tachorpm

Extract RPM signal from tachometer pulses

Description

rpm = tachorpm(x,fs) extracts a rotational speed signal, rpm, from a tachometer pulse signal vector, x, that has been sampled at a rate of fs Hz.

If you do not have a tachometer pulse signal, use rpmtrack to extract rpm from a vibration signal.

[rpm,t,tp] = tachorpm(x,fs) also returns the time vector, t, and the detected pulse locations, tp.

[___] = tachorpm(x,fs,Name,Value) specifies options using Name,Value pairs and any of the previous syntaxes.

example

tachorpm(___) with no output arguments plots the generated RPM signal and the tachometer signal with the detected pulses.

Examples

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Load a simulated tachometer signal sampled at 300 Hz.

Compute and visualize the RPM signal using tachorpm with the default values.

tachorpm(Yn,fs) Increase the number of fit points to capture the RPM peak. Too many points result in overfitting. Verify this result by zooming in on the area around the peak.

tachorpm(Yn,fs,'FitPoints',600)

axis([0.47 0.65 1320 1570]) Choose a moderate number of points to obtain a better result.

tachorpm(Yn,fs,'FitPoints',100) Add white Gaussian noise to the tachometer signal. The default pulse-finding mechanism misses pulses and returns a jagged signal profile. Verify this result by zooming in on a two-second time interval.

rng default
wgn = randn(size(Yn))/10;
Yn = Yn+wgn;

[rpm,t,tp] = tachorpm(Yn,fs,'FitPoints',100);

figure
plot(t,Yn,tp,mean(interp1(t,Yn,tp))*ones(size(tp)),'+')
hold on
sl = statelevels(Yn);
plot(t,sl(1)*ones(size(t)),t,sl(2)*ones(size(t)))
hold off
xlim([9 10]) Adjust the state levels to improve the pulse finding.

sl = [0 0.75];

[rpm,t,tp] = tachorpm(Yn,fs,'FitPoints',100,'StateLevels',sl);

plot(t,Yn,tp,mean(interp1(t,Yn,tp))*ones(size(tp)),'+')
hold on
plot(t,sl(1)*ones(size(t)),t,sl(2)*ones(size(t)))
hold off
xlim([9 10]) Input Arguments

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Tachometer pulse signal, specified as a row or column vector.

Example: double(chirp((-1.5:1/2e2:1.5),14,1.1,8,'quadratic')>0.98) resembles a tachometer signal, sampled for three seconds at 200 Hz, and obtained during a quadratic run-up/coast-down test.

Sample rate, specified as a positive scalar expressed in Hz.

Name-Value Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: 'PulsesPerRev',3,'OutputFs',1e3 specifies that there are three tachometer pulses per revolution and that the returned RPM signal is to be sampled at 1 kHz.

Number of tachometer pulses per revolution, specified as the comma-separated pair consisting of 'PulsesPerRev' and a real scalar.

State levels used to identify pulses, specified as the comma-separated pair consisting of 'StateLevels' and a two-element real vector. The first element of the vector corresponds to the low-state level and the second element corresponds to the high-state level. Choose the state levels so that all pulse edges cross within 10% of both of them. If this option is not specified, then tachorpm computes the levels automatically using the histogram method, as in the statelevels function.

Output sample rate, specified as the comma-separated pair consisting of 'OutputFs' and a real scalar.

Fitting method, specified as the comma-separated pair consisting of 'FitType' and one of either 'smooth' or 'linear'.

• 'smooth' — Fit a least-squares B-spline to the pulse RPM values.

• 'linear' — Interpolate linearly between pulse RPM values.

B-spline breakpoints, specified as the comma-separated pair consisting of 'FitPoints' and a real scalar. The number of breakpoints is a trade-off between curve smoothness and closeness to the underlying data. Choosing too many breakpoints can result in overfitting. This argument is ignored if 'FitType' is set to 'linear'.

Output Arguments

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Rotational speeds, returned as a vector expressed in revolutions per minute. rpm has the same length as x.

Time vector, returned as a vector of positive values expressed in seconds.

Pulse locations, returned as a vector of positive values expressed in seconds.

Algorithms

The tachorpm function performs these steps:

1. Uses statelevels to determine the low and high states of the tachometer signal.

2. Uses risetime and falltime to find the times at which each pulse starts and ends. It then averages these readings to locate the time of each pulse.

3. Uses diff to determine the time intervals between pulse centers and computes the RPM values at the interval midpoints using RPM = 60 / Δt.

4. If 'FitType' is specified as 'smooth', then the function performs least-squares fitting using splines. If 'FitType' is specified as 'linear', then the function performs linear interpolation using interp1.

 Brandt, Anders. Noise and Vibration Analysis: Signal Analysis and Experimental Procedures. Chichester, UK: John Wiley & Sons, 2011.

 Vold, Håvard, and Jan Leuridan. “High Resolution Order Tracking at Extreme Slew Rates Using Kalman Tracking Filters.” Shock and Vibration. Vol. 2, 1995, pp. 507–515.