Estimation of bridge displacement responses using FBG sensors and theoretical mode shapes

Bridge vibration displacements have been directly measured by LVDTs (Linear Variable Differential Transformers) or laser equipment and have also been indirectly estimated by an algorithm of integrating measured acceleration. However, LVDT measurement cannot be applied for a bridge crossing over a river or channel and the laser technique cannot be applied when the weather condition is poor. Also, double integration of accelerations may cause serious numerical deviation if the initial condition or a regression process is not carefully controlled. This paper presents an algorithm of estimating bridge vibration displacements using vibration strains measured by FBG (Fiber Bragg Grating) sensors and theoretical mode shapes of a simply supported beam. Since theoretically defined mode shapes are applied, even high modes can be used regardless of the quality of the measured data. In the proposed algorithm, the number of theoretical modes is limited by the number of sensors used for a field test to prevent a mathematical rank deficiency from occurring in computing vibration displacements.89The proposed algorithm has been applied to various types of bridges and its efficacy has been verified. The closeness of the estimated vibration displacements to measured ones has been evaluated by computing the correlation coefficient and by comparing FRFs (Frequency Response Functions) and the maximum displacements.