KEYWORDS: Time-frequency analysis, Signal processing, Nonlinear optics, Data processing, Interference (communication), Modulation, Wave propagation, System identification, Damage detection, Space telescopes
Membrane dynamics is often nonlinear and nonstationary because of geometric nonlinearity induced by high local
flexibility, non-uniform pre-tension, light weight, dynamic coupling with surrounding air, wave propagation, supportinduced
nonlinearity, and others. Hence, dynamics characterization and health monitoring of membrane structures
require advanced time-frequency analysis, and the focus is on how to obtain accurate time-varying frequency and
amplitude of a nonlinear nonstationary signal. Here we propose the use of a conjugate-pair decomposition (CPD) method
with the empirical mode decomposition (EMD) for characterization of membrane dynamics. First, EMD with signal
conditioning techniques is used to separate a compound membrane response into well-behaved intrinsic mode functions
(IMFs) without assuming the signal to be harmonic. Then, a pair of sliding conjugate functions is used to accurately
extract the time-varying frequency and amplitude of each IMF by using only three neighboring data points for each time
instant. Because the variations of frequencies and amplitudes of IMFs contain system characteristics, they can be used
for system identification and damage detection. Experimental nonlinear responses of a horizontally tensioned Kapton
membrane subjected to a transverse harmonic excitation provided by a shaker at one end are used to validate the proposed methodology. Results show that the clamped-clamped supports and pre-tension cause the first-mode vibration to have a hardening cubic nonlinearity, and several other nonlinear phenomena are identified.
KEYWORDS: Dynamical systems, Signal processing, Inspection, Time-frequency analysis, Nonlinear optics, Complex systems, Data processing, System identification, Fourier transforms, Data analysis
This paper presents a conjugate-pair decomposition (CPD) method for offline damage inspection and online health
monitoring of dynamical systems. Responses of damaged dynamical systems are often nonlinear and nonstationary. For
a nonlinear non-stationary signal, empirical mode decomposition (EMD) uses the apparent time scales revealed by the
signal's local maxima and minima to sequentially sift intrinsic mode functions (IMFs) of different time-varying scales,
starting from high- to low-frequency ones. For offline detailed damage inspection, CPD uses one or more pairs of
windowed adaptive harmonics and function orthogonality to track time-varying frequency and amplitude of each IMF.
Because CPD processes only time-domain data, it is free from the edge effect caused by Gibbs' phenomenon and other
mathematical and numerical problems caused by the use of Hilbert transform. Hence, results from CPD are valuable for
accurate identification of dynamical systems. For parametric identification, one can compare the time-varying frequency
and amplitude from CPD with those from perturbation analysis to determine the type and order of nonlinearity and
system parameters. For online health monitoring, CPD tracks the instantaneous frequency of an arbitrary signal without
signal decomposition by processing three or more most recent data to estimate its instantaneous frequency and
amplitude. Numerical results show that CPD is versatile for system identification, damage inspection, and health
monitoring of different linear/nonlinear dynamical systems.
The backscattering coefficient and intensities of soot particles were calculated using Mie scattering theory for the
different incidences laser wavelengths and particle radii with complex refractive index also talked into consideration.
The calculation results indicated that at a scatter angle of 180°,the backscattering intensities can go up by 30% of
forward scattering intensities at different radii of particles if the resource laser wavelength is properly selected. This
conclusion provides a theoretical basis for the selection of laser sources and detector aiming at enhancing Signal Noise
Ratio.
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