###### Abstract  
With the development of industrial robots and other mechanical equipment to a higher degree of automation, mechanical systems have become increasingly complex. This represents a huge challenge for condition monitoring. The separation of vibration source signals plays an important role in condition monitoring and fault diagnosis. The key to the separation method of the vibration source signal is prior knowledge, such as of the statistical features of the vibration source signal, the number of vibration sources, and so forth. However, effective prior knowledge is difficult to obtain in engineering applications. This study found that low rank is a common feature of rotating machinery vibration source signals. To address the problem of the difficulty obtaining the signal feature of a vibration source, the multi-low-rank constrained vibration source signal separation method was proposed. Its advantages and effectiveness have been verified through simulations and experimental tests. Compared with the blind source separation method of independent component analysis (BSS-ICA) and the ensemble empirical mode decomposition (EEMD) methods, it obtained better clustering results and higher signal-to-signal ratio (SSR) values. fault diagnosis; low rank; vibration source signal; separation; robotic bearings Article  
Vibration Source Signal Separation of Rotating Machinery Equipment and Robot Bearings Based on Low Rank Constraint  
[PERSON], [PERSON], [PERSON], [PERSON], M.  
The denoising separation method is widely applied in condition monitoring. The signal features and filters (e.g., time domain, frequency domain, or time-frequency domain filters) are used to separate signals of interest from multiple component signals. First, the mixed vibration signal is decomposed into multiple components. Second, some components are discarded or retained, according to the prior features of the signal. Finally, the retained components are reconstructed as the vibration source signal. For example, [PERSON] et al. [5] used the complex wavelet transform to separate the fault vibration source signal. [PERSON] et al. [6] proposed an enhanced adaptive noise denoising algorithm. In this, the noise feature is used to separate the gear noise component and retain the bearing fault component. [PERSON] et al. [7] proposed a framework using the sailfish optimization (SO) algorithm and Gini index (GI) as a criterion to adaptively select the optimum variational mode decomposition (VMD) parameters for each fault signal. For this method, the bearing fault signal is automatically separated based on maximum GI values. [PERSON] et al. [8] proposed a novel compound fault separation algorithm based on parallel dual-Qfactors and improved maximum correlation kurtosis deconvolution (IMCKD), and separated the inner ring and outer ring bearing fault signals. However, the separation effect of this method is determined by the accuracy of dual-Qfactors. The above studies in the literature reflect that accurate signal prior features are the key to separating the source signal in the denoising separation method. Since the 21 st century [9; 10], the BSS method has been applied to mechanical fault diagnosis. [PERSON] et al. [11] proposed a novel perspective on blind filtering of vibration signals with the purpose of fault detection in rotating machinery, and successfully separated the vibration source signals of the bearing outer ring fault. [PERSON] et al. [12] proposed an adaptive blind source separation method to solve the non-stationary problem, and applied it to separate wheel fault vibration source signals. [PERSON] et al. [13] proposed a sparse component analysis (SCA) method based on linear clustering for the purpose of underdetermined blind source separation of vibration signals, and separating rolling bearing fault signals. In order to solve the underdetermined BSS problem, [PERSON] et al.