Research On Source Number Estimation And Feature Separation Extraction Method Of Mechanical Composite Fault Under Underdetermined Conditions

The general structure and operating conditions of mechanical equipment are very complicated,and their operating status greatly affects production safety.When abnormal conditions occur in the equipment,it is impossible to accurately determine the number of fault sources.Due to the complexity of the equipment structure and economic cost,the number of installed sensors will be limited,which will cause the number of observation signals of mechanical vibration to be less than the number of fault sources.In addition,the signal picked up by the sensor usually shows that multiple unknown vibration source signals are coupled to each other after being transmitted through an unknown route.Therefore,the in-depth study of source number estimation and blind source separation in the case of mechanical equipment underdetermination is particularly critical.In this article,the source number estimation and feature extraction of mixed signals under underdetermined conditions are mainly studied.Aiming at the shortcomings of general source number estimation methods,an improved source number estimation algorithm is studied;when the number of sources is solved,an underdetermined blind source separation method based on the combination of kurtosis and FastICA is proposed.The main content of the article is as follows:For the problem that the number of vibration sources is difficult to estimate under underdetermined conditions,a source number estimation method based on Variational Mode Decomposition(VMD)and Singular Value Decomposition(SVD)is proposed.Firstly,the Intrinsic Mode Function(IMF)is formed by VMD decomposition of the fault vibration signals.Then,the IMF is recombined to obtain multidimensional observation signals and its covariance matrix is obtained.Finally,the number of signal sources is estimated accurately according to the eigenvalues of singular value decomposition.In addition,a blind extraction method based on VMD and FastIndependent Component Analysis(FastICA)is proposed to solve the problem of mechanical vibration signal separation under underdetermined conditions.First,a single channel observation signal is processed by VMD to obtain multidimensional component signals.Then,according to the kurtosis criterion,the component signals which are the same as the number of signal sources are selected and recombined,so that the single-channel signal in the underdetermined case is transformed into the multi-channel signal in the positive definite case.Finally,the FastICA method is used to analyze the multi-channel signals processed by morphological filtering to realize the blind source separation of mechanical vibration signals.