【作者】 孙长江；

【导师】 宋雷鸣；

【作者基本信息】 北京交通大学 ， 环境工程， 2008， 硕士

【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。更多还原

【Abstract】 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.更多还原