基于Beamforming的阵列噪声源识别仿真和算法研究
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摘要
随着我国社会生产力和国民经济持续高速发展,交通噪声污染越来越严重地影响着人们的学习、工作和生活。控制噪声源是噪声治理最根本、最有效的方法。通过噪声源识别,可以了解噪声源的位置分布及其各部分的发声特性,为从原理上降低噪声提供理论依据。
本文在对几种传统噪声源识别方法进行分析比较的基础上,选用了阵列噪声源识别方法;并根据本文研究对象的特点,采用了波束形成信号处理算法。
本文根据波束形成法的原理推导出了阵列接收声源的数学模型,并用LabVIEW仿真得到了相应的声源识别相控扫描图。分析仿真结果可知,相控波束识别法具有较高的分辨率,只是当声音的频率、传感器的间距、传感器与声源的距离等相互关系不满足算法特征要求时,分辨率比较低或出现旁瓣和栅瓣。为此,本文提出了基于阵列方向图矩阵的空间扫描算法,并通过理论推导和仿真比较证明了此算法的优越性。该方法进一步提高了识别的分辨率,消除了传统波束形成算法中旁瓣和栅瓣的影响。
根据工程测试的实际需求,将基于阵列方向矩阵的空间扫描算法引入工程问题,将其原理描述为工程化方程。该工程化方程属于第一类Fredholm积分方程的范畴,本文采用人工神经网络方法来求解该数学物理反问题,这也是本文研究的重点和难点。
首先将方程求解问题转化为非线性单目标数学优化问题;然后用连续型Hopfield神经网络来解决该优化问题,通过构造能量函数和选取合适的网络参数,使得网络的能量函数收敛到全局最小值时输出方程的最优解;最后在以经典例题为例验证了本算法可行性和正确性的基础上求解了该工程化方程,并对求解结果进行了相应的分析。
本文应用连续型Hopfield神经网络求解出了第一类Fredholm积分方程的经典例题,这在目前的工程数学上是一个不小的突破,很有现实意义和工程价值,为今后的相关研究提供了新的理论基础。
With development of the social productivity and national economy, the noise pollution of traffic is influencing people's life, work and study more and more seriously. Controlling the noise source is the most basic and effective method to reduce noise. Using noise identification, we can know the position distribution of noise, analyze its characteristic and offer the theoretical foundation for reducing the noise.
This paper compared several kinds of traditional methods, then chose the array noise source identify method. According to the characteristic of the object, adopted the beamforming algorithm.
According to the principle of time delay of beamforming, calculated the mathematical model of array receiving noise source and simulate it, then gained the figure of scanning. The results indicate that the beamforming has higher precision, but petal and bar petal can appear when the frequency of noise is high. For this reason, on the basis of traditional methods of the beamforming, this text had put forward the space scan algorithms basing on direction matrix of the array, calculated the mathematical model of array receiving noise source and simulated it. The results had much higher precision than the traditional beamforming, removed the influence of petal and bar petal of the traditional beamforming and verified the feasibility of this idea in theory, then put the equation into the projects.
The engineer equation is the first type Fredholm integral equation. This paper solved the reversed problem of physical&mathematics by artificial neural network. Firstly, transformed the equation into non-linear and single objective mathematics model of optimization, then solved the problem with continuous Hopfield neural network, then chose a set of suitable parameters and built the energy function, and output the solution when the energy function converged to the global minimum. Finally, proved accuracy and feasibility of the algorithm on the basis of the classical example, solved the equation of engineer, and analyzed the result.
This text successfully solved the classical example of Fredholm equation, which is break-through at mathematics, have much realistic and project value.
本文在对几种传统噪声源识别方法进行分析比较的基础上,选用了阵列噪声源识别方法;并根据本文研究对象的特点,采用了波束形成信号处理算法。
本文根据波束形成法的原理推导出了阵列接收声源的数学模型,并用LabVIEW仿真得到了相应的声源识别相控扫描图。分析仿真结果可知,相控波束识别法具有较高的分辨率,只是当声音的频率、传感器的间距、传感器与声源的距离等相互关系不满足算法特征要求时,分辨率比较低或出现旁瓣和栅瓣。为此,本文提出了基于阵列方向图矩阵的空间扫描算法,并通过理论推导和仿真比较证明了此算法的优越性。该方法进一步提高了识别的分辨率,消除了传统波束形成算法中旁瓣和栅瓣的影响。
根据工程测试的实际需求,将基于阵列方向矩阵的空间扫描算法引入工程问题,将其原理描述为工程化方程。该工程化方程属于第一类Fredholm积分方程的范畴,本文采用人工神经网络方法来求解该数学物理反问题,这也是本文研究的重点和难点。
首先将方程求解问题转化为非线性单目标数学优化问题;然后用连续型Hopfield神经网络来解决该优化问题,通过构造能量函数和选取合适的网络参数,使得网络的能量函数收敛到全局最小值时输出方程的最优解;最后在以经典例题为例验证了本算法可行性和正确性的基础上求解了该工程化方程,并对求解结果进行了相应的分析。
本文应用连续型Hopfield神经网络求解出了第一类Fredholm积分方程的经典例题,这在目前的工程数学上是一个不小的突破,很有现实意义和工程价值,为今后的相关研究提供了新的理论基础。
With development of the social productivity and national economy, the noise pollution of traffic is influencing people's life, work and study more and more seriously. Controlling the noise source is the most basic and effective method to reduce noise. Using noise identification, we can know the position distribution of noise, analyze its characteristic and offer the theoretical foundation for reducing the noise.
