基于核方法的非线性系统辨识，均衡和信号分离及在故障诊断中的应用
发布时间：2018-08-19 17:41
【摘要】：本论文在国家自然科学基金(50775208、51075372)、湖南省机械设备健康维护重点实验室开放基金(200904)和河南省教育厅自然科学基金(2008C460003)资助下,将核函数方法(Kernel Methods)应用到非线性系统的辨识,均衡和信号分离中,深入研究了基于核方法的机械故障诊断方法,并进行了仿真对比与实验研究,取得了一些创新性成果。本文的主要内容包括： 第一章,简述了本课题的研究意义,综述了核函数方法及其在机械故障诊断中的国内外研究现状,概述了本文的主要内容和创新之处。 第二章,论述了核函数的基础理论,介绍了常用的核函数,核函数的非线性映射以及构造核函数的条件,为将核函数方法应用到机械故障诊断中奠定理论基础。这一章的内容是整篇论文的理论基础。 第三章,论述了核递推最小二乘辨识思想和三种典型算法即ALD-KRLS、 SW-KRLS和FB-KRLS,通过仿真研究,比较了传统最小二乘(LMS)辨识算法、递推最小二乘(RLS)辨识算法和核递推最小二乘(KRLS)辨识算法对非线性系统的辨识能力。仿真研究表明,不论是在辨识精度,稳定性还是抗干扰性方面,KRLS辨识算法明显优于传统LMS、RLS辨识法。在这三种典型的KRLS辨识算法,SW-KRLS法比其他两种KRLS辨识算法获得了更好的辨识效果。SW-KRLS法特别适用于时变非线性系统辨识。在此基础上,提出了基于核递推最小二乘辨识的机械故障方法,并应用到转子系统的故障诊断中,实验结果表明提出的方法是有效的。 第四章,针对传统的自适应均衡方法存在的不足,提出了一种基于KRLS的非线性系统自适应均衡方法。该方法通过引入核函数,将原始的非线性数据映射到高维特征空间,然后在高维特征空间中实施标准最小二乘算法。提出的方法并与传统的非线性系统均衡方法进行了对比分析,仿真研究表明,提出的方法优于传统的均衡方法,能很好的消除传递通道的影响,有效地提取出弱冲击性成分。最后,将提出的方法应用到转子系统的弱冲击性故障提取中,实验结果进一步验证了提出的方法的有效性。 第五章,详细论述了独立分量分析、核函数独立分量分析的基本思想和算法。KICA是一种非线性算法,它是将传统ICA方法在高位特征空间中的推广,它具有更加优异的性能,可以解决一些经典的ICA方法无法解决的难题,例如非线性混合的盲信号分离问题。针对传统的独立分量分析在处理非线性混合的故障源分离的不足,提出了一种基于核独立分量分析(KICA)的非线性混合的机械故障源盲分离方法,该方法利用核函数的优点,将信号从低维的非线性原始空间变换到高维线性特征空间,从而可以采用线性ICA方法进行分离。仿真结果表明,与传统的ICA方法相比,提出的方法在处理非线性混合的源盲分离具有明显的优势。最后,将提出的方法应用到轴承故障信号的盲分离中,实验结果进一步验证了提出的方法的有效性。 第六章,总结了全文的工作,并提出了值得进一步研究的一些问题。
[Abstract]:In this paper, the Kernel Method is applied to the identification, equalization and signal separation of nonlinear systems with the support of the National Natural Science Foundation of China (50775208, 51075372), the Open Fund of Hunan Key Laboratory of Mechanical Equipment Health Maintenance (200904) and the Natural Science Foundation of Henan Education Department (2008C460003). Some innovative results have been obtained by comparing the simulation results with the experimental results. The main contents of this paper include:
In the first chapter, the research significance of this subject is briefly described, and the research status of kernel function method and its application in mechanical fault diagnosis at home and abroad is summarized.
In the second chapter, the basic theory of kernel function is discussed, and the common kernel function, the nonlinear mapping of kernel function and the conditions of constructing kernel function are introduced, which lays a theoretical foundation for applying kernel function method to mechanical fault diagnosis.
In the third chapter, the idea of kernel recursive least squares identification and three typical algorithms, namely ALD-KRLS, SW-KRLS and FB-KRLS, are discussed. Through simulation study, the identification ability of traditional least squares (LMS) identification algorithm, recursive least squares (RLS) identification algorithm and kernel recursive least squares (KRLS) identification algorithm for nonlinear systems are compared. The KRLS identification algorithm is superior to the traditional LMS and RLS identification algorithms in terms of identification accuracy, stability and anti-jamming. SW-KRLS identification algorithm achieves better identification results than the other two KRLS identification algorithms in the three typical KRLS identification algorithms. SW-KRLS method is especially suitable for time-varying nonlinear system identification. The mechanical fault diagnosis method based on kernel recursive least squares identification is applied to rotor system fault diagnosis. The experimental results show that the proposed method is effective.
