Simcenter Testing Solutions OMA in Simcenter Testlab

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OMA in Simcenter Testlab

Snowboarding gif

Operational Modal Analysis (OMA) is a technique used to identify the modal parameters (natural frequencies, damping, and mode shapes) of a structure or object during operation.  By measuring and understanding the modal parameters, engineers, architects and designers can help create structures, machines and devices that perform better, last longer, and are more comfortable for their users or occupants.  

This article serves as a follow-up to this introductory OMA article, and will provide a walk-thru of the Operational Modal Analysis module in Simcenter Testlab, providing practical suggestions on settings and interpreting results.  The database used in this article comes from a recent ski holiday experiment by Siemens engineers.  You can read more about the experiment and the conclusions by reading the Simcenter blog!


1.  Review of Operational Modal Analysis process
2.  Starting Operational Modal Analysis in Simcenter Testlab
     2.1  Loading OMA Add-ins
     2.2  OMA curve-fitter options
     2.3  Extra options
3.  Operational Data Collection tab
     3.1  Loading time histories
     3.2  Processing of Crosspowers & Correlation functions
          3.2.1.  Selecting references
Time lags & Frequency resolution
          3.2.3.  Exponential windowing
Operational Data Selection tab
Loading operational data
Reviewing included crosspowers
Operational PolyMAX tab
     5.1  Calculating mode shapes

1.   Review of Operational Modal Analysis (OMA)

Operational modal analysis is a technique to investigate the structural dynamics of a system while it is in operation.  OMA is performed in-situ under real-world load conditions which ensures that the forces acting upon the structure are realistic with respect to level, location/direction of application, as well as frequency/order content.  However, performing the test during operation means the input forces are not able to be quantified as they are in other techniques.  OMA is a response-only technique, meaning no input forces are measured during the test, and the starting point is time-history response data.   The OMA process is shown in Figure 1 below.

Overview of the operational modal analysis process.
Figure 1: Summary of operational modal analysis process.

For this article, we will be using data taken on a snowboard during a ski outing.  Accelerometers were attached at several locations along the snowboard, and data was acquired while going down the slope.  The wireframe and measurement node names can be seen in Figure 2 below.

Wireframe model of a snowboard
Figure 2.  Wireframe geometry of a snowboard to be used in an operational modal analysis.

2.  Starting Operational Modal Analysis in Simcenter Testlab

2.1  Loading OMA Add-ins
Operational Modal Analysis can be launched directly from the folder structure of the Testlab installation (\Start Menu\Programs\Simcenter Testlab <version>\Testlab Structures Analysis\Operational Modal Analysis), or by starting the Desktop application and loading the OMA Add-in.  Add-ins can be found under “Tools” in the menu of the Testlab Desktop (see Figure 3).   OMA requires 60 Tokens.

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Figure 3.  Operational Modal Analysis Add-in can be loaded via Tools > Add-ins (left).  OMA uses 60 Tokens.

Once loaded, the OMA Add-in will populate the Desktop with the following tabs, or pages along the bottom of the screen (tab order is configurable, and may appear differently): Op. Data Collection, Op. Data Selection, Op. Time MDOF, Op. Synthesis, Op. Validation, Multi-Run Modal.  This article will review each of these tabs.  Multi-run modal is covered in this article and will not be covered here. 
2.2  Operational PolyMAX Curve-fitter Option

In addition to the default curve-fitter that is automatically loaded with the OMA Add-in (Op. Time MDOF), one can also load the PolyMAX curve-fitter for use on operational data.  The PolyMAX curve-fitter is an advanced modal parameter estimator that gives a very clear stabilization diagram and can greatly simplify the modal analysis process.  This Add-in uses 26 Tokens and can be loaded by selecting “Operational PolyMAX Modal Analysis” in the Add-ins menu.  The PolyMAX option will be used for this article.
2.3  Extra Options

There are a couple additional Add-ins which can be added onto Operational Modal Analysis which offer some unique benefits.  They are listed below:
  • Automatic Modal Parameter Selection (AMPS) – 8 Tokens
AMPS selects poles based on an automated assessment of the stabilization diagram.  It not only speeds up the parameter estimation process, but also makes the pole selection user-independent.  AMPS is used for the purpose of this article.
  • Operational PolyMAX Plus – 11 Tokens
PolyMAX Plus is an extension on top of the PolyMAX curve-fitter mentioned previously.  PolyMAX Plus provides uncertainty bounds on frequency and damping estimates of selected poles, as well as iterates on the frequency and damping values selected.
3.  Operational Data Collection Tab

3.1  Loading Time Histories
Operational modal analysis starts with response measurements from the structure as time-histories, in the form of an LDSF file.  Pointing Testlab to the time data we want to use for our OMA is the first step of the process. 

