528 A. Vemuri et al. Instantanneous RPM estimate skipping 18 pulses Instantanneous RPM estimate skipping 18 pulses Instantanneous speed (rpm) Instantanneous speed (rpm) 2.75 2.65 2.55 2.45 2.4 15 15.5 16.5 17.5 Time(sec) Time(sec) 16 17 18 2.5 2.6 2.7 x 104 x 104 2.54 2.52 2.5 2.48 2.46 X: 15.25 Y: 2.482e+04 X: 15.26 Y: 2.482e+04 2.44 15.245 15.25 15.255 15.26 15.265 a b Fig. 46.8 (a) Instantaneous RPM estimate with 18 pulses skipped and (b) reduction in fluctuations with 18 pulses skipped Fig. 46.9 FromTop to Bottom: RPM estimation procedure with no pulses skipped; RPM estimation with 3 pulse skipped starting with the first, second, third and fourth pulses. Vertical bars denote the time instances to which the RPM has been assigned and the small explosions denote the time instances of zero crossings; Different colors represent different initiating pulses Skipping ‘ n’ pulses provides a smooth instantaneous speed curve that can be seen to have lesser fluctuations. However, a lot of data is being discarded in the process which can be used for a statistical advantage. There is no reason to believe that it is beneficial to start with one particular pulse and skip ‘n’ pulses rather than to start with the next pulse and skip ‘ n’ pulses and so on to starting with the .n 1/ th pulse and skip ‘n’ pulses. Thus, there are nC1estimates of speed over the same data set when skipping the same ‘ n’ number of pulses. This is represented pictorially in Fig. 46.9. There is very little difference in the speed profile generated from these cases. One use that immediately comes to mind is to average the estimates for a smooth RPM curve. However, this cannot be done straight away as the time instances associated with the estimated speeds are not the same for all the curves. Different estimates of speed are assigned to different time instances and a logical way to use all of this information is to combine them as shown in Fig. 46.10. This also provides the benefit of obtaining an instantaneous speed estimate at intervals consistent with the case where every pulse is used without skipping. This is very convenient as the instantaneous velocity will now be estimated at the same sampling times as any other response data that is recorded. Clearly, the corresponding curve from
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