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基于Transformer模型的滚动轴承剩余使用寿命预测方法

周哲韬 刘路 宋晓 陈凯

周哲韬,刘路,宋晓,等. 基于Transformer模型的滚动轴承剩余使用寿命预测方法[J]. 北京航空航天大学学报,2023,49(2):430-443 doi: 10.13700/j.bh.1001-5965.2021.0247
引用本文: 周哲韬,刘路,宋晓,等. 基于Transformer模型的滚动轴承剩余使用寿命预测方法[J]. 北京航空航天大学学报,2023,49(2):430-443 doi: 10.13700/j.bh.1001-5965.2021.0247
ZHOU Z T,LIU L,SONG X,et al. Remaining useful life prediction method of rolling bearing based on Transformer model[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(2):430-443 (in Chinese) doi: 10.13700/j.bh.1001-5965.2021.0247
Citation: ZHOU Z T,LIU L,SONG X,et al. Remaining useful life prediction method of rolling bearing based on Transformer model[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(2):430-443 (in Chinese) doi: 10.13700/j.bh.1001-5965.2021.0247

基于Transformer模型的滚动轴承剩余使用寿命预测方法

doi: 10.13700/j.bh.1001-5965.2021.0247
基金项目: 国家重点研发计划(2018YFB1702703)
详细信息
    通讯作者:

    E-mail:songxiao@buaa.edu.cn

  • 中图分类号: V229+.2;TH133.33;TP183

Remaining useful life prediction method of rolling bearing based on Transformer model

Funds: National Key R & D Program of China (2018YFB1702703)
More Information
  • 摘要:

    准确的滚动轴承剩余使用寿命(RUL)预测对保证机械安全运行和减小维修损失起着至关重要的作用。为提高滚动轴承RUL预测准确率,提出一种基于Transformer模型的轴承RUL预测方法,充分利用其自注意力机制与编码器-解码器结构的优势,解决轴承RUL预测中序列过长而导致的记忆力退化问题,挖掘出输入特征与轴承RUL之间复杂映射关系。同时,采用三角函数变换与累积变换来修正输入特征的单调性与趋势性,使其能更好地表征滚动轴承的退化过程。在PHM2012数据集上的实验结果表明:所提方法相比于对比方法平均绝对误差分别降低了9.25%、28.63%、34.14%,平均得分分别提高了2.78%、19.79%、29.38%;在XJTU-SY数据集上的实验结果表明,所提方法相比于对比方法均方根误差降低了17.4%,平均得分提高了18.6%,进一步证明了其可行性与优越性。

     

  • 图 1  基于Transformer的轴承RUL预测模型

    Figure 1.  Bearing RUL prediction model based on Transformer

    图 2  滚动轴承RUL预测流程

    Figure 2.  Flow chart of RUL prediction for rolling bearings

    图 3  PRONOSTIA采集平台

    Figure 3.  The PRONOSTIA platform

    图 4  三角特征与传统特征对比

    Figure 4.  Comparison of trigonometric features and classical features

    图 5  累积特征与传统特征对比

    Figure 5.  Contrasts of cumulative features and classical features

    图 6  轴承1_4预测结果

    Figure 6.  Bearing 1_4 prediction results

    图 7  轴承2_5预测结果

    Figure 7.  Bearing 2_5 prediction results

    图 8  得分Al与误差El的函数关系

    Figure 8.  Function of Al and error El

    图 9  滚动轴承实验台

    Figure 9.  Testbed of rolling element bearings

    图 10  退化轴承照片

    Figure 10.  Photographs of normal and degraded bearings

    表  1  特征和相应的计算公式

    Table  1.   Feature and corresponding formulas

    特征公式
    反正切值标准差$ {X_{{\text{atan}}}} = \sigma \left( {\ln [{x_i} + \sqrt {{x_i}^2 + 1} ]} \right) $
    反双曲正弦标准差${X_{ {\text{asinh} } } } = \sigma \left( {\dfrac{i}{2}\ln \left( {\dfrac{ {i + {x_i} } }{ {i - {x_i} } } } \right)} \right)$
    标准差${X_{ {\text{sd} } } } = \sqrt {\dfrac{1}{n}{ {\displaystyle\sum\limits_{i = 1}^n {\left( { {x_i} - \mu } \right)^2} }} }$
    峰值${X_{\text{P} } } = {\rm{max}}\left| X \right|$
    峰峰值${X_{ {\text{p - p} } } } = {\rm{max}}\left( { {x_i} } \right) - {\rm{min}}\left( { {x_i} } \right)$
    均方根${X_{ {\text{rms} } } } = \sqrt {\dfrac{1}{n}{ {\displaystyle\sum\limits_{i = 1}^n { {x_i}^2 } }} }$
    上边界${X_{ {\text{upper} } } } = {\rm{max} }\left( { {x_i} } \right) + \dfrac{1}{2}\dfrac{ { {\rm{max} }\left( { {x_i} } \right) - {\rm{min}}\left( { {x_i} } \right)} }{ {n - 1} }$
    脉冲因子${X_{ {\text{if} } } } = \dfrac{ { {X_{\text{P} } } } }{ {\dfrac{1}{n}\displaystyle\sum\limits_{i = 1}^n {\left| { {x_i} } \right|} } }$
    峰值因子${X_{ {\text{cf} } } } = \dfrac{ { {X_{\text{P} } } }}{ { {X_{ {\text{rms} } } } } }$
    裕度系数${X_{ {\text{mf} } } } = \dfrac{ { {X_{\text{P} } } } }{ { { {\left( {\dfrac{1}{n}\displaystyle\sum\limits_{i = 1}^n {\sqrt {\left| { {x_i} } \right|} } } \right)}^2} } }$
    能量${X_{\text{e} } } = {\displaystyle\sum\limits_{i = 1}^n { {x_i} } ^2}$
    峭度${X_{\text{k} } } = \dfrac{ {\dfrac{1}{n}{ {\displaystyle\sum\limits_{i = 1}^n {\left( { {x_i} - \mu } \right)^4} }} } }{ { {X_{ {\rm{sd} } ^4} } } }$
    平均绝对值${X_{ {\text{mav} } } } = \dfrac{1}{n}\displaystyle\sum\limits_{i = 1}^n {\left| { {x_i} } \right|}$
    偏度${X_{ {\text{sk} } } } = \dfrac{ {\dfrac{1}{n}{ {\displaystyle\sum\limits_{i = 1}^n {\left( { {x_i} - \mu } \right)^3} }} } }{ { {X_{ {\text{sd} } } }^3} }$
    下载: 导出CSV

