Parallel Factor Analysis And Its Application In Blind Separation Of Multi-fault Sources

This work was supported by a grant from National Natural Science Foundation of China(NSFC,Grant No.51675258,51075372),The State Key Laboratory of Mechanical Transmissions(SKLMT-KFKT-201514),National key R & D program(No.2016YFF0203000)and Foundation for Postgraduate Innovation of Nanchang Hangkong University(YC2016050).Considering the existing problem of traditional blind source separation of the mechanical fault sources,this paper put forward some new blind source separation algorithms by introducing parallel factor analysis theory to mechanical fault diagnosis,and these new methods had applied in blind source separation of multiple fault.With a series of simulations and experiments,the results verified the feasibility and validity of the proposed algorithms.The main chapter and work of this paper were presented as follows:In Chapter one: The background and significance of this paper was illuminated firstly.Then,the theory of blind source separation and its development in mechanical fault diagnosis were discussed.Meanwhile,the principle of parallel factor analysis and its worldwide applications were also summarized.Finally,the main contents and the innovation points of this dissertation were presented.In Chapter two: Considering the deficiencies of the traditional mechanical vibration source estimation,this chapter proposed the new source number estimation algorithm based on the combination of parallel factor analysis and the core consistency diagnostic.The simulation results showed that the new source number estimation algorithm can accurately estimated the vibration source number from the non-stationary signal under the condition of the complete mixture and underdetermined mixture.Moreover,with the noise interference,the proposed method in this chapter also finished the estimation of vibration source number in mechanical system.At last,the algorithm was applied to the experiment of bearing multiple fault source estimation and the multi-source mechanical vibration test,and the experiment results further verified the effectiveness of the approach.In Chapter three: The traditional independent component analysis would not solve blind source separation in noisy environment.To meet this deficiency,the new blind source separation based on parallel factor analysis was presented in this chapter.The PARAFAC model was constructed from observed signals firstly.Then,the PARAFAC model was decomposed by trilinear alternative least square(TALS)in order to get the corresponding load matrix,i.e.the mixing matrix estimation.Finally,the estimated source signals would be obtained.Under the condition of underdetermined mixture,the source signals were recovered by the shortest-path method on the basis of above knowledge.In this simulation,we set different SNR of noise environment.The proposed method in this chapter was compared with the traditional blind source separation method under the condition of complete mixture.Meanwhile this method also was compared with LMD-UBSS under the condition of underdetermined mixture.The simulation results showed that the proposed method was superior to traditional blind source separation method.Finally,this algorithm was applied to the blind source separation experiment of bearing multiple fault and the multi-source mechanical vibration test,and the experiment results further verified the effectiveness of the approach.In Chapter four: In the arbitrarily underdetermined condition,blind source separation would not achieved by the Traditional PARAFAC method.Based on the deficiency above,this chapter put forward two new underdetermined blind source separation methods,Underdetermined Blind Source Separation Method Based on Local Mean Decomposition and Parallel Factor Analysis(LMD-PARAFAC)and Underdetermined Blind Source Separation Method Based on empirical mode decomposition and Parallel Factor Analysis(EMD-PARAFAC)respectively.the proposed two methods could obtain their respectively sub-signals of observed signals firstly.These sub-signals and original observed signals were combined into new observed signals.This two methods were compared with the traditional PARAFAC method.Meanwhile,this proposed two algorithms were compared in different SNR of noise environment from two indexes that convergence accuracy and computational efficiency respectively.The simulation results show that the ideal separation effect could be achieved by the proposed two methods.However,the traditional PARAFAC method obtained the bad separation effect.EMD-PARAFAC was superior to LMD-PARAFAC from convergence accuracy and computational efficiency without considering the influence of end effect.Finally,EMD-PARAFAC method was applied to underdetermined blind source separation experiment of bearing multiple fault.LMD-PARAFAC method was applied to the multi-source mechanical vibration test.the experiment results further verified the effectiveness of the approach.In Chapter five: Parallel Factor is the tensor data processing method.the uniqueness of PARAFAC model decomposition has important practical value,which successfully applied in blind source separation.In practical engineering,the mixed model of source signal is Nonlinear.However the original algorithms based on Parallel Factor analysis have assumed that source signals are linear mixed.Based on this deficiency,an blind source separation method of nonlinear mixture based on kernel parallel factor analysis was proposed.In proposed method,nonlinear observation signals were mapped from low dimensional space to high dimensional kernel feature space.Then the treated observation signals in kernel feature space were analyzed by parallel factor analysis.The simulation results showed that the proposed algorithm can accurately estimated the source signals from the nonlinear mixtures of non-stationary signal.Finally,the proposed method was applied to the separation of mixed faults of rolling bearing,and the experiment results further verified the effectiveness of the approach.In Chapter six: The conclusions were presented and some advanced topics in the proposed methodology that need further investigation in future were presented and addressed.