Optimal strain sensor layouts for shape sensing of thin-walled structures using the single sensor based inverse Finite Element Method

The reconstruction of the displacement field of a structure from discrete strain measurements, commonly referred to as shape sensing, has become essential for the development of efficient Structural Health Monitoring (SHM) frameworks and for the monitoring of morphing structures. Among the various methodologies developed in recent years, the inverse Finite Element Method (iFEM) has proven to be both accurate and computationally efficient. However, iFEM traditionally requires a large number of strain sensors and imposes constraints such as back-to-back sensor configurations, i.e. strain sensors need to be placed on both of the free surfaces of a thin-walled structure for each sensorized location. This last limitation has recently been addressed through the development of a Single Sensor Based iFEM (SSB-iFEM) formulation. This work explores, for the first time, the features of this novel formulation, not only to eliminate the back-to-back constraint, but also as a viable approach that, coupled with sensor pattern optimization, reduces the number of sensors required for iFEM-based displacement reconstructions. The analysis, conducted for the shape sensing of an aluminum stiffened panel, demonstrates that the SSB-iFEM can achieve the same accuracy as the standard iFEM with a significantly reduced set of strain sensors.