基于l_1范数稀疏解的水下双层圆柱壳振动声辐射预报影响因素研究
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摘要
基于模态叠加法理论,采用l1范数稀疏解方法,实现了水下双层圆柱壳由内壳有限测点振速值重构得到内、外壳振速空间分布,进而基于边界元理论对结构水下辐射声场进行预报。通过数值计算,分析了模态数目、测点数目和模态振型误差等因素对振动声辐射预报结果的影响,为指导速度场重构时模态数目、测点数目的选取提供了一定的理论依据;结果表明基于l1范数稀疏解声学预报方法对模态振型误差有一定的鲁棒性。最后开展了水下典型双层圆柱壳结构振动声辐射预报的试验研究,可为工程领域结构的声振预报提供一定的指导思路。
Based on the theory of mode superposition, this paper proposes the l1-norm sparse solution which achieves the aim of vibration field reconstruction accurately through a few measuring points on the inner shell. Furthermore, the sound radiation field can be predicted through the analysis of relationship between vibration and sound field based on the theory of BEM. And the various influence on reconstruction results is discussed, such as the number of measurements, the number of modes, the error of modes, and so on,through numerical simulation research, which provides some theoretical guidance for reconstructing the velocity field, choosing the number of measurements and modes. The results show that the l1-norm sparse solution has the robustness to the error of structure modes. Finally, the experimental research is carried out on the reconstruction of vibration and sound field of a double cylindrical shell underwater, which can provide some guidance for prediction of structural vibration and sound in engineering field.
Based on the theory of mode superposition, this paper proposes the l1-norm sparse solution which achieves the aim of vibration field reconstruction accurately through a few measuring points on the inner shell. Furthermore, the sound radiation field can be predicted through the analysis of relationship between vibration and sound field based on the theory of BEM. And the various influence on reconstruction results is discussed, such as the number of measurements, the number of modes, the error of modes, and so on,through numerical simulation research, which provides some theoretical guidance for reconstructing the velocity field, choosing the number of measurements and modes. The results show that the l1-norm sparse solution has the robustness to the error of structure modes. Finally, the experimental research is carried out on the reconstruction of vibration and sound field of a double cylindrical shell underwater, which can provide some guidance for prediction of structural vibration and sound in engineering field.
引文
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[9]陶襄樊.水下双层圆柱壳振动声辐射预报测点布置及试验研究[C]//第十六届全国船舶水下噪声学术研讨会.中国贵阳,2017:194-203.Tao Xiangfan.Experimental and theoretical study on prediction of vibration and sound radiation for double cylindrical shell under water[C]//The 16th National Symposium on Underwater Noise of Ships.Guiyang,China,2017:194-203.
[10]陆鑫森.高等结构动力学[M].上海:上海交通大学出版社,1992:134-135.Lu Xinsen.Advanced structural dynamics[M].Shanghai:Shanghai Jiaotong University Press,1992:134-135.
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[12]Laulagnet B,Guyader J L.Sound radiation by finite cylindrical ring stiffened shells[J].Journal of Sound and Vibration,1990,138(2):173-191.
[13]邹经湘.结构动力学[M].哈尔滨:哈尔滨工业大学出版社,1996:64-65.Zou Jingxiang.Structural dynamics[M].Harbin:Harbin Institute of Technology Press,1996:64-65.
[14]Karvanen J,Cichocki A.Measuring sparseness of noise signals[C]//Proceedings of Fourth International Symposium on Independent Component Analysis and Blind Signal Separation.Japan,2003:125-130.
[15]Donoho D L.For most large underdetermined systems of linear equations the minimal L1-norm solution is also the sparsest solution[J].Communications on Pure and Applied Mathematics,2006,59(6):797-829.
[16]Li Y Q,Cichocki A,Amari S.Analysis of sparse representation and blind source separation[J].Neural Computation,2004,16(6):1193-1234.
[17]Bofill P,Zibulevsky M.Underdetermined blind source separation using sparse representations[J].Signal Processing,2001,81(11):2353-2362.
[18]Takigawa I,Kudo M,Toyama J.Performance analysis of minimum l1-norm solutions for underdetermined source separation[J].IEEE Transactions on Signal Processing,2004,52(3):582-591.
