ABSTRACT This paper presents a new class of the equation error estimator using de-noised displacement by the temporal–spatial filter for the system identification in an elastic solid. The finite element method is employed to discretize the equation of motion for an elastic solid, and the Young’s modulus of each finite element is estimated by the proposed approach. The temporal–spatial filter is applied to de-noise measured nodal displacements and to reconstruct nodal accelerations. The equation of motion modified for the de-noised dynamic responses is derived, and the equation error estimator (EEE) for the system identification is defined with the modified equation of motion. The proposed EEE represents the residual error of the modified equation of motion over a measurement interval, and results in a nonlinear equation, which is solved by the successive substitution method. The sensitivity of the temporal–spatial filter required to solve the nonlinear equation is derived by the direction differentiation of the analytical expressions of the filter. The validity and accuracy of the proposed approach are tested through numerical simulation studies. It is shown that the proposed method yields accurate and stable solutions without regularization for all cases tested in this study.

中文翻译：

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使用时空滤波器降噪的测量位移方程误差估计器的公式，用于弹性固体的系统识别

摘要 本文提出了一类新的方程误差估计器，它使用时空滤波器的降噪位移来识别弹性固体中的系统。采用有限元方法离散化弹性固体的运动方程，并通过所提出的方法估计每个有限元的杨氏模量。时空滤波器用于对测量的节点位移进行降噪并重建节点加速度。推导出为去噪动态响应修正的运动方程，并用修正的运动方程定义用于系统辨识的方程误差估计器（EEE）。提议的 EEE 表示在测量间隔内修正的运动方程的残余误差，并导致非线性方程，用逐次代换法求解。求解非线性方程所需的时空滤波器的灵敏度是通过滤波器解析表达式的方向微分推导出来的。通过数值模拟研究测试了所提出方法的有效性和准确性。结果表明，对于本研究中测试的所有案例，所提出的方法无需正则化即可产生准确且稳定的解决方案。