基于融合灰色熵和自助马尔科夫链的滚动轴承振动性能退化趋势预测

程立; 马文锁; 夏新涛; 王良文

doi:10.13224/j.cnki.jasp.20220038

基于融合灰色熵和自助马尔科夫链的滚动轴承振动性能退化趋势预测

doi: 10.13224/j.cnki.jasp.20220038

程立¹,
马文锁^2,*, ,,
夏新涛²,
王良文³

1.
河南科技大学信息工程学院，河南洛阳 471023
2.
河南科技大学机电工程学院，河南洛阳 471003
3.
郑州轻工业大学机电工程学院河南省机械装备智能制造重点实验室，郑州 450002

基金项目: 国家自然科学基金（51475144，52075500）

详细信息

作者简介:
程立（1990-），男，博士，主要从事轴承性能与复合材料研究

通讯作者:
马文锁（1969-），男，教授，博士，主要从事轴承性能与复合材料研究。E-mail：mawensuo@haust.edu.cn

中图分类号: V233.1；TH133.33
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- 文章访问数: 84
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- 被引次数: 0
出版历程
- 收稿日期: 2022-01-20
- 网络出版日期: 2023-07-26

Degradation trend prediction of rolling bearing vibration performance based on fusion grey entropy and bootstrap Markov chain

1.
School of Information Engineering， Henan University of Science and Technology，Luoyang Henan 471023，China
2.
School of Mechatronics Engineering， Henan University of Science and Technology，Luoyang Henan 471003，China
3.
Henan Provincial Key Laboratory of Intelligent Manufacturing of Mechanical Equipment， School of Mechanical and Electrical Engineering， Zhengzhou University of Light Industry，Zhengzhou 450002，China

摘要

摘要:
针对现有的基于熵的非线性动力学方法存在计算结果与非线性动力学系统不一致、计算结果在不同尺度上不一致、计算所需数据长度较长的缺点，提出一种新的非线性时间序列复杂性测度：融合灰色熵算法，并将其用于滚动轴承退化特征提取。针对滚动轴承退化趋势序列数据长度短、预测困难的问题，提出了自助马尔科夫链预测模型。试验研究结果表明，融合灰色熵对数据长度要求较低，并且在不同尺度上的计算结果具有一致性。同时，所提的自助马尔科夫链预测模型的平均相对误差仅为8.4973%，低于GM模型的平均相对误差。这说明所提模型能够有效地对滚动轴承的振动性能退化趋势进行预测。
- 滚动轴承 /
- 融合灰色熵 /
- 非线性动力学 /
- 自助法 /
- 马尔科夫链 /
- 退化趋势预测
Abstract:
In view of the shortcomings of existing entropy-based nonlinear dynamics methods that the calculation results are inconsistent with the nonlinear dynamics system at different scales and the data length required for the calculation is long, the fusion gray entropy algorithm, a new measure of nonlinear time series complexity, was proposed and then used to extract the degradation features of rolling bearing. Considering the problems of very short data length of the rolling bearing degradation trend sequence that it is difficult for prediction, Bootstrap Markov chain prediction model was proposed. The experimental results showed that the data length requirement of fusion gray entropy was low, and the calculation results of the fusion gray entropy at different scales were consistent. Meanwhile, the average relative error of the proposed bootstap Markov chain prediction model was only 8.4973%, which was lower than that of the GM model. This showed that the proposed model can effectively predict the vibration performance degradation trend of rolling bearings.
- rolling bearing /
- fusion grey entropy /
- nonlinear dynamics /
- bootstrap method /
- Markov chain /
- degradation trend prediction

HTML

图 1 滚动轴承寿命强化试验设备

Figure 1. Experimental setup of rolling bearing test system

下载: 全尺寸图片幻灯片

图 2 滚动轴承振动时间序列波形图

Figure 2. Waveform diagram of rolling bearing vibration time series

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图 3 滚动轴承振动时间序列的融合灰色熵与样本熵（N=400和N=800）

Figure 3. Fusion grey entropy and sample entropy of rolling bearing vibration time series （N=400 and N=800）

下载: 全尺寸图片幻灯片

图 4 滚动轴承振动时间序列的融合灰色熵与样本熵（N=1000和N=1600）

Figure 4. Fusion grey entropy and sample entropy of rolling bearing vibration time series （N=1000 and N=1600）

下载: 全尺寸图片幻灯片

图 5 滚动轴承振动时间序列的融合灰色熵与模糊熵（N=400和N=800）

Figure 5. Fusion grey entropy and fuzzy entropy of rolling bearing vibration time series （N=400 and N=800）

下载: 全尺寸图片幻灯片

图 6 滚动轴承振动时间序列的融合灰色熵与模糊熵（N=1000和N=1600）

Figure 6. Fusion grey entropy and fuzzy entropy of rolling bearing vibration time series （N=1000 and N=1600）

下载: 全尺寸图片幻灯片

图 7 滚动轴承振动性能退化趋势预测结果

Figure 7. Prediction results of vibration performance degradation trend of rolling bearings

下载: 全尺寸图片幻灯片

表 1 GM模型预测与残差

Table 1. GM model predictions and residuals

序号	融合灰色熵	GM模型预测	残差
1	0.38616	0.38616	0
2	0.434173	0.426765	0.007408
3	0.393394	0.420918	−0.02752
4	0.421035	0.415151	0.005883
5	0.402322	0.409464	−0.00714
6	0.430665	0.403854	0.026811
7	0.429364	0.39832	0.031043
8	0.364764	0.392863	−0.0281
9	0.381094	0.38748	−0.00639
10	0.380181	0.382172	−0.00199

下载: 导出CSV

表 2 马尔科夫状态区间

Table 2. Markov state interval

区间符号	区间值
ΔI₁	[0, 0.0078]
ΔI₂	[0.0078, 0.0155]
ΔI₃	[0.0155, 0.0233]
ΔI₄	[0.0233, 0.0310]

下载: 导出CSV

表 3 第11个残差状态预测

Table 3. The 11th residual state prediction

序号	绝对残差	初始状态	转移步数	状态ΔI₁	状态ΔI₂	状态ΔI₃	状态ΔI₄
10	0.00199	ΔI₁	1	0.8168	0.1761	0.0071	0
9	0.00639	ΔI₁	2	0.8177	0.1751	0.0072	0
8	0.0281	ΔI₄	3	0.7857	0.1767	0.0220	0.0156
7	0.031043	ΔI₄	4	0.8097	0.1755	0.0109	0.0039
概率分布P\|_ΔIj				3.2299	0.7034	0.0472	0.0195

下载: 导出CSV

表 4 预测结果的平均相对误差和平均绝对误差

Table 4. Averaged relative errors and absolute errors of prediction results

模型	平均相对误差/%	平均绝对误差
GM	9.2616	0.0273
自助马尔科夫链	8.4973	0.0253

下载: 导出CSV

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