基于子结构的非线性参数系统动力反演方法研究

Nonlinear system parameters inversion method based on substructure

研究了输入、输出不完备情况下的非线性参数系统动力反演问题。将子结构技术与分解算法相结合,引入广义逆,无需迭代,直接求得待识别参数的极小范数最小二乘解,反演获得未知输入荷载。本文从理论上论证了该方法的收敛性和严格的适用条件,为有限测点条件下非线性参数系统的动力反演问题提供了一个较好的解决方法。与全量补偿算法相比,计算效率大大提高,具有广泛的工程实际应用前景。数值算例表明该方法具有很好的参数识别精度及荷载反演效果。

The nonlinear system parameter identification problem with incomplete input and output information is studied. The consideration of Rayleigh-type proportional damping introduces a nonlinear system parameters identification problem. In this paper, combined with decomposition algorithm, the proposed method obtains minimal norm least square solution of the unknown system parameter and the unknown input in one step by using Moore-Penrose Pseudo-inverse. The substructure method offers an efficient approach for the dynamic detection of engineering structures with limited observations. Compared with Compensation Method, the method is more efficient and has a wider application background. The numerical example shows that the proposed approach can effectively identify the structural parameters from incomplete measurements. The algorithm is expected to provide an economical, simple, efficient,and robust system identification technique that can be used as a nondestructive defect detection procedure in the future.