Hilbert-Huang变换及其在目标方位估计和水声通信中的应用研究
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摘要
具有时变特性的非平稳信号广泛的存在于各个领域中，要想揭示非平稳信号的本征特征需要借助于各种时频分析方法，而Hilbert-Huang变换方法是一种新颖的时频分析方法，它可以不利用任何先验知识仅根据信号自身的特点自适应的将任意复杂的非平稳信号分解为若干个本征模态函数之和，每个本征模态函数在某一时刻只含有一个振动模态，因此可以得到具有物理意义的瞬时频率。Hilbert-Huang变换方法具有自适应分解信号和时频分辨率高的突出特点，相比与其他的时频分析方法，在非平稳信号分析与处理中具有显著的优势，Hilbert-Huang变换方法自诞生以来就引起了人们极大的关注，人们纷纷使用这种方法来处理各领域内的非平稳数据，目前Hilbert-Huang变换方法已经被广泛的应用到了科研与工程的各个领域中。
本文对Hilbert-Huang变换算法中的均值曲线拟合、端点效应和模态混叠等问题进行了研究，并提出了相应的解决方案。论文中提出了一种利用分段高级样条直接拟合均值曲线的方法，该方法利用分段高阶样条获得更精确的均值点，对均值点序列直接进行拟合来得到均值曲线，该方法使得使得EMD方法在筛选本征模态函数时可以获得更为精确的均值曲线，从而实现准确的模态提取，同时相对于传统的方法，该方法具有更快的分解速度。本文中对模态混叠问题也进行了研究，分析了产生模态混叠现象的根本原因，提出了一种基于平移不变小波变换和EMD尺度滤波的消除模态混叠的方法，利用该方法可有效的剔除信号中引起模态混叠现象的高频间断信号，从而达到克服模态混叠现象的目的。传统的Hilbert-Huang变换算法存在着运算量过大的缺点，为了使Hilbert-Huang变换算法在硬件上能够实时实现，本文针对水声信号处理中信号的特点，对Hilbert-Huang变换方法从均值曲线拟合、端点效应处理、筛选本征模态函数的终止条件、EMD分解的终止条件、计算Hilbert变换等几个方面对其进行了算法改进，使得在保证Hilbert-Huang变换性能的基础上，大大减少了Hilbert-Huang变换算法的运算量。
针对水声信号的特点，本文将Hilbert-Huang变换应用到水声信号处理领域，发展了基于Hilbert-Huang变换的目标方位估计方法和水声通信方法。本文将Hilbert-Huang变换方法与矢量声信号处理技术相结合，发展了一种基于Hilbert-Huang变换的目标方位估计方法，该方法对矢量水听器输出的各路信号分别利用EMD方法进行分解，再利用同阶本征模态函数的解析信号得到复瞬时声能流，从而得到某一目标的瞬时方位。该方法可以将矢量水听器输出的合成矢量信号分解为单分量信号之和，从而实现对不同方位目标的识别。
具有不同起始频率和调频斜率的两个线性调频信号在进行合成的时候由于相位变化速度的不同，合成的信号中将出现一些局部反相的情况，造成附近出现小尺度信号的情况。对这样的合成信号利用EMD进行分解并利用Hilbert变换得到其一阶本征模态函数的瞬时频率曲线上将出现一些峰值，而采取一定的方法对合成后的信号进行改造会使具有峰值的地方变得平坦甚至凹陷。在此基础上可以发展出一种基于Hilbert-Huang变换方法的水声通信方法，该方法利用尺度上的信息进行编码，利用本征模态函数的瞬时频率进行解码，本章对该方法从仿真实验、水池实验和湖上实验等方面验证这种新的水声通信方法的有效性。
The non-stationary signals with the characteristic of time variant widely exist in manyfields, and time-frequency analysis methods are essential to reveal the essential characteristicof the non-stationary signals. Hilbert-Huang transform is a new kind of time-frequencyanalysis method and it can adaptively decompose any complicated non-stationary signal intosome intrinsic mode functions without any prior knowledge of the signal. Any intrinsic modefunction only has one vibration mode at any time, and instantaneous frequency with physicalmeaning can be obtained. Hilbert-Huang transform has the advantages of decomposing signaladaptively and having higher time-frequency resolution. Compared with other time-frequencyanalysis methods, Hilbert-Huang transform has many advantages in non-stationary signalanalyzing and processing. Since its birth, Hilbert-Huang transform attracts many attentionsfrom researchers, and more and more researchers use this method to process thenon-stationary signals in their fields.
