Modal identification based on Gaussian continuous time autoregressive moving average model

A new time-domain modal identification method of the linear time-invariant system driven by the non-stationary Gaussian random force is presented in this paper. The proposed technique is based on the multivariate continuous time autoregressive moving average (CARMA) model. This method can identify physical parameters of a system from the response-only data. To do this, we first transform the structural dynamic equation into the CARMA model, and subsequently rewrite it in the state-space form. Second, we present the exact maximum likelihood estimators of parameters of the continuous time autoregressive (CAR) model by virtue of the Girsanov theorem, under the assumption that the uniformly modulated function is approximately equal to a constant matrix over a very short period of time. Then, based on the relation between the CAR model and the CARMA model, we present the exact maximum likelihood estimators of parameters of the CARMA model. Finally, the modal parameters are identified by the eigenvalue analysis method. Numerical results show that the method we introduced here not only has high precision and robustness, but also has very high computing efficiency. Therefore, it is suitable for real-time modal identification.