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.

中文翻译：

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从有缺陷的测量中重建物理坐标中的结构响应

摘要 对于结构健康监测，监测数据仅限于空间中的多个位置。为了克服测量的不完整性，已经开发了许多方法，例如形状传感和动态缩减扩展。然而，测量噪声会影响计算出的位移。然后，结合卡尔曼滤波器，开发了无偏滤波方法来估计输入并同时更新状态。本研究提出了一种无偏输入估计和状态更新方法，该方法可以使用缺陷测量处理复杂过程（本文中的复杂过程表明该过程包含动态和准静态分量）。所提出的方法包括两个步骤：第一步采用主成分分析来求解欠定方程，并得到噪声化的完整位移向量；第二步使用 Gillijns De Moor 滤波器消除测量噪声，得到所有位置的无偏位移。与以往的论文不同，本研究在物理坐标中表达结构的运动，而不是在模态坐标中，因为模态坐标不足以描述静态和准静态响应。此外，这项研究没有假设，也没有输入的先验知识，甚至输入位置也是未知的。使用二十层框架和三跨连续桥的数值模拟验证了该方法在存在白噪声的情况下是有效和准确的。最后，通过实验验证了采用两跨连续梁桥模型的算法，