共轭梯度最小二乘迭代正则化算法在冲击载荷识别中的应用

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摘要结构动载荷识别反问题是典型的病态问题，需要应用正则方法克服其病态特性而获得稳定的解。与直接正则化算法Tikhonov方法相比，共轭梯度最小二乘 (Conjugate Gradient Least Squares, CGLS) 迭代算法在载荷识别反问题的正则化过程有无须对传递矩阵求逆、无须明确正则化参数的优点。本文提出共轭梯度最小二乘迭代正则化算法和启发式迭代收敛终止准则，用于三自由度仿真模型和壳结构试验模型的冲击载荷识别，并与经典的Landweber迭代正则化算法和直接正则化算法Tikhonov方法比较。仿真和实验结果表明：CGLS迭代正则化算法在识别精度、收敛速度、计算效率和抗噪性方面有明显优势。

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	卢立勤1
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	陈雪峰1

关键词 ：共轭梯度最小二乘算法, Landweber算法, 冲击载荷识别, 正则化

Abstract：

Regularization methods should be developed to overcome the ill-posedness of inverse problem of structural dynamic load identification for a stable solution. The conjugate gradient least squares (CGLS) iterative regularization algorithm has several advantages over direct regularization methods such as Tikhonov method on solving inverse problem: the inversion of matrix is not required; no explicit regularization parameter is required. In this paper, the CGLS iteration regularization algorithm with the heuristic stopping rule is proposed to reconstruct the impact load acting on the three-degrees-of-freedom system and the shell structure, compared to the classical Landweber iteration regularization algorithms and Tikhonov regularization method. Simulation and experiment demonstrates that the CGLS algorithm for impact load identification works better in accuracy, convergence rate, cost time and anti-noise.

Key words： conjugate gradient least squares algorithm Landweber algorithm impact load identification regularization method

收稿日期: 2015-05-28 出版日期: 2016-11-15

引用本文:

卢立勤1,2，乔百杰1，张兴武1，陈雪峰1. 共轭梯度最小二乘迭代正则化算法在冲击载荷识别中的应用[J]. 振动与冲击, 2016, 35(22): 176-182.
LU Li-qin1,2, QIAO Bai-jie1, ZHANG Xing-wu1, CHEN Xue-feng1. The application of conjugate gradient least squares iteration regularization algorithm in impact load identification. JOURNAL OF VIBRATION AND SHOCK, 2016, 35(22): 176-182.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2016/V35/I22/176

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