A multiscale approach to the smart deployment of micro-sensors over flexible plates

In former studies, we proposed a topology optimization approach to maximize the sensitivity to damage of measurements collected through a network of sensors deployed over flexible, thin plates. Within such frame, damage must be intended as a change of the structural health characterized by a reduction of the relevant load-carrying capacity. By properly comparing the response of the healthy, undamaged structure and the response of the damaged one, independently of the location of the source of damage, a procedure to optimally deploy a given set of sensors was provided. In this work we extend the aforementioned approach within a multiscale frame, to account for (at least) three different length-scales: a macroscopic one, linked to the dimensions of the structure to be monitored; a mesoscopic one, linked to the characteristic size of the damaged region(s); a microscopic one, linked to the size of inertial microelectromechanical systems (MEMS) to be used within a marginally invasive health monitoring system. Results are provided for a square plate fully clamped along its border, to show how the micro-sensors are to be deployed to maximize the sensitivity of measurements to damage, and to also discuss the speedup obtained with the proposed multiscale approach in comparison with a standard single-scale one.