Since physical parameters are much more sensitive than modal parameters, structural parameter identification with an extended Kalman filter (EKF) has received extensive attention in structural health monitoring for civil engineering structures. In this paper, EKF-based parameter identification technique is studied with numerical and experimental approaches. A four-degree-of-freedom (4-DOF) system is simulated and analyzed as an example. Different integration methods are examined and their influence to the final identification results of the structural stiffness and damping is also studied. Furthermore, the effect of different kinds of noise is studied as well. Identification results show that the convergence speed and estimation accuracy under Gaussian noises are better than those under non-Gaussian noises. Finally, experiments with a five-story steel frame are conducted to verify the damage identification capacity of the EKF. The results show that stiffness with different damage degrees can be identified effectively, which indicates that the EKF is capable of being applied for damage identification and health monitoring for civil engineering structures.

Based on the classical Timoshenko beam theory, the rotary inertia caused by shear deformation is further considered and then the equation of motion of the Timoshenko beam theory is modified. The dynamic characteristics of this new model, named the modified Timoshenko beam, have been discussed, and the distortion of natural frequencies of Timoshenko beam is improved, especially at high-frequency bands. The effects of different cross-sectional types on natural frequencies of the modified Timoshenko beam are studied, and corresponding simulations have been conducted. The results demonstrate that the modified Timoshenko beam can successfully be applied to all beams of three given cross sections, i.e., rectangular, rectangular hollow, and circular cross sections, subjected to different boundary conditions. The consequence verifies the validity and necessity of the modification.