Displacement responses of a bridge as a result of external loadings provide crucial information regarding structural integrity and current conditions. Due to the relative characteristic of displacement, the conventional measurement approach requires reference points to firmly install the transducers, while the points are often unavailable for bridges. In this paper, a displacement estimation approach using Kalman filter-based data fusion is proposed to provide a practical means for displacement measurement. The proposed method enables accurate displacement estimation by optimally utilizing acceleration and strain in combination that have high availability and are free from reference points for sensor installation. The Kalman filter is formulated using a state-space model representing the double integration of acceleration and model-based strain-displacement relationship. The validation of the proposed method is conducted successfully by a numerical simulation and a field experiment, which shows the efficacy and accuracy of the proposed approach in bridge displacement measurement.

Response estimation at unmeasured locations using the limited number of measurements is an attractive topic in the field of structural health monitoring (SHM). Because of increasing complexity and size of civil engineering structures, measuring all structural responses from the entire body is intractable for the SHM purpose; the response estimation can be an effective and practical alternative. This paper investigates a response estimation technique based on the Kalman state estimator to combine multi-sensor data under non-zero mean input excitations. The Kalman state estimator, constructed based on the finite element (FE) model of a structure, can efficiently fuse different types of data of acceleration, strain, and tilt responses, minimizing the intrinsic measurement noise. This study focuses on the effects of (a) FE model error and (b) combinations of multi-sensor data on the estimation accuracy in the case of non-zero mean input excitations. The FE model error is purposefully introduced for more realistic performance evaluation of the response estimation using the Kalman state estimator. In addition, four types of measurement combinations are explored in the response estimation: strain only, acceleration only, acceleration and strain, and acceleration and tilt. The performance of the response estimation approach is verified by numerical and experimental tests on a simply-supported beam, showing that it can successfully estimate strain responses at unmeasured locations with the highest performance in the combination of acceleration and tilt.

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