Frequency-RPM map for order analysis
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Syntax
map = rpmfreqmap(x,fs,rpm)
map = rpmfreqmap(x,fs,rpm,res)
map = rpmfreqmap(___,Name,Value)
[map,freq,rpm,time,res]= rpmfreqmap(___)
rpmfreqmap(___)
Description
example
map = rpmfreqmap(x,fs,rpm)
returnsthe frequency-RPM map matrix, map
, that resultsfrom performing frequency analysis on the input vector, x
. x
ismeasured at a set rpm
of rotational speeds expressedin revolutions per minute. fs
is the sample ratein Hz. Each column of map
contains root-mean-square(RMS) amplitude estimates of the spectral content present at eachvalue of rpm
. rpmfreqmap
usesthe short-time Fourier transform to analyze the spectral content of x
.
example
map = rpmfreqmap(x,fs,rpm,res)
specifiesthe resolution bandwidth of the map in Hz.
example
map = rpmfreqmap(___,Name,Value)
specifiesoptions using Name,Value
pairs in addition tothe input arguments in previous syntaxes.
[map,freq,rpm,time,res]= rpmfreqmap(___)
returns vectors with thefrequencies, rotational speeds, and time instants at which the frequencymap is computed. It also returns the resolution bandwidth used.
example
rpmfreqmap(___)
with no outputarguments plots the frequency map as a function of rotational speedand time on an interactive figure. The plot is also known as a Campbelldiagram.
Examples
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Frequency-RPM Map of Chirp with 4 Orders
Open Live Script
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.
rpmfreqmap(x,fs,rpm)
Frequency-RPM Map of Helicopter Vibration Data
Open Live Script
Analyze simulated data from an accelerometer placed in the co*ckpit 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.
rpmfreqmap(vib,fs,rpm,1.5);
Waterfall Plot of Frequency-RPM Map
Open Live Script
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 rpmfreqmap
withoutoutput arguments.
Load a file containing simulated vibrational data from an accelerometer placed in the co*ckpit of a helicopter. The data is sampled at a rate of 500 Hz for 10 seconds. Remove the linear trend in the data. Call rpmfreqmap
to generate an interactive plot of the frequency-RPM map. Specify a frequency resolution of 2 Hz.
load helidata.matrpmfreqmap(detrend(vib),fs,rpm,2)
Move the crosshair cursors in the figure to determinethe RPM and the RMS amplitude at a frequency of 25Hzafter 5seconds.
Click the Zoom X button in the toolbar to zoom into the time region between 2 and 4seconds. 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 6seconds.
Input Arguments
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res
— Resolution bandwidth
fs
/128 (default) | positive scalar
Resolution bandwidth of the frequency-RPM map, specified asa positive scalar. If res
is not specified, then rpmfreqmap
setsit to the sample rate divided by128. If the signalis not long enough, then the function uses the entire signal lengthto compute a single frequency estimate.
Data Types: single
| double
Name-Value Arguments
Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN
, where Name
is the argument name and Value
is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose Name
in quotes.
Example: 'Scale','dB','Window','hann'
specifiesthat the frequency map estimates are to be scaled in decibels anddetermined using a Hann window.
Amplitude
— Frequency-RPM map amplitudes
'rms'
(default) | 'peak'
| 'power'
Frequency-RPM map amplitudes, specified as the comma-separatedpair consisting of 'Amplitude'
and one of 'rms'
, 'peak'
,or 'power'
.
'rms'
— Returns the root-mean-squareamplitude for each estimated frequency.'peak'
— Returns the peakamplitude for each estimated frequency.'power'
— Returns the powerlevel for each estimated frequency.
OverlapPercent
— Overlap percentage between adjoining segments
50 (default) | scalar from 0 to 100
Overlap percentage between adjoining segments, specified asthe comma-separated pair consisting of 'OverlapPercent'
anda scalar from 0 to 100. A value of 0 means that adjoining segmentsdo not overlap. A value of 100 means that adjoining segments are shiftedby one sample. A larger overlap percentage produces a smoother mapbut increases the computation time. See rpmordermap formore information.
Data Types: double
| single
Scale
— Frequency-RPM map scaling
'linear'
(default) | 'dB'
Frequency-RPM map scaling, specified as the comma-separatedpair consisting of 'Scale'
and either 'linear'
or 'dB'
.
'linear'
— Returns a linearlyscaled map.'dB'
— Returns a logarithmicmap with values expressed in decibels.
Window
— Analysis window
'hann'
(default) | 'chebwin'
| 'flattopwin'
| 'hamming'
| 'kaiser'
| 'rectwin'
Analysis window, specified as the comma-separated pair consistingof 'Window'
and one of these values:
'hann'
specifies a Hann window. See hann for more details.'chebwin'
specifies a Chebyshevwindow. Use a cell array to specify a sidelobe attenuation in decibels.The sidelobe attenuation must be greater than 45dB.If not specified, it defaults to 100dB. See chebwin for more details.'flattopwin'
specifies a flat topwindow. See flattopwin formore details.'hamming'
specifies a Hamming window. See hamming for 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, itdefaults to 0.5. See kaiser formore details.'rectwin'
specifies a rectangularwindow. See rectwin for moredetails.
Example: 'Window','chebwin'
specifies a Chebyshevwindow with a sidelobe attenuation of 100dB.
Example: 'Window',{'chebwin',60}
specifiesa Chebyshev window with a sidelobe attenuation of 60dB.
Example: 'Window','kaiser'
specifies a Kaiserwindow with a shape parameter of 0.5.
Example: 'Window',{'kaiser',1}
specifiesa Kaiser window with a shape parameter of 1.
Data Types: char
| string
| cell
Output Arguments
collapse all
map
— Frequency-RPM map
matrix
Frequency-RPM map, returned as a matrix.
freq
— Frequencies
vector
Frequencies, returned as a vector.
rpm
— Rotational speeds
vector
Rotational speeds, returned as a vector.
time
— Time instants
vector
Time instants, returned as a vector.
res
— Resolution bandwidth
scalar
Resolution bandwidth, returned as a scalar.
References
[1] Brandt, Anders. Noise and Vibration Analysis:Signal Analysis and Experimental Procedures. Chichester,UK: John Wiley & Sons, 2011.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Version History
Introduced in R2015b
expand all
R2023b: Use gpuArray
objects
The rpmfreqmap
function supports gpuArray
objects. You must have Parallel Computing Toolbox™ to use this functionality.
See Also
orderspectrum | ordertrack | orderwaveform | rpmordermap | rpmtrack | spectrogram | tachorpm
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