System identification method by using inverse solution of equations of motion in time domain and noisy condition

In direct system identification (DSI) method, inverse solution of the equations of motion is applied to obtain physical parameters of a linear system (structural mass, damping, and stiffness matrices). With the small error in measurement, caused by sensor drift or signal noise, these physical parameters are identified with a significant drift. In this paper, a new simple post-processing method is proposed, for error reduction in DSI in the time domain in a manner that structural properties are identified without applying the optimization process. In noisy condition, baseline correction is applied through a nonic curve-fitting approach. The modified signals are partitioned into a number of sub-signals, and their mean is applied for system identification. The number of sub-signals is optimized so that the root mean square (RMS) of off-diagonal components of the mass matrix becomes near zero. Seeking more precision, the residual force in every time step at all degrees of freedom (DOFs) is minimized. The validity of the proposed method is tested on a multistory structure, subjected to a random force at the foundation level. In terms of incomplete measurement and 5% noise, identified parameters including mass, stiffness and damping matrices, have satisfying mean errors of 0.094%, 0.545%, and 4.42% with the coefficient of variations of 0.35%, 1.38% and 6.98%, respectively. The sensitivity of the proposed method to the noise level is also investigated. It is observed that the baseline slop of velocity and displacement signals are sharply increased when the noise level goes beyond 3%.