# Fault Diagnosis of Rolling Bearings Based on Acoustic Signals in Strong Noise Environments
## 4 Simulation Verification Analysis
Furthermore, the fault extraction capabilities of the EMD and CEEMD methods for simulated signals are inherently constrained. The proposed methods, i.e., S-FMD, C-VMD, EMD, CEEMD, and fixed-parameter FMD, presented in this article were employed to denoise the bearing inner raceway simulation signal after the introduction of noise. The RNF and ISEI obtained by the two methods in the figure have the same change trend, that is, the ISEI is as feasible as the RFN in selecting the best components. Each method yields multiple intrinsic mode function (IMF) components, from which the optimal components are selected for further analysis. The relative fault number (RFN) and Integrated Signal Energy Index (ISEI) are then calculated for these optimal components. Figure 16 illustrates the RFN and ISEI values of the optimal components obtained by each method. The figure indicates that the S-FMD method proposed in this article achieves the highest RFN and ISEI values, thereby retaining the most fault information. This finding aligns with the envelope spectrum derived from the proposed method, which distinctly reveals the fault characteristic frequency (\(f_{i}\)) along with multiple harmonics. Furthermore, it demonstrates that the fixed-parameter FMD method exhibits superior capabilities in extracting noise effects and fault features compared to C-VMD, EMD, and CEEMD. This suggests that the proposed method is effective for conducting bearing fault diagnosis in environments with strong noise, thereby affirming its feasibility for diagnosing faults based on rolling bearing sound signals. Additionally, it is noteworthy from Figure 16 that the adaptive C-VMD method shows higher RFN and ISEI values than EMD, CEEMD, and fixed-parameter FMD, indicating a better noise reduction effect compared to these three methods. Consequently, this article compares C-VMD, which demonstrates improved noise reduction effects, with the proposed S-FMD method for analyzing the measured sound signals. Relying solely on one set of parameters may impose certain limitations. To address this, we introduced two additional simulated experiments with Gaussian white noise levels of \(-11\) dB and \(-9\) dB, respectively, to mitigate deviations and provide a more comprehensive evaluation of the fault detection performance of the S-FMD method under varying noise conditions. Figures 17 and 18 illustrate the time domain diagrams corresponding to SNRs of \(-9\) dB and \(-11\) dB, while Figures 19 and 20 present the envelope spectrum following noise reduction processing using this method, clearly revealing the inner ring fault. The  
Figure 5.3 Each method decomposes the signal and selects the ISEI and RFN of the best components (simulation with inner raceway fault). The test device is a certain type of test bench from Schaeffler Trading (Shanghai, China) Co., Ltd.--Shanghai R&D Center, as shown in Figure 5.4 As shown in Figure 23, the red box is the position of the sound sensor, the radial position of the test bearing, and the radial data from the test bearing. The sound signal is picked up by a sound sensor composed of an AWA14423 microphone and an AWA14604 preamplifier. The data are sampled by NI acquisition card 9234. The sampling frequency and number of sampling points are both set to 51.2 kHz. The size and appearance of the microphone are shown in Figure 5.5 The sensor performance indicators are shown in Figure 5.6