Upcoming Feature: SSI-UPCX - New Powerful SSI Technique with Uncertainty Estimation
As a part of the upcoming release of ARTeMIS Modal Pro 5.0, a new powerful Stochastic Subspace Identification technique will be 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 long-term collaborators at 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. Uncertainties associated with the measured data are propagated to uncertainties associated with the estimated modal parameters.
Uncertainty Estimation of Modal Parameters - Benefits
There are several benefits of this new technique compared to today's modal analysis estimation techniques:
- 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.
Below, these benefits are explained in more
Visualizing Uncertainties using Confidence Bounds
Modal estimation methods that make use of Stabilization Diagrams only present, in general, 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. An example of a typical Stabilization Diagram resulting from the use of the SSI-UPC technique is shown below.
Click picture to view full application window
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. It would therefore be beneficial to have a method to estimate both mean values of the modal parameters as well as their corresponding covariance. From the covariance, it is possible to visualize the uncertainty in terms of confidence bounds around the mean values. And this is what the SSI-UPCX technique does. The Stabilization Diagram for the same data used for the example above, but calculated with the SSI-UPCX technique is shown below. The confidence bounds represented by the grey horizontal bars clearly show the uncertainty for each mode in the Stabilization Diagram.
Click picture to view full application window
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.
So the conclusion is that the estimated modal parameters returned by SSI-UPCX are more reliable than conventional modal estimation techniques that rely on "mean value" clustering techniques.
Now, it is in fact possible to answer the question: How uncertain are the modal parameter estimates?
Not only the mathematical complexity, but also the computational burden in estimating the confidence bounds, have been key reasons why there have been no commercially available techniques so far. However, with SSI-UPCX these are now solved issues. In case of the above example, it is from a dataset of 36 channels with 51200 samples in each. To estimate the mean values in both SSI-UPC and SSI-UPCX requires approximately 1 minute to process the data once it has been loaded into the program. To obtain the covariances using the SSI-UPCX technique, another 30 seconds are required to process the data. The estimation of the covariances and display of confidence bounds are made automatically as a second step, after the mean values are displayed in the Stabilization Diagram.
The release of this exciting new feature is planned for September 2016. All new customers will get this technique when they order ARTeMIS Modal Pro. Existing customers having a valid maintenance service for ARTeMIS Modal Pro will also have access to this powerful technique.
M. Döhler & L. Mevel: Efficient multi-order
uncertainty computation for stochastic subspace identification.
Mechanical Systems and Signal Processing. Vol. 38, Issue 2, 2013, pp.
M. Döhler, L. Mevel & P. Andersen:
Efficient uncertainty computation for modal parameters in stochastic
subspace identification. Processing of ISMA 2012, Leuven, Belgium.
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