Mechanical Fault Diagnostic Method Based On Extended Parallel Factor Analysis

This work was supported by a grant from National Natural Science Foundation of China(NSFC,Grant No.51675258),The State Key Laboratory of Mechanical Systems and Vibration(No.MSV201914)and Foundation for Postgraduate Innovation of Nanchang Hangkong University of China(YC2017049).Considering the limitations of traditional parallel factors in some applications,the extended parallel factor analysis algorithm is introduced into mechanical fault diagnosis,and the mechanical fault diagnosis method based on extended parallel factor analysis is studied.Some simulations and experiments were carried out to verify the effectiveness of the proposed method,and good results were obtained.The main contents of the thesis are as follows:1.Based on the shortcomings in the traditional parallel source-based blind source separation method(PARAFAC-BSS),i.e.in the PARAFAC-BSS method,the uniqueness of PARAFAC decomposition needs to be satisfied the condition that the three bearer matrices cannot contain any related columns,and this shortcomings limits the application of PARAFAC-BSS method.On this basis,PARAFAC-BSS is extended,and a blind source separation method based on extended parallel factor(PARAFAC2-BSS)is proposed.The advantage of the proposed method is that the established PARAFAC2 model only requires one mode matrix set to have the same factors,other matrices can have different factors,thus overcoming the deficiencies of the PARAFAC-BSS method.When the established model changes in a certain dimension,the model is still valid,and the traditional PARAFAC-BSS method must re-establish the model.At the same time,the comparison between PARAFAC2-BSS and PARAFAC-BSS is carried out.The simulation results show that PARAFAC2-BSS has obvious advantages in terms of performance indicators and similarity coefficient analysis.Finally,the proposed method is applied to the blind separation of rolling bearing faults,and the blind separation PARAFAC2 model of rolling bearing fault is constructed.The experimental results further verify the effectiveness of the proposed method.2.Combining the respective advantages of EMD,LMD and PARAFAC2,two mechanical fault underdetermination blind separation methods are proposed,which arethe blind separation method of EMD-PARAFAC2 and the blind separation method of LMD-PARAFAC2.The proposed method first decomposes the observed signal into several effective components and recombines them into new observation signals,achieving the effect of increasing the dimension,so that the number of observed signals is greater than or equal to the number of source signals,and transforming the underdetermined blind separation problem into overdetermined or positive definite blind separation problem.At the same time,the two mechanical fault underdetermined blind separation methods are compared with the EMD-PARAFAC and LMD-PARAFAC methods.The simulation results show that the separation effect of EMD-PARAFAC2 is better than that of the traditional EMD-PARAFAC.The separation effect of LMD-PARAFAC2 is better than that of the traditional LMD-PARAFAC.The EMD-PARAFAC2 blind separation method is more advantageous in convergence accuracy.The LMD-PARAFAC2 blind separation method is more advantageous in suppressing the end effect and retaining the signal information integrity.Finally,the proposed method is applied to the underdetermined blind separation experiment of rolling bearings.The experimental results show that the proposed method is effective.3.The existing method of blind separation of mechanical faults based on parallel factors is based on the assumption that the system is an instantaneous hybrid model.However,there is a time shift problem with the signal received by the sensor.when using the PARAFAC-BSS method to solve the time shift problem,it is required to consider re-modeling every time shift,which brings great inconvenience and affects the rapidity of fault separation,re-modeling is required to be considered for each time shift,therefore,it brings great inconvenience and also affects the rapidity of fault separation.In order to reduce this complexity,combined with the advantages of tensor decomposition,adaptive modeling can also be carried out in the case of dimensional changes.A blind separation method based on PARAFAC2 for time domain convolution non-stationary signals is proposed.Combined with the time division method,third-order tensor data is established from the multi-channel mixing matrix,then,using the time domain PARAFAC2 method,the data set of PARAFAC2 in each time dimension is established.Combined with the time division method,third-order tensor data is established from the multi-channel mixing matrix,then,using the time domain PARAFAC2 method,a data set of PARAFAC2 in each time dimension is established.The simulation results show that the separation effect of the PARAFAC2-based convolution blind separation method is better than the PARAFAC convolution blind separation in the presence of time delay.Finally,the method is successfully applied to the blind separation of mechanical fault sources.4.TUCKER decomposition is a new extended parallel factor model that can be seen as a high-order PCA.The characteristic is that the amount of compressed data obtained by the TUCKER decomposition of the constructed three-dimensional tensor is much smaller than the original data,and the data can be greatly compressed.Therefore,it is more conducive to feature extraction of data.The advantage of deep belief network(DBN)can train the whole neural network to generate training data according to the maximum probability by training the weight between its neurons,which is very beneficial for identification and classification.In this paper,combined with the respective advantages of TUCKER decomposition and deep belief network(DBN),a fault identification method based on TUCKER-DBN is proposed.In the proposed method,the third-order tensor state samples are constructed and normalized.Then,the core tensor is obtained by TUCKER decomposition,the hidden information in the data is mined,and the obtained core tensor is input into the DBN classifier for training and recognition.The method is applied to engine fault diagnosis.Experiments show that the proposed method is effective and has a good recognition effect.Compared with the traditional DBN recognition method,the proposed method has significantly improved the recognition speed.