Legendre Polynomials-Based Displacement Field Reconstruction of Plate-Type Structures With Quasi-Distributed FBG Sensors

Structural deformation estimation is of great interest for many engineering fields, such as aerospace structures, antenna panels, and so on. During operation, however, the direct measurement of global displacements is often difficult, due to the limits of installation space and electromagnetic interference. This article proposed a displacement field reconstruction method for deformed plate-type structures using discrete curvature measurements and a polynomial superposition approach. Specifically, the displacement field is expressed as a linear superposition of the Legendre polynomial basis functions, where the weight coefficients are calculated using the discrete curvatures captured by a quasi-distributed fiber Bragg grating (FBG) sensor array and the given boundary conditions. This method overcomes the drawback of error accumulation in other curvature-based methods due to the use of recursion operations. In addition, the curvature fitting and the determination of the number of polynomial basis functions were also presented to obtain the best reconstruction quality. Simulations and experiments have been conducted to validate the proposed method. The simulation results show that the displacement reconstruction precisions are more than 99% for two types of complex deformations. Experiments were carried out on an aluminum plate and a phased-array antenna panel, respectively. The results show that the reconstructed displacements of the reference points match well with those measured displacements, and the reconstruction precision exceeds 96%. This proposed curvature-based approach has high potential to global displacement monitoring of plate-type structures used in aerospace and antenna industrial fields.