Higher-order spectra have become a useful tool in spectral analysis, particularly for identifying the presence and
sometimes type of nonlinearity in a system. Two such spectra that have figured prominently in signal processing
are the bispectrum and trispectrum. The bispectrum is well-suited to capturing the presence of quadratic
nonlinearities in system response data while the trispectrum has proved useful in detecting cubic nonlinearities.
In a previous work, the authors developed an analytical solution for the auto-bispectrum for multi-degree-of-freedom
systems. Here this analysis is extended to the trispectrum. Specifically, an expression is developed for
the trispectral density of a multi-degree-of-freedom system subject to Gaussian excitation applied at an arbitrary
location. The analytical expression is compared to those obtained via estimation using the direct method.
Higher-order spectra (HOS) appear often in the analysis and identification of nonlinear systems. The auto-bispectrum
is one example of a HOS and is frequently used in the analysis of stationary structural response data
to detect the presence of structural nonlinearities. In this work we derive an expression for the auto-bispectrum
of a multi-degree-of-freedom structure with quadratic nonlinearities. A nonlinearity detection strategy, based on
estimates of the bispectrum, is then described. The performance of several such detectors is quantified using
Receiver Operator Characteristic (ROC) curves illustrating the trade-off between Type-I error and power of
detection (1-Type-II error).
This paper discusses modeling, simulations and experimental aspects of active aeroelastic control on aircraft wings by
using Synthetic Jet Actuators (SJAs). SJAs, a particular class of zero-net mass-flux actuators, have shown very
promising results in numerous aeronautical applications, such as boundary layer control and delay of flow separation. A
less recognized effect resulting from the SJAs is a momentum exchange that occurs with the flow, leading to a
rearrangement of the streamlines around the airfoil modifying the aerodynamic loads. Discussions pertinent to the use of
SJAs for flow and aeroelastic control and how these devices can be exploited for flutter suppression and for aerodynamic
performances improvement are presented and conclusions are outlined.
Higher order spectral analysis techniques are often used to identify nonlinear interactions in modes of dynamical systems. More specifically, the auto and cross- bispectra have proven to be useful tools in testing for the presence of quadratic nonlinearities based on a system's stationary response. In this paper a class of mechanical system represented by a second-order nonlinear equation of motion subject to random forcing is considered. Analytical expressions for the second-order auto- and cross-spectra are determined using a Volterra functional approach and the presence and extent of nonlinear interactions between frequency components are identified. Numerical simulations accompany the analytical solutions to show how modes may interact nonlinearly producing intermodulation components at the sum and/or difference frequency of the fundamental modes of oscillation. A closed-form solution of the Bispectrum can be used to help identify the source of non-linearity due to interactions at specific frequencies. Possible applications include structural health monitoring where damage is often modeled as a nonlinearity. Advantages of using higher-order spectra techniques will be revealed and pertinent conclusions will be outlined.
Higher-order spectra (HOS) appear often in the analysis and identification of nonlinear systems. The auto-bispectrum
is one example of a HOS and is frequently used in the analysis of stationary structural response data
to detect the presence of certain types structural nonlinearities. In this work we use a closed-form expression
for the auto-bispectrum, derived previously by the authors, to find the bispectral frequency most sensitive to
the nonlinearity. We then explore the properties of nonlinearity detectors based on estimates of the magnitude
of the auto-bispectrum at this frequency. We specifically consider the case where the bispectrum is estimated
using the direct method based on the Fourier Transform. The performance of the detector is quantified using
a Receiver Operator Characteristic (ROC) curve illustrating the trade-off between Type-I error and power of
detection (1-Type-II error). Theoretically derived ROC curves are compared to those obtained via numerical
simulation. Results are presented for different levels of nonlinearity. Possible consequences are discussed with
regard to the detection of damage-induced nonlinearities in structures.
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