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Seismic Damage Detection of Moment Resisting Frame Structures Using Time-Frequency Features

To detect seismic damage of moment resisting frame (MRF) structures, a data-driven method using the fractal dimension (FD) of time-frequency feature (TFF) of structural seismic dynamic responses at measured stories is extended and refined. The TFF is defined as the real part of Gabor wavelet transform of translational interstory displacement, and FD is used to give a quantitative value to describe the calculated TFF. Static condensation method is first used to reduce the degrees-of-freedom (DOFs) of MRF and to express the rotational displacements using translational displacements. For linear MRF, the FDs of TFFs at all stories are the same using the definition of TFF and modal superposition principle. For damaged MRF with plastic hinges at the ends of beams and columns, the force analogy method is implemented to establish transformation matrix from plastic hinge rotations to translational interstory inelastic displacements. Due to the sparseness of the transformation matrix, plastic hinges only generate interstory inelastic displacements, which are low-frequency contents, in the vicinity of plastic hinges. Correspondingly, the FDs of TFFs of interstory displacements with inelastic component are different from the FDs of TFFs of the interstory displacements that do not contain inelastic component. A numerical simulation on a 16-story MRF was conducted. The simulation included 10 cases such as no damage or linear structure, plastic hinges in single-story beams, plastic hinges in single-story columns, plastic hinges in single-story beams and columns, and plastic hinges in multiple story beams and columns. The robustness to measurement noise was also investigated. The seismic damage detection results demonstrated that the proposed method was capable of locating the stories where the plastic hinges occurred.