In closed loop sine control testing, the estimation method of the sine amplitude is often overlooked, or taken for granted. Typically a filter, which tracks the control frequency, is used to determine the sine wave amplitude. Because the filter ignores amplitude from any harmonics of the control drive frequency, the displayed amplitude often under represents the vibration that the actual test object, or Device Under Test (DUT), sees during the test. This filter is often referred to as a harmonic tracking filter.
This situation, where the harmonically estimated amplitude is lower, can happen on both control and measurement accelerometers. It is important to understand that the reported amplitudes can be lower than the actual vibration amplitude that the DUT actually experiences. Measuring other estimator methods in parallel (peak, RMS, average) the true vibration levels can be better understood.
In this article, different estimation methods for the sine amplitude will be discussed, including how estimators work, when to use them, and how to interpret vibration levels from different methods.
Contents: 1. Sine Control Background 2. Harmonic Distortion 3. Amplitude Estimation Methods 3.1 Harmonic Filter 3.2 RMS 3.3 Average 3.4 Peak 4. Control vs. Measurement Channels 5. Additional Measurement Functions 5.1 Total Harmonic Distortion (THD) 5.2 Frequency Response Function (FRF) 6. Conclusion
1. Sine Control Test Background
In a sine control test, sinusoidal vibrations are reproduced on a test object, or DUT, by a shaker system as shown in Figure 1.
Figure 1: Sine Control Vibration Control System: highlighted in green is the amplitude estimation step of control sine wave
Typically, the vibration levels being reproduced are monitored at either one or more key accelerometer control locations, and the drive output to the shaker is constantly updated to achieve the desired vibration levels. This constant updating is considered a ‘closed loop’.
The desired vibration levels are defined by a reference control profile. This profile contains two pieces of information:
Frequency - A sine tone is swept between the lowest frequency of interest and the highest frequency of interest as dictated by the vibration control profile. This is defined in units of Hertz.
Amplitude - The profile also specifies the vibration amplitude to be achieved at each frequency, typically specified in g’s of acceleration.
This profile may come from industry standards, or may be developed from measured field data.
In a closed loop vibration control test, accelerometers may play two different roles – control or measurement:
Control accelerometers are actively monitored during the test, and the drive is updated based on the levels seen by these accelerometers.
Measurement accelerometers have the data collected and analyzed, but are not used in the control loop.
A key step in the process is to determine the amplitude of the reproduced sine wave on the object, which is highlighted in green in Figure 1. This is not always straightforward due to harmonics and other noise.
Part of the difficulty of determining the amplitude is due to harmonic distortion. An environment dominated by sine vibration is characterized by a fundamental frequency and harmonics (multiples) of that fundamental. The harmonics that are generated during a sine test are referred to as harmonic distortion, as shown in Figure 2.
Figure 2: Vibration spectrum during sine control test with harmonic distortion
Where do these harmonics come from, when ostensibly, only one frequency is being input into the structure and controlled?
Harmonics are created when the sine wave vibration is not matching an ideal sine wave. For example, a shaker system may not move as a perfect sine wave due to:
Friction or rubbing in the shaker armature or bearings
Armature resonance
Moments created by a bent or bowed shaker armature
Moments caused by the test article center of gravity not directly over the center of shaker, which causes the shaker armature not to move straight up and down
Loose parts rattling
And more…
A illustration of a Device Under Test (DUT) mounted on and off the center of gravity on a shaker is shown in Figure 3.
Figure 3: Mounting the test article center of gravity aligned with the center of a shaker (left) produces less harmonic distortion compared to mounting the test article off center (right)
A less than perfect sine wave generates harmonics of the main frequency, thus creating harmonic distortion.
Harmonic distortion is a non-linear phenomenon, which in this case means that exciting at a specific frequency produces responses at that frequency and other frequencies. When harmonic distortion is combined with lightly damped test object resonances, vibration levels can suddenly change at given test frequency. This is challenging for the sine control loop.
In defining a closed loop Sine Control test in Simcenter Testlab (formerly called LMS Test.Lab), the operator must decide how the amplitude of the sine control frequency and measurement channels are to be calculated. This is done by selecting one of the estimator (Harmonic, RMS, Average, or Peak) methods.
The selected amplitude estimator impacts the control loop, the success of completing the test without interruption, and the final analysis of the all the measured data. In Figure 4, an averaged control spectrum is shown, which appears to be within the limits defined for the test.
Figure 4: A 2 g sine control reference profile and control spectrum results within test tolerance limits
However, depending on the amplitude estimation method selected, the actual vibration levels experienced by the test object could be different than what is shown on the screen.
