Real-Time Virtual Sensing for Dynamic Vibration of Flexible Structure via Fiber Bragg Grating Sensors

Real-time monitoring of the dynamic vibrations of beam-type structures indicates important implications in aerospace engineering applications, in which the additional sensing information about vibration parameters, including displacements, rotational angles, angular rates, as well as accelerations, facilitates the improvement of the system’s safety. This article proposed a virtual sensing method with the usage of fiber Bragg grating (FBG) strain sensors to directly estimate the vibration parameters from the measured strains. The algebraic relationships of displacement–strain and rotation–strain on the sensor’s installing points as well as the boundary points are obtained based on the Birkhoff interpolation method, and meanwhile, the explicit expressions on angular rates and accelerations are derived. Furthermore, a tracking differentiator is used to recover the strain signals and their first- and second-order derivatives from the noisy measurements in order to real-time estimate the angular rates and accelerations of the vibrating beam. Differing from the classical modal-based method, complex modal decomposition is not required in the proposed method. The comparison of numerical simulation results reveals that the proposed method has advantages over the modal-based method in accuracy and efficiency. Furthermore, the laboratory experiments indicate that the proposed method is effective for real-time estimating vibration parameters from the noisy measured strains.