广义Tikhonov正则化工况传递路径分析

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (24) : 270-277.

论文

唐中华1，昝鸣1，张志飞1，徐中明1，晋杰2

作者信息 +

Operational transfer path analysis with generalized Tikhonov regularization method #br#

TANG Zhonghua1, ZAN Ming1, ZHANG Zhifei1, XU Zhongming1, JIN Jie2

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文章历史 +

摘要

工况传递路径分析是定位振动噪声问题的有效方法，广泛应用于各类工程领域中。但工况传递路径分析在估计传递率函数矩阵时，是一个病态的反问题，常用标准Tikhonov正则化法来改善病态性。标准Tikhonov正则化法以单位矩阵为正则化矩阵，经奇异值分解，得到的奇异向量振荡较严重，构成的正则化解准确度较低，因此路径贡献量的计算精度较低。针对此不足，以一阶偏导矩阵作为正则化矩阵，结合广义奇异值分解，得到振荡幅度更小的广义奇异向量。以广义奇异向量为基向量，并采用L曲线法选取正则化参数，得到广义Tikhonov正则化解，从而实现工况传递路径分析。最后通过工况传递路径分析仿真与实验验证了广义Tikhonov正则化工况传递路径分析方法的有效性，结果表明，与标准Tikhonov正则化相比，各路径贡献量的准确度更高，有效地提高了工况传递路径分析的精度。

Abstract

Operational transfer path analysis (OTPA) is an effective method to locate vibration and noise problems, which is widely used in various engineering fields. However, estimating the transmissibility matrix is an ill-conditioned inverse problem and the standard Tikhonov regularization method is often used to improve the ill-conditioning. The standard Tikhonov regularization, which takes an identity matrix as a regularization matrix, is decomposed by singular value decomposition to obtain the singular vector. However, the oscillation of the singular vector is relatively serious. Therefore, the accuracy of the regularized solution constructed by the singular vector is low and the accuracy of individual contribution is low, too. To improve the accuracy, the generalized Tikhonov regularization which takes the matrix approximating the first derivative operator as the regularization matrix is used to estimate the transmissibility matrix. After generalized singular value decomposition, the generalized singular vector whose oscillation is smaller than that of singular vector is used as the basis vector of the solution. The regularization parameter is selected by the L-curve method. Finally, the effectiveness of the generalized Tikhonov regularization method for OTPA is verified by simulation and experiment. The results show that the accuracy of individual contribution of the generalized Tikhonov regularization method is higher than that of the standard Tikhonov regularization method, and the accuracy of OTPA is improved effectively.

导出引用

唐中华1，昝鸣1，张志飞1，徐中明1，晋杰2. 广义Tikhonov正则化工况传递路径分析[J]. 振动与冲击, 2022, 41(24): 270-277

TANG Zhonghua1, ZAN Ming1, ZHANG Zhifei1, XU Zhongming1, JIN Jie2. Operational transfer path analysis with generalized Tikhonov regularization method #br#[J]. Journal of Vibration and Shock, 2022, 41(24): 270-277

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