3. Amplitude Estimation Methods
Four different methods of estimating the sine amplitudes are available in Simcenter Testlab Vibration Control. They include:
Harmonic Filter – Default setting, filtered to the control frequency
RMS - Sine amplitude is RMS acceleration value over one period, data not filtered to the control frequency
Average - Sine amplitude is Average acceleration value over one period, data not filtered to the control frequency
Peak – Sine amplitude is maximum acceleration value over one period, data not filtered to the control frequency
Only one estimation method can be used when performing closed loop control with the control accelerometer during a sine test. However, all four methods can be used in reporting the amplitudes of the control and measurement channels.
The control estimator is selected in the right-hand window pane of the Sine Setup page as shown in Figure 5.
Figure 5: Control channel estimators from Simcenter Testlab
In the Measurements area of the Sine Control worksheet, estimators for the resulting measurements can be selected as show in Figure 6. More than one estimator can be selected and stored during the test.
Figure 6: Estimator options for measurement channels in Simcenter Testlab
Even if the control is being done with a harmonic estimator, it is often helpful to look at the results via the other estimator methods.
If all the data collected was a pure sine wave with no noise, all the estimator methods would yield the same result. In a real test, there is bound to be noise on top of the sinusoidal data. This noise is handled differently by the methods which yields different amplitude results.
Note that in Figure 6, the THD (Total Harmonic Distortion) is not an estimation method, but a separate measurement that will be calculated and stored during the measurement.
3.1 Harmonic Filtered
Harmonic Sine estimation is the default method in Sine Control, and is commonly used. The harmonic filter method, which works in the time domain, offers a reliable estimate for the amplitude of the fundamental frequency and provides harmonic rejection. It is helpful to think of the harmonic estimator as using a tracking filter on the data that is always centered on the control frequency as shown in Figure 7.
Figure 7: Harmonic filtered for sine control
The harmonic estimator uses the known sine wave output of the DAC and a series of equations to do a least squares fit to determine the amplitude. See the online help (C:\Program Files (x86)\LMS\LMS Test.Lab 16A\central\Help – File:LMS Test.Lab Sine Control) OR (C:\Program Files (x86)\Simcenter\Testlab 18\central\Help\EnvTestingSine.chm). The method works well for common test objects, as well as with test objects (DUTs) that have a very non-linear responses with high amounts of harmonic distortion.
A vibration spectrum measurement calculated with harmonic amplitude estimation during a sine vibration control test is shown in Figure 8.
Figure 8: Harmonic estimation method vibration spectrum from measurement channel
The harmonic filter method preserves magnitude and phase responses. This can be useful when doing transfer functions using sine dwell or follow-on operational deflection shape work.
Using the harmonic estimator for control is the least conservative test from a vibration point of view. In this case, least conservative means that the total vibration levels of this test will be typically higher compared to using the RMS, average, or peak estimators for control. Because the harmonic estimator ignores all noise and harmonics outside of the drive frequency, the drive voltages will be the highest to achieve the control frequency target vibration.
The data in Figure 8 will be used as a comparison for the other estimation methods in the rest of the article.
3.2 RMS
The RMS estimator calculates the average of the squared values of all (N) time samples available for one period as shown in Figure 9:
Figure 9: RMS Estimator
This RMS average is then multiplied by the factor √2 (square root of 2, or 1.414) which is the ratio of the Peak to RMS value for an ideal sine wave. Even though the method is called RMS, the software displays a peak value derived from this RMS method.
A comparison of RMS amplitude estimation versus harmonic amplitude estimation is shown in Figure 10. For this particular sine test, the results of the harmonic estimator and RMS estimator are very similar, except at the frequency circled in green.
Figure 10: Comparison of RMS Estimator to Harmonic Estimator, results are similar at most frequencies. Differences are circled in green.
The RMS method takes into account the complete signal, including the fundamental signal and its harmonics. In this test, the RMS estimator had higher values at some frequencies than the Harmonic estimator.
3.3 Average
The Average estimator calculates the linear average of the absolute values of all (N) time samples available for one period as shown in Figure 11. Note that the absolute value of each sample is used, otherwise the average amplitude of the sine wave would be close to zero.
Figure 11: Average Sine Estimator
This average is then multiplied by the factor Pi/2, where Pi = 3.1415926…, which is the ratio of the peak to average value for an ideal sine wave. The software will display a peak vibration derived from the average estimator method.
