动载荷反演问题的正则化求解

Regularization Solution to Inverse Problem of Dynamic Force Identification

将状态空间的结构振动方程时域离散化,建立动态载荷反演的力学模型。在问题求解过程中,由于结构矩阵的病态特性以及测量噪声的影响,常规最小二乘法往往失效,通过对载荷反演模型详细的剖析,指出该病态问题的本质,提出了相应的正则化求解方法。数值模拟表明了本文方法的有效性,其可以得到满足工程要求的稳定近似解。

In this paper, a discrete formulation of force identification in time domain is presented. The inverse problem of force identification is always ill-posed due to the inverse process of structural matrix and the noise in measured vibration responses, and the ordinary least square method always obtains meaningless solution. Therefore, a regularization technique is used to solve this inverse problem in order to alleviate the ill-posedness due to the inverse process of structural matrix and measurement noise in engineering. The numerical simulation results show that the regularized solution to force identification problem is valid.