This paper compared several kinds of traditional methods, then chose the array noise source identify method. According to the characteristic of the object, adopted the beamforming algorithm.
According to the principle of time delay of beamforming, calculated the mathematical model of array receiving noise source and simulate it, then gained the figure of scanning. The results indicate that the beamforming has higher precision, but petal and bar petal can appear when the frequency of noise is high. For this reason, on the basis of traditional methods of the beamforming, this text had put forward the space scan algorithms basing on direction matrix of the array, calculated the mathematical model of array receiving noise source and simulated it. The results had much higher precision than the traditional beamforming, removed the influence of petal and bar petal of the traditional beamforming and verified the feasibility of this idea in theory, then put the equation into the projects.
The engineer equation is the first type Fredholm integral equation. This paper solved the reversed problem of physical&mathematics by artificial neural network. Firstly, transformed the equation into non-linear and single objective mathematics model of optimization, then solved the problem with continuous Hopfield neural network, then chose a set of suitable parameters and built the energy function, and output the solution when the energy function converged to the global minimum. Finally, proved accuracy and feasibility of the algorithm on the basis of the classical example, solved the equation of engineer, and analyzed the result.
This text successfully solved the classical example of Fredholm equation, which is break-through at mathematics, have much realistic and project value.
引文
[1]刘惠玲.环境噪声控制.哈尔滨.哈尔滨工业大学出版社.2002.10
[2]Omologo M,Svaizer P.Acoustic Event Localization Using a Crosspower-Spectrum Phase Based Technique.ICASSP' 94.1994.Vol 2:19-22
[3]陈南.汽车振动与噪声控制.北京.人民交通出版社.2005.8
[4]王永良等.空间谱估计理论与算法.北京.清华大学出版社.2004.11
[5]E.Skudrzyk.The Foundations of Acoustics.New York.Springer-Verlag Wien.1971.7
[6]周福洪.水声换能器及其阵.北京.国防工业出版社.1984.9
[7]朱广信、陈彪等、金蓉.基于传感器阵列的声源定位.电声技术.2003.1
[8]陈可.声源定位系统的研究.合肥.中国科学技术大学.2003.5
[9]严素清.传感器阵列的声源定位研究.扬声器与传声器.2004.12
[10]邵怀宗等.基于麦克风阵列的声源定位研究.云南民族大学学报(自然科学).2004.12
[11]Serpedin E,Giannakis G B.Blind Channel Identifications and Equalizations with ModulationInduced Cyclostationarity.IEEE Trans Signal Processing.1998:46,1930-1944
[12]Stoica P and A.Nehorai.Performance Comparison of Subspace Rotation and Music Methods of Direction Estimation.IEEE Trans.on SP.1991.Vol.39.No.2:446-453
[13]F.A.Reed,P.L.Feintuch,N.J.Bershad.Time Delay Estimation Using the LMS Adaptive Filter-Static Behavior.IEEE Trans.On Acoustics Speech and Signal Processing.1981.Vol.ASSP-29 n.3
