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Identification of joint structural state and earthquake input based on a generalized Kalman filter with unknown input

机译：基于通用卡尔曼滤波器的联合结构状态和地震输入的识别

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摘要

Accurate and real-time information of structural states and earthquake input is the prerequisite for structural seismic safety assessment and vibration control. When the earthquake input to a structure is not measured, it has been tried to identify structural state and the unknown earthquake input using the measured structural responses as an inverse problem. However, only structural absolute acceleration responses instead of the relative ones can be measured in this case, which limits the real-time performance of the existing Kalman filter with unknown input (KF-UI). In this paper, a generalized Kalman filter with unknown input (GKF-UI) is proposed to identify structural states and unknown earthquake inputs in real-time. Structural motion equations are established in the relative coordinate system and the observation equations are structural absolute acceleration-only measurements. The analytical derivation of the proposed GKF-UI is a direct extension of the classical Kalman filter (KF). It is also proven that the identification by the proposed GKF-UI using the absolute acceleration-only measurements under unknown earthquake excitation does not lead to the so-called drifted results in the previous identifications under unknown external excitations. Moreover, structural modeling errors can be considered in the identification by the proposed method. Then, it is extended to investigate the identification of the structural state of high-rise shear buildings and unknown earthquake inputs by combining the proposed GKF-UI with the modal expansion. Hybrid dynamic motion equations in modal space and observation equations in physical space are established to both reduce the state dimension and keep the one-dimension of unknown earthquake input instead of the increased number of unknown modal inputs. In addition, absolute accelerations are used in the observation equations, which avoids the dilemma that absolute accelerations cannot be converted into relative modal accelerations in the relative coordinate system under unknown earthquake input. Some numerical examples are used to verify the proposed method. Moreover, a shaking table test is adopted to further validate the performances of the proposed method.
机译：结构状态和地震投入的准确性和实时信息是结构地震安全评估和振动控制的先决条件。当未测量结构的地震输入时，已经尝试使用测量的结构响应作为逆问题识别结构状态和未知地震输入。然而，在这种情况下，只能测量结构绝对加速响应而不是相对的加速度响应，这限制了现有卡尔曼滤波器的实时性能，其中具有未知输入（Kf-UI）。在本文中，提出了一种具有未知输入（GKF-UI）的通用卡尔曼滤波器，以实时识别结构状态和未知地震输入。结构运动方程在相对坐标系中建立，并且观察方程是仅结构绝对加速度测量。所提出的GKF-UI的分析推导是经典卡尔曼滤波器（KF）的直接扩展。还证明了所提出的GKF-UI使用在未知地震激励下仅使用绝对加速度的测量的识别不会导致所谓的漂移导致在未知的外部激励下的先前识别。此外，通过所提出的方法可以在识别中考虑结构建模误差。然后，通过将所提出的GKF-UI与模态扩展组合来延长识别高层剪切建筑物和未知地震输入的识别。建立模态空间中的混合动态运动方程和物理空间中的观察方程，以减少状态尺寸，并保持未知地震输入的一维，而不是增加数量的未知模态输入。另外，在观察方程中使用绝对加速度，这避免了绝对加速度不能转换为在未知地震输入的相对坐标系中的相对模态加速度的困境。一些数值例子用于验证所提出的方法。此外，采用振动台测试来进一步验证所提出的方法的性能。

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