Frequency-RPM map for order analysis
the frequency-RPM map matrix,
map = rpmfreqmap(
map, that results
from performing frequency analysis on the input vector,
measured at a set
rpm of rotational speeds expressed
in revolutions per minute.
fs is the sample rate
in Hz. Each column of
map contains root-mean-square
(RMS) amplitude estimates of the spectral content present at each
the short-time Fourier transform to analyze the spectral content of
rpmfreqmap(___) with no output
arguments plots the frequency map as a function of rotational speed
and time on an interactive figure. The plot is also known as a Campbell
Frequency-RPM Map of Chirp with 4 Orders
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 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 order-4 chirp has twice the amplitude of the others. 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; ph = 2*pi*cumtrapz(rpm/60)/fs; x = [1 1 2 1]*cos([o1 o2 o3 o4]'*ph);
Visualize the frequency-RPM map of the signal.
Frequency-RPM Map of Helicopter Vibration Data
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 frequency estimation.
load('helidata.mat') vib = detrend(vib);
Plot the nonlinear RPM profile. The rotor runs up until it reaches a maximum rotational speed of about 27,600 revolutions per minute and then coasts down.
plot(t,rpm) xlabel('Time (s)') ylabel('RPM')
Compute the frequency-RPM map. Specify a resolution bandwidth of 2.5 Hz.
[map,freq,rpmOut,time] = rpmfreqmap(vib,fs,rpm,2.5);
Visualize the map.
imagesc(time,freq,map) ax = gca; ax.YDir = 'normal'; xlabel('Time (s)') ylabel('Frequency (Hz)')
Repeat the computation using a finer resolution bandwidth. Plot the map using the built-in functionality of
rpmfreqmap. The gain in frequency resolution comes at the expense of time resolution.
Waterfall Plot of Frequency-RPM Map
Generate a signal that consists of two linear chirps and a quadratic chirp, all sampled at 600 Hz for 15 seconds. The system that produces the signal increases its rotational speed from 10 to 40 revolutions per second during the testing period.
Generate the tachometer readings.
fs = 600; t1 = 15; t = 0:1/fs:t1; f0 = 10; f1 = 40; rpm = 60*linspace(f0,f1,length(t));
The linear chirps have orders 1 and 2.5. The component with order 1 has half the amplitude of the other. The quadratic chirp starts at order 6 and returns to this order at the end of the measurement. Its amplitude is 0.8. Create the signal using this information.
o1 = 1; o2 = 2.5; o6 = 6; x = 0.5*chirp(t,o1*f0,t1,o1*f1)+chirp(t,o2*f0,t1,o2*f1) + ... 0.8*chirp(t,o6*f0,t1,o6*f1,'quadratic');
Compute the frequency-RPM map of the signal. Use the peak amplitude at each measurement cell. Specify a resolution of 6 Hz. Window the data with a flat top window.
[map,fr,rp] = rpmfreqmap(x,fs,rpm,6, ... 'Amplitude','peak','Window','flattopwin');
Draw the frequency-RPM map as a waterfall plot.
[FR,RP] = meshgrid(fr,rp); waterfall(FR,RP,map') view(-6,60) xlabel('Frequency (Hz)') ylabel('RPM') zlabel('Amplitude')
Interactive Frequency-RPM Map
Plot an interactive frequency-RPM map by calling
Load a file containing simulated vibrational data from an accelerometer placed in the cockpit
of a helicopter. The data is sampled at a rate of 500 Hz for 10 seconds.
Remove the linear trend in the data. Call
generate an interactive plot of the frequency-RPM map. Specify a frequency
resolution of 2
load helidata.mat rpmfreqmap(detrend(vib),fs,rpm,2)
Move the crosshair cursors in the figure to determine the RPM and the RMS amplitude at a frequency of 25 Hz after 5 seconds.
Click the Zoom X button in the toolbar to zoom into the time region between 2 and 4 seconds. A panner appears in the bottom plot.
Click the Waterfall Plot button in the toolbar to display the frequency-RPM map as a waterfall plot. For improved visibility, rotate the plot clockwise using the Rotate Left button three times. Move the panner to the interval between 4 and 6 seconds.
res — Resolution bandwidth
fs/128 (default) | positive scalar
Resolution bandwidth of the frequency-RPM map, specified as
a positive scalar. If
res is not specified, then
it to the sample rate divided by 128. If the signal
is not long enough, then the function uses the entire signal length
to compute a single frequency estimate.
comma-separated pairs of
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
'Scale','dB','Window','hann'specifies that the frequency map estimates are to be scaled in decibels and determined using a Hann window.
Amplitude — Frequency-RPM map amplitudes
'rms' (default) |
Frequency-RPM map amplitudes, specified as the comma-separated
pair consisting of
'Amplitude' and one of
'rms'— Returns the root-mean-square amplitude for each estimated frequency.
'peak'— Returns the peak amplitude for each estimated frequency.
'power'— Returns the power level for each estimated frequency.
OverlapPercent — Overlap percentage between adjoining segments
50 (default) | scalar from 0 to 100
Overlap percentage between adjoining segments, specified as
the comma-separated pair consisting of
a scalar from 0 to 100. A value of 0 means that adjoining segments
do not overlap. A value of 100 means that adjoining segments are shifted
by one sample. A larger overlap percentage produces a smoother map
but increases the computation time. See
Scale — Frequency-RPM map scaling
'linear' (default) |
Frequency-RPM map scaling, specified as the comma-separated
pair consisting of
'Scale' and either
'linear'— Returns a linearly scaled map.
'dB'— Returns a logarithmic map with values expressed in decibels.
Window — Analysis window
'hann' (default) |
Analysis window, specified as the comma-separated pair consisting
'Window' and one of these values:
'hann'specifies a Hann window. See
hannfor more details.
'chebwin'specifies a Chebyshev window. Use a cell array to specify a sidelobe attenuation in decibels. The sidelobe attenuation must be greater than 45 dB. If not specified, it defaults to 100 dB. See
chebwinfor more details.
'flattopwin'specifies a flat top window. See
flattopwinfor more details.
'hamming'specifies a Hamming window. See
hammingfor more details.
'kaiser'specifies a Kaiser window. Use a cell array to specify a shape parameter, β. The shape parameter must be a positive scalar. If not specified, it defaults to 0.5. See
kaiserfor more details.
'rectwin'specifies a rectangular window. See
rectwinfor more details.
'Window','chebwin' specifies a Chebyshev
window with a sidelobe attenuation of 100 dB.
a Chebyshev window with a sidelobe attenuation of 60 dB.
'Window','kaiser' specifies a Kaiser
window with a shape parameter of 0.5.
a Kaiser window with a shape parameter of 1.
map — Frequency-RPM map
Frequency-RPM map, returned as a matrix.
freq — Frequencies
Frequencies, returned as a vector.
rpm — Rotational speeds
Rotational speeds, returned as a vector.
time — Time instants
Time instants, returned as a vector.
res — Resolution bandwidth
Resolution bandwidth, returned as a scalar.
 Brandt, Anders. Noise and Vibration Analysis: Signal Analysis and Experimental Procedures. Chichester, UK: John Wiley & Sons, 2011.