Monitor of Remote Control Vehicle via Approximate Gabor Transform of Their Acoustic Signatures

Abstract

This study employs the Fourier sine spectrum and Gabor sine spectrogram to monitor the vibration modes of three unmanned aircrafts whose data are collected by a portable acoustic data acquisition system. To capture both dominant and miuor modes, procedures to generate the spectrum and spectrogram are carefully constructed to avoid errors as much as possible. The uousiuusoidai trend is first removed via the iterative Gaussian smoothing method. Zero points around the two ends of the high-frequency part are identified by searching and interpolation procedures. After dropping segments beyond the two zero euds, the Fourier sine spectrum is obtahied. The timefrequency transform imposes a finite bandwidth Gaus.sian window upon the spectrum centered at a giveu frequency. Finally, the inverse fast Fourier tran.sform of the spectral band gives the spectrogram coefficient. The resulting spectrum aud spectrogram capture a great deal of information couceruing the dominant modes aud corresponding harmonics that clearly reveal the operating conditions. According to the nonlinear subharmonic theory of von Círoll and Ewins ("A Mechanism of Low Subharmonic Response in Rotor/Stator Contact-Measuremeuts and Simulations," analyses of acoustic signatures of three remote control aerial vehicles indicate they do not have significant nonalignment between components. The test ofa remote control helicopter even shows the capability of resolving the change ofa fiowfield. All of the tests show that the proposed system is a potential tool to monitor both the operational and healthy conditions of a system.

Frequency Identification of Vibration Signals Using Video Camera Image Data

“…To demonstrate further the capability of the high-speed camera and webcam image systems, the vibration signals emitted from an electrodynamics modal exciter type 4809 [9,19] were tested too. An accelerometer system and an acoustic data acquisition system with a small commercial microphone Figure 2(a,b) were also employed to validate the image data.…”

“…For convenience, these time series data strings are written in the following form [1,7–9,19]: $\begin{array}{cc}{y}_j=\sum _{l=0}^{J-1}false[b_{l}cos\frac{2\pi t_j}{{\lambda }_l}+c_{l}sin\frac{2\pi t_j}{{\lambda }_l}false]+\sum _{n=0}^N{a}_n{t}_j^n,& 0<j<J\end{array}$where y j is the gray-level summation at t = t j , the second summation represents the non-sinusoidal trend, and N represents the largest power for which a n →0 for all n > N . In most engineering applications, N = 250 is a reasonable value.…”

“…The non-sinusoidal trend is interpreted as the sum of monotonic parts and all of the Fourier modes, in which the wavelengths are longer than the data span T = J Δ t . The iterative Gaussian smoothing method in the spectral domain is used as a high-passed filter and yields the following high-frequency response [7–9,19–21]: $y_m^{\prime }=\sum _{l=0}^{J-1}{false[1-afalse(\sigma /{\lambda }_{l}false)false]}^m\left[b_{l}cos\left(\frac{2\pi t}{{\lambda }_l}\right)+c_{l}sin\left(\frac{2\pi t}{{\lambda }_l}\right)\right]$where the iteration parameter m and smoothing factor σ use the values of 127 and 0.8 T , respectively. Since m > 125 is corresponding to N > 250, the trend is ultimately removed, because this result is derived by assuming the data span running from –∞ to ∞, small errors are thus induced by using the missing data beyond the two ends.…”

“…Instrumental data are often contaminated by a mean trend resulting from processes other than those of primary interest [17–18]. Before applying the spectral method, this embedded trend should be removed to prevent the resulting spectrum from being contaminated [7–9,19–21]. To examine the periodic part, the Fourier method is applied to problems in which wave components involve only fixed amplitudes and frequencies [22–23].…”

“…To examine the periodic part, the Fourier method is applied to problems in which wave components involve only fixed amplitudes and frequencies [22–23]. To resolve the time-dependent amplitude and frequency, the iterative Gaussian filter and modified Gabor transform [1,7–9,19,23–26] are used to remove the trend and perform time frequency analysis, respectively.…”