Inverse WKB recursive solution method for dynamic load identification of linear time-varying structural systems

To perform the accurate and efficient dynamic load identification (DLI) on time-varying (TV) structural systems, this paper proposes a novel time-domain dynamic load identification method, which we call the inverse Wentzel-Kramers-Brillouin (WKB) real function recursive solution. The proposed method can identify the dynamic loads of TV structural systems with different masses, damping, and stiffness online. Based on the WKB real function recursive solution, we first derive the acceleration recursive solution for linear time-varying (LTV) dynamic systems. Then, by reversing the acceleration recursive solution, we obtain the recursive formula for the dynamic load as a function of time. At each time step, this method performs recursion using the load and response of the previous time step to derive the current load. Finally, we demonstrate through numerical simulations that this algorithm has higher identification accuracy and computational efficiency than the inverse Wilson-theta method, and reduces the computation time significantly.