基于主分量、独立分量分析的盲信号处理及应用研究
摘要
本文以统计信号处理理论为基础,针对现有传统信号分析方法的不足,研究混合信号中独立分量提取的相关理论和计算方法; 面向工程实际应用的需要,研究算法在实际应用中需考虑的快速性、稳定性和自适应性,并以工业现场的实际信号为对象,研究独立分量分离在实际工程应用中的作用与价值。
本文首先集中讨论了与主分量分析(PCA)和独立分量分析(ICA)相关的理论和方法; 论述了“独立”与“不相关”的关系; 论述了白化理论及其工程应用的方法,对“白化”解相关的特性进行了研究。结果表明,对信号进行白化处理,可以大幅度降低信号之间的互相关程度。
研究了PCA 的一些计算方法以及主分量选取的原则,并根据这一原则——贡献率的大小,来决定主分量的数量。应用这一理论,对实际的工程信号进行了PCA 分析,为传感器数量的选取提供了理论依据。研究了采用PCA 方法对信号进行白化预处理的理论与方法。
分析了ICA 所用的比照函数,给出了若干比照函数的数学模型,总结了比照函数的选用原则; 指出基于神经网络的独立分量估计算法的核心是梯度下降法; 在随机梯度算法的基础上,提出了一种改进的非线性ICA 算法。研究结果表明,该算法对同类峭度符号的信号的分离具有较好的效果。
针对传统时频信号处理中存在的“同频干扰不可分”问题,进行了基于PCA 白化预处理的ICA 盲源分离的仿真研究,并对实际的工程信号进行了ICA 分析。其结果表明,盲源分离可以令人满意地解决由多个频率成份相互重叠的信号混合后的分离问题。研究了如何采用ICA 方法剔除中厚板轧机主传动轴的振动信号在传输过程中所受到的同频噪声干扰。
论述了基于峭度比照函数的定点算法和基于其它高次非线性函数的比照函数的定点算法的一般算式; 在Hyvarien“定点算法”的基础上,提出了采用其它非线性函数作为比照函数的定点算法,并提出了增强稳定性的改进方法; 应用不同的非线性函数所构成的比照函数对不同分布类型的独立分量的提取进行了仿真研究; 针对盲源分离过程中信号次序的不确定性,研究了分离信号次序重排的方法。
研究了中厚板轧机主传动系统的主要结构特点,分析了主传动系统的固有振动频率,建立了主传动系统的振动模型,指出了主传动系统中易受破坏的的关键传动部件——万向联轴器的破坏机理; 设计并开发了一套基于DataSocket 的Internet 通信方式
Aim to the limitation of traditional signal processing, the theories and methodologies based on statistical signal processing, which are used to extrat the independent components from mixture signals, have been researched. To meet the needs of engineering, the rapidity, stability and self-adaptability of the methodology have been researched. Faces to the real signal of engineering, the applications of independent component analysis (ICA) have been researched.
First, the theories and methodologies of principal component analysis (PCA) and independent component analysis have been discussed. The relationships of independent and irrelevance have been explained. The white theory and its application in engineering have been expounded. The feature of decorrelation based on whitening has been researched. The result shows the correlative level of signals can be reduced mostly after whitening them.
The contributiveness-based methodology of principal component selection has been researched. The number of principal component can be determined according this principle. Applied this theory on real signal of engineering, the minimal number of sensor can be determined by using. The theory and methodology for signal whitening based on PCA have been researched.
The contrast functions have been analyzed, the selected methodology for contrast function has been summarized, and several contrast functions have been proposed. The key of independent estimation based on neural calculating is gradient decent. On the based of stochastic gradient decent algorithm, an improved nonlinear ICA algorithm has excellent effect for the signals that have the same sign of kurtosis.
Aim to the problem of dis-separating for the same frequency mixed signal, the simulation for blind source separation based on PCA whitening has been researched, and applying the method on real engineering signal —the roll machine vibration signals disturbed by the same frequency noises on signal transmission. The result shows that the blind source separation can excellently separate the signals, which their components are overlapped in frequency domain.
Fixed-point algorithm based on kurtosis contrast function and others fixed-point algorithms based on high-order nonlinear contrast function. On the fundamental of
fixed-point algorithm proposed by Hyvarien, the other nonlinear contrast functions have been proposed in this thesis, and the reliability improved methods has been proposed also. The simulations for different distributed components have been processing by using different nonlinear contrast functions. Aim to the un-determination of order of the component occurs in separating, the order resorting has been researched, and a order resorting algorithm of component has been proposed. The character of main driving system of rolling machine and its inherent frequency has been analyzed. The vibrant model of the main driving system has been created. The mechanism of failed of couple, which is damageable component in the main driving system of rolling machine, has been pointed out. A set of monitoring system of the main driving system of roll machine has been developed. This monitoring system is developed by using DataSocket programming. The communications between workstations and server can be over Internet. A self-adaptive filter has been designed to smooth the vibration signals that are disturbed by power pause in the space. A set of FM wireless communication for torsion monitoring has been designed and been applied also. This torsion monitoring system is easy to mount. The problem, which the signals disturbed by same frequency noises over the transmission in space can’t be demodulated correctly, has been solved by using ICA. This thesis indicated the ICA can solved the problem, which can’t be completed correctly by using traditional signal processing methods.