    表  2  PHM2012数据集工况信息

    Table  2.   Operating condition information of PHM2012 dataset

    工况径向力/N转速/(r·min−1训练集测试集
    工况140001800轴承1_1、轴承1_2轴承1_3、轴承1_4、轴承1_5 轴承1_6 轴承1_7
    工况242001650轴承2_1、轴承2_2轴承2_3、轴承2_4、轴承2_5、轴承2_6、轴承2_7
    工况350001500轴承3_1、轴承3_2轴承3_3
    下载: 导出CSV

    表  3  累积变换前后比较

    Table  3.   Comparison before and after cumulative transformation

    传统特征单调性趋势性累积特征单调性趋势性
    反双曲正弦标准差0.570.71反双曲正弦标准差11
    反正切值标准差0.580.76反正切值标准差11
    能量0.500.64能量11
    偏度0.600.83偏度11
    峭度0.390.80峭度11
    上边界0.260.36上边界11
    均方根0.500.61均方根11
    脉冲因子0.540.78脉冲因子11
    峰值因子0.520.75峰值因子11
    峰峰值0.270.37峰峰值11
    裕度系数0.510.77裕度系数11
    标准差0.500.60标准差11
    平均绝对值0.590.70平均绝对值0.870.96
    下载: 导出CSV

    表  4  实验数据(PHM2012轴承数据集)

    Table  4.   Experimental data(PHM2012 Datasets)

    数据集划分轴承编号非全寿命时间/(10s)全寿命时间/
    (10s)
    训练集1_12803
    1_2871
    2_1911
    2_2797
    3_1515
    3_21637
    测试集 1_318022375
    1_411391428
    1_523022463
    1_623022448
    1_715022259
    2_312021955
    2_4612751
    2_520022311
    2_6572701
    2_7172230
    3_3352434
    下载: 导出CSV

    表  5  运行速度对比结果

    Table  5.   Running speed comparison results

    预测模型运行时间/ms
    Transformer2.15
    LSTM3.47
    GRU3.33
    BiLSTM4.00
    下载: 导出CSV

    表  6  所提方法与其他2种方案的构成

    Table  6.   Composition of the proposed prediction method and other two schemes

    预测方法特征提取模型预测模型
    所提方法累积特征编码器-解码器结构
    Transformer模型
    方案1经典统计特征编码器-解码器结构
    Transformer模型
    方案2累积特征单编码器结构
    Transformer模型
    下载: 导出CSV

    表  7  所提方法和对比方法在PHM 2012数据集RUL预测结果

    Table  7.   The RUL prediction results of the proposed method and comparison method in the PHM 2012 dataset

    轴承型号误差El
    所提方法方案1方案2文献[11]文献[25]文献[26]
    1_374.17−413167.667.6254.73−1.04
    1_4−0.69 23.31−98.8169.7738.4885.81
    1_59.9336.7510.45−72.57−99.4−278.2
    1_6−12.33102.39−7.180.93−120.019.18
    1_783.62132.3282.4885.9970.65−7.13
    2_361.35 90.1465.0881.2475.5310.49
    2_45.06−196.314.499.0419.8151.8
    2_5−70.22 60.04−53.9928.198.228.8
    2_60.78102.825.1324.9217.87−20.93
    2_744.83 77.4447.0319.061.6944.83
    3_31.22118.27−1.232.092.93−3.66
    下载: 导出CSV

    表  8  表7的预测结果比较

    Table  8.   Comparison of predicted results in Table 7

    方法平均绝对误差$|E|$平均得分s
    所提方法33.050.4589
    方案1448.300.0697
    方案241.230.3460
    文献[11]36.420.4465
    文献[25]46.310.3831
    文献[26]50.180.3547
    下载: 导出CSV

    表  9  实验方案

    Table  9.   The experimental scheme

    径向力/N转速/(r·min−1)训练集测试集
    110002250轴承2_1
    轴承2_2
    轴承2_3
    轴承2_4
    轴承2_5
    100002400轴承3_1
    轴承3_2
    轴承3_3
    轴承3_4
    轴承3_5
    下载: 导出CSV

    表  10  XJTU-SY数据集RUL预测结果与比较

    Table  10.   RUL prognostics results and comparisons on XJTU-SY dataset

    模型RMSE平均得分
    DSCN0.07490.4165
    RCNN0.08030.3586
    RVM0.10820.2911
    TCN-RSA0.06590.4803
    所提方法0.05440.5697
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-05-10
  • 录用日期:  2021-07-04
  • 网络出版日期:  2021-07-12
  • 整期出版日期:  2023-02-28

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