Figure 12 shows the difference between average estimation method versus harmonic estimation method during the same sine control test.
Figure 12: Harmonic versus Average Sine Estimator
The Average method, similar to the RMS method, takes into account the complete signal, including the fundamental signal and its harmonics. In this test, the Average estimator had both higher and lower vibration values at some frequencies than the Harmonic estimator.
3.4 Peak
The Peak estimator determines the maximum amplitude of the sample time signal as shown in Figure 13.
Figure 13: Peak amplitude estimator
If the system is non-linear, with harmonic distortion, this peak value may surpass the RMS or Harmonic Estimator values by a considerable margin. An example of the difference between peak and harmonic estimation is shown in Figure 14.
Figure 14: Peak estimator (Cyan) is higher than harmonic estimator (Magenta) for the same accelerometer during the same test
If the peak value and the harmonic estimator amplitudes are very different, this may indicate that there is lot of harmonic content. This may explain difficulties experienced in performing the control during the sine test if a harmonic estimator method is not used.
More importantly, the peak indicates the total amplitude of the vibration that the test object experiences. The peak estimator amplitude includes vibration from the main control frequency, all harmonics, and any noise from rattles, etc.
Using the peak estimator for control is the most conservative test from a vibration point of view. In this case, most conservative means that the vibration levels of this test will be typically higher compared to using harmonic, average, or peak estimators for control. Because the peak amplitude estimation method includes all noise and harmonics outside of the drive frequency, the drive voltages will be the lowest to achieve the control frequency target vibration.
Because the peak estimator includes all content in the vibration signal (including noise), the peak control may not be always be stable compared to the harmonic estimator (which considers only the control frequency and rejects all other noise).
4. Control vs. Measurement Channels
There are other averaging methods available for measurement channels that are not available for control channels. As shown in Figure 15, the averaging mode is user definable.
Figure 15: Advanced Control setup in Simcenter Testlab
These additional averaging methods are available to help facilitate matching averaging methods used in collection of the original field data. By using a similar averaging method, the comparison between the test and field data should be more straightforward.
Besides the vibration spectrum itself, there are other measurements that can be calculated during the sine control test.
5.1 Total Harmonic Distortion (THD)
Total harmonic distortion (THD) is a function versus frequency. It is the ratio of the energy in the measured signal that is not related to the control sine tone (Equation 1):
Equation 1: Total Harmonic Distortion (THD)
THD has a value between zero and 1 as shown in Figure 16.
Figure 16: Total Harmonic Distortion
A value close to zero means that the signal is approaching a pure or ideal sine wave. A value close to 1 means that the energy component of the signal due to the control sine tone is very limited, and that there is a high amount of harmonic distortion.
Dividing the spectra obtained during a sweep obtains the Frequency Response Functions(FRFs) for a sine test as shown in Figure 17.
Figure 17: Frequency Response Function (FRF) between control signal voltage and accelerometer
The FRF function obtained in vibration control is not necessarily a classical FRF. A classical FRF is the ratio of an output divided by an input. For example, for a mechanical system, an input is a force, and a response is an acceleration. The units of the FRF would be Acceleration/Force.
In Sine vibration control, this definition is not enforced. A FRF could be the ratio of two accelerometers (which are really both outputs) on the structure, which would be unit less. It could also be the ratio of an accelerometer (g) divided by the output drive signal (Volts), for FRF units of g/V.
If different estimators are active, different FRFs will result and the annotation will indicate which spectra were used to obtain the FRF.
Note: As only the harmonic estimator yields phase information, all FRFs obtained from spectra originating from other estimators will only contain amplitude information.
The amplitude estimation method in a sine control test can often be overlooked or taken for granted. There are four estimation methods (harmonic, average, RMS, and peak):
Control Channels: Use the harmonic estimator whenever possible. Selecting the harmonic estimator facilitates control, even if the presence of high levels of harmonic distortion. It is the only method that calculates phase in additional to amplitude. Harmonic is the most conservative of the four methods - the drive voltage levels for harmonic are higher than the other methods. This causes higher amounts of vibration on the test article for the harmonic estimator when compared to the other methods. Peak estimation method is the least conservative, drive levels are lower than the other methods and the total vibration on the test article is the lowest.
Measurement Channels: It is a good practice to calculate and store measurements with all four estimation methods. This way, both the total vibration (peak) and harmonic vibration can be understood easily.
It is helpful to understand the different methods and how they are calculated. A minimum, it is important to understand that the Harmonic Estimation method may report lower amplitudes than the Device Under Test actually experiences.
