Before starting testing, you can verify the quality of the Virtual Point Transformation, based on your test setup.
In this video, I’ll show you a workflow to check your test setups for Virtual Point measurements in DIRAC. DIRAC uses positions and orientations to calculate the VP Transformation. So when you’re preparing a test setup in DIRAC, it’s important to check if it can capture all Degrees of Freedom of your Virtual Point. The VP Transformation card in DIRAC helps you to do just this. Here’s how.
In the VP Transformation card, you can review the conditioning of the transformation matrices, and the contributions of the sensors and impacts. But before looking at any details of the transformation, we need to make sure that we have correctly assigned all our impacts and sensors to the VP. The table shows you how many sensor channels and excitations are connected to the Virtual Points. When you click into the tables, DIRAC will highlight all sensors and impacts that are used for the VP. I like to use this feature to check if I forgot or wrongly assigned any of my impacts.
When I check Virtual Point Transformation, I start by looking at the overall conditioning number. The conditioning number is computed separately for the transformation matrix of the responses and the forces. In a nutshell, it represents how sensitive the VP Transformation is to errors in the placement and measurements of the forces and responses. So your goal should be to make it as small as possible. Good VP setups usually have a conditioning below 100. When your setup does not allow to identify all your VP DoFs, the overall conditioning will be highlighted in red. This is the case when you have only assigned two triaxial sensors to measure a 6-DoF VP because they cannot observe the rotation around the axis that connects them. That’s why you always need at least three sensors to capture the response of a 6-DoF VP. If the conditioning number is still too high, you can use the information in the individual VP DoF conditioning to improve it.
The overall conditioning of the VP Transformation can be broken down to the individual response and reference DoFs of the VP. These boxes relate to the different VP DoFs and illustrate how well a Degree of Freedom can be identified relative to all the others. Darker colors represent higher values. Since our measurements should be equally sensitive to all Degrees of Freedom, we aim at getting all values to 1. Rotational Degrees of Freedom are often more difficult to identify than translations, but they should never be below 0.1. Here we see that the rotation around the x axis has a relatively bad conditioning. This leads to the high overall conditioning of the transformation of the responses. We can improve this by moving the third sensor further out. If you want to improve a badly conditioned VP DoF, you can also use the information from the contribution matrix.
The contribution matrix has one column for every Virtual Point Degree of Freedom and one row for every excitation point when you display the reference matrix. For the response matrix, the rows correspond to all sensor channels. The entries in the matrix show how each impact contributes to the identification of the Degrees of Freedom of the VP. Here, we have low conditioning of the moment around the z axis of the VP because our impacts only have a low contribution to this Degree of Freedom. If we move one of the impacts to better excite this moment and refresh, the conditioning of the z moment improves. Another important use case for the contribution matrix is to check the overdetermination for each Degree of Freedom of the VP. Without any overdetermination, an error in a single impact or sensor channel leads to bad quality of the VP FRF. But a simple way to check it is by removing the VP assignment of an impact with high contribution and recalculate. If the conditionings are still good for the Degree of Freedom, you have enough overdetermination. When you follow these steps, you and your VPs are in great condition to start measuring.
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