Strain Pre-Extrapolation Methods for Shape Sensing: A Comparative Study between Modal Virtual Sensor Expansion and Smoothing Element Analysis

Abstract

Reconstructing the displacement field from discrete strain measurements, commonly referred to as shape sensing, has become a key component in developing effective Structural Health Monitoring (SHM) systems. Tracking displacements during a structure’s service life provides valuable insights for preventive maintenance and supports the implementation of digital twin models. Among the various shape sensing techniques, the inverse Finite Element Method (iFEM) has gained a lot of attention in the literature. Despite its numerous successful applications, its broader adoption as a practical monitoring tool for in-service structures is limited by the need for many strain sensors. Therefore, the algorithm is often coupled with strain pre-extrapolation techniques, which can virtually expand the information from a few physical sensors. The most widely used method to operate this task is the Smoothing Element Analysis (SEA). Although it has proven effective in different scenarios, its effectiveness and applicability are limited when it comes to addressing built-up structures with complex geometrical domains. An algorithm which overcomes this limitation has been recently proposed, the Modal Virtual Sensor Expansion (Modal VSE). This method, based on the extrapolation through modal strain shapes, has proven to be effective, but has never been compared with existing methods. In this work, the Modal VSE is benchmarked against SEA on the strain pre-extrapolation and consequent shape sensing of a composite stiffened panel. The Modal VSE shows a higher accuracy and adaptability in the process than SEA. These results are confirmed when the signal from strain sensors is perturbed by uncertainties typical of experimental scenarios.

Keywords: Structural health monitoring, Modal VSE, SEA, shape sensing, strain pre-extrapolation