At the top of the Operational Data Collection tab is a box labelled “Data source”.  This dialog allows the user to specify where Testlab should look for the LDSF.  By clicking on the “…” a pop-up window will appear (see Figure 4 below).  The user can select “Most Recent Run”, specify a folder in the Active Section of the current Project, or select the Input Basket.

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Figure 4.  Load time-history data by selecting a location.

Once the data source is selected, the data will appear in the Data Set window (Figure 5), along with checkboxes to exclude certain channels (OnOff checkboxes) as well as select Reference channels, which will be discussed in the next section.  Also displayed are the Channel Group, engineering unit (Y Unit), segment used for processing (X Axis), and sampling frequency (Fs).

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Figure 5.  Time histories to be analyzed.  Channels can be excluded from the analysis by unchecking the OnOff box.  Specify Reference channels by checking a box in the Reference column.

3.2  Processing of Crosspowers & Correlation Functions

3.2.1  Selecting References
As there are no measured input forces available in OMA, at least one response measurement location needs to be designated as the reference for the cross-power and cross-correlation functions to be used in the curve-fitting process.   While there are no restrictions in the number of references selected, or which locations can be used, there are a few guidelines. 

First, depending on the size of the structure, it is often advantageous to select references from multiple regions, such that all the measurements are somewhat near at least one reference location.  This ensures that the relationship between the response and reference transducers is dominated by the structure’s modal response, and not noise or other outside signals.

For the snowboard in this example, two references are selected: one in the front of the board (front right:+Z) and one in the rear of the board, on the opposite side (back left:+Z) (see Figure 2).  This ensures that for all responses, at least one reference is physically close-by, and all areas of the board (front, back, left, right) are covered with a reference.  Additional references could also be added, though little new information will likely be gained about the structure, and it will only lengthen the time required to perform the analysis.

3.2.2  Time Lags & Frequency Resolution
With the time histories loaded and the reference locations specified, the next step is to process the crosscorrelation and crosspower functions.  In the bottom of the left side of the window is a section called “Processing of Crosspowers” (see Figure 6) where the user can specify the “Number of time lags” and cutoff for an exponential window.  The user can also save the resulting functions by typing in the Run Name box.

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Figure 6.  Processing of Crosspowers section of Op. Data Collection page.

The number of time lags setting is related to the correlation functions used in the creation of the autopower and crosspower functions.  It is analogous to the acquisition time in a traditional FFT, and determines the frequency resolution of the resulting crosspowers according to the equation in Figure 7.  In the current snowboard example, the sampling frequency of the data was set to 256 Hz, which results in a bandwidth of 128 Hz.  By setting the number of time lags to 512, it results in a frequency resolution of 0.5 Hz. 

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Figure 7.  Spectral resolution of calculated crosspowers is determined by sampling frequency of the time data and specified number of time lags for the correlation function.

Figure 8 shows a comparison of several different time lag values and the corresponding effect on the resulting crosspower function.  Like any autopower or crosspower function, finer frequency resolution (smaller Df) results in reduced amplitude, as there are more spectral lines to spread out the energy. 

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Figure 8.  Effect of # of time lags (frequency resolution) on crosspower function.  Too many time lags can result in a spiky crosspower function (red curve), which may complicate curve-fitting.  Too few time lags can cause modes to be lumped together (magenta curve) and be missed during curve-fitting.

Choosing the number of time lags is a balance between being able to separate closely spaced modes and having a clear crosspower function that will aid in parameter estimation.  Each test and structure will be different, so some experimentation with resolution is encouraged.

3.2.3  Exponential Windowing
Another important setting in the Processing of Crosspowers section is the exponential window percentage.  This setting controls the exponential window applied to the correlation functions, which is used to reduce the effect of leakage and the influence of the higher time lags, which have a larger variance.  The application of the exponential window to the correlation functions is equivalent to the usage in impact testing: to ensure the response of the structure is zero before the end of the observation time.  The damping effects of the exponential window are automatically compensated for later in the operational modal analysis process.

The Quick Function window can be used to check the effect of the window and number of time lags on both the crosspower function as well as the crosscorrelation function for a given response location and reference (see Figure 9).  After selecting a response location and a reference, the user can select to view the Crosspower, Crosspower and Unwindowed Crosspower, Crosscorrelation, or Crosscorrelation and Unwindowed Crosscorrelation functions. 

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Figure 9.  The Quick Function window can be used to determine the optimal number of time lags and exponential window percentage for the processing of crosspowers.

