基于Mindlin理论Winkler地基参数的Kalman滤波识别

提出了Winkler地基参数的Kalman滤波识别方法。引入Mindlin理论后，推导了Winkler地基上板的控制微分方程。利用Fourier变换，推求了Winkler地基上简支板的Fourier闭式解。推导了Winkler地基参数的Kalman滤波方程，研究了Winkler地基参数的Kalman滤波识别的具体计算步骤。研究表明，运用Kalman滤波理论进行Winkler地基参数的识别，能有效地估计Winkler地基参数；Winkler地基参数的滤波收敛速度和精度受地基参数初始值选取和位移实测资料的影响，且Kalman滤波理论也可用于其他地基模型地基参数的识别。

Kalman filtering identification of Winkler foundation's parameter based on Mindlin theory

Based on Kalman filtering theory, an identification method of Winkler foundation’s parameter is put forward. After Mindlin theory is introduced, the differential equations of Mindlin plate on Winkler foundation are derived. Through applying Fourier transformative technology, the corresponding solutions to the pinned plate on Winkler foundation are obtained. Kalman filtering equations of Winkler foundation’s parameter are established ; and the steps of Kalman filtering identification of Winkler foundation’s parameter are studied. Research shows that Winkler foundation’s parameter can be efficiently identified by applying Kalman filtering theory ; and the convergence velocity and precision of Winkler foundation’s parameter are depended on both the initial information of Winkler foundation’s parameter and the measured displacement data at the studied nodes. And this identification method can also be applied to the problem of identification of parameters of other foundation models.