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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2021, Vol. 55 Issue (10): 1937-1947    DOI: 10.3785/j.issn.1008-973X.2021.10.016
    
Remaining useful life prediction of turbofan engine based on similarity in multiple time scales
Yu-hui XU(),Jun-qing SHU,Ya SONG,Yu ZHENG,Tang-bin XIA*()
State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China
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Abstract  

A novel method based on health index similarity in multiple time scales with autoencoder (AE MTS-HI) was proposed aiming at the shortage of the traditional similarity-based method in extracting health index and similarity matching. Autoencoder was applied to construct the health index based on monitoring data, which can minimize the loss of nonlinear information. The health index in multiple time scales was developed for similarity matching by considering the fluctuation of the length of test degradation trajectories. The method can remove the accuracy limitation caused by fixed time scales and enhance the prediction robustness. Performance of the proposed method was evaluated on public turbofan engines datasets. Results demonstrate that the method can improve the remaining useful life (RUL) prediction accuracy and provide stable support for predictive maintenance.

Key words： remaining useful life (RUL)      multiple time scale      autoencoder      similarity-based method      turbofan engine     
Received: 03 November 2020      Published: 27 October 2021
CLC:  TH 17  
Fund:  国家自然科学基金资助项目（51875359）；上海市自然科学基金资助项目（20ZR1428600）；上海商用飞机系统工程科创中心联合研究基金资助项目（FASE-2021-M7）；教育部-中国移动联合基金建设项目（MCM20180703）
Corresponding Authors: Tang-bin XIA     E-mail: xuyuhui@sjtu.edu.cn;xtbxtb@sjtu.edu.cn
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Yu-hui XU
Jun-qing SHU
Ya SONG
Yu ZHENG
Tang-bin XIA
Cite this article:

Yu-hui XU,Jun-qing SHU,Ya SONG,Yu ZHENG,Tang-bin XIA. Remaining useful life prediction of turbofan engine based on similarity in multiple time scales. Journal of ZheJiang University (Engineering Science), 2021, 55(10): 1937-1947.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2021.10.016     OR     https://www.zjujournals.com/eng/Y2021/V55/I10/1937


基于多时间尺度相似性的涡扇发动机寿命预测

针对传统相似性方法在提取健康指标和相似性匹配上存在的不足，提出结合自编码器神经网络的基于多时间尺度健康指标相似性的预测方法（AE MTS-HI）. 采用自编码器从状态监测数据中提取表征发动机退化状态的健康指标，降低提取过程非线性信息的损失. 将测试退化轨迹长度的波动纳入考量，针对性地设计多时间尺度的健康指标进行相似性匹配. 这不仅可以克服单一时间尺度匹配导致的精度限制，而且可以提高预测的鲁棒性. 在涡扇发动机的公开数据集上验证所提方法的性能. 结果表明，利用该方法能够显著提升剩余使用寿命（RUL）的预测精度，为预知维护提供有力支撑.


关键词： 剩余使用寿命（RUL）,  多时间尺度,  自编码器,  相似性方法,  涡扇发动机 
Fig.1 Schematic diagram of condition monitoring parameters
Fig.2 Structure of autoencoder
Fig.3 Framework of AE MTS-HI
层 神经元数 激活函数
输入层 $ {d}_{\mathrm{i}\mathrm{n}} $ —
隐含层1 $ {d}_{\mathrm{i}\mathrm{n}}/2 $ ReLU函数
隐含层2 $ {d}_{\mathrm{o}\mathrm{u}\mathrm{t}} $ 线性激活函数
隐含层3 $ {d}_{\mathrm{i}\mathrm{n}}/2 $ ReLU函数
输出层 $ {d}_{\mathrm{i}\mathrm{n}} $ tanh函数
Tab.1 Parameters setting of autoencoder
Fig.4 Schematic diagram of similarity matching and RUL prediction
数据集 样本个数 数据总量 最小运行周期数 最大运行周期数
训练集 100 20631 128 362
测试集 100 13096 31 303
Tab.2 Detailed descriptions of FD001
Fig.5 Distributions of running cycles in FD001
Fig.6 Classification based on tendency of signals
分类 传感器编号
增长型 2，3，4，8，9，11，13，14，15，17
衰减型 7，12，20，21
固定型 1，5，6，10，16，18，19
Tab.3 Classification of sensor signals
Fig.7 Schematic diagram of RUL rectification
测试样本运行长度 测试样本数量 选用时间尺度
$30\leqslant {t}_{i} < 50$ 7 30
$50\leqslant {t}_{i} < 70$ 7 30,50
$70\leqslant {t}_{i}$ 86 30,50,70
Tab.4 Time scales for similarity matching
Fig.8 Experimental results of parameter tuning of autoencoder
Fig.9 Degradation model reference library
Fig.10 RUL prediction results
方法 RMSE Score
SVM[24] 29.822 —
CNN[9] 18.448 1 286.7
LSTM[10] 16.14 338
Similarity-based[16] 19.87 —
Similarity-based with SVR[25] — 388
Similarity-based with KTST[15] 16.87 377.08
AE MTS-HI 14.07 291.67
Tab.5 Comparison results with methods proposed by other researchers
降维方法 RMSE Score
多元线性回归 16.32 486.50
等距特征映射 14.50 339.95
主成分分析 14.29 302.95
自编码器 14.07 291.67
Tab.6 Comparison results with other dimensionality reduction methods
隐含层个数 隐含层神经元数 RMSE
1 1 14.31
3 4，1，4 14.17
3 7，1，7 14.07
3 10，1，10 14.12
5 10，6，1，6，10 14.13
5 7，7，1，7，7 14.09
Tab.7 Comparison results with other autoencoder structures and parameters
样本长度 样本数量 Score
L=30 L=50 L=70 多时间尺度
$30\leqslant {t}_{i} < 50$ 7 26.30 — — 26.30
$50\leqslant {t}_{i} < 70$ 7 8.41 8.86 — 6.56
$70\leqslant {t}_{i}$ 86 337.70 276.23 284.35 258.81
所有样本 100 372.41 — — 291.67
Tab.8 Effects of multiple time scales on predicting results
Fig.11 Effects of single time scale size on predicting results
样本编号 样本长度 RUL e
L=30 L=50 L=70 多时间尺度
23 130 113 4.40 4.99 ?2.77 2.21
60 147 100 4.81 1.61 ?7.17 ?0.25
61 159 21 2.32 5.88 4.69 4.30
76 205 10 0.12 ?1.80 ?1.83 ?1.17
49 303 21 ?2.36 ?3.82 ?4.08 ?3.42
Tab.9 Description and prediction error of typical instances
Fig.12 Health indexes of medium-length instances
Fig.13 Health indexes of end-of-life instances
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