Viewing the windowed and unwindowed crosscorrelation functions as shown in Figure 9 can aid in determining the optimal amount of damping to apply with the exponential window.  The percentage value entered corresponds to the amplitude of the correlation function at the end of the time window:
  • A value of 100% means the function will maintain 100% of its original amplitude, so there is effectively no window applied. 
  • A value of 1% means the windowed function will have an amplitude at the end of the time segment equal to 1% of the unwindowed function. 
The window’s function is to ensure the crosscorrelation function is zero or near zero by the end of the time window to avoid leakage.  The exponential window percentage is another setting which may require some trial and error, and multiple response locations should be checked, as demonstrated in Figure 9.   

Once the number of time lags and exponential window percentage are determined, click “Start Calculation” and a set of crosspower functions will be calculated and stored in the active section of the project with the name shown in the “Run Name” box.  Sometimes it is helpful to include the number of lags and window percentage in the Run Name, particularly if several different sets of crosspowers are calculated. 
For example, in this case we are using 512 lags (for a spectral resolution of 0.5 Hz) and a window percentage of 1%, so the run name may be something like “Oper Pre-Processing  0_5Hz_1%”.  One may choose to calculate several crosspower sets with different settings and see which gives the best OMA results.

4.  Operational Data Selection Tab
4.1  Loading Operational Data

Once the crosspowers have been calculated, the next step is to load them for processing.  In the Navigator tab, find the operational pre-processing run created in the previous section (see Figure 10).  Inside the run folder will be a folder of Operational Crosspowers, with a sub-folder for each reference location.  Right-click on each reference folder and place all crosspowers into the Input Basket.

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Figure 10.  Add all operational crosspower functions to the Input Basket to prepare for the curve-fitting process.

Now on the Op. Data Selection tab of Testlab, click on the Input Basket radio button to specify the crosspower location as shown in Figure 11, and click “Refresh Function Table” at the top of the screen. 

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Figure 11.  Load crosspowers into Function Table for inspection.

The crosspowers are loaded into the function table, one column for each reference location, and a row for each response location.

4.2  Reviewing Included Cross-powers
Once all the crosspowers are loaded into the Function Table, it is a good opportunity to visualize each function to ensure the quality of the calculations.  It is often helpful to view the individual functions and compare them to the sum of all the functions (see Figure 12 below).  By summing all the included crosspowers, peaks that appear in several of the crosspower functions at particular frequencies (as one might expect to see at natural frequencies) will also appear in the sum function.  As such, the sum function offers a convenient way to visualize the modal behavior of the structure captured by all the crosspower functions at once.  While the function is named “Sum”, it is really a complex average of all the included functions.

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Figure 12.  Individual crosspowers can be reviewed and compared to the Sum of all included crosspowers as a quality check. 

In the event that a particular measurement location went bad or seems to be corrupting the dataset for some other reason, a family of crosspowers can be excluded from the analysis.  Exclude crosspowers by right-clicking on row or column headers of the Function Table to exclude a set of crosspowers from the curve-fitting calculations.  Excluding a row will remove a given response location from all references, and excluding a column will exclude all crosspowers for a given reference location.

5.  Operational PolyMAX Tab
Now that a set of crosspower functions have been calculated and collected the next step is to perform some curve-fitting to extract the structure’s modal parameters.  The curve-fitting process in Simcenter Testlab for OMA is identical to the process followed in experimental modal analysis.  The process is outlined in great detail in this article, and will not be repeated in detail here.
5.1  Calculating mode shapes

Figure 13 below shows the four mode shapes calculated for the snowboard using the process outlined in the “Getting Started with Modal Curvefitting” article.

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Figure 13.  Mode shapes for a snowboard while in use.

During operation, the presence of the snowboarder has a profound effect on the mode shapes of the snowboard.   Note the middle section of the board barely participates in any of the mode shapes seen in Figure 13, as the weight of the snowboarder constrains this portion of the snowboard structure.  Mode 1 (18.8 Hz) shows a front-dominated bending mode, Mode 2 (25.4 Hz) is a rear-dominated bending mode.  Mode 3 (54.3 Hz) shows front and rear in-phase torsion, while Mode 4 (55.8 Hz) shows front and rear torsion modes out-of-phase.
Finally, the same tools available in standard modal analysis to validate your modes are obviously also extremely useful in OMA. In the picture below (Figure 14), the synthesized crosspowers using the estimated operational modes are shown. Despite the noisy data, the model is able to capture the overall dynamics visible in the data, which confirms that all main modes are correctly identified.

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Figure 14.  Operational Synthesis tab can be used to verify the operational modal model captures the modal characteristics of the system.  Synthesized crosspowers (red curves) are compared to measured crosspowers (green curves).

Questions?  Post a Reply, email Scott MacDonald, or contact Siemens Support Center.

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