Mechanical Fault Diagnosis Method Based On Variational Bayesian Mixture Of Independent Component Analysis

This thesis introduces variational Bayesian mixture of independent component analysis theory to the mechanical fault diagnosis, and makes more advanced exploration and research to the blind source separation of the mechanical fault, which is funded by the National Natural Science Foundation of China (50775208, 51075372) and Hunan Provincial Key Laboratory of Mechanical Equipment Health Maintenance Open Fund (200904). In this process, the mechanical fault diagnosis method based on variational Bayesian mixture of independent component analysis is proposed, and then simulation and experimental study have been made and a number of innovative achievements have been gained. The main contents include the following:The first chapter introduces the background and the meaning of this subject in detail, and reviews the research status of the theory of variational Bayesian and independent component analysis comprehensively, and then presents the main contents and innovations of this paper.The second chapter discusses the basic principle of variational Bayesian independent component analysis (vbICA) and its two algorithms (vbICA1 algorithm and vbICA2 algorithm). The separation performances of these two algorithms are compared by experiment. The results show that the effects of blind source separation with these two algorithms in the noise environment are both good. However, during the separation process, vbICA2 algorithm can be better than vbICA1 separation algorithm, and, as the noise increased, the more obvious advantages for separation performance of the vbICA2 algorithm. On this basis, the chapter leads to the sense of variational Bayesian miture of independent component analysis proposed, and discusses variational Bayesian mixture of independent component analysis theory and algorithms in detail. This chapter is the theoretical basis of the whole thesis.The third chapter shows that Decomposing and representing data using independent component analysis assumes that the whole data distribution is adequately described by one coordinate frame. However, if the observed data consists of various self-similar, non-Gaussian manifolds, enforcing a single, global representation is not appropriate and will produce a sub-optimal representation. In order to make up the lack of ICA in blind sources separations, blind separation of mechanical fault sources based on variational Bayesian mixture of independent component analysis is presented based on variational Bayesian theory in this paper. To consider the source signals from multiple frames, the method creats a mixture model of independent component analysis in multiple frameworks for learning the observed signals and separating them. Simulation results show that the method is very effective. Finally, the proposed method is applied to the source separation of bearing inner and outer fault, the experimental results also show that the proposed method is very effective.The fourth chapter discusses the deficiency of the existing methods of mechanical fault source number estimation, that they can only estimate the upper limit of sources, and can not accurately estimate the number of sources, and do not consider the effect of noise. In order to overcome the deficiency, a new method to estimate the number of mechanical fault sources based on variational Bayesian mixture of independent component analysis is proposed in this paper. The proposed method is based on Bayesian network, combining mixture of independent component analysis and variational Bayesian. And then the optimal number of hidden sources is estimated using negative free energy (Negative Free Energy, NFE) gained by maximizing the objective function. Simulation and experimental results show that the proposed method is very effective.The fifth chapter discusses the deficiency of underdetermined blind source separation method of mechanical fault sources, that the existing methods of underdetermined blind source separation don't consider the noise. In order to overcome the deficiency, a underdetermined blind source separation method of mechanical fault sources based on variational Bayesian mixture of independent component analysis is proposed, combining mixture of independent component analysis and Bayesian inference. This method assumes that source signals come from different clusters (ie, manifolds), and a ICA model is created for each cluster, thus the mixture model of ICA is created. And then the mixture model of ICA is learned combining with variational Bayes. The mixing matrix can be estimated out and the source signal can be recovered from observed signal through learning. Simulation and experimental results show that the method which is used into underdetermined blind source separation is very satisfactory.The sixth chapter summaries research work of this paper comprehensively, and puts forward to further work.