希尔伯特—黄变换在水声信号处理中的应用研究
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摘要
声波是目前唯一能进行水下远程探测、通讯的信息载体,因而水声技术在人类探索海洋、开发利用海洋、海洋军事防卫等方面扮演着举足轻重的角色。
水声信号常常伴随有非线性和非平稳性,而黄鄂博士提出的Hilbert-Huang变换(Hilbert-Huang Transform, HHT)是一种针对非线性、非平稳信号分析的有效手段,所以本文主要致力于HHT方法在水声信号处理领域中的应用的研究,内容主要集中在以下三个方面：首先是探讨HHT的物理意义及其工程实现中的相关问题；其次是HHT在矢量信号处理中的应用研究；再次是利用HHT方法进行了混凝土缺陷检测识别的可行性研究,通过实测数据的分析,检验了该方法在水声信号处理中的应用效果。据此,本论文的所做工作如下：
1.HHT技术的概念及其实现问题研究。针对HHT中所用到的重要概念做了详细的阐述,其中包括瞬时频率、单分量信号与多分量信号、时间尺度和本征模态函数(Intrinsic Mode Function, IMF)的概念。详细说明了经验模态分解(Empirical Mode Decomposition, EMD)方法和希尔伯特谱,对EMD实现过程中涉及的曲线拟合、边界点预测、停止准则等做了讨论。
2.EMD在水声信号处理中的实用性研究。针对利用EMD进行信号分析可能遇到的几个问题进行了讨论,并利用仿真数据作了验证。主要包括以下三个方面：
(1)根据白噪声在EMD下的统计特性——IMF的能量密度和其对应的平均周期的乘积是一个常数,提出了一种自适应去噪算法。通过仿真验证,该方法取得了很好的去噪效果,该方法的优点是不存在参数选择的问题。
(2)利用EMD对双音信号(两个纯音信号和)的分析,进行了对EMD频率分辨力的研究,给出了EMD能够正确分离双音信号的条件。
(3)针对EMD中可能出现的模态混叠现象,提出了一种新的处理办法,即利用差分运算结合累计求和分离混叠模态；并进行了实际数据仿真分析,取得了比较好的结果。
3.讨论了HHT在矢量水听器信号处理中应用的几个问题。对复数EMD的三种实现方法——正负频率法、差分向量法、投影法进行分析对比,说明三种算法在实现上的利弊。然后将其应用于矢量水听器多目标方位估计,并且讨论了不同合成矢量信号的方法对复数EMD的影响,得到了不同信号形式的适用条件。
4.HHT算法应用于混凝土模型缺陷目标检测与识别的可行性研究。结合坝体缺陷检测课题,设计了一个实验系统,对模拟的混凝土缺陷模型回波信号进行采集和存贮,利用EMD和其他算法对实验数据进行分析,提取了回波信号特征,实现了对混凝土模型缺陷的初步识别。
Underwater sound is the only information carrier in the long-range underwater detection and communications. And thus the underwater acoustic plays an important role in the ocean exploration, the ocean development, the ocean utilization, and the marine military defense etc.
Underwater acoustic signal is often non-linear and non-stationary, and Hilbert-Huang Transform (HHT) proposed by Dr. Norden E. Huang is an effective method to analyze the non-linear, non-stationary signal. So this dissertation focuses on the application of HHT to the underwater acoustic signal processing, and the research fix attention on the following three aspects:at first, the physical significance of the HHT has been explored, and the related issues of its realization have been discussed. Secondly, the HHT has been used to process the vector signals. And then, the HHT method has applied to detect and identify the defect in the concrete models, and by analyzing experimental data to estimate the effect of using the method to process the underwater acoustic signal. Accordingly, this paper arranged as follows:
1. Research has been carried on the related concepts of HHT and its realization. The important concepts using in HHT were expounded in detail, which were the instantaneous frequency, single-component signal, multi-component signal, the time scale and the intrinsic mode function (IMF) and so on. Empirical mode decomposition (EMD) and the Hilbert spectrum have been explained. And some problems involved in the implementation of EMD, such as the curve fitting, the end points forecast and the stop criteria were discussed.
2. The practicability research of using EMD in the underwater acoustic processing has been carried. A few problems encountered in signal analysis using EMD has been discussed in this thesis, and some new solutions have been proposed. And the solutions have been verified though analysis the simulation data. And this part includes the following three aspects:
1) An adaptive de-noise algorithm has been proposed using the statistical properties of the white noise after EMD analysis, which is the product of the energy density of IMFs and its corresponding average period is a constant. The simulations shown that the proposed method has a good effect in signal de-noise, and it needs not to choose the parameters as the wavelet analysis.
2) The research of the frequency resolution of EMD has been carried using EMD to analyze the two-tone signal (the sum of two tone signals). And the conditions of EMD to correctly separate the two-tone signals were given.
3) For the mode mixing problem occurred possibly in EMD, a new approach has been put forward which combines the differential operator and the cumulative sum. And the new method has been compared to other algorithm though the simulation and it can achieve good results relatively.
3. Some problems using HHT analyze vector hydrophone signal has been discussed. There were three methods to realize the plural EMD, which is positive and negative frequency method, the first-order difference vector method, the projection method. And the three methods have been contrasted though simulation, and the advantages and disadvantages in their implementation were pointed out. Complex EMD was applied to estimate the azimuth of the multi-targets with a single vector. The different plural signal forms have been discussed, and its influence to the Complex EMD has been also discussed; and the application condition of the various signal forms has been obtained.
4. The feasibility study of using HHT to detect and identify the defect in the concrete model has been processed. Combined the task of dam defect detection for the underwater robot, a test system has been designed, and it see to collect and store the underwater acoustic echo signal. The EMD algorithm and other methods were used to analysis the data and extract the characteristics of the signals, and the identification of the different defects with concrete model has been realized initially.
