An Improved Inverse Finite Element Framework for Shape Sensing: Application of SVD-Based Extended Data-Driven Approach in Preregression

The inverse finite element method (iFEM) is an advanced shape-sensing framework that serves as a powerful tool for structural health monitoring (SHM). It enables real-time reconstruction of structural deformations through in situ strain measurements. However, the precision of the iFEM reconstruction heavily relies on the number and placement of strain sensors. In this study, the proposed approach is able to break through the limitations of regularity in sensor placement (SP), while further reducing the requirement for the number of sensors. One major contribution of this article is to leverage an extended data-driven approach based on singular value decomposition (SVD) to realize strain field preregression. The combination of the SVD-based extended data-driven approach with the iFEM framework containing physical information improves the credibility and interpretability, rendering it more appealing for practical applications. The use of SVD method makes iFEM better resistant to noise disturbances. Furthermore, it exhibits strong scalability and is not restricted by specific data-driven algorithms. To validate the feasibility of the proposed improved iFEM framework, the precision of the preregressed smooth strain measurements and iFEM predictions based on different types of inverse elements with varying orders is evaluated. The research results show that precise reconstruction of structural deformations can be realized, even with sparser strain SP. It provides a new perspective for the development of iFEM-based SHM technologies.