[14]L.Z.QU,N.J.Bershad.Comments on 'Time Delay Estimation Using the INS Adaptive Filter-Static Behavior'.IEEE Trans.On Acoustics Speech and Signal Processing.1985.Vol.ASSP-33 n.6
[15]佐川明朗.日本高速铁路噪声对策.中日高速铁路环境技术交流会讲义.2008.1.23
[16]J.J.Christensen and J.Hald.Beam forming.TECHNIC AL REVIEW.2004 NO.1.3-4
[17]宋雷鸣.基于相控阵列的噪声源识别及仿真研究.铁道学报.2005.Vol.27 No.6
[18]张光义.相控阵雷达系统.北京.国防工业出版社.1994.8.36-44,46-49
[19]杜功焕.声学基础.南京.南京大学出版社.2001
[20]张贤达.现代信号处理.北京.清华大学出版社.1995:125-140
[21]李庆扬等.数值分析.第四版.北京.清华大学出版社、施普林格出版社.2001.8
[22]史荣昌.矩阵分析.北京.北京理工大学出版社.1996.1
[23]同济大学应用数学系.高等数学.北京.高等教育出版社.2001.10
[24]宋雷鸣.一种改善beamforimg“延迟求和”算法精度的方法.电子测量与仪器学报.2007.Vol.21 No.5
[25]李春芳、赵葆常.Fredholm第一类积分方程数值解的可靠性.应用科学学报.1998.03
[26]肖庭延、于慎根、王彦飞.反问题的数值解法.北京.科学出版社.2003.9
[27]刘继军.不适定问题的正则化方法.北京.科学出版社.2005.9
[28]李明忠.第一种Fredholm积分方程的数值解法.应用科学学报.1985.4
[29]陈祥光,裴旭东.人工神经网络技术及应用.北京.中国电力出版社.2003:104-106
[30]朱大奇.人工神经网络原理及应用.北京.科学出版社.2006.3
[31]王伟.人工神经网络原理入门与应用.北京.北京航空航天大学出版社.1995.4
[32]韩力群.人工神经网络理论、原设计及应用.北京.化学工业出版社.2007.2
[33]J.H.Winters.Superresolution for Ultrasoniclmaging in Air Using Neural Networks.IEEE Int Conf on Neural Net 1.1988
[34]J.J.Hopfield.Neurons With Graded ResponseHave Collective Computational Properties LikeThose of Two-State Neurons.Proc Natl Acad Sci USA.1984
[35]C.R.Vogel.Numerical Solution of a Non-LinearIll-Posed Problem Arising in Inverse Scattering.Inverse Problems.1985
[36]吴麒.自动控制原理.北京.清华大学出版社.2005.10
[37]叶世伟、王海娟.神经计算原理.北京.机械工业出版社.2007.1
[38]F.salam,etal.On the Analysis Of DynmicFeedback Neural Nets.IEEE Trans on Circuits and Sys.No.2.1991.38
[39]Kate Smith,Marimuthu Palaniswami and Mohan Krishnamoorthy."Neural Techniques for Combinatorial Optimization with Applications".IEEE Transactions On Neural Networks.Vol.9,No.6,November1998,p1301 - 1318
[40]高隽.人工神经网络原理及仿真实例.北京.机械工业出版社.2003.9
[41]施海蓉.基于MATLAB的人工神经网络在穆斯堡尔谱学中的应用.南京.南京大学.2000:35-36
[42]David L.Phillips.A Technique for the Numerical Solution of Certain Integral Equations of the First Kind.J.Ass.Comput.Mach.1962
[43]顾树生、王建辉.自动控制原理.北京.冶金工业出版社2001.9
[44]赵新泉.Hopfield神经网络全局指数稳定性的几个新判据.许昌学院学报.2003.10Vol.22 No.2
[45]唐焕文、秦学志.实用最优化方法.大连.大连理工大学出版社.2004.1
[46]陈周立.机械设计优化方法.北京.冶金工业出版社.1984.6
[47]孙靖民.机械优化设计.北京.机械工业出版社.2001.1
[48]赛特达.iSIGHT培训教程(试验设计).北京.赛特达公司.2005.9
[49]易国伟.多学科设计优化中的质量工程.北京.北京航空航天大学.2004.3
[50]艾娜.70t级集装箱专用平车车体结构优化设计.北京.北京交通大学.2006.3
[51]孔晨.多学科设计优化方法与技术的应用.北京.北京航空航天大学.2004.3
[52]曾庆良等.一种结构优化方法的研究与实现.机械制造.2006.5 Vol.44 No.6
[2]Omologo M,Svaizer P.Acoustic Event Localization Using a Crosspower-Spectrum Phase Based Technique.ICASSP' 94.1994.Vol 2:19-22
[3]陈南.汽车振动与噪声控制.北京.人民交通出版社.2005.8
[4]王永良等.空间谱估计理论与算法.北京.清华大学出版社.2004.11
[5]E.Skudrzyk.The Foundations of Acoustics.New York.Springer-Verlag Wien.1971.7
[6]周福洪.水声换能器及其阵.北京.国防工业出版社.1984.9
[7]朱广信、陈彪等、金蓉.基于传感器阵列的声源定位.电声技术.2003.1
[8]陈可.声源定位系统的研究.合肥.中国科学技术大学.2003.5
[9]严素清.传感器阵列的声源定位研究.扬声器与传声器.2004.12
[10]邵怀宗等.基于麦克风阵列的声源定位研究.云南民族大学学报(自然科学).2004.12
