## 1 Introduction  
Rolling bearing is one of the most widely used parts in rotating machinery. The operational status of the rolling element bearing often directly affects the performance of the whole machine. Consequently, the fault identification and diagnosis of rolling bearings are of great significance to ensure the safe and reliable operation of mechanical equipment [1; 2; 3]. Vibration signals caused by rolling bearing faults have been extensively studied and powerful diagnostic methods have been proposed. In recent years, the emerging artificial intelligence diagnosis technologies have been widely concerned by many scholars. A large number of artificial intelligent methods such as support vector machine [4], fuzzy diagnosis method [5], convolutional neutral network [6], and recurrent neutral network [7] were proposed to diagnose the mechanical faults. Furthermore, the sparse representation methods have also been widely used because of the signals sparsity. Adaptive impulse dictionary [8], combined time-frequency dictionary [9], matching pursuit [10], and dictionary learning method [11] were presented to diagnose faults of rotating machinery. In addition to the above mentioned two popular methods, many other research methods such as fault quantitative diagnosis [12], fault mechanism research [13; 14], fault diagnosis of low speed machinery [15] and fault location diagnosis [16] also gained attention. Some traditional methods such as Fourier transform, envelope analysis method, empirical mode decomposition, wavelet transform, spectral kurtosis, and morphological filtering have shown their advantages on single fault detection [17; 18; 19]. However, these diagnosis methods all take the rolling bearing with single point of failure as the research object. In the actual conditions, the failure of rolling bearing usually manifests itself as a compound fault including the outer race defect, the inner race defect or the rollers defect. In general, due to the influence of operating environment, the interaction between multiple noise source and compound fault, the compound fault features are mutually coupled and interfere with each other, which causes major difficulty in compound faults detection [20]. Therefore, the separation of the compound fault components from strong background noise is a difficult problem in the field of mechanical fault diagnosis [21; 22]. In order to solve the problem issued above and improve the monitoring level of rolling bearings' running state, some methods have been proposed for compound faults diagnosis, such as demodulation algorithm, variational mode decomposition, clustering algorithm, and blind source separation technique [23; 24; 25; 26]. Reference [27] proposed a method of combining wavelet analysis with blind source separation for roller bearing compound faults separation that needs multiple signal channels to analyze. However, composite signals analyzed by blind source separation are usually exported from different channels by multiple sensors. Therefore, multiple sensors need to be installed in the diagnosis process, which may bring a lot of inconvenience to engineering applications. [PERSON] et al. [28] proposed a novel method named maximum correlated kurtosis deconvolution (MCKD), which is an effective tool for separating out the periodic impulse fault components from the vibration signal in circumstances of intense background noise. In recent years, MCKD has been widely used to extract periodic pulses for fault diagnosis [29; 30; 31]. However, some shortcomings in practical application of MCKD limit its performance to extract the transient process in noisy vibration signal. One problem is that, like most of the existing technologies, the main concern of MCKD is the detection of a single fault located in the outer race, inner race or rolling element, i.e., MCKD is not suitable for extracting multiple fault-impact components simultaneously in compound fault diagnosis.