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摘要: 针对稀疏自动编码器(Sparse auto encoder, SAE)采用sigmoid激活函数容易造成梯度消失的问题, 用一种新的Tan函数替代原有的sigmoid函数; 针对SAE采用Kullback-Leibler (KL) 散度进行稀疏性约束在回归预测方面的局限性, 以dropout机制替代KL散度实现网络的稀疏性. 利用改进SAE对滚动轴承振动信号进行无监督深层特征自适应提取, 无需人工设计标签进行有监督微调. 同时, 考虑到滚动轴承剩余使用寿命(Remaining useful life, RUL)预测方法一般仅考虑过去信息而忽略未来信息, 引入双向长短时记忆网络(Bi-directional long short-term memory, Bi-LSTM)构建滚动轴承RUL的预测模型. 在2个轴承数据集上的实验结果均表明, 所提基于改进SAE和Bi-LSTM的滚动轴承RUL预测方法不仅可以提高模型的收敛速度而且具有较低的预测误差.Abstract: Since the sigmoid activation function of sparse auto-encoder (SAE) is easy to cause the gradient to disappear, a new Tan function is used to replace the original sigmoid function. In SAE, for the limitations in regression prediction when Kullback-Leibler (KL) divergence is used for sparseness constraints, KL divergence is replaced with the dropout mechanism to achieve network sparsity. And the improved SAE is used to perform unsupervised adaptive deep feature extraction for the vibration signals of rolling bearings, without designing labels manually for supervised fine adjustment. Meanwhile, for the remaining useful life (RUL) prediction method of rolling bearing, generally only the past information is considered and the future information is ignored, the bi-directional long short-term memory (Bi-LSTM) is introduced to construct an RUL prediction model of the rolling bearing. Using two bearing data sets, experimental results both show that the proposed RUL prediction method of a rolling bearing based on improved sparse auto encoder and Bi-LSTM can improve the convergence speed of the model and has lower prediction error.
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图 7 轴承1_1时域振动信号及归一化后的频域幅值谱
Fig. 7 The time domain vibration signal and normalized amplitude spectrum of the bearing1_1
图 9 本文方法预测轴承1_7的当前p值
Fig. 9 The current p value of bearing 1_7 predicted by the proposed method
图 10 本文方法对轴承1_7的RUL预测结果
Fig. 10 RUL prediction result of bearing 1_7 by the proposed method
图 11 特征提取所消耗时间的对比(PHM2012轴承数据集)
Fig. 11 Comparison of the time consuming of feature extraction (PHM2012 bearing datasets)
图 12 3种方案对轴承1_7的RUL预测结果
Fig. 12 RUL prediction results of bearing 1_7 by three schemes
图 13 特征提取所消耗时间的对比(XJTU-SY轴承数据集)
Fig. 13 Comparison of the time consuming of feature extraction (XJTU-SY bearing datasets)
表 1 实验数据(PHM2012轴承数据集)
Table 1 Experimental data (PHM2012 bearing datasets)
数据集划分 不同轴承 非全寿数据 (组) 全寿数据 (组) 训练集 1_1 — 2803 1_2 — 871 2_1 — 911 2_2 — 797 3_1 — 515 3_2 — 1637 测试集 1_3 1802 2375 1_4 1139 1428 1_5 2302 2463 1_6 2302 2448 1_7 1502 2259 2_3 1202 1955 2_4 612 751 2_5 2002 2311 2_6 572 701 2_7 172 230 3_3 352 434 
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表 2 3种优化算法的训练误差
Table 2 Training error of three optimization algorithms
不同优化算法 Adam RMSProp SGDM MSE 0.0008 0.0011 0.0009 MAE 0.0450 0.0794 0.0485 MAPE 0.2292 0.3302 0.3394 MSPE 0.0183 0.0213 0.0406 RMSE 0.0624 0.0985 0.0651 误差之和 0.3557 0.5304 0.4945
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表 3 本文预测方法与其他3种方案的构成
Table 3 The composition of the proposed prediction method and other three schemes
预测方法 特征提取模型 预测模型 本文方法 改进 SAE Bi-LSTM 方案 1 SAE Bi-LSTM 方案 2 改进 SAE LSTM 方案 3 SAE LSTM
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表 4 不同轴承RUL预测误差结果对比(PHM2012轴承数据集) (%)
Table 4 Comparison of RUL prediction results of different bearings (PHM2012 bearing datasets) (%)
不同轴承 本文方法 方案 1 方案 2 方案 3 文献[20] 文献[21] 1_3 8.03 0.52 0.70 −6.98 43.28 −31.76 1_4 −8.30 0.70 −3.81 2.42 67.55 62.76 1_5 −44.72 −26.09 −45.34 −110.56 −22.98 −136.03 1_6 −2.74 −23.29 21.92 −13.70 21.23 −32.88 1_7 −3.04 7.13 −9.51 −33.03 17.83 −11.09 2_3 −4.12 −20.85 −15.94 −1.73 37.84 44.22 2_4 0.72 −3.60 −0.72 −27.30 −19.42 −55.40 2_5 −6.15 16.83 −38.51 12.62 54.37 68.61 2_6 3.10 −37.21 −13.95 −6.20 −13.95 −51.94 2_7 1.72 −1.72 5.17 −1.72 −55.17 −68.97 3_3 −15.85 2.44 2.44 17.07 3.66 −21.96 平均误差 −6.49 −7.74 −9.81 −15.37 32.48 53.24 平均得分 0.576 0.522 0.477 0.425 0.263 0.065
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表 5 实验数据(XJTU-SY轴承数据集)
Table 5 Experimental data (XJTU-SY bearing datasets)
数据集划分 不同轴承 非全寿数据 (组) 全寿数据 (组) 训练集 1_1 — 123 1_2 — 161 2_1 — 491 2_2 — 161 3_1 — 2538 3_2 — 2496 测试集 1_3 126 158 1_4 98 122 1_5 42 52 2_3 426 533 2_4 34 42 2_5 271 339 3_3 297 371 3_4 1212 1515 3_5 91 114
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表 6 不同轴承 RUL 预测误差结果对比(XJTU-SY 轴承数据集) (%)
Table 6 Comparison of RUL prediction results of different bearings (XJTU-SY bearing datasets) (%)
不同轴承 本文方法 方案 1 方案 2 方案 3 1_3 15.63 21.88 12.50 18.75 1_4 8.33 −8.33 −4.17 20.83 1_5 −10.00 −30.00 20.00 −10.00 2_3 −24.30 −21.78 15.89 −23.36 2_4 −12.50 −25.00 −25.00 −12.50 2_5 10.29 27.94 14.71 22.06 3_3 31.08 23.78 17.57 22.97 3_4 −18.25 5.83 −50.83 −36.96 3_5 4.35 −26.09 −8.70 −39.13 平均误差 0.51 −3.53 −0.89 −4.15 平均得分 0.419 0.282 0.418 0.267
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