10 PolyMAX Modal Analysis Exercise

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Tutorial Category: LMS Test.Lab Structures – Modal Testing & Analysis Topic: PolyMAX Modal Analysis compared to Time MDOF

In this tutorial we will see in detail what are the main advantages of this new parameter estimation method, PolyMAX: extremely clear stabilization diagrams even for broadband and high-order analyses. Easy-to-interpret stabilization diagrams considerably facilitate the modal analysis process and imply the potential for automating like in Automatic Modal Parameter Selection (AMPS). Overview: A brief PolyMAX theory concept introduction ................................................................................ 2 Time MDOF and PolyMAX comparison ......................................................................................... 3 Automatic Modal Parameter Selection (AMPS) ............................................................................. 8 Results comparison ....................................................................................................................... 9 Considerations ............................................................................................................................ 11

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Prerequisites  

full set of FRF’s measured on the disc LMS Test.Lab Modal Analysis and PolyMax license or tokens to use them

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1

A brief PolyMAX theory concept introduction The PolyMAX method is a further evolution of the least-squares complex frequency-domain (LSCF) estimation method. The LSCF method identifies a so-called common-denominator model and was introduced to find initial values for the iterative maximum likelihood method. Quickly it was found that these “initial values” yielded already very accurate modal parameters with a very small computational effort: the most important advantage of the LSCF estimator over the available and widely applied parameter estimation techniques, is the fact that very clear stabilization diagrams are obtained. It was found that the identified common-denominator model closely fitted the measured FRF data. However, when converting this model to a modal model by reducing the residues to a rank-one matrix using the singular value decomposition (SVD), the quality of the fit decreased. Another feature of the common-denominator implementation is that the stabilization diagram can only be constructed using pole information (eigenfrequencies and damping ratios). Neither participation factors nor mode shapes are available at first instance. The theoretically associated drawback is that closely spaced poles will erroneously show up as a single pole. These two reasons provided the motivation for a polyreference version of the LSCF method, which is called “PolyMAX”. These two reasons provided the motivation for a polyreference version of the LSCF method, using a so-called right matrix-fraction model. In this approach, also the participation factors are available when constructing the stabilization diagram. The main benefits of the polyreference method are the facts that the SVD step to decompose the residues can be avoided and that closely spaced poles can be separated.

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Time MDOF and PolyMAX comparison The first step to be done is to add the PolyMAX workbook by activating the PolyMAX Modal Analysis Add-in like shown here below:

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Let’s choose a broadband range (i.e. bandwidth 600 ÷ 7560 Hz; model size 64) and compare the stabilization diagram we get and the way the poles pop up in those two.

Time MDOF

PolyMAX

We can already see what we introduced in the theoretical introduction: with PolyMAX the poles are much more stable and less scattered compared to what we got in the Time MDOF.

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Let’s zoom in on some natural frequencies to better check these differences. For the next 6 pictures the X-axis scaling has been kept constant (80 Hz) to give an idea about how the different techniques cope with closely spaced natural frequencies.

Time MDOF

PolyMAX

For modes about 15 Hz from each other, the two methods seem to give both good results.

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Question: What if we chose two closer modes?

Time MDOF

PolyMAX

We can now observe that for an approximate distance of 5 Hz, the Time MDOF method starts having some troubles compared to PolyMAX.

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Question: What if we have two modes even closer?

Time MDOF

PolyMAX

We can clearly see that Time MDOF has quite some troubles in giving stable and well aligned poles.PolyMAX can still cope with them without any problem. Let’s choose now some poles and proceed with the mode shape calculation; we will afterwards compare the two methods.

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Automatic Modal Parameter Selection (AMPS) To speed up the whole procedure, we will exploit the Automatic Modal Parameter Selection Add-in. This tool uses an algorithm which follows the choice criteria used by experienced engineers. Starting from the Stabilization Diagram, those steps can be listed as:    

Detects a vertical column visually Finds a sequence of stable poles at the lowest possible order Compares damping ratio with next order poles If damping ratio is sufficiently constant  select pole



The idea in the algorithm implementation is to group the poles in clusters based on damping ratio, select the best cluster and finally out of the latter one selects the best pole.

PolyMAX

As we can see there are some modes which have been selected even if they do not belong to a Sum function peak. We can then play with the advanced parameters of this tool such are the Modal Density and Maximum damping ratio. 

Modal Density: with this parameter you can indicate whether a high or a low number of modes is expected in the selected frequency band. This will influence how the algorithm subdivides the band into sub-bands for analysis



Maximum damping ratio: poles with a damping ratio larger than the set maximum damping ratio will not be selected.

If some ‘strange’ modes are still selected, they can be manually deselected; this procedure allows to save quite some time.

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4

Results comparison After having found out what the mode shapes with the two methodologies are, we can pass them to the Modal Validation worksheet and make a comparison through the Cross MAC (Modal Assurance Criterion) and make some considerations:

Because of the mathematical definition of the MAC, the values on the major diagonal should be close to 100 and the others to 0. This is the case for our data apart from the 5th mode where we have a value of 66.252.

Mode No. Frequency [Hz]

(A) 1 1235.8

(A) 2 1238.0

(A) 3 2632.0

(A) 4 2808.2

(B) 1

1235.5

99.175

0.687

0.004

0.062

(B) 2

1237.7

0.802

98.749

0.003

0.009

(B) 3 (B) 4

2630.6 2807.4

0.002 0.041

0.007 0.027

99.996 0.065

0.031 99.467

(B) 5 (B) 6 (B) 7 (B) 8 (B) 9 (B) 10

2810.8 3174.7 3190.0 3409.8 3515.5 3928.1

0.078 0.008 0.094 20.337 0.178 0.002

0.275 0.063 0.017 0.196 19.196 0.007

0.023 0.048 0.038 0.003 0.067 5.925

0.24 0.003 0.009 0.081 0.002 0.01

(A) 5 2811.5

(A) 6 3175.0

(A) 7 3190.1

(A) 8 3409.9

(A) 9 3516.3

(A) 10 3928.5

0.011 0.243 0.012 44.866

0.012 0.06 0.059 0.001

0.092 0.025 0.033 0.016

20.969 0.091 0.001 0.082

0.022 19.412 0.045 0.016

0.002 0.007 5.81 0.009

66.252 0,014

0.019 99.996

0.066 0.231

0.12 0.175

0.261 0.003

0.015 0.068

0.055

0.124

99.967

0.071

0.017

0.042

0.025

0.153

0.07

99.98

0.089

0.009

0.163 0.002

0.005 0.068

0.014 0.042

0.043 0.007

99.982 0.015

0.015 99.999

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By clicking on the value itself the compared modes are animated in the geometry display below (chose left/right display).

PolyMAX

Time MDOF

Looking carefully you will see that there is a kind of standing wave on the Mode Shape coming out of the Time MDOF which might explain the small difference noticed in the Cross MAC between PolyMAX and Time MDOF.

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Considerations Time MDOF drawbacks:  

To identify stable poles, the stabilization diagram has to be calculated for frequency subranges (bands) in which the total bandwidth has to be divided. This is time consuming!. Repeated roots are difficult to identify: if they are very close to each other (2 – 5 Hz), the stabilization diagram gives a very high density of closely spaced poles making the selection of poles difficult.

Advantages of PolyMAX   

LSCE based: clear stabilization diagrams. The poles in the stabilization diagram are clearly identified over the entire bandwidth. Only one (or few zoomed) stabilization diagrams are necessary. This is a huge time gain. Repeated roots are easily identifiable. Polyreference analysis.

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