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# Sine Control: Amplitude Estimation Methods

Siemens Theorist

Sine Control: Amplitude Estimation Methods

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 Unit Under Test (UUT), 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 UUT actually experiences. If possible, this over testing should be avoided, or at a minimum, should be recorded.

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.

Sine Control Test Background

In a sine control test, sinusoidal vibrations are reproduced on a test object, or UUT, by a shaker system as shown in Figure 1. 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’.

Figure 1: Sine Control Vibration Control System: highlighted in green is the amplitude estimation step of control sine wave

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.

Harmonic Distortion

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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
• And more…

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 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 3, an averaged control spectrum is shown, which appears to be within the limits defined for the test.

Figure 3: A 2g 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.

Amplitude Estimation Methods

Four different methods of estimating the sine amplitudes are available in LMS Test.Lab 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 4.

Figure 4: Control channel estimators from LMS Test.Lab

In the Measurements area of the Sine Control worksheet, estimators for the resulting measurements can be selected as show in Figure 5. More than one estimator can be selected and stored during the test.

Figure 5: Estimator options for measurement channels in LMS Test.Lab

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.

In Figure 5, the THD (Total Harmonic Distortion) is not an estimation method, but a separate measurement that is covered later in this article.

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 6.

It is important to remember that the harmonic filtering/rejection is not changing the vibration levels that the test object experiences.  It is only affecting the amplitude of vibration reported via the software, and the behavior of the control algorithm.

Figure 6: Harmonic filtered for sine control

In reality, 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).  The method works well for common test objects, as well as with test objects (UUTs) 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 7.

Figure 7: Harmonic estimation method vibration spectrum from measurement channel

The data in Figure 7 will be used as a comparison for the other estimation methods in the rest of the article.

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.

RMS

The RMS estimator calculates the average of the squared values of all (N) time samples available for one period as shown in Figure 8:

Equation 8: 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 9. 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 9: 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.

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 10. Note that the absolute value of each sample is used, otherwise the average amplitude of the sine wave would be close to zero.

Figure 10: 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 11 shows the difference between average estimation method versus harmonic estimation method during the same sine control test.

Figure 11: 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.

Peak

The Peak estimator determines the maximum amplitude of the sample time signal as shown in Figure 12.

Figure 12: Peak amplitude estimator

If the system is very non-linear, with lots of 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 13.

Figure 13: Peak Estimator (Cyan) is higher than Harmonic Estimator (Magenta) for the same accelerometer during the same testIf 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 includes vibration from the main control frequency and all harmonics.

Looking only at the harmonic estimator amplitude can be misleading.  The amplitude would appear to be less because the harmonics are not included.

Control vs. Measurement Channels

There are other averaging methods available for measurement channels that are not available for control channels.  As shown in Figure 14, the averaging mode is user definable.

Figure 14: Advanced Control setup in LMS Test.Lab

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.

For a better description of how averaging works, see the Knowledge Base article on Averaging methods’.

Besides the vibration spectrum itself, there are other measurements that can be calculated during the sine control test.

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 can have a value between zero and 1 as shown in Figure 15.

Figure 15: 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.

FRF

Dividing the spectra obtained during a sweep obtains the Frequency Response Functions (FRFs) for a sine test as shown in Figure 16.

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.

Figure 16: Frequency Response Function (FRF) between control signal voltage and accelerometer

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.

In the LMS Test.Lab Documentation, there is extensive documentation in the “LMS Test.Lab Sine Control” manual.  The documentation is located in “Start->Programs-> LMS Test.Lab 17A->Documentation”.

Conclusion

The amplitude estimation method in a sine control test can often be overlooked or taken for granted.  It is helpful to understand the different methods, and understand that the Harmonic Estimation method may report lower amplitudes than the Unit Under Test actually experiences.

Some best practices:

• Measurement Channels - It is also 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.
• Control Channels – Use the harmonic estimator whenever possible. Selecting the harmonic estimator facilitates control, even if the presence of high levels of harmonic distortion.

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Siemens Experimenter

I really liked this article.  On the surface "sine control" seems simple, but this highlights the complexities truly in play.  I understand better why a closed loop controller needs to be involved, and why the amplitude estimation technique makes a difference.

The most provocative part for me was when I read the statement: "a non-linear phenomenon, which in this case means that exciting at a specific frequency produces responses at that frequency and other frequencies."  By my personal education and experience - I tend to only think of non-linearity in the time domain context only.  That statement helps me think about the effect of nonlinearities in the frequency domain; in a different way than I had before.

The more and more I think about that statement, the more I buy it and the more I like it.  I think I got a little bit smarter today :-)

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