基于Warshall-Floyd算法的船舶结构噪声传递路径研究
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摘要
结构振动是船舶主要的噪声源,传统测试方法难以有效分析结构噪声的传递路径。根据统计能量分析(SEA)理论中的振动子系统概念,利用赋权图方法分析结构噪声的传递规律。将相似模态群抽象成赋权图的顶点,结合能量平衡方程中SEA矩阵建立顶点之间的邻接关系,采用路径效率方法和统计熵方法两种分析方法,将物理模型转化为最短路径问题的权值矩阵。通过Warshall-Floyd最短路径算法找出权值矩阵中任意两个顶点之间的前N条最短路径,得出任意空间位置的结构噪声源到目标舱室的前N条主要传递路径,对比能量传递路径在不同频带和不同振动模态群的差异,并分析各主要路径在能量传递过程中的权重,揭示船舶结构噪声源传递的一般规律,为降低船舶结构噪声提供指导。
The structural vibration is the main noise source for ships, while the traditional test method is difficult to identify the transmission path of structure noises. Based on the concept of vibration subsystems in the statistical energy analysis(SEA) theory, the transfer paths of structure noises were analyzed by using the weight graph method. Abstructing the similar modes groups into points in the graph, and introducing the adjacent relationships among vertex set up by the SEA matrix in the energy balance equation, the physical model was translated into the weighted matrix of a shortest path problem by virtue of the path efficiency method and statistical entropy method. With the Warshall-Floyd algorithm, the first N shortest paths between any two points in the graph were figured out, and the first N dominant transfer paths from the noise source at any position to the targeted cabin were also offered. With the comparison of transfer paths in different frequency bands and different vibration modes groups and with the analysis of the weights of each dominant transfer path, some general rules for the ship's structure-borne noise transmission were revealed, which provide constructive guidance for the reduction of structure-borne noises.
The structural vibration is the main noise source for ships, while the traditional test method is difficult to identify the transmission path of structure noises. Based on the concept of vibration subsystems in the statistical energy analysis(SEA) theory, the transfer paths of structure noises were analyzed by using the weight graph method. Abstructing the similar modes groups into points in the graph, and introducing the adjacent relationships among vertex set up by the SEA matrix in the energy balance equation, the physical model was translated into the weighted matrix of a shortest path problem by virtue of the path efficiency method and statistical entropy method. With the Warshall-Floyd algorithm, the first N shortest paths between any two points in the graph were figured out, and the first N dominant transfer paths from the noise source at any position to the targeted cabin were also offered. With the comparison of transfer paths in different frequency bands and different vibration modes groups and with the analysis of the weights of each dominant transfer path, some general rules for the ship's structure-borne noise transmission were revealed, which provide constructive guidance for the reduction of structure-borne noises.
引文
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[23] MARTINS E,PASCOAL M,DOS SANTOS J.The k shortest paths problem[J].European Journal of Operational Research,1998,165(1):97-107.
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[26] BOT A L,CARBONELLI A,PERRET-LIAUDET J.Entropy:a counterpart in statistical energy analysis[C]//Proceedings of the 18th International Congress on Sound and Vibration.Riode Janeiro:ICSV,2011.
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[28] CORMEN T H.Introduction to algorithms[M].Cambridge:MIT Press,2009.
[2] 姚德源,王其政.统计能量分析原理及其应用[M].北京:北京理工大学出版社,1995.
[3] LYON R H,DEJONG R.Theory and application of statistical energy analysis[M].Boston:Butterworth-Heinemann,1995.
[4] LE BOT A,CARBONELLI A,LIAUDET J P.On the usefulness of entropy in statistical energy analysis[Z].Acoustics,2012.
[5] NORTON M P,KARCZUB D G.Fundamentals of noise and vibration analysis for engineers[M].Cambridge:Cambridge University Press,2003.
[6] CRAIK R J M.The effect of a ventilation duct on the transmission of sound between two rooms[M].Edinburgh:Heriot-Watt University,1977.
[7] CRAIK R J M.The noise reduction of the acoustic paths between two rooms interconnected by a ventilation duct[J].Applied Acoustics,1979,12(3):161-179.
