基于动态响应灵敏度同步反演结构物理参数与输入的算法

Simultaneous identification of structural physical parameters and input based on dynamic response sensitivity

提出一种基于动态响应灵敏度概念,仅利用结构少数测点上的动态响应同步反演结构物理参数和输入的方法。首先,将结构的输入力进行正交多项式分解,推导了结构动态响应对输入力的正交系数和结构物理参数的灵敏度计算公式;然后,构造结构参数与输入同步反演的识别方程,并采用阻尼最小二乘法求解方程,同时识别结构物理参数变化与输入力时程;最后,分别利用一个五层平面框架结构和一个九榀三维刚架结构验证了方法的有效性。研究结果表明,该方法可以克服测量噪声和初始模型误差的影响,同步精确地识别结构的输入力和局部损伤引起的结构物理参数变化。

A new method was proposed to simultaneously identify structural physical parameters and input from several dynamic responses of a structure based on dynamic response sensitivity. The input forces on the structure were represented by using orthogonal polynomial approximation,and the sensitivity of the structural dynamic response with respect to the orthogonal coefficients of input forces and the physical parameters of the structure was derived analytically. The identification equation was set up and was solved with the damped least-squares method to simultaneously identify input forces and structural parameters. A five-story plane frame and a nine-bay three-dimensional frame were taken as examples for validating the proposed method,respectively. Numerical simulations with noisy measured accelerations and initial model errors showed that the proposed method could accurately identify the input forces and detect the changes of structural physical parameters caused by structural local damages.