A novel shape sensing approach based on the coupling of Modal Virtual Sensor Expansion and iFEM: Numerical and experimental assessment on composite stiffened structures

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Shape sensing, i.e. the reconstruction of the displacement field of a structure from discrete strain measurements, is becoming crucial for the development of a modern Structural Health Monitoring framework. Nevertheless, an obstacle to the affirmation of shape sensing as an efficient monitoring system for existing structures is represented by its requirement for a significant amount of sensors. Two shape sensing methods have proven to exhibit complementary characteristics in terms of accuracy and required sensors that make them suitable for different applications, the inverse Finite Element Method (iFEM) and the Modal Method (MM). In this work, the formulations of these two methods are coupled to obtain an accurate shape sensing approach that only requires a few strain sensors. In the proposed procedure, the MM is used to virtually expand the strains coming from a reduced number of strain measurement locations. The expanded set of strains is then used to perform the shape sensing with the iFEM. The proposed approach is numerically and experimentally tested on the displacement reconstruction of composite stiffened structures. The results of these analyses show that the formulation is able to strongly reduce the number of required sensors for the iFEM and achieve an extremely accurate displacement reconstruction.