基于变分贝叶斯混合独立分量分析的机械故障诊断方法研究

发布时间：2018-09-09 12:13

【摘要】：本论文在国家自然科学基金(50775208,51075372)和湖南省机械设备健康维护重点实验室开放基金(200904)资助下,通过将变分贝叶斯混合独立分量分析理论引入到机械故障诊断中,提出了基于变分贝叶斯混合独立分量分析的机械故障诊断方法,并进行了仿真和实验研究,取得了一些创新性成果。其主要内容包括以下几个方面：第一章,详细介绍了本课题的选题背景、意义,全面综述了变分贝叶斯理论和独立分量分析理论的研究现状及其应用现状,在此基础上,提出了本论文的研究内容与创新之处。第二章,论述了变分贝叶斯独立分量分析(vbICA)的基本原理及其两种算法(vbICA1算法和vbICA2算法)。并通过实验比较了这两种算法的分离性能。实验结果表明,在噪声环境下的信号盲源分离,用这两种算法都能得到很好的分离效果。然而,在分离过程中,vbICA2算法能够得到比vbICA1算法更好的分离效果,而且,随着噪声的增强,vbICA2算法的分离性能的优越性越明显。在此基础上,给出了变分贝叶斯混合独立分量分析提出的意义,详细论述了变分贝叶斯混合独立分量分析理论和算法。本章的内容是整篇论文的理论基础。第三章,指出用ICA分解和表示数据时,假设整个数据分布完全可以用一个坐标系来描述。然而,当观测数据是由许多自相似的、非高斯的流形组成时,则硬是用一个单独的、全局的表示是不合适的,这样会产生一个次优的表示。针对ICA在盲源分离中的不足,本文在变分贝叶斯理论的基础上,提出了一种基于变分贝叶斯混合独立分量分析的机械故障源盲分离方法。该方法是考虑到源信号来自于多个坐标系,然后在多个坐标系下建立独立分量分析混合模型对观测信号进行学习分离。仿真结果验证了该方法的有效性。最后,将提出的方法应用到轴承内、外圈故障的源分离中,实验结果也验证了提出的方法的有效性。第四章,针对现有的机械故障源数估计方法存在的不足,即它只能给出源数估计的上限,并不能准确估计源数,而且未考虑噪声干扰的影响,提出了一种基于变分贝叶斯混合独立分量分析的机械故障源数估计方法,提出的方法以贝叶斯网络为基础,将混合独立分量分析与变分贝叶斯结合起来,并通过最大化目标函数得到负自由能(Negative Free Energy,NFE)来估计出最佳的隐藏信源数目。仿真和实验结果表明,本文提出的方法是非常有效的。第五章,论述了机械故障诊断欠定盲分离方法中存在的不足,即现有的欠定盲分离并没有考虑在噪声环境下,针对此不足,在变分贝叶斯和混合独立分量分析理论的基础上,提出了一种基于变分贝叶斯混合独立分量分析的机械故障诊断欠定盲源分离方法。该方法是假设源信号来自不同的簇(即流形),对每个簇建立一个ICA模型,这样就产生了ICA混合模型,然后结合变分贝叶斯对ICA混合模型进行学习,通过学习可以从观测信号中估计出混合矩阵以及恢复出源信号。仿真研究和实验研究表明,该方法对观测信号数目少于源信号数目的欠定盲源分离的效果非常满意。第六章,对本论文的研究工作进行了全面总结,并对进一步开展的工作做了展望。
[Abstract]:In this paper, with the support of the National Natural Science Foundation of China (50775208, 51075372) and the Open Fund of the Key Laboratory of Health Maintenance of Mechanical Equipment of Hunan Province (200904), by introducing the theory of Variational Bayesian Mixed Independent Component Analysis into mechanical fault diagnosis, a method of mechanical fault diagnosis based on Variational Bayesian Mixed Independent Component Analysis is proposed. The main contents include the following aspects:
In the first chapter, the background and significance of this topic are introduced in detail. The research status and application status of variational Bayesian theory and independent component analysis theory are summarized. On this basis, the research contents and innovations of this paper are put forward.
In the second chapter, the basic principle of variational Bayesian independent component analysis (vbICA) and its two algorithms (vbICA1 algorithm and vbICA2 algorithm) are discussed. The separation performance of the two algorithms is compared through experiments. The experimental results show that the two algorithms can achieve good separation performance in noise environment. In the process of separation, vbICA2 algorithm can get better separation effect than vbICA1 algorithm, and with the increase of noise, the superiority of vbICA2 algorithm is more obvious. On this basis, the significance of variational Bayesian Mixed Independent Component Analysis is given, and the theory of variational Bayesian Mixed Independent Component Analysis and the theory of variational Bayesian Mixed Independent Component Analysis are discussed in detail. Algorithm. The content of this chapter is the theoretical basis of the whole paper.
In Chapter 3, it is pointed out that when ICA is used to decompose and represent data, it is assumed that the whole data distribution can be completely described in a coordinate system. However, when the observed data are composed of many self-similar, non-Gaussian manifolds, it is inappropriate to simply use a single, global representation, which results in a suboptimal representation. In this paper, based on the variational Bayesian theory, a method of blind source separation for mechanical faults based on the variational Bayesian hybrid independent component analysis is proposed. The simulation results verify the effectiveness of the proposed method. Finally, the proposed method is applied to the source separation of bearing inner and outer ring faults. The experimental results also verify the effectiveness of the proposed method.
In Chapter 4, aiming at the shortcomings of the existing methods for estimating the number of mechanical fault sources, that is, they can only give the upper limit of the number of sources, can not accurately estimate the number of sources, and do not consider the influence of noise interference, a method of estimating the number of mechanical fault sources based on variational Bayesian mixed independent component analysis is proposed. Based on the network, the hybrid independent component analysis (HICA) and variational Bayesian are combined to estimate the optimal number of hidden sources by maximizing the Negative Free Energy (NFE) of the objective function.
In the fifth chapter, the shortcomings of under-determined blind separation method for mechanical fault diagnosis are discussed, that is, the existing under-determined blind separation method does not take into account the noise environment. To overcome this shortcomings, a mechanical fault diagnosis method based on variational Bayesian and mixed independent component analysis is proposed. This method is based on the assumption that the source signals come from different clusters (i.e. manifolds), and an ICA model is established for each cluster. Thus, a ICA hybrid model is generated. Then the ICA hybrid model is studied by using the variational Bayesian method. The mixed matrix can be estimated from the observed signals and the source signals can be recovered by learning. Research and experimental results show that this method is very satisfactory for under-determined blind source separation with less than the number of observed signals.
In the sixth chapter, the research work of this paper is summarized comprehensively, and the further work is prospected.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：TH165.3

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