水声信号常常伴随有非线性和非平稳性,而黄鄂博士提出的Hilbert-Huang变换(Hilbert-Huang Transform, HHT)是一种针对非线性、非平稳信号分析的有效手段,所以本文主要致力于HHT方法在水声信号处理领域中的应用的研究,内容主要集中在以下三个方面：首先是探讨HHT的物理意义及其工程实现中的相关问题；其次是HHT在矢量信号处理中的应用研究；再次是利用HHT方法进行了混凝土缺陷检测识别的可行性研究,通过实测数据的分析,检验了该方法在水声信号处理中的应用效果。据此,本论文的所做工作如下：
1.HHT技术的概念及其实现问题研究。针对HHT中所用到的重要概念做了详细的阐述,其中包括瞬时频率、单分量信号与多分量信号、时间尺度和本征模态函数(Intrinsic Mode Function, IMF)的概念。详细说明了经验模态分解(Empirical Mode Decomposition, EMD)方法和希尔伯特谱,对EMD实现过程中涉及的曲线拟合、边界点预测、停止准则等做了讨论。
2.EMD在水声信号处理中的实用性研究。针对利用EMD进行信号分析可能遇到的几个问题进行了讨论,并利用仿真数据作了验证。主要包括以下三个方面：
(1)根据白噪声在EMD下的统计特性——IMF的能量密度和其对应的平均周期的乘积是一个常数,提出了一种自适应去噪算法。通过仿真验证,该方法取得了很好的去噪效果,该方法的优点是不存在参数选择的问题。
(2)利用EMD对双音信号(两个纯音信号和)的分析,进行了对EMD频率分辨力的研究,给出了EMD能够正确分离双音信号的条件。
(3)针对EMD中可能出现的模态混叠现象,提出了一种新的处理办法,即利用差分运算结合累计求和分离混叠模态；并进行了实际数据仿真分析,取得了比较好的结果。
3.讨论了HHT在矢量水听器信号处理中应用的几个问题。对复数EMD的三种实现方法——正负频率法、差分向量法、投影法进行分析对比,说明三种算法在实现上的利弊。然后将其应用于矢量水听器多目标方位估计,并且讨论了不同合成矢量信号的方法对复数EMD的影响,得到了不同信号形式的适用条件。
4.HHT算法应用于混凝土模型缺陷目标检测与识别的可行性研究。结合坝体缺陷检测课题,设计了一个实验系统,对模拟的混凝土缺陷模型回波信号进行采集和存贮,利用EMD和其他算法对实验数据进行分析,提取了回波信号特征,实现了对混凝土模型缺陷的初步识别。
Underwater sound is the only information carrier in the long-range underwater detection and communications. And thus the underwater acoustic plays an important role in the ocean exploration, the ocean development, the ocean utilization, and the marine military defense etc.
Underwater acoustic signal is often non-linear and non-stationary, and Hilbert-Huang Transform (HHT) proposed by Dr. Norden E. Huang is an effective method to analyze the non-linear, non-stationary signal. So this dissertation focuses on the application of HHT to the underwater acoustic signal processing, and the research fix attention on the following three aspects:at first, the physical significance of the HHT has been explored, and the related issues of its realization have been discussed. Secondly, the HHT has been used to process the vector signals. And then, the HHT method has applied to detect and identify the defect in the concrete models, and by analyzing experimental data to estimate the effect of using the method to process the underwater acoustic signal. Accordingly, this paper arranged as follows:
1. Research has been carried on the related concepts of HHT and its realization. The important concepts using in HHT were expounded in detail, which were the instantaneous frequency, single-component signal, multi-component signal, the time scale and the intrinsic mode function (IMF) and so on. Empirical mode decomposition (EMD) and the Hilbert spectrum have been explained. And some problems involved in the implementation of EMD, such as the curve fitting, the end points forecast and the stop criteria were discussed.
2. The practicability research of using EMD in the underwater acoustic processing has been carried. A few problems encountered in signal analysis using EMD has been discussed in this thesis, and some new solutions have been proposed. And the solutions have been verified though analysis the simulation data. And this part includes the following three aspects:
1) An adaptive de-noise algorithm has been proposed using the statistical properties of the white noise after EMD analysis, which is the product of the energy density of IMFs and its corresponding average period is a constant. The simulations shown that the proposed method has a good effect in signal de-noise, and it needs not to choose the parameters as the wavelet analysis.
2) The research of the frequency resolution of EMD has been carried using EMD to analyze the two-tone signal (the sum of two tone signals). And the conditions of EMD to correctly separate the two-tone signals were given.
3) For the mode mixing problem occurred possibly in EMD, a new approach has been put forward which combines the differential operator and the cumulative sum. And the new method has been compared to other algorithm though the simulation and it can achieve good results relatively.
3. Some problems using HHT analyze vector hydrophone signal has been discussed. There were three methods to realize the plural EMD, which is positive and negative frequency method, the first-order difference vector method, the projection method. And the three methods have been contrasted though simulation, and the advantages and disadvantages in their implementation were pointed out. Complex EMD was applied to estimate the azimuth of the multi-targets with a single vector. The different plural signal forms have been discussed, and its influence to the Complex EMD has been also discussed; and the application condition of the various signal forms has been obtained.
4. The feasibility study of using HHT to detect and identify the defect in the concrete model has been processed. Combined the task of dam defect detection for the underwater robot, a test system has been designed, and it see to collect and store the underwater acoustic echo signal. The EMD algorithm and other methods were used to analysis the data and extract the characteristics of the signals, and the identification of the different defects with concrete model has been realized initially.
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