4. Checking the quality of the results

The quality of the identification carried out is verified by calculating the value RMS of the difference between the measured movements and the re-synthesized movements.

The reference value to be reached is zero, with an accuracy of \({10}^{\mathrm{-}3}\), compared to the value of the RMS of the measured displacement (of the order of \({10}^{1}\)).

This verification can be carried out in the real case where we do not know the efforts applied (since we want to identify them), and the only quality criterion for the result of the opposite problem is the ability of the efforts to find the movements measured. But it should not be forgotten that several different inputs can lead to the same measured displacement. The choice of the initial location of the efforts is important. It should be noted that for the inverse problem to be over-determined, it is necessary to respect the double inequality \({\mathit{nb}}_{\mathit{mes}}>{\mathit{nb}}_{\mathit{modes}}>{\mathit{nb}}_{\mathit{act}}\), where \({\mathit{nb}}_{\mathit{mes}}\) is the number of measurement points, \({\mathit{nb}}_{\mathit{modes}}\) is the number of modes used in the modal decomposition, and \({\mathit{nb}}_{\mathit{act}}\) is the number of points for the location of the efforts chosen a priority.

In the case where one seeks to identify a fluid force applied to a linear structure, one is generally satisfied with identifying an « equivalent » force applied to a point of the structure.