Element level system identification with unknown input with Rayleigh damping

A novel system identification procedure is proposed for nondestructive damage evaluation of structures. It is a finite element-based time-domain linear system identification technique capable of identifying structures at the element level. The unique features of the algorithm are that it can identify a structure without using any input excitation information and it can consider both viscous and Rayleigh-type proportional damping in the dynamic models. The consideration of proportional damping introduces a source of nonlinearity in the otherwise linear dynamic algorithm. However, it will also reduce the total number of damping coefficients to be identified, reducing the size of the problem. The Taylor series approximation is used to transform a nonlinear set of equations to a linear set of equations. The proposed algorithm, denoted as the modified iterative least square with unknown input algorithm, is verified with several examples considering various types of structures including shear-type building, truss, and beams. The algorithm accurately identified the stiffness of structures at the element level for both viscous (linear) and proportional (nonlinear) damping cases. It is capable of identifying a structure even with noise-contaminated response information. An example shows how the algorithm could be used in detecting the exact location of a defect in a defective element. The algorithm is being developed further and is expected to provide an economical, simple, efficient, and robust system identification technique that can be used as a nondestructive defect detection procedure in the near future.