动态载荷时域识别的联合去噪修正和正则化预优迭代方法

系统响应可表示为单位脉冲响应函数与激励载荷的卷积，将其离散化一组线性方程组，则载荷识别问题即转化为求解线性方程组的反问题。针对响应中带有噪音时载荷识别的困难，提出了联合奇异熵去噪修正和正则化预优的共轭梯度迭代识别方法。一方面对含噪信号进行基于奇异熵的去噪处理，提高反问题求解中输入数据的精度。另一方面利用正则化方法对共轭梯度迭代算法进行预优，改善反问题的非适定性。由于从输入的响应数据去噪和正则化算法两方面同时改善动态载荷识别反问题的求解，因此可以有效地抑制噪声，提高识别精度。通过数值算例分析，表明在不同的噪声水平干扰下，其识别精度均优于常规的正则化方法，能够实现有效稳定地识别动态载荷。最后通过实验研究进一步验证了该方法的正确性和有效性。

A joint method of denoising correction and regularization preconditioned iteration for dynamic load identification in time domain

It is difficult to directly measure the dynamic load due to the complex forms of the structure and the excitation. Therefore, how to accurately identify the dynamic load by indirect method is of great significance. The dynamic loads in the time domain are expressed as the superposition of a series of kernel function, and the response of the linear system can be obtained by the convolution integral of the kernel function and dynamic loads. Load identification is transformed into an inverse problem through discretizing the convolution integral into a set of linear equations. To solve the difficulties of load identification from the noisy response, a method of dynamic load identification is proposed based on the combination of the singular entropy denoising and the regularization preconditioned conjugate gradient iteration. In order to improve the accuracy of input data in solving the load identification problem, the singular entropy denoising method is introduced in the noisy response signal. Furthermore, the conjugate gradient iterative algorithm is preconditioned by Tikhonov regularization method to alleviate the ill-posedness from the inverse problem. Since the solution of load identification inverse problem is improved at two respects: the input response data denoising and regularization algorithm, the proposed method can effectively suppress noise and improve the identification accuracy. The numerical example indicates that it can identify dynamic load more accurately and stably compared with the other conventional regularization method under the different noise levels of interference. Finally the validity and the feasibility of the proposed method are demonstrated by the experiment.