基于自适应乘法正则化的结构随机激励识别

针对结构随机激励识别存在的激励位置未知以及重构效率偏低问题，本文提出了一种基于自适应乘法正则化的结构随机激励识别方法。该方法无需依赖于激励位置的先验信息，仅通过结构响应即可实现激励的准确定位和高效重构。首先，利用不同响应功率谱之间的传递特性来计算任意指定激励位置的定位误差，进而通过最小化定位误差来识别目标激励位置；在此基础上，借助自适应乘性正则化方法，定义全局正则化项来构造新的重构优化函数；然后，引入广义迭代加权最小二乘算法对优化函数进行求解，从而实现了结构随机激励识别；最后通过数值算例验证了所提方法的有效性。结果表明：所提方法能够精准的定位结构随机激励位置，且在与Tikhonov方法重构精度相似的基础上，提高了识别效率约15倍，同时具备良好的抗噪能力，为结构外部作用效应的获取提供了一种新思路。

Structural random excitation identification based on adaptive multiplicative regularization

In order to solve the problems of unknown excitation position and low reconstruction efficiency in structural random excitation identification, a method of structural random excitation identification based on adaptive multiplicative regularization is proposed in this paper. The method does not rely on the priori information of the excitation position, and can realize the accurate positioning and efficient reconstruction of the excitation only through the structural response. Firstly, the transfer characteristics between different response power spectra were used to calculate the location error of any specified excitation position, and then the target excitation position was identified by minimizing the location error. On this basis, with the help of adaptive multiplicative regularization method, the global regularization term is defined to construct a new reconstruction optimization function. Then, the generalized iterative weighted least squares algorithm is introduced to solve the optimization function, so as to realize the structure random excitation identification. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method. The results show that the proposed method can accurately locate the random excitation position of the structure, and on the basis of the reconstruction accuracy similar to that of Tikhonov method, the recognition efficiency is improved by about 15 times. At the same time, it has a good anti-noise ability, which provides a new idea for obtaining the external effect of the structure.