Numerical and experimental verification of an inverse-direct approach for load and strain monitoring in aeronautical structures

Aeronautical structures are increasingly aging, and the occurrence of unexpected loads could reduce their operability. A health and usage monitoring system would enable the continuous monitoring of the state of health of a structure and track its aging by a load monitoring system, which aims at the real-time reconstruction of the loads acting on a structure. However, sometimes the loads and the induced strain and stress fields are difficult to be reconstructed exactly, as for complex loading due to flight maneuvers. In this work, the full strain and load fields of a structure are reconstructed by an inverse-direct approach, leveraging on the calibration matrix approach. The latter exploits a least-squares minimization of an error functional, defined as the comparison between measured strains in discrete positions and a numerical formulation of the same, to reconstruct an equivalent, however representative, load set. By assuming a linear relationship between strain and load through a calibration matrix, this minimization can be performed analytically, leading to a computationally very efficient algorithm that can be operated online. Once the equivalent load set is computed, the full strain field can be estimated relying on a second calibration matrix linking the external loads to the strain field of the complete structure. The method has been numerically tested with an unmanned aerial vehicle (UAV) subjected to aerodynamic pressure loads simulating flight maneuvers. Finally, the results are experimentally validated during a ground test program on a real UAV, proving the robustness to different experimental uncertainties.