Real-time response estimation of structural vibration with inverse force identification

This study aimed to develop a virtual sensing algorithm of structural vibration for the real-time identification of unmeasured information. First, certain local point vibration responses (such as displacement and acceleration) are measured using physical sensors, and the data sets are extended using a numerical model to cover the unmeasured quantities through the entire spatial domain in the real-time computation process. A modified time integrator is then proposed to synchronize the physical sensors and the numerical model using inverse dynamics. In particular, an efficient inverse force identification method is derived using implicit time integration. The second-order ordinary differential formulation and its projection-based reduced-order modeling is used to avoid two times larger degrees of freedom within the state space form. Then, the Tikhonov regularization noise-filtering algorithm is employed instead of Kalman filtering. The performance of the proposed method is investigated on both numerical and experimental testbeds under sinusoidal and random excitation loading conditions. In the experimental test, the algorithm is implemented on a single-board computer, including inverse force identification and unmeasured response prediction. The results show that the virtual sensing algorithm can accurately identify unmeasured information, forces, and displacements throughout the vibration model in real time in a very limited computing environment.