[2]陶建成,邱小军.两种模态展开法预测结构辐射声功率时振动传感器数目的要求研究[J].应用声学,2009,28(4):283~290.Tao Jiancheng,Qiu Xiaojun.Velocity sensor number requirements on using mode decomposition methods for structure borne sound power prediction[J].Applied Acoustics,2009,28(4):283-290.
[3]孙超,何元安,尚德江,等.基于波叠加方法的水下声源辐射声场预报及实验研究[J].振动与冲击,2013,32(10):130-140.Sun Chao,He Yuanan,Shang Dejiang,et al.Prediction of underwater sound source radiation based on wave superposition method and relevant experiments[J].Journal of Vibration and Shock,2013,32(10):130-140.
[4]王斌.基于表面振动监测的大型水下结构辐射噪声预报研究[D].上海:上海交通大学,2008.Wang Bin.Research on prediction of noise radiated by large underwater structures via surface vibration monitoring[D].Shanghai Jiaotong University,2008.
[5]何卫平.基于模态理论的圆柱壳声振分析及有源控制方法研究[D].武汉:华中科技大学,2010.He Weiping.The research on vibration and sound radiation from a cylindrical shell and the noise active control based on mode theory[D].Wuhan:Huazhong University of Science and Technology,2010.
[6]余鹏.圆柱壳结构水下声振响应预报的测点布置研究[D].武汉:华中科技大学,2016.Yu Peng.Optimal sensor placement for predicting vibration and acoustic radiation of cylindrical shell under water[D].Wuhan:Huazhong University of Science and Technology,2016.
[7]阮竹青,彭伟才,张俊杰,等.基于表面响应预报水下圆柱壳声辐射的振动测点布置研究[J].中国舰船研究,2013,8(1):80-97.Ruan Zhuqing,Peng Weicai,Zhang Junjie,et al.Transducer arrangement for radiated power prediction of cylindrical shells based on velocity distribution[J].Chinese Journal of Ship Research,2013,8(1):80-97.
[8]陶襄樊,陈美霞,魏建辉.欠定盲分离方法预报水下双层加筋圆柱壳辐射声场[J].舰船科学技术,2012,34(11):8-13.Tao Xiangfan,Chen Meixia,Wei Jianhui.Prediction of radiated acoustic field for double cylinder shell under water using underdetermined blind source separation[J].Ship Science and Technology,2012,34(11):8-13.
[9]陶襄樊.水下双层圆柱壳振动声辐射预报测点布置及试验研究[C]//第十六届全国船舶水下噪声学术研讨会.中国贵阳,2017:194-203.Tao Xiangfan.Experimental and theoretical study on prediction of vibration and sound radiation for double cylindrical shell under water[C]//The 16th National Symposium on Underwater Noise of Ships.Guiyang,China,2017:194-203.
[10]陆鑫森.高等结构动力学[M].上海:上海交通大学出版社,1992:134-135.Lu Xinsen.Advanced structural dynamics[M].Shanghai:Shanghai Jiaotong University Press,1992:134-135.
[11]Stepanishen P R.Modal coupling in the vibration of fluid-loaded cylindrical shells[J].Journal of Acoustic Society of America,1982,71(4):813-823.
[12]Laulagnet B,Guyader J L.Sound radiation by finite cylindrical ring stiffened shells[J].Journal of Sound and Vibration,1990,138(2):173-191.
[13]邹经湘.结构动力学[M].哈尔滨:哈尔滨工业大学出版社,1996:64-65.Zou Jingxiang.Structural dynamics[M].Harbin:Harbin Institute of Technology Press,1996:64-65.
[14]Karvanen J,Cichocki A.Measuring sparseness of noise signals[C]//Proceedings of Fourth International Symposium on Independent Component Analysis and Blind Signal Separation.Japan,2003:125-130.
[15]Donoho D L.For most large underdetermined systems of linear equations the minimal L1-norm solution is also the sparsest solution[J].Communications on Pure and Applied Mathematics,2006,59(6):797-829.
[16]Li Y Q,Cichocki A,Amari S.Analysis of sparse representation and blind source separation[J].Neural Computation,2004,16(6):1193-1234.
[17]Bofill P,Zibulevsky M.Underdetermined blind source separation using sparse representations[J].Signal Processing,2001,81(11):2353-2362.
[18]Takigawa I,Kudo M,Toyama J.Performance analysis of minimum l1-norm solutions for underdetermined source separation[J].IEEE Transactions on Signal Processing,2004,52(3):582-591.