广义Tikhonov正则化工况传递路径分析

摘要
图/表
参考文献(23)
相关文章 (15)

全文: PDF (2193 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

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。

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	唐中华1
	昝鸣1
	张志飞1
	徐中明1
	晋杰2

关键词 ：振动噪声, 工况传递路径分析, 广义奇异值分解, 广义Tikhonov正则化

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.

Key words： noise and vibration operational transfer path analysis generalized Tikhonov regularization generalized singular value decomposition

收稿日期: 2021-09-01 出版日期: 2022-12-28

引用本文:

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#. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(24): 270-277.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I24/270

[1] VAN DER SEIJS M V, DE KLERK D, RIXEN D J. General framework for transfer path analysis: History, theory and classification of techniques[J]. Mechanical Systems and Signal Processing, 2016, 68-69: 217-244.
[2] DIEZ-IBARBIA A, BATTARRA M, PALENZUELA J, et al. Comparison between transfer path analysis methods on an electric vehicle[J]. Applied Acoustics, 2017, 118: 83-101.
[3] 屠翔宇, 蒋伟康, 朱志勇, 等. 乘用车油箱的燃油晃动噪声工况传递路径分析[J]. 振动与冲击, 2017, 36(18): 184-188.
TU Xiangyu, JIANG Weikang, ZHU Zhiyong, et al. Operational transfer path analysis on the fuel tank sloshing noise of automotives[J]. Journal of Vibration and Shock, 2017, 36(18): 184-188.
[4] DE KLERK D, OSSIPOV A. Operational transfer path analysis: Theory, guidelines and tire noise application[J]. Mechanical Systems and Signal Processing, 2010, 24(7): 1950-1962.
[5] CERVANTES-MADRID G, PERAL-ORTS R, CAMPILLO-DAVO N, et al. Inverse transfer path analysis, a different approach to shorten time in NVH assessments[J]. Applied Acoustics, 2021, 181: 108178.
[6] 高阳, 朱自未, 谢素明, 等. 高速列车转向架上方客室噪声传递路径分析[J]. 机械工程学报, 2020, 56(04): 168-176.
GAO Yang, ZHU Ziwei, XIE Suming, et al. Transfer Path Analysis of Interior Noise above Bogie Area of High-speed Train[J]. Journal of Mechanical Engineering, 2020, 56(04): 168-176.
[7] 袁旻忞, SHEN A, 鲁帆, 等. 高速列车运行工况下噪声传递路径及声源贡献量分析[J]. 振动与冲击, 2013, 32(21): 189-196.
YUAN Minmin, SHEN Anne, LU Fan, et al. Operational transfer path analysis and noise sources contribution for China railway high-speed(CRH)[J]. Journal of Vibration and Shock, 2013, 32(21): 189-196.
[8] 张磊, 曹跃云, 杨自春, 等. 水下圆柱壳体结构噪声的工况传递路径分析[J]. 振动测试与诊断, 2012, 32(06): 897-902+1032.
ZHANG Lei, CAO Yueyun, YANG Zichun, et al. Structure-borne noise of submerged Cylindrical shell based on operational transfer path analysis [J]. Journal of Vibration ,Measurement and Diagnosis, 2012, 32(06): 897-902+1032.
[9] GAJDATSY P, JANSSENS K, DESMET W, et al. Application of the transmissibility concept in transfer path analysis[J]. Mechanical Systems and Signal Processing, 2010, 24(7): 1963-1976.
[10] CHENG W, LU Y, ZHANG Z. Tikhonov regularization-based operational transfer path analysis[J]. Mechanical Systems and Signal Processing, 2016, 75: 494-514.
[11] HANSEN P C. Rank-Deficient and Discrete Ill-Posed Problems[M]. Philadelphia: SIAM, 1998.
[12] 成玮, 卢英英, 陆建涛, 等. Tikhonov正则化在运行工况传递路径分析的应用[J]. 振动测试与诊断, 2017, 37(01): 57-64+199.
CHENG Wei, LU Yingying, LU Jiantao, et al. Tikhonov regularization for operational transfer path analysis[J]. Journal of Vibration ,Measurement and Diagnosis, 2017, 37(01): 57-64+199.
[13] LI R, BU W. Multi-parameter Tikhonov regularization-based OTPA with application to ship-radiated noise evaluation[J]. AIP Advances, 2021, 11(1): 015240.
[14] CHRISTENSEN-DALSGAARD J, HANSEN P, THOMPSON M. Generalized Singular Value Decomposition Analysis of Helioseismic Inversions[J]. Monthly Notices of the Royal Astronomical Society, 1993, 264: 541.
[15] BUCCINI A, PASHA M, REICHEL L. Generalized singular value decomposition with iterated Tikhonov regularization[J]. Journal of Computational and Applied Mathematics, 2020, 373: 112276.
[16] WEI Y, XIE P, ZHANG L. Tikhonov Regularization and Randomized GSVD[J]. SIAM Journal on Matrix Analysis and Applications, 2016, 37(2): 649-675.
[17] BECK A, BEN-TAL A. On the Solution of the Tikhonov Regularization of the Total Least Squares Problem[J]. SIAM Journal on Optimization, 2006, 17(1): 98-118.
[18] GAUTHIER P A, CAMIER C, PASCO Y, et al. Beamforming regularization matrix and inverse problems applied to sound field measurement and extrapolation using microphone array[J]. Journal of Sound and Vibration, 2011, 330(24): 5852-5877.
[19] HANSEN P C, O’LEARY D P. The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems[J]. SIAM Journal on Scientific Computing, 1993, 14(6): 1487-1503.
[20] CHOI H G, THITE A N, THOMPSON D J. Comparison of methods for parameter selection in Tikhonov regularization with application to inverse force determination[J]. Journal of Sound and Vibration, 2007, 304(3-5): 894-917.
[21] WANG Z, ZHU P. A system response prediction approach based on global transmissibilities and its relation with transfer path analysis methods[J]. Applied Acoustics, 2017, 123: 29-46.
[22] VAITKUS D, TCHERNIAK D, BRUNSKOG J. Application of vibro-acoustic operational transfer path analysis[J]. Applied Acoustics, 2019, 154: 201-212.
[23] SHIN K. An alternative approach to measure similarity between two deterministic transient signals[J]. Journal of Sound and Vibration, 2016, 371: 434-445.