For decades, the damage or collapse of structures due to structural deterioration has occurred in countries around the world. In order to prevent the occurrence of the disaster, structure health monitoring and diagnosis become an essential issue. In this paper, first, autoregressive with exogenous input (ARX) model and the proper orthogonal decomposition (POD) method in time domain are used to identify system parameters of a small-scaled column specimen such as natural frequencies and modal shapes based on measured time-history response of the column. Then, numerical results through finite element simulation by the software “Nastran” are obtained to compare with the result of system identification by the ARX model and POD method. These comparisons can validate the correctness of system identification. Furthermore, for structure health diagnosis, model shapes, modal shape curvatures, and modal strain energy indices are utilized as indices to detect damage. First, mode shapes are generated by numerical simulation. Then, modal shape curvatures are obtained by the central difference method. Finally, modal strain energy indices can be derived according to the formula of strain energy of beams and calculated by numerical integration. The numerical results show that modal shape curvatures and modal strain energy indices are sensitive to damage location and can identify damage location accurately. Next, these two damage indices are applied to real experimental data. However, the results of detecting damage location are not satisfied. Because the only four accelerometers in testing are used to collect acceleration response, mode shape data from system identification is incomplete. Although more mode shape data may be generated by applying curve fitting to the identified four mode shape data, the calculation of modal strain energy indices based on the augmented mode shape data is still not accurate.