基于Tikhonov正则化迭代求解的结构损伤识别方法

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摘要求解以结构物理与模态信息所构成的线性方程组，而获得结构的损伤位置和损伤程度，是进行结构损伤检测的一种常用做法。然而，在噪声影响下，其求解往往会出现振荡发散的情况，导致损伤检测结果不准确。Tikhonov正则化方法广泛应用于噪声条件下的线性系统求解，该方法执行的关键是选择合理的正则化矩阵及正则化参数。文章提出了一种迭代化的Tikhonov正则化方法，通过迭代的方式重构正则化矩阵，在充分抑制噪声的同时，保留了真实的损伤信息。同时，提出了奇异值二分法，自适应地调整正则化参数，避免了传统“L-曲线”方法选取正则化参数时需要进行大量试算等诸多问题。选取一海洋平台结构对提出方法的有效性进行验证，并与传统Tikhonov正则化方法进行对比，结果表明：提出的迭代型Tikhonov正则化方法具有更好的损伤识别结果。

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关键词 ：海洋平台, 损伤检测, 交叉模态应变能, Tikhonov正则化, 噪声鲁棒性

Abstract：Solving a linear equation set constructed with structural physical and modal information to acquire a structure’s damage location and damage level is a common method in structural damage detection.However, under effects of noise, oscillation and divergence phenomena may appear in solving to cause incorrect structural damage detection results.Tikhonov regularization method is widely used to solve linear systems under noise condition, and the key point to correctly apply this method is choosing an appropriate regularization matrix and regularization parameters.Here, a Tikhonov regularization iterative method (TRIM) was proposed to reconstruct regularization matrix through iteration, effectively suppress noise and retain actual damage information.Meanwhile, the singular value dichotomy was proposed to adaptively adjust regularization parameters and avoid mass trial calculation for selecting these parameters using the traditional "L-curve" method.An offshore platform structure was selected to verify the effectiveness of the proposed method, and compare the results using TRIM with those using the traditional Tikhonov regularization method.The results showed that the proposed TRIM has better damage identification results.

收稿日期: 2018-03-16 出版日期: 2019-08-28

引用本文:

夏志鹏，王树青，徐明强，王皓宇. 基于Tikhonov正则化迭代求解的结构损伤识别方法[J]. 振动与冲击, 2019, 38(17): 251-259.
XIA Zhipeng WANG Shuqing XU Mingqiang WANG Haoyu . Structural damage identification based on TRIM. JOURNAL OF VIBRATION AND SHOCK, 2019, 38(17): 251-259.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2019/V38/I17/251

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