基于變分貝葉斯混合獨(dú)立分量分析的機(jī)械故障診斷方法研究
發(fā)布時間：2018-09-09 12:13
【摘要】：本論文在國家自然科學(xué)基金(50775208,51075372)和湖南省機(jī)械設(shè)備健康維護(hù)重點(diǎn)實(shí)驗(yàn)室開放基金(200904)資助下,通過將變分貝葉斯混合獨(dú)立分量分析理論引入到機(jī)械故障診斷中,提出了基于變分貝葉斯混合獨(dú)立分量分析的機(jī)械故障診斷方法,并進(jìn)行了仿真和實(shí)驗(yàn)研究,取得了一些創(chuàng)新性成果。其主要內(nèi)容包括以下幾個方面： 第一章,詳細(xì)介紹了本課題的選題背景、意義,全面綜述了變分貝葉斯理論和獨(dú)立分量分析理論的研究現(xiàn)狀及其應(yīng)用現(xiàn)狀,在此基礎(chǔ)上,提出了本論文的研究內(nèi)容與創(chuàng)新之處。 第二章,論述了變分貝葉斯獨(dú)立分量分析(vbICA)的基本原理及其兩種算法(vbICA1算法和vbICA2算法)。并通過實(shí)驗(yàn)比較了這兩種算法的分離性能。實(shí)驗(yàn)結(jié)果表明,在噪聲環(huán)境下的信號盲源分離,用這兩種算法都能得到很好的分離效果。然而,在分離過程中,vbICA2算法能夠得到比vbICA1算法更好的分離效果,而且,隨著噪聲的增強(qiáng),vbICA2算法的分離性能的優(yōu)越性越明顯。在此基礎(chǔ)上,給出了變分貝葉斯混合獨(dú)立分量分析提出的意義,詳細(xì)論述了變分貝葉斯混合獨(dú)立分量分析理論和算法。本章的內(nèi)容是整篇論文的理論基礎(chǔ)。 第三章,指出用ICA分解和表示數(shù)據(jù)時,假設(shè)整個數(shù)據(jù)分布完全可以用一個坐標(biāo)系來描述。然而,當(dāng)觀測數(shù)據(jù)是由許多自相似的、非高斯的流形組成時,則硬是用一個單獨(dú)的、全局的表示是不合適的,這樣會產(chǎn)生一個次優(yōu)的表示。針對ICA在盲源分離中的不足,本文在變分貝葉斯理論的基礎(chǔ)上,提出了一種基于變分貝葉斯混合獨(dú)立分量分析的機(jī)械故障源盲分離方法。該方法是考慮到源信號來自于多個坐標(biāo)系,然后在多個坐標(biāo)系下建立獨(dú)立分量分析混合模型對觀測信號進(jìn)行學(xué)習(xí)分離。仿真結(jié)果驗(yàn)證了該方法的有效性。最后,將提出的方法應(yīng)用到軸承內(nèi)、外圈故障的源分離中,實(shí)驗(yàn)結(jié)果也驗(yàn)證了提出的方法的有效性。 第四章,針對現(xiàn)有的機(jī)械故障源數(shù)估計(jì)方法存在的不足,即它只能給出源數(shù)估計(jì)的上限,并不能準(zhǔn)確估計(jì)源數(shù),而且未考慮噪聲干擾的影響,提出了一種基于變分貝葉斯混合獨(dú)立分量分析的機(jī)械故障源數(shù)估計(jì)方法,提出的方法以貝葉斯網(wǎng)絡(luò)為基礎(chǔ),將混合獨(dú)立分量分析與變分貝葉斯結(jié)合起來,并通過最大化目標(biāo)函數(shù)得到負(fù)自由能(Negative Free Energy,NFE)來估計(jì)出最佳的隱藏信源數(shù)目。仿真和實(shí)驗(yàn)結(jié)果表明,本文提出的方法是非常有效的。 第五章,論述了機(jī)械故障診斷欠定盲分離方法中存在的不足,即現(xiàn)有的欠定盲分離并沒有考慮在噪聲環(huán)境下,針對此不足,在變分貝葉斯和混合獨(dú)立分量分析理論的基礎(chǔ)上,提出了一種基于變分貝葉斯混合獨(dú)立分量分析的機(jī)械故障診斷欠定盲源分離方法。該方法是假設(shè)源信號來自不同的簇(即流形),對每個簇建立一個ICA模型,這樣就產(chǎn)生了ICA混合模型,然后結(jié)合變分貝葉斯對ICA混合模型進(jìn)行學(xué)習(xí),通過學(xué)習(xí)可以從觀測信號中估計(jì)出混合矩陣以及恢復(fù)出源信號。仿真研究和實(shí)驗(yàn)研究表明,該方法對觀測信號數(shù)目少于源信號數(shù)目的欠定盲源分離的效果非常滿意。 第六章,對本論文的研究工作進(jìn)行了全面總結(jié),并對進(jìn)一步開展的工作做了展望。
[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.
【學(xué)位授予單位】：鄭州大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2011
【分類號】：TH165.3
本文編號：2232331
[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.
【學(xué)位授予單位】：鄭州大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2011
【分類號】：TH165.3
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