This example shows how to isolate a shaft fault from simulated measurement data for machines with varying rotation speeds and develop features that can help detect the fault.
The example assumes that you are already familiar with basic operations with the app. For a tutorial on using the app, see Identify Condition Indicators for Predictive Maintenance Algorithm Design.
The following figure illustrates a drivetrain with six gears. The motor for the drivetrain is fitted with a vibration sensor and a tachometer. In this drivetrain:
Gear 1 on the motor shaft meshes with gear 2 with a gear ratio of 17:1.
The final gear ratio, or the ratio between gears 1 and 2 and gears 3 and 4, is 51:1.
Gear 5, also on the motor shaft, meshes with gear 6 with a gear ratio of 10:1.
Twenty simulated machines use this drivetrain. Each machine operates with a nominal rotation speed within 1 percent of the design rotation speed of 1800 rpm. Therefore, the nominal rotation speed for each machine ranges between 1782 rpm and 1818 rpm.
Ten of the machines include a fault developing on the shaft of gear 6.
To start, load the data into your MATLAB® workspace and open Diagnostic Feature Designer.
load(fullfile(matlabroot, 'toolbox', 'predmaint', 'predmaintdemos', ... 'motorDrivetrainDiagnosis', 'machineData3'), 'motor_data') diagnosticFeatureDesigner
Import the data. To do so, in the Feature Designer tab, select
Import > Import Multi-Member Ensemble and then choose
motor_data as your ensemble variable.
Complete the import process in the subsequent dialog boxes by accepting the
default configuration and variables. The ensemble includes two data
Signal/vib, which contains the vibration signal, and
Tacho/pulse, which contains the tachometer pulses. The ensemble also
includes the condition variable
In the Data Browser, select both signals and plot them together using Signal Trace.
Note that the
Tacho pulse clusters widen with each pulse
because of rotation-speed variation. If the
Tacho pulses are not visible,
click Group Signals twice to bring the
to the front.
Now group the data by fault condition by selecting Ensemble View Preferences > Group by "Health". Use the panner to expand a slice of the signal.
The plot shows small differences in the peaks of the groups, but the signals look similar otherwise.
Time-synchronous averaging (TSA) averages a signal over one rotation, substantially reducing noise that is not coherent with the rotation. TSA-filtered signals provide the basis for much rotational-machinery analysis, including feature generation.
In this example, the rotation speeds vary within 1 percent of the design value. You
capture this variation automatically when you use the
Tacho signal for
To compute the TSA signal, select Filtering & Averaging > Time-Synchronous Signal Averaging. In the dialog box:
Confirm the selection in Signal.
In Tacho Information, select Tacho signal and confirm the signal selection.
Select Compute nominal speed (RPM). This option results in
the computation of a set of machine-specific nominal speeds, or operating points, from
Tacho signal. You can use this information when you perform
follow-on processing, such as TSA signal filtering. Since your tachometer variable is
Tacho, the app stores these values as the condition variable
Accept all other settings.
The TSA-averaged signals are cleaner than the raw signals. The peak heights are clustered by health condition, just as they were before, but the plot does not show enough information to indicate the source of the fault.
The TSA filtering options in the app all start with a TSA signal and subtract various components from that signal to produce a filtered signal. Each filtered signal type yields unique features that you can use to detect specific faults in the gear train. One of these filtered signals is the difference signal. The TSA difference signal contains the components that remain after you subtract all of the components that are due to the drivetrain design for components that are not in your area of interest. Specifically, the TSA difference-signal processing subtracts:
Shaft frequency and harmonics
Gear-meshing frequencies and harmonics
Sidebands at the gear-meshing frequencies and their harmonics
For this example, you are interested in the mesh defect between gear 5 and gear 6. To focus on signals arising from this defect, filter out signals associated with the other gears. To do so, use the successive gear ratios described in the model description as you move down the drivetrain. The ratio between gears 1 and 2 is 17. The ratio between gears 1/2 and 3/4 is 51. These ratios become your rotation orders.
To compute the TSA difference signal, select Filtering & Averaging > Filter Time-Synchronous Averaged Signals. In the dialog box:
Set Signal to the TSA signal
In Signals to Generate, select Difference signal.
In Speed Settings, select Nominal rotation speed
(RPM) and then
Confirm that Domain is
Set Rotation orders to
When you group the plotted data by
Health, you also see the
Tacho_rpm in the option list.
The resulting plot shows a clear oscillation. Group the data by
faulty labels. The oscillation is
present only for the
faulty machines. Using the data cursors, you can
show that the period of this oscillation is about 0.0033 seconds. The corresponding
frequency of the oscillation is about 303 Hz or 18,182 rpm. This frequency has roughly a
10:1 ratio with the primary shaft speed of 1800 rpm, and is consistent with the 10:1 gear
ratio between gear 5 and gear 6. The difference signal therefore isolates the source of the
In the preceding sections, you use tachometer pulses to precisely generate TSA signals and difference signals. If you do not have tachometer information, you can use a constant rpm value to generate these signals. However, the results are less precise.
See if you can isolate the defect without using the
Compute both the TSA signal and the difference signal with an ensemble-wide rotation speed
of 1800 rpm.
The new TSA signal has the name
Signal_tsa_1/vib. As the plot shows,
generating a TSA signal without tachometer information produces a less clear signal then
generating a signal with tachometer information.
Compute the difference signal using
Signal_tsa_1/vib and the
Constant rotation speed (RPM) setting.
In the resulting plot, you can still see the oscillation for the
faulty set of machines, but as with the TSA signal, the oscillation is
much less clear than the previous difference signal. The unaccounted-for 1-percent rpm
variation has a significant impact on the results.
Use the TSA and difference signals
Signal_tsa_tsafilt/x_Difference to compute time-domain rotational
To compute these features, select Time-Domain Features > Rotating Machinery Features. In the dialog box, select the signals to use for TSA signal and Difference signal and then select all the feature options that use TSA or difference signals.
The resulting histogram plots indicate good separation between
faulty groups for all of the
TSA-signal-based features, and for FM4 (kurtosis) in the difference-signal-based features.
Since the difference signal displays a clear oscillation that is limited to the
faulty group, spectral features are also likely to differentiate well
faulty groups. To calculate
spectral features, you must first compute a spectral model. To do so, click
Spectral Estimation > Order Spectrum. As before, select your
difference signal as Signal and your tachometer signal as
The resulting plot displays the oscillation of the defect as the first peak in the plot at roughly order 10.
Compute the spectral features by clicking Spectral Features. In the dialog box:
Confirm the selection for Spectrum.
Move the order range slider to cover the range from 0 to 200. As you move the slider, the order spectrum plot incorporates the change.
The resulting histograms indicate good differentiation between groups for
shows a small amount of group overlap.
Rank the features using the default T-test ranking. To do so, click Rank
Features and select
FeatureTable1. The app
automatically ranks the features and plots the scores.
the two top places with scores significantly higher than the other features.
take the third and fourth places with scores much lower than the spectral features,
but still significantly higher than the remaining features.
The remaining features are likely not useful for detecting faults of this type.
Using these high-ranking features, you could now move on to export the features to Classification Learner for training or to your MATLAB workspace for algorithm incorporation.