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

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Journal of Vibration and Shock ›› 2022, Vol. 41 ›› Issue (24) : 270-277.

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

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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.

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noise and vibration / operational transfer path analysis / generalized Tikhonov regularization / generalized singular value decomposition

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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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