## 4 Simulation Experiment and Analysis  
A simulation noisy signal with 50 Hz is used to prove the effectiveness of the proposed method. The simulation signal is \(S(t)=0.1 sin(2\times\pi\times 50\times t)+n(t)\), and \(n(t)\) is Gaussian white noise with an intensity of 0.5. The sampling frequency of the signal is 3 kHz, and the sampling number is 3000. Its frequency domain waveform is shown in Figure 5. Due to too much interference noise, it is impossible to extract the fault characteristics. The SNR is \(-27.58\) Db by calculation, which indicates that the characteristic frequency is heavily polluted by noise. The original signal is passed into the high-pass filter, and the frequency domain waveform is shown in Figure 6. The CASTSR is used to extract the features of weak signals. The output spectrum of the first-order adaptive second-order trigtable system and second-order adaptive second-order trigtable system is shown in Figures 7 and 8.  
As can be seen from Figure 7, after the input signal goes through the first-order stochastic resonance, noise energy is transferred from the high frequency to the low frequency. As a result, the high-frequency noise is weakened, while the fault feature of the low frequency is strengthened. However, there is still a little noise around the characteristic frequency of 50 Hz, and the characteristic frequency is extracted, but it is weak. As can be seen from Figure 8, after the second stage of stochastic resonance is carried out, noise energy is transferred from the high frequency to the low frequency, and the fault characteristics of the  
Figure 4: Fault diagnosis flow based on CASTSR and EMD.  
Figure 5: The frequency domain waveform of the original signal.  
The processing results of the original noisy signals by EMD are shown in Figure 9.  
As can be seen from Figure 9, the decomposition results of the original signal show that the first four orders are high-frequency noise-containing components, and the characteristic frequency of 50 Hz appears in IMF5, but there is a lot of interference noise around it, so fault features cannot be accurately extracted. The proposed CASTSR was used to extract the weak signal features.  
The proposed CASTSR was used to extract the weak signal features. The processing results of the first-order stochastic resonance output are shown in Figure 10. The processing results of the second-order stochastic resonance output are shown in Figure 11.  
In Figure 10, IMF1 is a high-frequency interference component, in which the characteristic frequency is submerged. The characteristic frequency appears in IMF2, where the surrounding noise is less, and the characteristic frequency can be clearly identified. Compared with the result without denoising, the IMF order of EMD decomposition decreases by two orders after denoising. According to the processing results of the second-order stochastic resonance output in Figure 11, it can be seen that the characteristic frequency appears in IMF1. Compared with the first-order result, the ambient noise is effectively  
Figure 8: The output spectrum of the second cascade system.  
Figure 9: The processing results of the original noisy signals.  
transferred to the characteristic frequency, and the IMF order of EMD decomposition is reduced by one order.  
From Figures 9-11, after the pretreatment of the noise signal by CASTSR is carried out, the high-frequency interference noise is transferred into the low frequency to increase the characteristic frequency. Compared with the result of direct EMD decomposition without noise reduction, the IMF component obtained by EMD is more accurate and clearer with fewer noise-interference components and more prominent characteristic frequency information. In addition, from the perspective of the IMF order of EMD decomposition, the IMF order of EMD decomposition decreases with the increase in CASTSR order, and the most direct result is the improvement in computing efficiency.