The measurement matrix provides a graphical overview of the complete FRF matrix in terms of the response channels (rows) and excitation points (columns). The order of the DoFs is determined by the order of sensors / impacts / VPs as defined in Prepare. Clicking on a box within the matrix will display the corresponding FRF within the Graphing card and corresponding information in the Validate card. Right-click on an entry and choose “Focus on Excitation”, “Focus on Response” or “Focus on Virtual Point” to immediately focus on that measurement point in the 3D viewer.
The colors and values of the entries in the matrix each represent a certain statistic quality value, as described below. The FRF matrices can now be shown for any combination of raw and Virtual Point-transformed channels, as described next.
The matrix is shown for the measured FRF data by default, but several other options are available for reviewing the matrix with VP-transformed data.
The matrix mode can be changed by selecting the desired mode in the taskbar above the matrix. Additional presets are also available; the matrix modes displayed in the taskbar can be toggled on/off by selecting them in the additional context menu, as shown in Figure 7‑2.
Figure 7‑2 also shows the option to add a custom preset within the context menu. Using the custom presets, any combination of raw and VP-transformed data can be shown in the measurement matrix. The creation of custom presets is discussed further in the following paragraphs and descriptions of the default presets are discussed next.
Figure 7-2: Selection of matrix modes displayed in the taskbar
The following videos explains how to use the matrix viewer in Analyze.
In Measured mode, statistics on the raw FRF matrix are shown. This is typically used right after or during measurement, to ensure the collected data are of high quality. Here you can even do additional measurements to optimize certain excitation points; if an impact is triggered while in this mode, the software will confirm if it is intentional and add it to the impact location that is currently selected in the matrix.
In VP mode, the VP FRF matrix is shown as a result of transformation of all responses and excitations that are associated with virtual points. The matrix will become square, and the specific VP DoFs follow from the definitions as set for the respective virtual points in Prepare. This is useful for e.g. mount characterization and Dynamic Substructuring.
In All mode, statistics are shown for both the measured FRF data and the VP FRF data, for a grand overview of all possible FRFs. Obviously, any update to the data takes the longest time to refresh in this mode, as every VP DoF gets recomputed.
In VP+ mode, statistics are shown similar to VP mode, but also including any microphones, additional sensors and control impacts that are not associated to any VP. This is useful for e.g. Dynamic Substructuring where it is desired to include additional impact or response data in the component model.
In Response-VP mode, the matrix is shown as a result of VP transformation of only the responses, with the excitations kept in the original framework. This is not used for most typical applications.
In Force-VP mode, the matrix is shown as a result of VP transformation of only the excitations, with the responses kept in the original framework. This is useful for many source characterization and transfer path analysis applications, as it typically results in a matrix that has more rows than columns, with the forces/moments located exactly at the desired (Virtual Point) interfaces.
Custom presets can also be defined to study any combination of measured and VP transformed excitations and responses. Custom presets can be generated from the context menu shown in Figure 7‑2 to open the window in Figure 7‑3. Here, the desired excitations and responses are selected. Note that you can also click on the “Type” and “Virtual Point” buttons near the top to sort and filter the channels.
Creating a custom selection is useful to focus on e.g. the left side of the car, a subset of VPs, etc. Additionally, to export a certain subset of data to ATFX or MAT (see 8.1: Export options), it must first be defined in a custom preset here.
Figure 7-3: Selection of response and reference channels for a custom preset in the measurement matrix
Just below the matrix, there are options to edit the data displayed in the matrix; see Figure 7‑4. This includes: frequency range, averaging, and quality mode (coherence, consistency, or reciprocity).
The frequency range over which the statistics are calculated can be edited using the slider bars or by entering values manually. Some presets are included for Low (0 – 100 Hz), High (0 – 3000 Hz), and Focus (20 – 1000 Hz) frequencies. The presets can be edited by right-clicking on them with a certain frequency range already selected. Averaging can be set to Mean, Minimum and Maximum: this defines the averaging over the selected frequency range.
The range for the values in the matrix can be edited by dragging the color bar on the right. Right-click presets are available for 0–100%, 50–100% and 90–100%.
Figure 7-4: Setting the frequency range and quality modes in the measurement matrix
There are several modes available for reviewing the quality of the measurement matrix. These options are accessed using the Mode: drop-down just below the matrix, as shown in Figure 7‑4. The available quality modes include: Coherence, Magnitude, Response/Force Consistencies and Reciprocity. The active mode can be easily recognized by the color displayed in the matrix.
The diagram shows the coherence over frequency. For measured FRFs, this is intuitive. For the various VP transformed FRFs, coherence is propagated from the measured FRFs. The VP transformation matrices are used here to calculate weighted averaged values of the “input” coherence.
The diagram shows the magnitude of the FRF over frequency. This is intuitive for any measured or VP transformed FRFs.
The diagram shows the specific response consistency over frequency for those response channels that are associated with a virtual point. For measured data, an additional curve is added to the graph in purple, which is the “VP-filtered” FRF for the selected FRF element.
For the various VP transformed FRFs, the consistencies are propagated from the measured FRF. The VP transformation matrices are used here to calculate weighted averaged values of the “input” consistencies.
This mode is similar to the response consistency mode, as described above, but for specific force consistency.
In reciprocity mode, only available for VP FRFs, the diagram shows the reciprocity between different VP DoF. Since the inputs and outputs of VP FRFs are truly collocated (some would say, “vectorially associated”), reciprocity can strictly be required on the matrix. Thus, the measurement matrix value shows the level of reciprocity between reciprocal entries. As a result, the diagonal is always 100%. Matrices with 100%-score throughout all entries are rarely seen; rather it is advised to focus on directions that have significant “coupling”, as a consequence of the structural nature of the component at hand. For diagonal entries, it is furthermore interesting to assess the passivity of the “driving-point” FRFs, by verifying if the phase angle is bound by 0–180 degrees.
In this mode, the graphing card shows the selected FRF (blue) together with reciprocal FRF (red), which is mirrored along the symmetry axis of the matrix. When blue is not seen, it means it is hidden by orange and you have in fact reached 100% reciprocity.
There are additional options that can be used to customize the display of the measurement matrix. These options are available using the buttons in the upper right corner of the measurement matrix card, as shown in Figure 7‑5.
It is possible to change the labels that are displayed for the response and reference channels. This is done by clicking the settings icon, and choosing the desired label type.
There are several scenarios when it may be desired to hide empty columns or rows. For example, if not all excitations have been measured, or if additional VPs are included in the project but have not been measured. The empty cells are hidden by clicking on the settings icon and selecting Hide empty cells.
For very large datasets, it may be desired to only display a subset of the channels in the matrix. This action is done using the filter icon, and toggling on or off the channels that should be displayed or hidden, respectively.
Note that filtering is only used for previewing data in the matrix, but a custom preset is required for exporting a subset of the matrix.
Figure 7-5: Options available for the measurement matrix
The Graphing card has a toggle button FL, which stands for “frequency lock”. When activated, the frequency range of the graphing card and the frequency range selection of the measurement matrix stay synchronized.
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