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Multi-Channel Vibration Signal Analysis Method for Rotor-Bearing Faults
DOI: 10.12677/MOS.2024.131085, PDF, HTML, XML, 下载: 112  浏览: 243

Abstract: This paper carried out research based on the Multivariate Empirical Mode Decomposition (MEMD) algorithm proposed by Rehman in 2011. The algorithm is an Empirical Mode Decomposition (EMD) applied to multi-channel data. Combining the basic theory of MEMD, a multi-channel vibration sig-nal analysis method is proposed. First, multi-channel vibration signals are collected. Then a series of Intrinsic Mode Function (IMF) components are obtained by the adaptive decomposition of mul-ti-channel vibration signals using MEMD. Then, IMF components containing fault information are selected according to the Kurtosis criterion. Finally, spectrum analysis and Hilbert envelope analy-sis are used to extract fault characteristics.

1. 引言

2. 滚动轴承故障信号特征

(1) 外圈故障

${f}_{0}=\frac{Z}{2}\left(1-\frac{d}{D}\mathrm{cos}\varphi \right){f}_{r}$ (1)

(2) 内圈故障

${f}_{i}=\frac{Z}{2}\left(1+\frac{d}{D}\mathrm{cos}\varphi \right){f}_{r}$ (2)

(3) 滚动体故障

Figure 1. Bearing failure diagram

${f}_{b}=\frac{1}{2}\cdot \frac{D}{d}\left(1-{\left(\frac{d}{D}\mathrm{cos}\phi \right)}^{2}\right){f}_{r}$ (3)

3. 理论基础

3.1. 多元经验模态分解方法原理

MEMD具体步骤如下：

(1) 采用Hammersley序列在(n − 1)维球面上选择K个分布均匀的采样点集，可以得到n维空间的K个方向向量 ${x}^{{\theta }_{k}}$

(2) 计算n维信号在方向向量集 ${x}^{{\theta }_{k}}=\left\{{x}_{1}^{k},{x}_{2}^{k},\cdots ,{x}_{n}^{k}\right\}$ 每个方向上的投影，记作 ${p}^{{\theta }_{k}}\left(t\right)$ ，形成投影集 ${\left\{{p}^{{\theta }_{k}}\left(t\right)\right\}}_{k=1}^{k}$

(3) 寻找投影集 ${\left\{{p}^{{\theta }_{k}}\left(t\right)\right\}}_{k=1}^{k}$ 中每个投影的极大值点，极大值点所对应的时间刻度为 $\left\{{t}_{i}^{{\theta }_{k}}\right\}$

(4) 用多元样条差值函数对极值点 $\left[{t}_{i}^{{\theta }_{k}},s\left({t}_{i}^{{\theta }_{k}}\right)\right]$ 插值，得到K个多元 $\left[{t}_{i}^{{\theta }_{k}},s\left({t}_{i}^{{\theta }_{k}}\right)\right]$

(5) 计算K个n维包络均值m(t)为：

$m\left(t\right)=\frac{1}{k}\underset{k=1}{\overset{k}{\sum }}{e}^{\theta }k\left(t\right)$ (4)

$s\left(t\right)=\underset{i=1}{\overset{q}{\sum }}{h}_{i}\left(t\right)+r\left( t \right)$

$s\left(t\right),{h}_{i}\left(t\right),r\left(t\right)\in {R}^{n}$ (5)

MEMD具有良好的降噪功能和对于多通道振动信号提取故障信息的能力，可以实现多通道同步分解，保证了不同IMF组尺度和数量上的对齐，且有效抑制了EMD方法容易造成的模态混叠，从而使得分解误差大大缩小。

3.2. 多通道振动信号分析方法

$K=\frac{E{\left(x-\mu \right)}^{4}}{{\sigma }^{4}}$ (6)

Figure 2. Flow chart of multi-channel vibration signal analysis method based on MEMD

4. 基于MEMD的多通道振动信号分析方法的仿真与验证

4.1. 仿真信号参数的设置与模型建立

$y\left(t\right)=x\left(t\right)+e\left(t\right)=\underset{k}{\sum }\mathrm{exp}\left\{\frac{-{\delta }_{0}}{\sqrt{1-{\delta }_{0}^{2}}}\cdot 2\pi {f}_{0}\left(t-{\tau }_{0}-k{T}_{0}\right)×\mathrm{sin}2\pi {f}_{0}\left(t-{\tau }_{0}-k{T}_{0}\right)\right\}+{A}_{n}n\left(t\right)$ (7)

Table 1. Simulate the relevant parameters of the signal model

Figure 3. Time-domain and spectrogram of a clean signal

Figure 4. The signal-to-noise ratio is −6 dB, −7 dB, −8 dB respectively

Figure 5. Spectrogram of a three-channel simulated signal

Figure 6. Three-channel simulated signal envelope spectrum

4.2. 基于MEMD方法的仿真分析

Figure 7. Time-domain plot of each component after MEMD decomposition

Figure 8. Spectrogram of each component after MEMD decomposition

Figure 9. Fault-related component envelope spectra of MEMD decomposition

Table 2. The awtosis values of each component after MEMD decomposition

4.3. 基于MEMD的多通道振动信号分析方法的实验验证

Table 3. Bearing geometry (mm)

Table 4. The multiple of the failure frequency of each component of the bearing

Figure 10. Rolling bearing three-channel experimental fault signal

Figure 11. Spectrogram of a three-channel experimental signal

Figure 12. Three-channel experimental signal envelope spectrum

Figure 13. Time domain plot of each component after MEMD decomposition

Figure 14. Spectrogram after MEMD decomposition

Table 5. The awtosis values of each component after MEMD decomposition

Figure 15. Envelope diagram after MEMD decomposition

5. 总结

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