Maximum Likelihood estimation of a Modal Model (MLMM)

Spending a lot of time finding the best poles in your stabilization diagram?

Stop wasting your time! Put the computer to work to find the optimal solution using the new Maximum Likelihood estimation of a Modal Model (MLMM) feature in Simcenter Testlab.

Released with LMS Test.Lab 17 (now called Simcenter Testlab), the new MLMM Modal Parameter estimator automatically iterates on the parameters of the initial modal model to optimize the fit between the identified model and the measured Frequency Response Function (FRF) data, resulting in the best fitting modal model.

Depending on the quality of the initial fit, the results can be significantly improved, as seen in Figure 1.

Figure 1: MLMM automatically improved this curve fit on a heavily damped structure, reducing error from 74% to 10% for this FRF synthesis

The initial modal model can be calculated either using Polymax or Time MDOF curve fitting routines, as is standard practice today. But instead of manually iterating one mode at a time between the stabilization diagram and the modal synthesis, the MLMM takes over! It automatically adjusts the frequency, damping, and modal participation values to reduce the difference between the modally calculated FRF and actual FRF for all identified modes.

For heavily damped structures and complex systems such as acoustic cavities or trimmed-body analysis, MLMM has significantly higher quality results. However, for other structures and curvefits, where the initial fit was very accurate, there is not significant improvements using MLMM.

Using MLMM

The Maximum Likelihood Modal Model is available for 26 tokens in Simcenter Testlab. From the main Simcenter Testlab menu, select “Tools -> Add-ins” to turn on “MLMM” as shown in Figure 2.

Figure 2: Tools -> Add-ins -> MLMM

At the top of the Polymax worksheet, an additional minor worksheet or tab is added to the Modal curve fitter as shown in Figure 3.

Figure 3: Stabilization diagram

Select poles from the stabilization diagram as normal. After creating the list of poles on the left side, press the “MLMM” button on top of the screen.

In the MLMM worksheet, set the “Maximum number of iterations”. This is the number of times that the frequency, damping, and modal participation factors will be adjusted. Press the “Calculate” button on the left side of the screen as shown in Figure 4.

Figure 4: With each iteration the error between the experimental FRFs and synthesized FRFs becomes smaller

In the middle of the screen the error between the synthesized FRFs of the model and the actual measured FRFs is shown. With each iteration, it should get progressively smaller. Eventually the changes become smaller and smaller.

Once the iterations are complete, the modal synthesis can be checked. Click on the ‘Modal Synthesis’ worksheet as shown in Figure 5.

Figure 5: Modal synthesis after MLMM

In the Modal Synthesis worksheet, there is a correlation and error percentage shown above the FRFs:

The correlation indicates how well the shape of the synthesized FRF follows the shape of the actual FRF. Ideally this should be 100%

The error indicates the difference between the amplitude of the calculated FRF and synthesized FRF. Ideally this should be 0%.

The arrow buttons, located in the lower left of the screen, can be used to view FRFs from different measurement locations.

Under the “Advanced…” button of the MLMM worksheet, some constraints can be set on the frequency and damping values as shown in Figure 6.

Figure 6: Known frequencies and maximum damping values can bet set as constraints in MLMM

The following constraints can be set:

Maximum percent variation between iterations

The “Keep mode frequency constant” can be checked to prevent frequencies from being adjusted

Limit modal damping to a maximum different than the default 70%. After iterating, any modes that MLMM did not think helpful for describing the FRFs get set with a large damping value. By default this value is 70%.

Enjoy using MLMM to speed up the curvefitting process.