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The necessary measurement points

By 19 July 2021No Comments

How many measurement points are needed to perform a modal analysis?

Basically, the simplest answer is that a sufficient number of measurement points must be measured to be able to uniquely describe the modal deformation of each mode. This answer may not be entirely obvious. Let us start with a model of a 7-storey building as shown in Figure 1.


We will consider 7 measurement points along one edge of the building, with one measurement point per floor, evenly distributed. To these 7 measurement points we add a measurement point at the base of the building. For this example, we are interested in the 2nd bending mode in the x direction. From figure 2 we can see that there are enough points to describe the shape of the mode completely.


Now consider only 6 measurement points, then 5, then 4 and finally 3 points along the structure. The modal deformations from these measurements are shown in Figure 3.

Comparison

If we compare the modal deformation with 8 points, 3 points or 4 points of measurement, we quickly realise that the description of the deformation is less complete. The "accurate description" of the modal deformation is lost. We already start to lose local information from 6 measurement points. This lack of information could be a problem when detecting/locating damage, for example.

Indeed, between 8 and 6 measurement points, the loss of information is localised at the level of the 1st and 4th floors. The deformation is locally modified when an event causes damage to one of these two floors. The other floors are not necessarily affected by this modification.

Would it be possible to measure the mode fairly well with the 8 differently distributed measurement points?

No, but this depends strongly on the mode of interest and the location of the 8 points. If these 8 measurement points are placed on several edges of the building, and if each measurement point is placed on a node of the modal deformation, the description will never be sufficient.