MAC and DPR-Based Embedded Optical Fiber Shape Sensing for Thin Flexible Space Membranes Using Modal Shapes Superposition

Thin and flexible composite structures are promising candidates for future space applications, particularly in large deployable systems such as antennas, reflectors, and solar sails. These gossamer-like structures offer high deployability and high weight-to-volume ratio, making them ideal for space missions requiring compact storage and in-orbit deployment. However, their performance is highly sensitive to deformation and shape inaccuracies. Ensuring structural integrity and proper shape configuration in orbit requires advanced Structural Health Monitoring (SHM) techniques capable of real-time shape sensing. This study presents an innovative methodology for shape reconstruction of thin and flexible composite structures using embedded Fiber Bragg Grating (FBG) sensors. The shape reconstruction is performed as a linear superposition of modal shapes, which form an orthogonal basis set for the structural deformation field. By leveraging this approach, the deformation state of the structure is expressed as a weighted sum of selected subset of modal shapes, allowing for a physically meaningful representation of arbitrary structural configurations. A novel optimization strategy, based on the Modal Assurance Criterion (MAC), is developed to identify optimal sensor locations that minimize modal aliasing, complexity of the structures and mass. Unlike conventional approaches that rely on dense sensor networks, this method exploits a reduced number of FBG sensors, strategically positioned along a path to maximize independent strain measurements. The methodology is validated through experimental studies on composite plate with embedded FBG sensors. The final prototype undergoes static shape reconstruction trials, where the reconstructed shapes are compared to numerical predictions to evaluate accuracy and consistency. The results demonstrate the feasibility of the proposed method for tracking the shape evolution of flexible structures subjected to external loads and boundary constraints. The proposed method offers a viable solution for HUMS/SHM in space applications, enabling precise shape monitoring of deployable structures with a minimal number of sensors. This work paves the way for future developments in autonomous in-orbit structural diagnostics, enhancing the reliability and performance of next-generation space structures.