Time domain SI Scheme
for TIme-invariant and Time-variant Structural System
Seung Keun Park
This paper presents a time domain system identification (SI) scheme for assessment of damping and stiffness parameters of time-invariant and time-variant structural system using measured acceleration.
In time-invariant structural system, structural parameters are estimated by using output error estimator (OEE) method and numerical algorithm for subspace state-space system identification (N4SID) method. Second-order dynamic equilibrium equation and discrete time state-space model is used for system equation in OEE method and N4SID method, respectively. In OEE method, an error function is defined as the time integral of the leastsquared errors between measured accelerations and calculated accelerations by a numerical model of a structure. Damping properties as well as stiffness properties of a structure are considered as system parameters. Structural damping is approximated by the Rayleigh damping model and Caughey damping model. To alleviate the ill-posedness of SI problems a regularization technique is employed. The regularization factor is determined by the geometric mean scheme. Numerical algorithm for subspace state-space system identification (N4SID) method is introduced. Input and output block Hankel matrix is used for extraction of system matrix. The main computational tools are the QR and singular value decompositions. The validity of the proposed method is demonstrated by an experimental laboratory study on a three-story shear building model, a numerical simulation study on a two-span truss bridge and an experimental laboratory study on cable vibration test.
In time-variant structural system, a moving time-window technique is proposed to trace abrupt changes in the structural parameters caused by sudden damage. The time window represents a finite time interval, in which the SI procedures are performed assuming time-invariant system parameters. As the time window moves forward, the variation of system parameters in time is identified. In the formulation of a new regularization function in time domain, a weighting factor is introduced to balance the relative regularization effect between stiffness and damping parameters. A truncated singular value decomposition scheme is applied to impose the regularization function on the minimization of the error function. Numerical simulation studies are presented to demonstrate the validity of the proposed method.
Time Domain System Identification, Ouput Error Estimator, N4SID, Regularization Technique, Estimation of Damping Ratio, Time Windowing Technique