This paper discussed some problems such as mean curve fitting, end effect and modemixing, and proposed corresponding solutions. A new method of directly fitting mean curveby piecewise high order spline was proposed in this paper, in which more accurate meanpoints were obtained by piecewise high order spline and mean curve was obtained by directlyfitting mean point sequence. The method made EMD method obtain more accurate meancurve when sifting intrinsic mode function and accomplish accurate mode extraction.Compared with traditional method, the new method had higher decomposing speed. Thispaper also discussed mode mixing problem, analyzed the basic reason leading to mode mixing,and proposed a method of eliminating mode mixing based on translation invariant wavelettransform and EMD scale filtering. The method could effectively remove high frequencydiscontinuous signal from useful signal, which is the main cause of mode mixing, andaccomplish the goal of eliminating mode mixing. Traditional Hilbert-Huang transformalgorithm had the disadvantage of too much computation, and to reduce the computationalburden of Hilbert-Huang transform and make it realizable on hardware realtime, this papermade some improvements on Hilbert-Huang transform, which included mean curve fitting,end effect treatment, terminating conditions of sifting intrinsic mode function, terminatingconditions of EMD decomposition and the calculation of Hilbert transform. Theseimprovements greatly reduced the computational burden of Hilbert-Huang transform, withperformance basically remaining unchanged.
According to the characteristics of underwater acoustic signals, Hilbert-Huang transformwas introduced into underwater acoustic signal processing field in this paper. A target azimuth estimating method and a method of underwater acoustic communication based onHilbert-Huang transform were proposed in this paper. By combining Hilbert-Huang transformwith vector underwater acoustic signal processing technology, a new target azimuthestimation method based on Hilbert-Huang transform was proposed in this paper. The newmethod decomposed the three channel signals into intrinsic mode functions by EMD,calculated the complex instantaneous acoustic energy flux by the analytic signals of the sameorder intrinsic mode functions, and then got the instantaneous azimuth of a certain target. Themethod decomposed the synthesizing vectors from vector hydrophone into the sum of simplecomponent signals and realized the identification of targets at the different azimuths.
The combining signal of two LFM signals, which had different initiation frequencies andchirp rates, had some time of local inversed phase, which resulted from the different speed ofphase variation. Thus the combining signal had many small scale signals in some localregions. After performing EMD on the combining signal, some intrinsic mode functions couldbe obtained. Perform Hilbert transform on the first order intrinsic mode function, and itsinstantaneous frequency curve could be obtained, in which there were some peaks. Modifyingthe combining signal by some methods could make the regions with peaks become flat oreven concave. Based on these characteristics, a new method of underwater acousticcommunication based on Hilbert-Huang transform was proposed in this paper, in whichinformation was encoded in the scale domain and decoded by the instantaneous frequency ofintrinsic mode function. The underwater acoustic communication method was validated bysimulation experiments, water pool experiments and lake experiments.
本文对Hilbert-Huang变换算法中的均值曲线拟合、端点效应和模态混叠等问题进行了研究，并提出了相应的解决方案。论文中提出了一种利用分段高级样条直接拟合均值曲线的方法，该方法利用分段高阶样条获得更精确的均值点，对均值点序列直接进行拟合来得到均值曲线，该方法使得使得EMD方法在筛选本征模态函数时可以获得更为精确的均值曲线，从而实现准确的模态提取，同时相对于传统的方法，该方法具有更快的分解速度。本文中对模态混叠问题也进行了研究，分析了产生模态混叠现象的根本原因，提出了一种基于平移不变小波变换和EMD尺度滤波的消除模态混叠的方法，利用该方法可有效的剔除信号中引起模态混叠现象的高频间断信号，从而达到克服模态混叠现象的目的。传统的Hilbert-Huang变换算法存在着运算量过大的缺点，为了使Hilbert-Huang变换算法在硬件上能够实时实现，本文针对水声信号处理中信号的特点，对Hilbert-Huang变换方法从均值曲线拟合、端点效应处理、筛选本征模态函数的终止条件、EMD分解的终止条件、计算Hilbert变换等几个方面对其进行了算法改进，使得在保证Hilbert-Huang变换性能的基础上，大大减少了Hilbert-Huang变换算法的运算量。
针对水声信号的特点，本文将Hilbert-Huang变换应用到水声信号处理领域，发展了基于Hilbert-Huang变换的目标方位估计方法和水声通信方法。本文将Hilbert-Huang变换方法与矢量声信号处理技术相结合，发展了一种基于Hilbert-Huang变换的目标方位估计方法，该方法对矢量水听器输出的各路信号分别利用EMD方法进行分解，再利用同阶本征模态函数的解析信号得到复瞬时声能流，从而得到某一目标的瞬时方位。该方法可以将矢量水听器输出的合成矢量信号分解为单分量信号之和，从而实现对不同方位目标的识别。
具有不同起始频率和调频斜率的两个线性调频信号在进行合成的时候由于相位变化速度的不同，合成的信号中将出现一些局部反相的情况，造成附近出现小尺度信号的情况。对这样的合成信号利用EMD进行分解并利用Hilbert变换得到其一阶本征模态函数的瞬时频率曲线上将出现一些峰值，而采取一定的方法对合成后的信号进行改造会使具有峰值的地方变得平坦甚至凹陷。在此基础上可以发展出一种基于Hilbert-Huang变换方法的水声通信方法，该方法利用尺度上的信息进行编码，利用本征模态函数的瞬时频率进行解码，本章对该方法从仿真实验、水池实验和湖上实验等方面验证这种新的水声通信方法的有效性。
