110 M.J. Ward et al. Fig. 11.7 A single frequency line of the spectrogram (middle) is tracked throughout the experiment to monitor the amplitude modulation (left) caused by non-linearity of the damage. When comparing to the angular position (right), it can be seen that the occurrence is periodic with the rotation of the apparatus identify the location of the damage in the system. However, the sample points acquired from the PocketAE system do not change uniformly with time. Therefore, an interpolation was performed to create a uniformly spaced time vector with which to perform the Discrete Fourier Transform (DFT). This new DFT was performed on the amplitude response of a single, constant frequency of the waveform data. The probing frequency input through the piezoelectric crystal was chosen so that the modulation by the pumping frequency might become apparent. A sliding window was employed to perform the DFT at sample intervals of 10 s for the 5 min tests. The result of this method was a new spectrogram with a resolution of approximately 0.05 Hz in the range of 0–75 Hz. This allowed viewing the pumping frequency modulation as the rotation rate of the experimental apparatus. These traits will be further described in the following results section. As previously mentioned, the constitutive model related to the damage behavior in this experiment was !2rDg, see Eq. (11.1). Therefore, as !was varied through the experiment, there reached an angular rate at which the damage became excited. Recording this angular velocity, a value r could be calculated which corresponded to the radial location of the damage. The angular position could also be computed using a statistical binning method which recorded a count for each peak in the PSD amplitude at the excitation frequency. As will be seen in the upcoming results section, this resulted in a normally distributed histogram for angular position. 11.4 Results 11.4.1 Localization Using VAM Spin-down VAM analysis was applied to accumulated acoustic emission data to create a spectrogram. This raw spectrogram, seen in Fig. 11.8, clearly shows a consistent amplitude peak over the course of the test at the probing frequency of 83 kHz. It also shows peaks at harmonics of this frequency. A shift in the data is clearly visible at around 45 s and can be attributed to the non-linearity caused by the damage beginning to react in the rotating gravitational field. A magnified view (highlighted by red box in Fig. 11.8a) of the probing frequency shows a periodicity in the amplitude of the probing signal that can be directly correlated to the angular position of the apparatus. As described in the previous section, extracting the probing line frequency data and performing a sliding window DFT results in a new spectrogram shown in Fig. 11.9.
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