532 A. Vemuri et al. Comparison of Raw Tach estimate Vs. Adaptive nth pulse estimate Instantaneous speed estimate (rpm) 3 2.5 2 1.5 1 0.5 0 0 5 10 15 20 Time(sec) 25 30 x 10 4 Raw Tach Adaptive nth pulse Fig. 46.14 Averaged nth pulse estimate vs raw tachometer estimate 46.4 Comparison and Other Examples There is no way to assert any degree of confidence in these algorithms as the true value of the instantaneous speed is not known. However, the two algorithms operate on independent philosophies. If they generate curves that are within bounds of the raw curve and are in close agreement with each other, it can be safe to proceed with one of them for further analysis. This section contains comparisons between the results from Bayesian and nth pulse algorithms for various systems. Figure 46.15 shows the comparison for the vacuum cleaner data. The overall error stays within 2 % throughout the data and is mostly within 0.2 %. The error is large initially when the order is not dominant enough to be estimated accurately by the Bayesian algorithm. This happens because the algorithm works on the criterion of amplitude of vibration. Figure 46.16 shows the results and comparison for data from a 6 cylinder engine powertrain. In contrast to the vacuum cleaner data, this system operates at very low speeds and has a low slew rate. The error mostly stays within 0.1 % and 1.5RPM. Figure 46.17 shows the results and comparison for data from a rotor rig. The overall error stays within 0.2 % and within 15 RPM for most of the data. As all the methods involve assumptions, comparison to the true value of instantaneous speed cannot be made. It can be seen that the estimates from the Bayesian and Adaptive nth Pulse Algorithms agree to within satisfactory limits. Moreover, they provide a smooth and precise estimate which stays within bounds of the raw estimate. 46.5 Conclusion The conventional way of estimating instantaneous speed involves fitting a curve (spline) to an initial estimate for which each consecutive pulse is considered in the formulation. The sampling process and error in interpolation give rise to unacceptable fluctuations in the instantaneous speed profile. The Adaptive nth Pulse Algorithm is an effective new technique which can address this issue. The main idea behind the algorithm is to increase the absolute time interval over which a single speed estimate is being calculated so that it is not affected by the errors (zero crossing uncertainty). The number of pulses to be skipped for different parts of the data has to be regulated according to the speed and rate of change of speed. This optimization is achieved by matching the time interval between estimates to a desired time resolution. The averaging technique presented generates a smooth curve which does not require a spline fit. The combination technique generates a curve with high signal to noise ratio to which a spline can be fit easily. It is a fairly simple procedure to apply and the operator/user does not have to be skilled in rotating systems analysis to understand it.
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