本文首先集中讨论了与主分量分析(PCA)和独立分量分析(ICA)相关的理论和方法; 论述了“独立”与“不相关”的关系; 论述了白化理论及其工程应用的方法,对“白化”解相关的特性进行了研究。结果表明,对信号进行白化处理,可以大幅度降低信号之间的互相关程度。
研究了PCA 的一些计算方法以及主分量选取的原则,并根据这一原则——贡献率的大小,来决定主分量的数量。应用这一理论,对实际的工程信号进行了PCA 分析,为传感器数量的选取提供了理论依据。研究了采用PCA 方法对信号进行白化预处理的理论与方法。
分析了ICA 所用的比照函数,给出了若干比照函数的数学模型,总结了比照函数的选用原则; 指出基于神经网络的独立分量估计算法的核心是梯度下降法; 在随机梯度算法的基础上,提出了一种改进的非线性ICA 算法。研究结果表明,该算法对同类峭度符号的信号的分离具有较好的效果。
针对传统时频信号处理中存在的“同频干扰不可分”问题,进行了基于PCA 白化预处理的ICA 盲源分离的仿真研究,并对实际的工程信号进行了ICA 分析。其结果表明,盲源分离可以令人满意地解决由多个频率成份相互重叠的信号混合后的分离问题。研究了如何采用ICA 方法剔除中厚板轧机主传动轴的振动信号在传输过程中所受到的同频噪声干扰。
论述了基于峭度比照函数的定点算法和基于其它高次非线性函数的比照函数的定点算法的一般算式; 在Hyvarien“定点算法”的基础上,提出了采用其它非线性函数作为比照函数的定点算法,并提出了增强稳定性的改进方法; 应用不同的非线性函数所构成的比照函数对不同分布类型的独立分量的提取进行了仿真研究; 针对盲源分离过程中信号次序的不确定性,研究了分离信号次序重排的方法。
研究了中厚板轧机主传动系统的主要结构特点,分析了主传动系统的固有振动频率,建立了主传动系统的振动模型,指出了主传动系统中易受破坏的的关键传动部件——万向联轴器的破坏机理; 设计并开发了一套基于DataSocket 的Internet 通信方式
Aim to the limitation of traditional signal processing, the theories and methodologies based on statistical signal processing, which are used to extrat the independent components from mixture signals, have been researched. To meet the needs of engineering, the rapidity, stability and self-adaptability of the methodology have been researched. Faces to the real signal of engineering, the applications of independent component analysis (ICA) have been researched.
First, the theories and methodologies of principal component analysis (PCA) and independent component analysis have been discussed. The relationships of independent and irrelevance have been explained. The white theory and its application in engineering have been expounded. The feature of decorrelation based on whitening has been researched. The result shows the correlative level of signals can be reduced mostly after whitening them.
The contributiveness-based methodology of principal component selection has been researched. The number of principal component can be determined according this principle. Applied this theory on real signal of engineering, the minimal number of sensor can be determined by using. The theory and methodology for signal whitening based on PCA have been researched.
The contrast functions have been analyzed, the selected methodology for contrast function has been summarized, and several contrast functions have been proposed. The key of independent estimation based on neural calculating is gradient decent. On the based of stochastic gradient decent algorithm, an improved nonlinear ICA algorithm has excellent effect for the signals that have the same sign of kurtosis.
Aim to the problem of dis-separating for the same frequency mixed signal, the simulation for blind source separation based on PCA whitening has been researched, and applying the method on real engineering signal —the roll machine vibration signals disturbed by the same frequency noises on signal transmission. The result shows that the blind source separation can excellently separate the signals, which their components are overlapped in frequency domain.
Fixed-point algorithm based on kurtosis contrast function and others fixed-point algorithms based on high-order nonlinear contrast function. On the fundamental of
fixed-point algorithm proposed by Hyvarien, the other nonlinear contrast functions have been proposed in this thesis, and the reliability improved methods has been proposed also. The simulations for different distributed components have been processing by using different nonlinear contrast functions. Aim to the un-determination of order of the component occurs in separating, the order resorting has been researched, and a order resorting algorithm of component has been proposed. The character of main driving system of rolling machine and its inherent frequency has been analyzed. The vibrant model of the main driving system has been created. The mechanism of failed of couple, which is damageable component in the main driving system of rolling machine, has been pointed out. A set of monitoring system of the main driving system of roll machine has been developed. This monitoring system is developed by using DataSocket programming. The communications between workstations and server can be over Internet. A self-adaptive filter has been designed to smooth the vibration signals that are disturbed by power pause in the space. A set of FM wireless communication for torsion monitoring has been designed and been applied also. This torsion monitoring system is easy to mount. The problem, which the signals disturbed by same frequency noises over the transmission in space can’t be demodulated correctly, has been solved by using ICA. This thesis indicated the ICA can solved the problem, which can’t be completed correctly by using traditional signal processing methods.
引文
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