2D shape reconstruction with Fiber Bragg Gratings embedded in rubbers using machine learning methods

This paper presents the development, signal analysis and application of an FBG array embedded smart rubber carpet for 2D shape reconstruction. The proposed sensor system is based on the optical fiber integration between two rubber layers, where the optical fibers have 7 FBGs for the quasi-distributed force assessment. The sensor system analysis is performed at room temperature in difference set of tests, namely the stability tests (without any applied force), the force characterization tests (forces applied directly on the FBG region) and the shape reconstruction tests (different forces applied at different positions in the carpet). The stability tests indicated a maximum variation below 0.02 nm considering all 7 FBGs, whereas the force characterization tests indicated a mean sensitivity of around 80 N/nm. However, it is worth to mention that there is a variation on the sensitivities considering all FBGs, which is related to minor thickness differences in the rubber layer that directly effects the strain transmission from the rubber layer to the optical fiber beneath it. Thereafter, the shape reconstruction occurs in two steps, the first one is the cubic interpolation between the FBGs, considering the boundary conditions on the carpet following the beam theory. Then, the k-nearest neighbors regression algorithm is used on the force distribution assessment with a dataset divided into training and testing with a 70/30 proportion. The shape reconstruction results indicate the feasibility of the proposed approach, where root mean squared errors below 0.65 N are obtained in the range of applied force between 3 N and 35 N. Therefore, the proposed smart carpet as a feasible option for different 2D shape reconstruction applications ranging from biomechanics to structural health monitoring.