526 A. Vemuri et al. Bayesian RPM estimate Accel 3 BS = 2048 - 87.2% overlap Instantaneous RPM (rpm) Time (sec) Frequency (Hz) Overlapping blocks Accel 3 Bayesian on Time Spectral map with BS = 2048 - 87.5% overlap 3 x 104 2 1 0 0 5 10 15 20 30 25 0.5 1.5 2.5 600 500 400 400 300 300 200 200 100 0 0 100 -10 -20 -30 -40 -50 -60 -70 -80 a b Fig. 46.5 (a) Spline fit to correct a small region and (b) final estimate over the time spectral map 10 15 20 25 30 0 0 0.5 1 1.5 2 2.5 3 Comparison of Initial Tach Vs. Bayesian estimate x 104 5 Time (sec) Bayesian Instantaneous speed estimate (rpm) Initial Tach Fig. 46.6 Final Bayesian estimate over the raw tachometer estimate interval between successive pulses is too small to be affected by the error (at high speeds or very low rate of change of speed or a combination of these), it would make sense to skip ‘n’ number of pulses to achieve a sufficiently large spacing. To demonstrate the reduction in error by the use of this method, the following error analysis is presented. t.2725/ t.2724/ D0:00244 s (46.A) t.2726/ t.2725/ D0:00238 s (46.B) Since the error in each time estimate can be ˙ t=2, the overall error in t.k/ – t .k 1/ for any ‘k’ can be ˙ t. Now, the true value of instantaneous RPM must satisfy the following, 60 t.k/ t .k 1/ C t .nC1/ True value of RPM 60 t.k/ t .k 1/ t .nC1/ (46.9)
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