Rolling bearing RUL prediction based on Pearson correlation coefficient statistical features
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摘要:
为了得到能够准确描述退化过程的健康因子，提出一种基于包络谱统计特征和皮尔逊相关系数的新健康因子用于剩余使用寿命预测。首先，基于Boostrap抽样方法和3 sigma原则提出一种第一预测时间识别方法，得到合适的全寿命退化阈值。其次，计算不同时间点的包络谱概率分布，并基于皮尔逊相关系数得到健康因子。最后，通过指数与线性回归混合模型预测轴承剩余寿命。实验结果表明：提出的健康因子可以有效性反映轴承退化趋势，并且指数与线性回归混合模型相较于其他预测模型预测准确性提升了23.7%。
Abstract:To obtain health indicators that can accurately describe the degradation process, a new health indicator based on envelope spectrum statistical features and Pearson correlation coefficient was proposed for remaining useful life prediction. Firstly, a first prediction time identification method was proposed based on the Boostrap sampling method and the 3 sigma principle to obtain a suitable full-life degradation threshold. Secondly, the envelope spectrum probability distributions at different time points were calculated and the health index was obtained based on the Pearson correlation coefficient. Finally, the remaining useful life of bearing was predicted by a hybrid model of exponential and linear regression. The experimental results showed that the proposed health index can effectively reflect the bearing degradation trend, and the prediction accuracy of the hybrid exponential and linear regression model was improved by 23.7% compared with other prediction models.
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表 1 数据集工况表
Table 1. Dataset working condition table
工况
编号转频/
Hz负载/
kN数据集
编号数据文件
数量故障类型 1 35 12 1-1 123 外圈故障 1-2 161 外圈故障 1-3 158 外圈故障 1-4 122 保持架故障 1-5 52 内圈外圈故障 2 37.5 11 2-1 491 内圈故障 2-2 161 外圈故障 2-3 533 保持架故障 2-4 42 外圈故障 2-5 339 外圈故障 
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表 2 时域特征计算
Table 2. Time domain feature calculation
特征 计算公式 T1 $ \mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n} （x） $ T2 $ \mathrm{s}\mathrm{t}\mathrm{d} （x） $ T3 $ （\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}\sqrt{\mathrm{a}\mathrm{b}\mathrm{s} （x） }） ^{2} $ T4 $ \mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n} （\mathrm{a}\mathrm{b}\mathrm{s} （x） ） $ T5 $ \mathrm{s}\mathrm{k}\mathrm{e}\mathrm{w}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s} （x） $ T6 $ \mathrm{k}\mathrm{u}\mathrm{r}\mathrm{t}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{s} （x） $ T7 $ \mathrm{r}\mathrm{m}\mathrm{s} （x） $ T8 $ \mathrm{m}\mathrm{a}\mathrm{x} （\mathrm{a}\mathrm{b}\mathrm{s} （x） ） $ T9 $ \mathrm{m}\mathrm{i}\mathrm{n} （\mathrm{a}\mathrm{b}\mathrm{s} （x） ） $ T10 $ \mathrm{m}\mathrm{a}\mathrm{x} （x） -\mathrm{m}\mathrm{i}\mathrm{n} （x） $ T11 $ -\displaystyle\sum P （x） \mathrm{l}\mathrm{o}\mathrm{g} （2,P （x） ） $ T12 $ {T}_{7}/{T}_{4} $ T13 $ {T}_{8}/{T}_{7} $ T14 $ {T}_{8}/{T}_{4} $ T15 $ {T}_{6}/ （{T}_{4}） ^{4} $ T16 $ {T}_{8}/{T}_{3} $ T17 $ {T}_{5}/ （{T}_{4}） ^{3} $ T18 $ \mathrm{s}\mathrm{t}\mathrm{d} （\mathrm{l}\mathrm{o}\mathrm{g} （2,x+ （{x}^{2}-1） ^{1/2}） ） $ T19 $ \mathrm{s}\mathrm{t}\mathrm{d} （\mathrm{l}\mathrm{o}\mathrm{g} （2,x+ （{x}^{2}+1{） }^{1/2}） ） $
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表 3 确定的FPT
Table 3. Determined FPT
工况 编号 FPT/min 1 1 309 2 224 3 1817 5 269 2 1 448 2 137 3 1301 4 121 5 481
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表 4 相关特征计算逻辑
Table 4. Correlation feature calculation logic
计算方法 时域 频域 包络谱 PCC T33原始信号 T34概率分布 T35原始信号 T36概率分布 T37原始信号 T38概率分布 互信息熵 T39原始信号 T40原始信号 T41原始信号
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表 5 线性回归模型得分
Table 5. Linear regression model score
数据集
编号指数模型 线性模型 综合模型 误差率/% 得分 误差率/% 得分 误差率/% 得分 1-1 0.256 0.415 0.452 0.212 0.361 0.289 1-2 0.485 0.187 0.736 0.079 0.610 0.121 1-3 −0.5 0 −0.5 0 −0.5 0 1-5 −0.5 0 0.070 0.787 0.070 0.787 2-1 −0.050 0.500 0.350 0.297 0.150 0.595 2-2 −0.224 0.045 0.258 0.411 0.020 0.932 2-3 0.879 0.048 0.997 0.032 0.938 0.039 2-4 −0.132 0.177 0.263 0.420 0.132 0.648 2-5 −0.396 0.004 0.045 0.879 0.045 0.879 平均 0.197 0.445 0.613
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表 6 对比模型得分结果
Table 6. Comparison of model score results
数据集
编号二次指数平滑模型 Winner模型 ARIMA模型 LSTM Bi_LSTM 综合模型 误差率/% 得分 误差率/% 得分 误差率/% 得分 误差率/% 得分 误差率/% 得分 误差率/% 得分 1-1 0.105 0.696 0.407 0.247 0 −0.5 0 −0.5 0 0.361 0.289 1-2 0.226 0.459 0.627 0.115 0 −0.226 0.044 −0.084 0.315 0.610 0.121 1-3 0.157 0.584 0 0.280 0.384 0.017 0.942 −0.105 0.238 −0.5 0 1-5 0.176 0.550 −0.035 0.620 −0.070 0.384 −0.5 0 −0.5 0 0.070 0.787 2-1 0.625 0.115 0.450 0.210 0.050 0.841 −0.5 0 −0.5 0 0.150 0.595 2-2 −0.5 0 −0.048 0.519 −0.272 0.024 −0.5 0 −0.5 0 0.020 0.932 2-3 −0.5 0 0.755 0.073 −0.5 0 −0.5 0 −0.5 0 0.938 0.039 2-4 −0.263 0.031 0.263 0.420 0 1.000 0.263 0.420 0.395 0.273 0.132 0.648 2-5 0.744 0.076 −0.143 0.197 0 −0.5 0 −0.5 0 0.045 0.879 综合得分 0.359 0.343 0.376 0.201 0.119 0.613
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