A Novel Advancing Signal Processing Method Based on Coupled Multi-Stable Stochastic Resonance for Fault Detection  
[PERSON]  
1 School of Locomotive and Rolling Stock Engineering, Dalian Jiaotong University, Dalian 116028, China; [EMAIL_ADDRESS] (H.C.); [EMAIL_ADDRESS] (Y.G.) [PERSON]  
1 School of Locomotive and Rolling Stock Engineering, Dalian Jiaotong University, Dalian 116028, China; [EMAIL_ADDRESS] (H.C.); [EMAIL_ADDRESS] (Y.G.) [PERSON]  
2 School of Computer Science, China West Normal University, Nanchong 637002, China 2  
an adaptive step-changed SR (SCSR), in which they use the entropy index to quantify SR performance. [PERSON] et al. [18] explained frequency-shifted and re-scaling SR. [PERSON] et al. [19] analyzed the multi-scale noise-regulated SR. For the detection of multi-frequency signals, [PERSON] et al. [20] used SR tuning multi-scale noise. The above methods use SR to play an important role in practical engineering applications. Other signal analysis methods are also proposed to process signals [21; 22; 23; 24; 25; 26]. In the process of using SR to detect weak signals, new parameter optimization methods and SR models have been continuously proposed. [PERSON] et al. [27] presented overdamped multi-stable stochastic resonance (MSR) with a tri-stable potential. [PERSON] et al. [28] introduced an MSR system which is applied to multi-frequency weak signal detection. In addition, some scholars have also studied the second-order SR system. [PERSON] et al. [29] analyzed the detection of weak signals in a second-order underdamped variable-step SR system. [PERSON] et al. [30] further studied the second-order MSR method and used it for the early fault diagnosis of bearings. Except for the first-order and second-order SR models, scholars have studied coupled SR systems less. The coupled SR system is an analysis of the SR model from another scale. [PERSON] et al. [31] applied the coupling bi-stable system for weak signal extraction, and the result shows that the coupled bi-stable SR is better in terms of detection effect than a single bi-stable SR system. [PERSON] et al. [32] further studied an adaptive coupling bi-stable SR method and its application. [PERSON] [33] analyzed a coupled bi-stable SR system under Levy noise. In addition, some combination methods with other algorithms have been proposed in recent years [34; 35; 36; 37; 38]. In sum, the SR, MSR, SNR, coupled SR system, et cetera, are proposed by some researchers to best detect motor bearing faults. These methods can better detect motor bearing faults, but they find it very difficult to detect the faults from weak motor bearing signals under the strong noise. For solving this problem, in this paper, a new advancing coupled multi-stable stochastic resonance method, with two first-order multi-stable stochastic resonance systems, namely the CMSR, is proposed to detect motor bearing faults. In this proposed CMSR, the effects of the output signal-to-noise ratio (SNR) for system parameters and coupling coefficients, are analyzed in-depth by numerical simulation technology. Then, the SOA is used to adaptively optimize and determine the system parameters of the SR by using the subsampling technique. Finally, the pre-processed signal is input into the CMSR to detect the faults of motor bearings by Fourier transform. The innovations and main contributions of this paper are described as follows:  
* A novel advancing signal processing method based on coupled multi-stable stochastic resonance is proposed to detect the faults of motor bearings;
* The output signal-to-noise ratio (SNR) for system parameters and coupling coefficients are analyzed in depth;
* The SOA is used to adaptively optimize and determine the system parameters of the SR by using the subsampling technique;
* The actual vibration data of induction motor bearings are used to prove the effectiveness of the proposed CMSR system. The rest of the paper is organized as follows.