# 8 Checking VP plausibility (passivity and reciprocity)

The Virtual Point Transformation is essential for high-quality test-based models. To validate the VP model, assess transformed data plausibility by checking the passivity of the driving point FRFs and the physical validity of reciprocal FRFs.

In particular, check that:

• For a passive system, the phase of a driving point FRF is positive.
• For a system with cross-coupling, reciprocal FRFs should be similar.

During the measurement process, to have a high-quality test-based model (link), check the plausibility of the VP transformed data after measuring each VP. It is very important that you do this quality check after ensuring that the data is free of overloads and when you are satisfied with the quality of the coherence and VP consistency. This is needed because VP data builds on good setup and signal quality.

## How to: Visualize VP transformed data

You can visualize the VP transformed FRFs in Analyze. Here, you evaluate their passivity and reciprocity.

1. The VP preset shows VP transformed data.
2. The matrix mode in reciprocity mode.
3. The main diagonal of the VP preset matrix represents true driving point FRFs.
4. In reciprocity mode, the graphs show the selected FRF and its reciprocal FRF.
5. The reciprocity plot shows the reciprocity between the both FRFs.

## How to: Check the passivity of a VP model

VP FRFs are true driving points (like in numerical models), so they must be passive. After selecting the VP preset and setting the matrix to reciprocity mode, the driving point VPs will stand out on the main diagonal of the matrix. To verify the passivity of the system, select each driving point and check in the graphing if the phase is passive (between 0° and 180°).

Good test-based models are passive. The phase of all driving point FRFs is between 0° and 180°.

## How to: Check the reciprocity of a VP model

After the passivity, check the reciprocity of the model. You can do it in Analyze, visualizing the matrix of the VP preset in reciprocity mode. There, find the transfer paths between the degrees of freedom where you expect high cross-coupling in your system. In the mount case shown below, an impact in X at the VP of the big cross will very likely generate a high response in X in the small cross. In the matrix viewer, find which cell corresponds to the identified reference and response channels and select it. In the graphs, you see the selected FRF and its reciprocal one, so you can easily verify whether the VP transformed FRFs are reciprocal or not.

## How to: Trace back problems in VP models

The VP plausibility checks are the last you perform. Reasons for issues in passivity and reciprocity are consequences of problems with the setup or signal quality, that you have probably missed.

If passivity and reciprocity have a low quality over the entire frequency range of interest, very likely your setup is not good. A common mistake is wrong VP assignments for sensors or excitations. Go back to the Prepare module and check the VP assignments, the conditioning and re-do the other setup checks.

When you spot a problem in a VP transformed FRF at a specific frequency (as in the example below), you very likely have signal problems. In this case, you need to trace back the error from VP level to the individual untransformed FRF that contribute to that VP DoF. For a better visualization, create a custom preset containing the measured and VP transformed FRFs of the problematic VP. Then, in the Validate card, toggle on and off the excitations or sensor channels that contribute the most to that VP DoF. You can use the contribution matrix in the Virtual Point Transformation card of the Prepare module to identify the excitation points and response channels that contribute the most to that specific VP DoF.

Once you identify the troublesome FRF, you can repeat the setup, signal and consistency checks to improve the model, paying additional attention to the direction and frequency range in which the VP transformed FRF is not passive. If needed, you should re-do the measurements of those FRFs.

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