Structural response reconstruction in physical coordinate from deficient measurements

Abstract For structural health monitoring, the monitored data is limited to several locations in space. To overcome the measurement incompleteness, many approaches have developed, such as the shape sensing and the dynamic reduction expansion. However, the measurement noise will affect the calculated displacement. Then, the unbiased filtering approaches have developed to estimate the input and to update the state simultaneously, combining with Kalman filter. This study proposes an unbiased input estimation and state updating method that can process the complex process using deficient measurements (the complex process in this paper indicates the process contains both dynamic and quasi-static components). The proposed approach involves two steps: the first step adopts the principal component analysis to solve an under-determined equation, and obtains the noised complete displacement vector; the second step uses the Gillijns De Moor filter to eliminate the measurement noise and gets the unbiased displacement at all positions. Different from previous papers, this study expresses the motion of a structure in the physical coordinate, not in the modal coordinate, because the modal coordinate is not sufficient to describe the static and quasi-static responses. Besides, this study makes no assumption and has no prior knowledge over the input, and even the input position is unknown. Numerical simulations, using a twenty-floor frame and a three-span continuous bridge, have validated that the approach is efficient and accurate under the existence of white noise. Finally, an experiment has been conducted to validate the algorithm adopting a two-span continuous beam bridge model, which has demonstrated that the approach is robust to modeling errors and applies to complex input.