the length of data signals from physical experiments can be a limitation in the convergence procedure. Overall, the MCS indicates that it is critical to track the convergence of the quadratic spectra since artificial, non-physical, coherence might exist.…”

Section: Iiia Monte Carlo Simulation On Spectral Hose and Coherencementioning

confidence: 99%

POD based spectral Higher-Order Stochastic Estimation

Tinney

Powers

2010

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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A new and unique analytical approach, capable of identifying both linear and higherorder coherences in multiple-I/O systems, is presented here in the context of turbulent flows. The technique is formed by combining two well-established methods: Proper Orthogonal Decomposition (POD) and Higher-Order Spectra Analysis; both of which were developed independently in the field of turbulence and system identification, respectively. The latter of these is based on known methods for characterizing nonlinear systems by way of Volterra functional series. In that, both linear and higher-order kernels are formed to quantify the nonlinear spectral transfer of energy between the system's input and output. This reduces essentially to spectral Linear Stochastic Estimation (LSE) when only the first-order terms are considered, and is therefore presented in the context of stochastic estimation as spectral Higher-Order Stochastic Estimation (HOSE). However, the trade-off to seeking higher-order transfer kernels is that the increased complexity restricts the analysis to single-I/O systems. Low-dimensional (POD based) analysis techniques are inserted to alleviate this void as the POD coefficients represent the dynamics of the so-called spatial structures (modes) of a multi degree-of-freedom system. At first, a Monte Carlo Simulation is performed to demonstrate the validity and characteristics of the higher-order Volterra series model. Next, the POD based spectral HOSE method is applied to an experimental data set comprising synchronous measures of the near-field pressure and far-field acoustics of a coaxial jet flow. Both near-field (line array of microphones) and far-field (arc array of microphones) signatures are decomposed independently using POD in order to obtain frequency dependent POD coefficients. The linear and quadratic kernels are computed using different combinations of POD coefficients. The results indicate that the acoustic signatures in the far-field of the jet are linearly related to the pressure signatures in the near-field pressure, as is expected in a subsonic Mach number jet flow.

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Quadratic phase coupling detection using higher order statistics

Cited by 16 publications

References 1 publication

Numerical investigation of the nonlinear interaction between the sinusoidal motion-induced and gust-induced forces acting on bridge decks

Numerical investigation of the nonlinear interaction between the sinusoidal motion-induced and gust-induced forces acting on bridge decks

Delay Differential Analysis of Time Series

POD based spectral Higher-Order Stochastic Estimation

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