When a multi-degree-of-freedom (MDOF) shear structure is excited by seismic excitation, the connections between structural and non-structural members may become loose or slight structural damage may arise, which cause the natural frequencies identified from the healthy structure shift. However, it is not easy to accurately re-identify the natural frequencies from the response recorded by one sensor. This paper presents a method to estimate the maximum inter-story drift and time histories of the relative displacement of all stories of the structure from the measured absolute response. First, the absolute acceleration and relative displacement are formulated in modal coordinates, and a state-space expression is derived. Then, a scheme to reduce the modeling error arising from shifts in the structural frequencies is devised that uses the genetic algorithm (GA) and a reasonably chosen fitness function. The applicability of this approach was investigated by conducting numerical simulations focusing on the rate of change in natural frequencies and selection of the lower bound of GA variables. Further simulations were conducted to investigate the robustness, installation location, and truncation error of the proposed method. Finally, the proposed approach was validated in a simple experiment. The results indicate that it can accurately estimate the time histories of the relative displacement and maximum inter-story drifts of all floors in the case of a significant change in natural frequencies and a large search range of GA variables. In addition, it is robust against environmental noise and performs well even when the model includes only lower modal responses.
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