Modal identification of system driven by lévy random excitation based on continuous time AR model

Based on the continuous time AR model, this paper presents a new time-domain modal identification method of LTI system driven by the uniformly modulated lévy random excitation. The structural dynamic equation is first transformed into the observation equation and the state equation (namely, stochastic differential equation). Based on the property of the strong solution of the stochastic differential equation, the uniformly modulated function is identified piecewise. Then by virtue of the Girsanov theorem, we present the exact maximum likelihood estimators of parameters. Finally, the modal parameters are identified by eigen analysis. Numerical results show that the method not only has high precision and robustness but also has very high computing efficiency.