## 1 Introduction  
Rotating machinery is a kind of widely used power equipment, so it is of great significance to implement intelligent operation and maintenance management [1; 2]. However, due to the complex structure and dynamic operating environment, the vibration of such equipment generally presents strong nonlinear and background noise characteristics [3; 4]. For many years, only the local vibration signals collected by a single sensor have been used to solve the problem of fault identification of rotating machinery system, which has led to obvious difficulties. Thus, we should make full use of a series of sensors arranged at several key sections of the rotating machinery, and implement intelligent fault decision-making technology based on as much information as possible. This view has gained consensus on the research prospect of industrial big data technology [5]. Obviously, the more sensors that collect fault information, the more dimensions the fault feature dataset will have. Therefore, in the process of researching the intelligent operation and maintenance of rotating machinery, a major question is how to effectively extract the sensitive quantitative features of its operational state from the nonlinear, strong noise, high-dimensional vibration signal fault feature dataset, which has significance for the development of intelligent decision-making technology driven by big data. The purpose of a vibration signal analysis of rotating machinery is to extract the operational information of the key rotating parts (e.g., gears, bearings, and rotors), and effective signal processing and feature extraction are key to completing the condition monitoring and fault diagnosis of rotating machinery. Therefore, more accurate and comprehensive extraction of vibration signal characteristics has been the pursuit of researchers in this field. The methods of feature extraction of vibration signal include empirical mode decomposition (EMD) [6; 7], minimum entropy deconvolution [8; 9], an adaptive filter [10; 11], matching tracking [12; 13], mathematical morphology analysis [14; 15; 16], cyclostationary signal analysis [17; 18], a Wiener filter [19; 20], wavelet transform [21; 22; 23], a Kalman filter [24; 25], and stochastic resonance [26; 27]--all of which help with the development of mechanical fault diagnosis. The above methods can effectively eliminate background noise and interference components, and extract a fault signal in a specific environment, but are not suitable for complex interference situations. In particular, when the interference signal in the vibration signal of rotating machinery is similar to the fault signal, it is more difficult to identify and eliminate the interference components and extract the fault signal with the above methods. Blind source separation (BSS) technology [28] can separate multiple aliased signals without the influence of time-frequency overlap of source signals. At the same time, the separation signal will not lose the weak signal characteristic information in the vibration signal of rotating machinery. There have been many effective blind source separation algorithms with different characteristics, including the fast fixed-point algorithm [3], natural gradient algorithm [29], Equivariant Adaptive Separation via Independence (EASI) algorithm [30], and Joint Approximation Diagonalization of Eigen-matrices (JADE) algorithm [31]. These have been widely used for fault diagnosis [32; 33], image processing [34], speech recognition [35], earthquake prediction [36], and other fields. [PERSON] et al. [37] proposed a source contribution quantitative estimation method based on underdetermined blind source separation to identify the major vibration and radiation noise. [PERSON] et al. [38] presented a new multiscale decomposition algorithm that enables the blind separation of convolutely mixed images. [PERSON] et al.