[11]Serpedin E,Giannakis G B.Blind Channel Identifications and Equalizations with ModulationInduced Cyclostationarity.IEEE Trans Signal Processing.1998:46,1930-1944
[12]Stoica P and A.Nehorai.Performance Comparison of Subspace Rotation and Music Methods of Direction Estimation.IEEE Trans.on SP.1991.Vol.39.No.2:446-453
[13]F.A.Reed,P.L.Feintuch,N.J.Bershad.Time Delay Estimation Using the LMS Adaptive Filter-Static Behavior.IEEE Trans.On Acoustics Speech and Signal Processing.1981.Vol.ASSP-29 n.3
[14]L.Z.QU,N.J.Bershad.Comments on 'Time Delay Estimation Using the INS Adaptive Filter-Static Behavior'.IEEE Trans.On Acoustics Speech and Signal Processing.1985.Vol.ASSP-33 n.6
[15]佐川明朗.日本高速铁路噪声对策.中日高速铁路环境技术交流会讲义.2008.1.23
[16]J.J.Christensen and J.Hald.Beam forming.TECHNIC AL REVIEW.2004 NO.1.3-4
[17]宋雷鸣.基于相控阵列的噪声源识别及仿真研究.铁道学报.2005.Vol.27 No.6
[18]张光义.相控阵雷达系统.北京.国防工业出版社.1994.8.36-44,46-49
[19]杜功焕.声学基础.南京.南京大学出版社.2001
[20]张贤达.现代信号处理.北京.清华大学出版社.1995:125-140
[21]李庆扬等.数值分析.第四版.北京.清华大学出版社、施普林格出版社.2001.8
[22]史荣昌.矩阵分析.北京.北京理工大学出版社.1996.1
[23]同济大学应用数学系.高等数学.北京.高等教育出版社.2001.10
[24]宋雷鸣.一种改善beamforimg“延迟求和”算法精度的方法.电子测量与仪器学报.2007.Vol.21 No.5
[25]李春芳、赵葆常.Fredholm第一类积分方程数值解的可靠性.应用科学学报.1998.03
[26]肖庭延、于慎根、王彦飞.反问题的数值解法.北京.科学出版社.2003.9
[27]刘继军.不适定问题的正则化方法.北京.科学出版社.2005.9
[28]李明忠.第一种Fredholm积分方程的数值解法.应用科学学报.1985.4
[29]陈祥光,裴旭东.人工神经网络技术及应用.北京.中国电力出版社.2003:104-106
[30]朱大奇.人工神经网络原理及应用.北京.科学出版社.2006.3
[31]王伟.人工神经网络原理入门与应用.北京.北京航空航天大学出版社.1995.4
[32]韩力群.人工神经网络理论、原设计及应用.北京.化学工业出版社.2007.2
[33]J.H.Winters.Superresolution for Ultrasoniclmaging in Air Using Neural Networks.IEEE Int Conf on Neural Net 1.1988
[34]J.J.Hopfield.Neurons With Graded ResponseHave Collective Computational Properties LikeThose of Two-State Neurons.Proc Natl Acad Sci USA.1984
[35]C.R.Vogel.Numerical Solution of a Non-LinearIll-Posed Problem Arising in Inverse Scattering.Inverse Problems.1985
[36]吴麒.自动控制原理.北京.清华大学出版社.2005.10
[37]叶世伟、王海娟.神经计算原理.北京.机械工业出版社.2007.1
[38]F.salam,etal.On the Analysis Of DynmicFeedback Neural Nets.IEEE Trans on Circuits and Sys.No.2.1991.38
[39]Kate Smith,Marimuthu Palaniswami and Mohan Krishnamoorthy."Neural Techniques for Combinatorial Optimization with Applications".IEEE Transactions On Neural Networks.Vol.9,No.6,November1998,p1301 - 1318
[40]高隽.人工神经网络原理及仿真实例.北京.机械工业出版社.2003.9
[41]施海蓉.基于MATLAB的人工神经网络在穆斯堡尔谱学中的应用.南京.南京大学.2000:35-36
[42]David L.Phillips.A Technique for the Numerical Solution of Certain Integral Equations of the First Kind.J.Ass.Comput.Mach.1962
[43]顾树生、王建辉.自动控制原理.北京.冶金工业出版社2001.9
[44]赵新泉.Hopfield神经网络全局指数稳定性的几个新判据.许昌学院学报.2003.10Vol.22 No.2
[45]唐焕文、秦学志.实用最优化方法.大连.大连理工大学出版社.2004.1
[46]陈周立.机械设计优化方法.北京.冶金工业出版社.1984.6
[47]孙靖民.机械优化设计.北京.机械工业出版社.2001.1
[48]赛特达.iSIGHT培训教程(试验设计).北京.赛特达公司.2005.9
[49]易国伟.多学科设计优化中的质量工程.北京.北京航空航天大学.2004.3
[50]艾娜.70t级集装箱专用平车车体结构优化设计.北京.北京交通大学.2006.3
[51]孔晨.多学科设计优化方法与技术的应用.北京.北京航空航天大学.2004.3
[52]曾庆良等.一种结构优化方法的研究与实现.机械制造.2006.5 Vol.44 No.6