Tikhonov正则化在运行工况传递路径分析的应用
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摘要
针对传统运行工况传递路径分析(operational transfer path analysis,简称OTPA)存在的不足,通过理论和试验分析,提出基于Tikhonov正则化方法的OTPA反问题模型。首先,分析Tikhonov正则化方法的理论优势,给出Tikhonov正则化参数选择的依据,同时调节电机转速获得不同运行工况数据,利用奇异值分解方法研究壳体结构的振动传递路径,分析传统OTPA算法总贡献量误差及路径贡献量估计精度;其次,分析运行工况数据是否满足Picard条件,提出基于Tikhonov正则化方法的OTPA算法,并分析Tikhonov正则化参数对所提出算法的影响。分析结果表明,所提出的方法显著减小了总贡献量和路径贡献量误差以及路径误判现象。该研究可为振动噪声监控与减振降噪提供理论依据。
To overcome the shortcomings of the traditional operational transfer path analysis(OTPA),this paper proposes a novel OTPA model for inverse problems based on Tikhonov regularization through theoretical and experimental analysis.First,we analyzed the theoretical advantages of Tikhonov regularization and provided the basic criteria for determining Tikhonov regularization parameters.We obtained operational data according to changing rotational speeds of the motors and studied the vibration transfer paths of the shell structure by singular value decomposition.Furthermore,we analyzed the errors of total contributions and path contributions for traditional OTPA.Next,we proposed a novel OTPA method based on Tikhonov regularization with Picard conditions and analyzd the effects of regularization parameters.Finally,the comparative study results showed that the proposed method reduced the errors of total contributions,path contributions,and path misjudgment.This study thus provides theoretical references for the monitoring,reduction and control of vibration and noise.
To overcome the shortcomings of the traditional operational transfer path analysis(OTPA),this paper proposes a novel OTPA model for inverse problems based on Tikhonov regularization through theoretical and experimental analysis.First,we analyzed the theoretical advantages of Tikhonov regularization and provided the basic criteria for determining Tikhonov regularization parameters.We obtained operational data according to changing rotational speeds of the motors and studied the vibration transfer paths of the shell structure by singular value decomposition.Furthermore,we analyzed the errors of total contributions and path contributions for traditional OTPA.Next,we proposed a novel OTPA method based on Tikhonov regularization with Picard conditions and analyzd the effects of regularization parameters.Finally,the comparative study results showed that the proposed method reduced the errors of total contributions,path contributions,and path misjudgment.This study thus provides theoretical references for the monitoring,reduction and control of vibration and noise.
引文
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[15]马超,华宏星.正则化技术在状态空间载荷识别中的应用[J].振动、测试与诊断,2014,34(6):1154-1158.Ma Chao,Hua Hongxing.The application of regularization technique for load identification in state space[J].Journal of Vibration,Measurement&Diagnosis,2014,34(6):1154-1158.(in Chinese)
[16]Hansen P C.The discrete picard condition for ill-posed problems[J].BIT Numerical Mathematics,1990,30(4):658-672.
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[18]Hansen P C.Analysis of discrete ill-posed problems by means of the l-curve[J].SIAM Review,1992,1(34):561-580.
[2]成玮,张周锁,何正嘉,等.基于独立分量分析的潜艇振源贡献量定量计算方法[J].机械工程学报,2010,46(7):83-87.Cheng Wei,Zhang Zhousuo,He Zhengjia,et al.Quantitative calculation of vibration source contributions of submarines based on independent component analysis[J].Journal of Mechanical Engineering,2010,46(7):83-87.(in Chinese)
[3]Li W,Wang D F,Chen S M,et al.Transfer path analysis of power train vibration on driver's noise[C]∥7th International Conference on Natural Computation(ICNC).Shanghai:IEEE,2011:2353-2357.
[4]Yoshida J,Noumura K.Method of transfer path analysis for interior vehicle sound using principal component regression method[J].Honda R&D Technical Review,2006,18(1):136-141.
[5]Janssens K,Mas P,Gajdatsy P,et al.A novel path contribution analysis method for test-based NVH trouble shooting[C]∥Proceedings of Acoustics 2008.Geelong,Victoria,Australia:[s.n.],2008:3673-3683.
[6]Roozen N B,Leclere Q,Sandier C.Operational transfer path analysis applied to a small gearbox test set-up[C]∥Proceedings of Acoustics 2012.Nantes,France:[s.n.],2012:3467-3473.
[7]Putner J,Lohrmann M,Fastl H.Contribution analysis of vehicle exterior noise with operational transfer path analysis[C]∥Proceedings of Meetings on Acoustics.Montreal,Canada:[s.n.],2013,19,040035(1-9).
[8]Yan Li,Jiang Weikang.Research on the procedure for analyzing the sound quality contribution of sound sources and its application[J].Applied Acoustics,2014,79:75-80.
[9]胥永刚,谢志聪,孟志鹏,等.基于奇异值分解的磁记忆信号特征提取方法[J].振动、测试与诊断,2014,34(6):1106-1109.Xu Yonggang,Xie Zhicong,Meng Zhipeng,et al.The signal feature extraction method of magnetic memory based on singular value decomposition[J].Journal of Vibration,Measurement&Diagnosis,2014,34(6):1106-1109.(in Chinese)
[10]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.
[11]Peter G,Karl J,Ludo G.Critical assessment of operational path analysis:mathematical problems of transmissibility estimation[J].The Journal of the Acoustical Society of America,2008,123(5):9359-9364.
[12]Hadamard J.Sur les problems aux derivees partielles et leur signification physique[R].Bulletin:Princeton University,1902.
[13]Tikhonov A N,Arsenin V Y.Solution of ill-posed problems[J].Mathematics of Computation,1978,32(14):491.
[14]Tikhonov A.Solution of incorrectly formulated problems and the regularization method[J].Doklady Akademii Nauk SSSR,1963,151(3):501-504.
[15]马超,华宏星.正则化技术在状态空间载荷识别中的应用[J].振动、测试与诊断,2014,34(6):1154-1158.Ma Chao,Hua Hongxing.The application of regularization technique for load identification in state space[J].Journal of Vibration,Measurement&Diagnosis,2014,34(6):1154-1158.(in Chinese)
[16]Hansen P C.The discrete picard condition for ill-posed problems[J].BIT Numerical Mathematics,1990,30(4):658-672.
[17]Golub G H,Heath M,Wahba G.Generalized crossvalidation as a method for choosing agood ridge parameter[J].Technometrics,1979,21(2):215-223.
[18]Hansen P C.Analysis of discrete ill-posed problems by means of the l-curve[J].SIAM Review,1992,1(34):561-580.