36 Assessment of Large Error Time-Differences for Localization in a Plate Simulation 373 Time(s) 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Normalized Amplitude -1 -0.5 0 0.5 1 Time (s) 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Normalized Amplitude -1 -0.5 0 0.5 1 Fig. 36.5 Time trace of acceleration response as seen at the point located at (11.7, 12.2) above and as seen at the point located at (36, 36) below for impact at location (15, 15) Frequency (Hz) 0 100 200 300 400 500 Normalized Power 0 0.2 0.4 0.6 0.8 1 Frequency (Hz) 0 100 200 300 400 500 Phase Velocity (in./sec) 0 1000 2000 3000 Fig. 36.6 Averaged power spectrum over all impacts and sensors; dispersion curve for the flexural wave mode the smallest RMSE. Conceptually, this issue is more likely to arise when the source is near the sensors, as the solution to the smallest difference-distance is not likely the minimum RMSE when the source is far from the sensors. The average accuracy for all impact locations is assessed over the entire velocity range 1–3000 in./s, which corresponds to the phase velocities derived in [11] for a thin plate of these properties. This is done to verify that no particular velocity assumption results in low RMSE results for all impacts. The dispersion curve of the flexural wave mode in the 500 Hz bandwidth of interest is shown in Fig. 36.6 along with the averaged power spectrum over all impacts for all sensors.
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