An Underdetermined Blind Source Separation Algorithm Based On Multisensory Time-Frequency Distribution And Its Application In Mechanical Multiple Fault Diagnosis

When the collected observation signals in the industrial field contain a variety of mechanical fault features,they interfere with each other.It is more difficult to identify and distinguish them than single fault features.In this paper,an underdetermined blind source separation algorithm based on Multisensory Time-Frequency Distribution,MTFD is studied and applied to mechanical multiple fault diagnosis.The specific research contents of the study are as follows:(1)The basic theory of blind source separation is studied,including three mathematical models of blind source separation,and a traditional blind source separation algorithm,such as fastICA algorithm.Meanwhile described the vibration signal characteristics of mechanical equipment which common parts are in fault mode,especially the fault characteristics of bearing multiple fault in time-frequency domain.(2)The blind source separation algorithm needs the accurate estimation of the number of sources,especially when the number of observations is smaller than the number of source signals,the smaller number of sources can be extracted,which is more difficult to obtain accurate estimation of the number of sources.In this paper,an underdetermined source number estimation method based on matrix non-negative low rank sparse representation is proposed.By multiple iterations of the observed signals and the build of non-negative low rank sparse graphs,the low rank sparse optimal solution matrix,the graph weight matrix related to the source signal and the size of their rank are all obtained.Then the accurate estimation of the source number is acquired.(3)Combined with the characteristics of MTFD and blind source separation,an underdetermined blind source separation method for mechanical multiple fault signals is proposed.Firstly,the Wigner-Ville distribution is used to transform the observed signals into a MTFD matrix.Secondly,whitening and noise threshold processing are performed on the matrix.Thirdly,select the automatic terms and cluster the feature vectors.Then,obtain the estimation of the Time-Frequency Distribution,TFD matrix of the source signal.Finally,the source signal is rebuilt and the accurate estimation of the source signal is obtained.The simulation and test results shown that the proposed method is effective in dealing with the underdetermined blind source separation of non-stationary signals.