ordertrack

Create a simulated signal sampled at 600 Hz for 5 seconds. The system that is being tested increases its rotational speed from 10 to 40 revolutions per second (or, equivalently, from 600 to 2400 revolutions per minute) during the observation period.

Generate the tachometer readings.

fs = 600;
t1 = 5;
t = 0:1/fs:t1;

f0 = 10;
f1 = 40;
rpm = 60*linspace(f0,f1,length(t));

The signal consists of four harmonically related chirps with orders 1, 0.5, 4, and 6. The amplitudes of the chirps are 1, 1/2, √2, and 2, respectively. To generate the chirps, use the trapezoidal rule to express the phase as the integral of the rotational speed.

o1 = 1;
o2 = 0.5;
o3 = 4;
o4 = 6;

a1 = 1;
a2 = 0.5;
a3 = sqrt(2);
a4 = 2;

ph = 2*pi*cumtrapz(rpm/60)/fs;

x = [a1 a2 a3 a4]*cos([o1 o2 o3 o4]'*ph);

Extract and visualize the magnitudes of the orders.

ordertrack(x,fs,rpm,[o1 o2 o3 o4])

Create a simulated vibration signal consisting of two crossing orders corresponding to two different motors. The signal is sampled at 300 Hz for 3 seconds. The first motor increases its rotational speed from 10 to 100 revolutions per second (or, equivalently, from 600 to 6000 revolutions per minute) during the measurement. The second motor increases its rotational speed from 50 to 70 revolutions per second (or 3000 to 4200 revolutions per minute) during the same period.

fs = 300;
nsamp = 3*fs;

rpm1 = linspace(10,100,nsamp)'*60;
rpm2 = linspace(50,70,nsamp)'*60;

The measured signal is of order 1.2 and amplitude 2√2 with respect to the first motor. With respect to the second motor, the signal is of order 0.8 and amplitude 4√2.

x = [2 4]*sqrt(2).*cos(2*pi*cumtrapz([1.2*rpm1 0.8*rpm2]/60)/fs);

Make the first motor excite a resonance at the middle of the frequency range.

rs = [1+1./(1+linspace(-10,10,nsamp).^4)'/2 ones(nsamp,1)];

x = sum(rs.*x,2);

Visualize the orders using rpmfreqmap.

rpmfreqmap(x,fs,rpm1)

Compute the order magnitudes for both motors as a function of RPM. Use the Vold-Kalman algorithm to decouple the crossing orders.

ordertrack(x,fs,[rpm1 rpm2],[1.2 0.8],[1 2],Decouple=true)

Analyze simulated data from an accelerometer placed in the cockpit of a helicopter.

Load the helicopter data. The vibrational measurements, vib, are sampled at a rate of 500 Hz for 10 seconds. Inspection of the data reveals that it has a linear trend. Remove the trend to prevent it from degrading the quality of the order estimation.

load("helidata.mat")

vib = detrend(vib);

Compute the order-RPM map. Specify an order resolution of 0.005.

[map,order,rpm,time,res] = rpmordermap(vib,fs,rpm,0.005);

Compute and plot the average order spectrum of the signal. Find the three highest peaks of the spectrum.

[spectrum,specorder] = orderspectrum(map,order);

[~,pkords] = findpeaks(spectrum,specorder,SortStr="descend",Npeaks=3);

findpeaks(spectrum,specorder,SortStr="descend",Npeaks=3)

Track the amplitudes of the three highest peaks.

ordertrack(map,order,rpm,time,pkords)