中文摘要：

提出一种利用结构在未知基底激励作用下，少数测点上的动态响应同步反演结构物理参数与基底激励的算法。首先，利用正交多项式展开结构基底激励，推导结构动态响应对结构物理参数和正交系数的灵敏度公式，并通过引入权值，克服由于不同待识别参数之间灵敏度向量的数量级差别较大而引起的灵敏度矩阵病态问题；然后，构造同步反演结构物理参数与基底激励的识别方程，并采用阻尼最小二乘法通过迭代计算求得方程最优解，完成结构物理参数与基底激励的同步反演；最后，采用一个12层的高层框架结构验证了算法的有效性。研究结果表明，该算法可利用少数测点响应同步精确反演结构的物理参数与未知基底激励。

英文摘要：

A new method is proposed to simultaneously identify structural physical parameters and support excitation from several structural dynamic responses under unknown support excitation. The support excitation on structures is represented by using orthogonal polynomial approximation, and the sensitivity of structural dynamic response with respect to structural physical parameters and orthogonal coefficients is derived. Weighted functions are adopted to overcome the ill condition of sensitivity matrix caused by the different magnitude scales of sensitivity vectors for different identified parameters. The identification equation is set Up and is solved with the damped least-squares method in an iterative process to simultaneously identify structural parameters and support excitation. A twelve-story frame is taken as an example for validating the proposed method. Research results show that the proposed method can accurately identify structural physical parameters and unknown support excitation from only several responses of structures.