Research and development of structural health monitoring (SHM) of a building is vigorously proceeded in the resent academic research, which can help early recovering of urban facilities after a serious disaster such as a strong earthquake or wind, or reliable checking of structural integrity of facilities against the deterioration. Of SHM, vibration based-damage detection (VBDD) is considered promising to make a structural diagnosis of a building, where modal properties or stiffness are compared before and after the severe event. Story stiffness identification is one of the powerful tools in the VBDD, which can detect damage locations and the amounts in a damaged building. In a steel moment frame building, however, the seismic failures can be often appeared locally to be concentrated to the parts of the beam-ends, since vibration energy is dissipated in the plastic hinges at beam ends in seismic design: therefore one must firstly evaluate whether beam-ends are damaged or not. The traditional story stiffness identification scheme might not be useful in the SHM of steel building, since changes in the story stiffness due to the beam-ends damage should appear simultaneously on the upper and lower stories.
In the paper, a vibration-based system identification procedure of a lumped mass-spring-stick typed fish-bone model is proposed, in order to detect damage locations and their amounts in a steel frame building suffered damages at beam-ends. The fish-bone model has a rotational stiffness on every story, therefore, by using distributions of rotational stiffness, one can easily detect a severe story damaged with beam-end ruptures. A system identification scheme of a fish-bone model using Extended Kalman filter (EKF) is proposed, where rotational stiffness estimates at each story are identified as unknown parameter under the assumption that no columns are damaged: i.e., bending and shear stiffness in columns can be given as a priori. The effectiveness of the proposed method is verified by numerical simulation using the three-dimensional (3-D) frame model, and by real-life records on shaking table tests conducted in the E-defense of the world-largest shake table. By evaluating the transition of the rotational stiffness on the steel frame specimen, detectability of beam-end damage is also discussed. The main results in the paper are summarized as follows:
1) The identification scheme to the fish-bone model is theoretically derived with applying to the EKF by using the partial differential inverse matrix formula. Firstly, the equations of motion and the identification scheme are derived with consideration only the bending deformation of the beams and columns. Secondly, the identification was extended to consider both bending and shear deformations of beams and columns in the fish-bone model. The derived identification scheme is verified in numerical simulation of the 3-D frame. As a result, the rotational stiffness of the beam can be well-identified even when the members behave in three-dimensional deformations such as bending, shear and axial deformations.
2) Beam stiffness of the shaking table test specimen is evaluated by the proposed identification scheme, where observation record of the closely real-life specimen and closely real-life damage were tested in the E-defense. Each identified parameter of rotational stiffness is converged to a constant value in those experimental demonstrations. It is clarified that rotational stiffness of the beam can be well-identified for applying the real-life records.
3) As a result on several identifications of the rotational stiffness in several quake-experienced states, it can be evaluated that the estimates of the rotational stiffness of the beam decreased with the progress of a series of the shaking table tests. The distributions of the rotational stiffness are shown promising to detect beam-ends ruptures on a steel moment resisting frame structure.
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