In the fourth chapter, aiming at the shortcomings of the traditional adaptive equalization methods, an adaptive equalization method for nonlinear systems based on KRLS is proposed. By introducing kernel function, the original nonlinear data is mapped into the high-dimensional feature space, and then the standard least squares algorithm is implemented in the high-dimensional feature space. The simulation results show that the proposed method is superior to the traditional equalization method, and can eliminate the influence of the transmission channel and extract the weak impulsive components effectively. Finally, the proposed method is applied to extract the weak impulsive faults of the rotor system, and the experimental results are further validated. The effectiveness of the proposed method is also discussed.
In the fifth chapter, the basic idea and algorithm of independent component analysis and kernel function independent component analysis are discussed in detail. KICA is a nonlinear algorithm, which extends the traditional ICA method in high-level feature space. It has more excellent performance and can solve some difficult problems that classical ICA methods can not solve, such as nonlinear mixing blindness. Signal separation problem. In order to overcome the disadvantage of traditional independent component analysis (ICA) in dealing with nonlinear hybrid fault source separation, a nonlinear hybrid blind source separation method based on Kernel Independent Component Analysis (KICA) is proposed, which utilizes the advantages of kernel function to transform signals from low-dimensional nonlinear original space to high-dimensional lines. Compared with the traditional ICA method, the proposed method has obvious advantages in dealing with the source blind separation of nonlinear mixtures. Finally, the proposed method is applied to the blind separation of bearing fault signals. The experimental results further verify the proposed method. Effectiveness.
The sixth chapter summarizes the work of this paper and puts forward some questions worthy of further study.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH165.3
[Abstract]:In this paper, the Kernel Method is applied to the identification, equalization and signal separation of nonlinear systems with the support of the National Natural Science Foundation of China (50775208, 51075372), the Open Fund of Hunan Key Laboratory of Mechanical Equipment Health Maintenance (200904) and the Natural Science Foundation of Henan Education Department (2008C460003). Some innovative results have been obtained by comparing the simulation results with the experimental results. The main contents of this paper include:
In the first chapter, the research significance of this subject is briefly described, and the research status of kernel function method and its application in mechanical fault diagnosis at home and abroad is summarized.
In the second chapter, the basic theory of kernel function is discussed, and the common kernel function, the nonlinear mapping of kernel function and the conditions of constructing kernel function are introduced, which lays a theoretical foundation for applying kernel function method to mechanical fault diagnosis.
In the third chapter, the idea of kernel recursive least squares identification and three typical algorithms, namely ALD-KRLS, SW-KRLS and FB-KRLS, are discussed. Through simulation study, the identification ability of traditional least squares (LMS) identification algorithm, recursive least squares (RLS) identification algorithm and kernel recursive least squares (KRLS) identification algorithm for nonlinear systems are compared. The KRLS identification algorithm is superior to the traditional LMS and RLS identification algorithms in terms of identification accuracy, stability and anti-jamming. SW-KRLS identification algorithm achieves better identification results than the other two KRLS identification algorithms in the three typical KRLS identification algorithms. SW-KRLS method is especially suitable for time-varying nonlinear system identification. The mechanical fault diagnosis method based on kernel recursive least squares identification is applied to rotor system fault diagnosis. The experimental results show that the proposed method is effective.
In the fourth chapter, aiming at the shortcomings of the traditional adaptive equalization methods, an adaptive equalization method for nonlinear systems based on KRLS is proposed. By introducing kernel function, the original nonlinear data is mapped into the high-dimensional feature space, and then the standard least squares algorithm is implemented in the high-dimensional feature space. The simulation results show that the proposed method is superior to the traditional equalization method, and can eliminate the influence of the transmission channel and extract the weak impulsive components effectively. Finally, the proposed method is applied to extract the weak impulsive faults of the rotor system, and the experimental results are further validated. The effectiveness of the proposed method is also discussed.
In the fifth chapter, the basic idea and algorithm of independent component analysis and kernel function independent component analysis are discussed in detail. KICA is a nonlinear algorithm, which extends the traditional ICA method in high-level feature space. It has more excellent performance and can solve some difficult problems that classical ICA methods can not solve, such as nonlinear mixing blindness. Signal separation problem. In order to overcome the disadvantage of traditional independent component analysis (ICA) in dealing with nonlinear hybrid fault source separation, a nonlinear hybrid blind source separation method based on Kernel Independent Component Analysis (KICA) is proposed, which utilizes the advantages of kernel function to transform signals from low-dimensional nonlinear original space to high-dimensional lines. Compared with the traditional ICA method, the proposed method has obvious advantages in dealing with the source blind separation of nonlinear mixtures. Finally, the proposed method is applied to the blind separation of bearing fault signals. The experimental results further verify the proposed method. Effectiveness.
The sixth chapter summarizes the work of this paper and puts forward some questions worthy of further study.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH165.3
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