Based on the multivariate continuous time autoregressive （CAR） model, this paper presents a new time-domain modal identification method of linear time-invariant system driven by the uniformly modulated Gaussian random excitation. The method can identify the physical parameters of the system from the response data. First, the structural dynamic equation is transformed into a continuous time autoregressive model （CAR） of order 3. Second, based on the assumption that the uniformly modulated function is approximately equal to a constant matrix in a very short period of time and on the property of the strong solution of the stochastic differential equation, the uniformly modulated function is identified piecewise. Two special situations are discussed. Finally, by virtue of the Girsanov theorem, we introduce a likelihood function, which is just a con- ditional density function. Maximizing the likelihood function gives the exact maximum likelihood estimators of model parameters. Numerical results show that the method has high precision and the computation is efficient.
A kind of method of modal identification subject to ambient excitation is presented. A new synthesis stationary signal based on structural response wavelet transform and wavelet coefficient processes co-integration is obtained. The new signal instead of structural response is used in identifying the modal parameters of a non- stationary system, combined with the method of modal identification under stationary random excitation-the NExT method and the adjusted continuous least square method. The numerical results show that the method can eliminate the non-stationarity of structural response subject to non-stationary random excitation to a great extent, and is highly precise and robust.
A new time-domain modal identification method of linear time-invariant system driven by the non-stationary Gaussian random excitation is introduced based on the continuous time AR model. The method can identify physical parameters of the system from response data. In order to identify the parameters of the system, the structural dynamic equation is first transformed into the continuous time AR model, and subsequently written into the forms of observation equation and state equation which is just a stochastic differential equation. Secondly, under the assumption that the uniformly modulated function is approximately equal to a constant matrix in a very short time period, the uniformly modulated function is identified piecewise. Then, we present the exact maximum likelihood estimators of parameters by virtue of the Girsanov theorem. Finally, the modal parameters are identified by eigenanalysis. Numerical results show that the method we introduce here not only has high precision and robustness, but also has very high computing efficiency. Therefore, it is suitable for real-time modal identification.
DU XiuLi1,2 & WANG FengQuan1 1 College of Civil Engineering, Southeast University, Nanjing 210096, China
