Software for Operational Modal Analysis
ARTeMIS

 

 

ARTeMIS Modal 5.0 Now Released

By September 1, 2016 we have released ARTeMIS Modal 5.0 (64 bit). This version has many new exciting features for modal estimation, modal validation and hardware control. In this newsletter we will introduce some of these and will continue in the newsletter for next month. If you wish to test the new version and you are not yet a customer, please go to the download page of our demo version. Should you wish to test the software with your own data please contact us at support@svibs.com. If you are already a customer, please go to customer download area and download this exciting new version.

 

SSI-UPCX - New Powerful SSI Technique with Uncertainty Estimation

In ARTeMIS Modal Pro 5.0 a new powerful Stochastic Subspace Identification technique is included. The name of this Crystal Clear Stochastic Subspace Identification technique is Extended Unweighted Principal Component, or in short SSI-UPCX. This technique has been developed in cooperation with the  Inria/IFSTTAR I4S Team in Rennes, France.

A unique aspect of the SSI-UPCX technique is that uncertainty estimation of the modal parameters is performed in a fast and memory-efficient way. The uncertainty estimation makes SSI-UPCX stand out, compared to today's modal analysis estimation techniques. Some of the benefits are:

 

- More accurate estimates of modal parameters than when using conventional "mean value" based clustering techniques.

- Effective elimination of computational (noise) modes and other unstable modes.

- Automatic modal estimation becomes more reliable in Structural Health Monitoring.

 

Visualizing Uncertainties using Confidence Bounds

In general, modal estimation methods that make use of Stabilization Diagrams only present the estimated mean values of the modal parameters. Typically, Stabilization Diagrams show the mean values of the natural frequencies of the estimated modes with respect to selected model dimensions. In a diagram like this, the search for stable modes is made on the basis of the mean values. Even if the stabilization is clear, it is still difficult to assess the level of confidence that can be associated with each of the presented modes.

In the SSI-UPCX technique it is possible to visualize the uncertainty of the individual estimates, in terms of confidence bounds around the mean values.  An example of this, is shown below.The confidence bounds represented by the grey horizontal bars clearly show the uncertainty for each mode in the Stabilization Diagram.

 

 

The confidence bounds shown above in the stabilization diagram can be further extended. Above, only the uncertainties of the natural frequencies are visualized. However, by selecting a specific state space model (Cursor Model), and selecting what modes to visualize in the Modes List, then by showing the new Frequency vs. Damping Diagram, the mean values and confidence ellipsoids of the natural frequency / damping ratio pairs can be visualized. The diagram showing the damping as a function of frequency can be seen below for some of the modes of the cursor model. The confidence level has been set to 95%:

 

 

In general, the additional covariance information enhance the assessment of the invidual modes. It is clear to see what modes can be trusted most.

 

Automatic Removal of Too Uncertain Modes

In addition to the display of confidence bounds in the Stabilization Diagram, the uncertainty information can also be used to remove modes that are too uncertain.

For each estimated modal parameter its Coefficient of Variation (CV) is calculated as the standard deviation divided with the mean value. Two screen-shots are shown below.  On the picture to the right, the mouse is pointing at a specific mode in the diagram.  As soon as the mouse pointer is placed over an estimated value, a tooltip appears. The tooltip presents the mean value, the standard deviation and the Coefficient of Variation for the natural frequency and the damping ratio. The picture on the left shows the Modal Indicator properties. These properties now include the maximum allowed Coefficients of Variations of the natural frequencies and damping ratios. These Coefficient of Variations are powerful dimensionless modal indicators that effectively help filter out the modes that have high uncertainty from the search for stable modes.

 

 

 

In the picture below, the maximum allowed Coefficient of Variation of the natural frequency has been set to 0.01 and to 0.1 for the damping ratio. By only showing the stable modes that are left, it is much easier now to extract the most accurate modes from the diagram. 

 

 

 

More accurate estimation of the final modal parameters

All the stable modes left in the above picture are like in the case of the other SSI techniques used for estimation a final set of modal parameters. Usually, the stable modes of different model orders are simply averaged to find the final estimate. However, in the SSI-UPCX technique we make use of the additional covariance information, in order to do an even better estimation of the final set of modal parameters. The algorithm used for this, is listed below:

 

1. The standard deviation is computed for each estimated mode (frequency+damping ratio) at the different model orders in the stabilization diagram by propagating the covariance of the data in a sensitivity analysis. The technical details of this procedure are explained in the paper (Mellinger et al., 2016).

2. In the stabilization diagram, estimates of the modes are available at different model orders with their uncertainty information. For each mode, one combined value (the final estimate) for its frequency and for its damping ratio is desired that is based on the (slightly different) estimates at different model orders within a stable range of the stabilization diagram. To combine the estimates at different model orders in a meaningful way, the uncertainty information is used: a weighted mean is built where the estimates at each model order are weighted with their inverse covariance. In this way, estimates with a high uncertainty (less quality) have less weight in the mean, and estimates of good quality having a low uncertainty, have more importance.

3. Finally, the covariance of the weighted mean is computed, taking into account the strong correlation between the estimates at the different model orders. The final estimate of a mode (containing the information of the different model orders) is delivered with the combined covariance matrix of the global frequency and damping ratio estimate.

 

These final estimates of the modal parameters can also be evaluated using the Frequency vs. Damping Diagram. In the case of the SSI-UPCX technique this diagram not only presents the mean values of the natural frequencies versus damping ratios, but also the confidence ellipsoids. The ellipsoids are coming from the estimated combined covariance matrix of the global natural frequency and damping ratio estimate.

 

 

 

This diagram gives a quick graphical overview over the estimation accuracy of the individual modes of the analysis. The larger confidence bounds a modal parameter has for a certain significance level, the more uncertain the estimation of the "true modal parameter" is. The ellipsoids also reveal the correlation between the natural frequency and the damping ratio. The first five modes e.g. show a reasonable uncorrelated nature . This is indicated by the "standing" confidence bound ellipses. In case of the fifth mode , there is correlation between the estimates of the natural frequency and the damping ratios. This is indicated by the "tilting" confidence bounds ellipses. It is tilting to the left which indicates that a higher frequency estimate at the same time most probable will result in a lower damping estimate.  

ARTeMIS Extractor - End of Life Notification

By the end of 2016 ARTeMIS Extractor has reached end of life after 17 years of service. Please contact us if you are still running ARTeMIS Extractor and wish to migrate to ARTeMIS Modal. We are running a special and very affordable migration campaign until December 31, 2016.

 

Meet us at ISMA and WindEnergy Hamburg, September, 2016 


SVS will be exhibiting at the ISMA conference on September 19-21 and at WindEnergy Hamburg exhibition on September 27-30. We will be showing ARTeMIS Modal 5.0, including the new SSI-UPCX technique and new tasks for controlling various data acquisition systems directly from the ARTeMIS workspace.

 


Structural Vibration Solutions A/S • Tel: +45 9635 4422 • sales@svibs.com

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