The non-stationary signals with the characteristic of time variant widely exist in manyfields, and time-frequency analysis methods are essential to reveal the essential characteristicof the non-stationary signals. Hilbert-Huang transform is a new kind of time-frequencyanalysis method and it can adaptively decompose any complicated non-stationary signal intosome intrinsic mode functions without any prior knowledge of the signal. Any intrinsic modefunction only has one vibration mode at any time, and instantaneous frequency with physicalmeaning can be obtained. Hilbert-Huang transform has the advantages of decomposing signaladaptively and having higher time-frequency resolution. Compared with other time-frequencyanalysis methods, Hilbert-Huang transform has many advantages in non-stationary signalanalyzing and processing. Since its birth, Hilbert-Huang transform attracts many attentionsfrom researchers, and more and more researchers use this method to process thenon-stationary signals in their fields.
This paper discussed some problems such as mean curve fitting, end effect and modemixing, and proposed corresponding solutions. A new method of directly fitting mean curveby piecewise high order spline was proposed in this paper, in which more accurate meanpoints were obtained by piecewise high order spline and mean curve was obtained by directlyfitting mean point sequence. The method made EMD method obtain more accurate meancurve when sifting intrinsic mode function and accomplish accurate mode extraction.Compared with traditional method, the new method had higher decomposing speed. Thispaper also discussed mode mixing problem, analyzed the basic reason leading to mode mixing,and proposed a method of eliminating mode mixing based on translation invariant wavelettransform and EMD scale filtering. The method could effectively remove high frequencydiscontinuous signal from useful signal, which is the main cause of mode mixing, andaccomplish the goal of eliminating mode mixing. Traditional Hilbert-Huang transformalgorithm had the disadvantage of too much computation, and to reduce the computationalburden of Hilbert-Huang transform and make it realizable on hardware realtime, this papermade some improvements on Hilbert-Huang transform, which included mean curve fitting,end effect treatment, terminating conditions of sifting intrinsic mode function, terminatingconditions of EMD decomposition and the calculation of Hilbert transform. Theseimprovements greatly reduced the computational burden of Hilbert-Huang transform, withperformance basically remaining unchanged.
According to the characteristics of underwater acoustic signals, Hilbert-Huang transformwas introduced into underwater acoustic signal processing field in this paper. A target azimuth estimating method and a method of underwater acoustic communication based onHilbert-Huang transform were proposed in this paper. By combining Hilbert-Huang transformwith vector underwater acoustic signal processing technology, a new target azimuthestimation method based on Hilbert-Huang transform was proposed in this paper. The newmethod decomposed the three channel signals into intrinsic mode functions by EMD,calculated the complex instantaneous acoustic energy flux by the analytic signals of the sameorder intrinsic mode functions, and then got the instantaneous azimuth of a certain target. Themethod decomposed the synthesizing vectors from vector hydrophone into the sum of simplecomponent signals and realized the identification of targets at the different azimuths.
The combining signal of two LFM signals, which had different initiation frequencies andchirp rates, had some time of local inversed phase, which resulted from the different speed ofphase variation. Thus the combining signal had many small scale signals in some localregions. After performing EMD on the combining signal, some intrinsic mode functions couldbe obtained. Perform Hilbert transform on the first order intrinsic mode function, and itsinstantaneous frequency curve could be obtained, in which there were some peaks. Modifyingthe combining signal by some methods could make the regions with peaks become flat oreven concave. Based on these characteristics, a new method of underwater acousticcommunication based on Hilbert-Huang transform was proposed in this paper, in whichinformation was encoded in the scale domain and decoded by the instantaneous frequency ofintrinsic mode function. The underwater acoustic communication method was validated bysimulation experiments, water pool experiments and lake experiments.
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