2 Checking VP conditioning

The VP conditioning indicates if all degrees of freedom of the Virtual Points can be identified with the defined sensors and excitations. The contribution matrices show how much each sensor channel and excitation contributes to the description of the DoFs of the Virtual Point.

This is the first quality check you have to perform, right after you have finished creating the design of experiment, before going to the test bench. Be aware that every time you make changes to the test setup, you need to check again the conditioning and contribution of your system. When you reach the desired quality of the test setup, you can start creating the physical setup.

  1. Conditioning and contribution information can be found in the VP Transformation card.
  2. You can expand the conditioning table to visualize more information. Refresh the table after making changes to the test setup.
  3. Check overall response and reference conditioning.
  4. Check the response and reference conditioning of each VP DoF.
  5. Change the VP to visualize the contribution of each VP of your system.
  6. Check both response and reference contribution of each VP to verify the overdetermination.

How to: Check the VP assignments

Before looking at any details of the transformation, make sure that all the impacts and sensors are correctly assigned to the VPs. In the conditioning table, you can see how many sensor channels and excitations are connected to each VP. For a better visualization, you can select a VP in the table and DIRAC will highlight in the 3D Viewer all sensors and impacts used for that VP. With this feature, you can check if you are missing any excitation or sensor and if you have wrongly assigned some of them.

How to: Interpret the overall conditioning number

When all sensors and impacts are correctly assigned, you can proceed to check the Virtual Point conditioning. To update the conditioning and contribution, hit the refresh button , to show the updated values.

To check the conditioning, 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 is to make it as small as possible.

Good test-based models have an overall reference and response conditioning below 100.

When your setup does not allow to identify all your VP DoFs, the overall conditioning will be infinite and highlighted in red. This is the case, for example:

  1. 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. If that is the case, you should either add a sensor for that VP or reduce the number of DoFs.
  2. When the excitations you have added do not excite all force and moment DoFs of the Virtual Point. If that is the case, you should either add one excitation for that VP or reduce the number of DoFs.

If after refreshing, the conditioning number is still too high, you can use the information of the individual VP DoF conditioning to improve it.

How to: Analyze the VP-DoF conditioning

The overall conditioning of the VP Transformation can be broken down to the individual response and reference DoFs of the VP. These can be visualized expanding the table by clicking on . These cells 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. Your measurements should be equally sensitive to all Degrees of Freedom, so you should aim at getting all values to 1. Rotational Degrees of Freedom are often more difficult to identify than translations, but they must never be below 0.1. If your VP is badly conditioned, try to add excitations or move sensors and excitations around to see if the conditioning improves. To understand which sensors and excitations to move, you can use the information from the contribution matrix.

Good test-based models have R-DoFs reference and response conditioning above 0.1.

How to: Use the contribution matrix

The contribution matrix shows how each impact or sensor channel contributes to the identification of the Degrees of Freedom of the VP. In the contribution matrix, each column corresponds to the Virtual Point Degrees of Freedom. When the matrix is set to Response, each row corresponds to a sensor channel. When the matrix is set to Reference, each row corresponds to an excitation point.

Let’s understand how you should use the contribution matrix to improve the conditioning of your test setup. In the example below, you can see that the conditioning of the Rz DoF or the references is low. By looking at the contribution matrix of the references of that VP, you can check which impacts contribute to Rz. You can notice that all impacts have a low contribution to Rz. To improve the conditioning, move one or more of these impacts to better excite the Rz moment. After refreshing you will see that the conditioning of the rotation around the Z axis has improved.

Another important use case for the contribution matrix is to check the overdetermination for each Degree of Freedom of the VP. You must avoid that one sensor channel or excitation dominates the contribution of one VP DoF. If that is the case, move the sensor or add an additional impact point to excite the specific DoF. You can check the percentage of contribution to the DoF by hovering over the matrix entry with the mouse. Without any overdetermination, an error in a single impact or sensor channel leads to bad quality of the VP FRF.

A simple way to check if you have enough overdetermination is by removing the VP assignment of an impact with high contribution and recalculating. If the conditionings are still good for the Degree of Freedom, you have enough overdetermination.

A good test-based model has an overdetermination of 1.5 or 2 for each VP Dof.

3-DoF VP6-DoF VP
Sensor channels69-12
Excitation points69-12

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