Numerical and experimental flight verifications of a calibration matrix approach for load monitoring and temperature reconstruction and compensation

Mechanical and aeronautical structures could experience unexpected loads during operations, potentially reducing their operability. A load monitoring system enables one to recover the actual load spectra of the component and track its aging continuously. However, complex loading can be difficult to be identified, as for complex aerodynamic loads due to operational maneuvers in aeronautical structures, especially when environmental conditions vary. This work proposes a method for recovering the full strain and displacement fields in the entire structure, leveraging on the Calibration Matrix approach and an equivalent set of lumped forces, including the thermal variation among the unknown parameters. A least-squares minimization of an error functional defined as a comparison between measured and numerical strain is exploited for load and temperature reconstruction, automatically compensating thermal effects on the strain measurements without requiring any training data sets. By assuming a linear relationship between strain and the unknowns through a calibration matrix, the minimization can be performed analytically offline, resulting in a computationally very efficient algorithm that can be operated in real-time at a reduced computational burden. Though the mathematical formulation is general for any arbitrary component geometry and loading condition, the method is tested with a full-scale Unmanned Aerial Vehicle (UAV) undergoing different operational maneuvers, both numerically and with actual flight tests. The results confirm the robustness of the method to real environmental disturbances, correctly reconstructing the strain and displacement fields due to aerodynamic loads through triangular equivalent forces and automatically adapting to different load scenarios and temperature changes.