[8] CRAIK R J M.Sound transmission paths through a statistical energy analysis model[J].Applied Acoustics,1990,30(1):45-55.
[9] CRAIK R J M.Sound transmission through buildings:using statistical energy analysis[M].Aldershot:Gower Publishing Company,1996.
[10] GUASCH O,ARAGONèS à.Finding the dominant energy transmission paths in statistical energy analysis[J].Journal of Sound and Vibration,2011,330(10):2325-2338.
[11] GUASCH O,ARAGONèS à,JANER M.A graph cut strategy for transmission path problems in statistical energy analysis[J].Mechanical Systems and Signal Processing,2012,30(7):343-355.
[12] ARAGONèS à.Graph theory applied to transmission path problems in vibroacoustics[J].Therapeutic Advances in Neurological Disorders,2015,5(6):349-358.
[13] CARCATERRA A.An entropy approach to statistical energy analysis[C]//INTER-NOISE and NOISE-CON Congress and Conference Proceedings.Christchurch:Institute of Noise Control Engineering,1998.
[14] CARCATERRA A.An entropy formulation for the analysis of energy flow between mechanical resonators[J].Mechanical Systems and Signal Processing,2002,16(5):905-920.
[15] LE BOT A.Entropy in statistical energy analysis[J].The Journal of the Acoustical Society of America,2009,125(3):1473-1478.
[16] LE BOT A,CARCATERRA A,MAZUYER D.Statistical vibroacoustics and entropy concept[J].Entropy,2010,12(12):2418-2435.
[17] LE BOT A.Statistical energy analysis and the second principle of thermodynamics[C]//IUTAM Symposium on the Vibration Analysis of Structures with Uncertainties.Berlin:Springer Netherlands,2011.
[18] LE BOT A.Foundation of statistical energy analysis in vibroacoustics[M].Oxford:Oxford University Press,2015.
[19] LYON R H,MAIDANIK G.Power flow between linearly coupled oscillators[J].The Journal of the Acoustical Society of America,1962,34(5):623-639.
[20] LYON R H.Fluctuation theory and (very) early statistical energy analysis (SEA)(L)[J].The Journal of the Acoustical Society of America,2003,113(5):2401-2403.
[21] 张文春,滕莉,段树林.舱室噪声传递路径分析的 SEA 赋权图法[J].大连海事大学学报(自然科学版),2017,43(1):67-71.ZHANG Wenchun,TENG Li,DUAN Shulin.SEA weighted digraph method for energy transfer path analysis of cabin noise[J].Journal of Dalian Maritime University(Science and Technology),2017,43(1):67-71.
[22] 高处,杨德庆.船舶舱室噪声传递路径分析的声振熵赋权图法[J].上海交通大学学报,2014,48(4):469-474.GAO Chu,YANG Deqing.Vibroacoustical entropy weighted graph method for sound transmission path analysis of ship cabin noise[J].Journal of Shanghai Jiaotong University,2014,48(4):469-474.
[23] MARTINS E,PASCOAL M,DOS SANTOS J.The k shortest paths problem[J].European Journal of Operational Research,1998,165(1):97-107.
[24] 柴登峰,张登荣.前N条最短路径问题的算法及应用[J].浙江大学学报(工学版),2002,36(5):531-534.CHAI Dengfeng,ZHANG Dengrong.Algorithm and its application to N shortest paths problem[J].Journal of Zhejiang University(Engineering Science),2002,36(5):531-534.
[25] 邦迪,默蒂,吴望名.图论及其应用[M].北京:科学出版社,1984.
[26] BOT A L,CARBONELLI A,PERRET-LIAUDET J.Entropy:a counterpart in statistical energy analysis[C]//Proceedings of the 18th International Congress on Sound and Vibration.Riode Janeiro:ICSV,2011.
[27] MICIKEVICIUS P.General parallel computation on commodity graphics hardware:case study with the all-pairs shortest paths problem[C]// International Conference on Parallel & Distributed Processing Techniques & Applications.[S.l.]:PDPTA,2004.
[28] CORMEN T H.Introduction to algorithms[M].Cambridge:MIT Press,2009.
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