A new Single Sensor Based iFEM formulation for shape-sensing of thin-walled structures instrumented with single-sided sensor configurations: Formulation, numerical assessment, and experimental validation

The reconstruction of the displacement field from discrete strain sensors, known as shape-sensing, is becoming an essential tool for realizing an efficient Structural Health Monitoring framework. In fact, monitoring displacements during service life can provide crucial information to guide preventive maintenance operations and can lead to the realization of the digital twin paradigm for the monitored structure. The shape-sensing method that has seen more success in the open literature is the inverse Finite Element Method. Although it has numerous successful applications, an obstacle to the definitive affirmation of its role as an applicable monitoring system for operating structures is the demanding requirements for numerous installed sensors. In particular, for thin-walled structures, the standard formulation of the method requires installing sensors on both faces of the structure. This configuration increases the number of sensors and is often impractical. In this work, a new Single Sensor Based inverse Finite Element (SSB-iFEM) formulation is proposed to allow the reconstruction of the deformed shape of thin-walled structures instrumented with strain sensors only on one face. The SSB-iFEM is tested numerically on a plate and on a rectangular-section box, and both numerically and experimentally on a C-section beam. The results show that extreme accuracy in monitoring can be achieved with both back-to-back and single-sided sensor configurations, thus expanding the possible applications of iFEM and opening new perspectives for its application to real operating structures.