On assessing the robustness of an input signal optimization algorithm for damage detection: the Info-Gap Decision Theory approach

The Info-Gap Decision Theory (IGDT) is here adopted to assess the robustness of a technique aimed at identifying the optimal excitation signal within a structural health monitoring (SHM) procedure. Given limited system response measurements and ever-present physical limits on the level of excitation, the ultimate goal of the mentioned technique is to improve the detectability of the damage increasing the difference between measurable outputs of the undamaged and damaged system. In particular, a 2 DOF mass-spring-damper system characterized by the presence of a nonlinear stiffness is considered. Uncertainty is introduced within the system under the form of deviations of its parameters (mass, stiffness, damping ratio ... ) from their nominal values. Variations in the performance of the mentioned technique are then evaluated both in terms of changes in the estimated difference between the responses of the damaged and undamaged system and in terms of deviations of the identified optimal input signal from its nominal estimation. Finally, plots of the performances of the analyzed algorithm for different levels of uncertainty are obtained, showing which parameters are more sensitive to the presence of uncertainty and thus enabling a clear evaluation of its robustness.