Empirical Fourier Decomposition Algorithm Based on Spectrum Reconstruction and Its Application in Bearing Fault Diagnosis
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摘要:
为解决经验傅里叶分解（EFD）方法处理轴承故障信号时易于发生频谱分割边界集中在局部窄带的问题，通过统计排序滤波器（OSF）简化采集的轴承振动信号的频谱，进行平均滑移处理和预分割；针对可能存在的过度分解问题，提出根据频域平方基尼指数（FDSGI）的边界融合算法，实现自适应地确定分割边界和分解模式数；并利用包络谱谐波显著度（ESHS）指标选择最佳分量，进而通过对最佳分量进行包络谱分析，达到轴承故障诊断目标. 轴承故障仿真信号和试验信号的对比试验证明了SREFD在频谱分割精确度方面优于EFD和经验小波变换（EWT），处理后的信号中能够更清晰地观察到轴承故障特征频率及其倍频，证明了所提方法的有效性和鲁棒性.
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关键词:
- 频谱重构 /
- 经验傅里叶分解 /
- 频谱重构经验傅里叶分解 /
- 边界融合 /
- 轴承故障诊断
Abstract:To address the tendency of spectral segmentation boundaries concentrating on local narrow bands when the empirical Fourier decomposition (EFD) method was applied to bearing fault signals, an order statistics filter (OSF) was used to simplify the frequency spectrum of the acquired bearing vibration signal, and then averaging and sliding processing and pre-segmentation were performed. To address the potential problem of excessive decomposition, a boundary fusion algorithm based on the frequency-domain squared Gini index (FDSGI) was proposed to adaptively determine segmentation boundaries and decomposition modes. The envelope spectrum harmonic significance (ESHS) indicator was used to select the optimal components. Further, bearing fault diagnosis was enabled through envelope spectrum analysis of the optimal components. The comparative test of bearing fault simulation signals and experimental signals demonstrates that empirical Fourier decomposition based on spectrum reconstruction (SREFD) outperforms EFD and empirical wavelet transform (EWT) in terms of spectral segmentation accuracy. The processed signals allow for clearer observation of bearing fault characteristic frequencies and their harmonics, which validates the effectiveness and robustness of the proposed method.
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图 3 基于SREFD的轴承故障诊断算法流程图
Figure 3. Flowchart of SREFD-based bearing fault diagnosis algorithm
图 4 $s(t)$及其分量的时域及其频域波形图
Figure 4. Waveforms of $s(t)$ and its components in the time and frequency domains
图 5 SREFD、EWT与EFD频谱分割结果与分解分量
Figure 5. Spectral segmentation results of SREFD, EWT, and EFD and their decomposition components
图 6 轴承故障仿真信号成分时域波形图
Figure 6. Time-domain waveform of signal components for bearing fault simulation
图 12 SREFD、EWT和EFD对轴承外圈故障信号的分解效果图
Figure 12. Decomposition effects of SREFD, EWT, and EFD for bearing outer ring fault signals
图 13 SREFD、EWT和EFD对轴承内圈故障信号的分解效果图
Figure 13. Decomposition effects of SREFD, EWT, and EFD for bearing inner ring fault signals
图 14 SREFD、EWT和EFD对轴承滚动体故障信号的分解效果
Figure 14. Decomposition effects of SREFD, EWT, and EFD for bearing ball fault signals
表 1 轴承外圈故障信号仿真参数
Table 1. Simulation parameters of bearing outer ring fault signal
参数 取值 参数 取值 参数 取值 ${M_1}$ 50 ${M_2}$ 1 ${M_3}$ 2 ${T_{\mathrm{a}}}$ 1/75 ${T_{{s}}}$ $ \begin{array}{*{20}{c}} {U(1\;000,} \\ {9\;000)} \end{array} $ $ {C_1} $ 0.025 $ A(t) $ 1 ${B_s}$ $ N(3.5,1) $ $ {C_2} $ 0.025 $ {f_{\mathrm{a}}} $ 3500 ${f_{\mathrm{d}}}$ 1500 ${f_1}$ 10 $ {\varphi _{\mathrm{a}}} $ 0 ${\varphi _{\mathrm{d}}}$ 0 $ {f_2} $ 20 $ {\xi _{\mathrm{a}}} $ 600 ${\xi _{\mathrm{d}}}$ 400 $ {\theta _1} $ $ {\text{π}} /6 $ ${\delta _{\mathrm{l}}}$ $ \begin{array}{*{20}{c}} {U( - 0.02{T_{\text{α}} },} \\ {0.02{T_{\text{α}} })} \end{array} $ $ {\theta _2} $ $ - {\text{π}} /3 $ 
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表 2 SREFD、EWT和EDF的各分解分量所对应的ESHS值
Table 2. ESHS values corresponding to each decomposition component of SREFD, EWT, and EDF
分量 SREFD EWT EDF 1 0.0072 0.0049 0.0077 2 0.0117 0.0018 0.0049 3 0.0087 0.0007 0.0083 4 0.0148 0.0034 0.0012 5 0.0122 0.0009 0.0024 6 0.0156 0.0098 0.0019 7 0.0030 0.0063 0.0110
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