BP Method with Rectified Linear Unit-based Nonlinear Decoupling for 3-axis FBG Force Sensor

A fiber Bragg grating (FBG) force sensor with a compact size has been designed which can achieve the detection of three force components (Fx, Fy, Fz). The sensor is mainly comprised of a deformable body, a support body, and 5 FBGs. Although the FBGs show advantageous sensitivity on forces, the coupled effect among the measured components along different directions brings difficulties in the precision improvement of the sensor. In this article, a Rectified Linear Unit (ReLU) -based Back Propagation (BP) method has been adopted to decouple the designed sensor and improve the precision. Its theoretical sensing model and nonlinear decoupling algorithm have been derived and introduced, respectively. Experiments have been implemented to investigate the feasibility of the adopted method. Compared with the linear method (LM) and sigmoid function-based BP method, the ReLU-based BP method has better measurement accuracy that the average relative errors are less than 2% of full scale (F.S.) for the designed 3-axis force sensor. Such a result validates the feasibility and effectiveness of the adopted method to decouple the nonlinear response of the designed sensor.