A physical parameter identification method of Lévy-driven vibratory systems based on multipower variation processes

In this paper, we put forward a physical parameter identification method of Lévy-driven engineering structures. Based on the properties of the quadratic variation and multipower variation processes, the structural dynamic equation is decomposed into the Gaussian continuous-time autoregressive (CAR) equation and the pure jump-driven CAR equation. Both equations have the same unknown parameters as those included in the Lévy-driven system. The parameters of the Lévy-driven system are identified by the maximum likelihood estimation method of the Gaussian CAR system. The numerical results demonstrate that the method works well.