留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

一种基于改进KELM的在线状态预测方法

朱敏 许爱强 陈强强 李睿峰

朱敏, 许爱强, 陈强强, 等 . 一种基于改进KELM的在线状态预测方法[J]. 北京航空航天大学学报, 2019, 45(7): 1370-1379. doi: 10.13700/j.bh.1001-5965.2018.0685
引用本文: 朱敏, 许爱强, 陈强强, 等 . 一种基于改进KELM的在线状态预测方法[J]. 北京航空航天大学学报, 2019, 45(7): 1370-1379. doi: 10.13700/j.bh.1001-5965.2018.0685
ZHU Min, XU Aiqiang, CHEN Qiangqiang, et al. An improved KELM based online condition prediction method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(7): 1370-1379. doi: 10.13700/j.bh.1001-5965.2018.0685(in Chinese)
Citation: ZHU Min, XU Aiqiang, CHEN Qiangqiang, et al. An improved KELM based online condition prediction method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(7): 1370-1379. doi: 10.13700/j.bh.1001-5965.2018.0685(in Chinese)

一种基于改进KELM的在线状态预测方法

doi: 10.13700/j.bh.1001-5965.2018.0685
基金项目: 

国家自然科学基金 11802338

山东省自然科学基金 ZR2017MF036

详细信息
    作者简介:

    朱敏  男, 博士研究生。主要研究方向:机载电子设备状态监测与故障诊断

    许爱强  男, 教授, 博士生导师。主要研究方向:复杂电子系统自动测试与诊断技术

    通讯作者:

    许爱强, E-mail: hjhyautotest@sina.com

  • 中图分类号: V243;TP181

An improved KELM based online condition prediction method

Funds: 

National Natural Science Foundation of China 11802338

Natural Science Foundation of Shandong Province ZR2017MF036

More Information
  • 摘要:

    针对核超限学习机(KELM)在线状态预测过程中,核矩阵阶数不断增长且难以跟踪时变动态特征的问题,提出了一个具有遗忘因子的稀疏KELM在线状态预测方法。通过引入遗忘因子构建新的目标函数,使稀疏字典中各元素依据时间远近具有不同权重,保证了模型对动态变化的有效跟踪;通过最小化字典的快速留一交叉验证(FLOO-CV)误差,选择具有预定规模的关键节点构成字典;基于当前字典,通过矩阵初等变换和分块求逆,实现相关参数的递推更新。某型飞机发动机的状态预测结果表明,与目前已有的3种在线序贯KELM相比,所提方法在6个监测项目上的平均训练时间分别缩短了7.5%、62.0%和81.9%,平均预测精度分别提升了44.0%、19.9%和50.9%。

     

  • 图 1  矩阵变换前的At

    Figure 1.  At before matrix transformation

    图 2  对Mackey-Glass混沌时间序列学习的训练样本数

    Figure 2.  Number of learned samples for chaotic Mackey-Glass time series

    图 3  不同方法的学习曲线(实验1)

    Figure 3.  Learning curves of different methods (Experiment 1)

    图 4  不同方法的预测曲线(实验1)

    Figure 4.  Prediction curves of different methods (Experiment 1)

    图 5  某发动机排气温度与滑油压力变化曲线

    Figure 5.  Curves of exhaust gas temperature and oil pressure of an aero-engine

    图 6  不同方法的学习曲线(实验2)

    Figure 6.  Learning curves of different methods (Experiment 2)

    图 7  滑油压力预测曲线

    Figure 7.  Prediction curves of oil pressure

    图 8  滑油压力绝对预测误差曲线

    Figure 8.  Absolute prediction error curves of oil pressure

    表  1  实验1参数设置

    Table  1.   Parameter setup in Experiment 1

    方法 正则化参数c 核参数σ 其他参数
    ReOS-ELM 2×103 L=50
    KB-IELM 10 10
    FF-KB-IELM 10 10 γ=0.999
    FOKELM 2×104 10 z=50
    FF-FOKELM 2×104 10 z=50, γ=0.999
    ALD-KOS-ELM 1×103 10 b=0.000 01
    NOS-KELM 2×104 10 m=50, δ=0.01, η=0.8
    FF-OSKELM 2×104 10 m=50, γ=0.999
    注:L为ReOS-ELM中隐层神经元个数;z为FOKELM中时间窗长度;ALD-KOS-ELM中的b表示ALD准则需要设置的阈值;NOS-KELM中的δη均是梯度下降法中运用动态学习率时需要设置的常数,详细请参见相关文献[17]。
    下载: 导出CSV

    表  2  实验1预测结果

    Table  2.   Prediction results of Experiment 1

    方法 训练 测试
    时间/s RMSE 时间/s RMSE MAPE MRPE
    ReOS-ELM 7.940 5 0.019 5 0.00 11 0.018 6 0.050 0 0.012 1
    KB-IELM 8.665 9 0.017 5 0.010 7 0.015 3 0.042 0 0.010 8
    FF-KB-IELM 8.632 2 0.015 3 0.010 1 0.013 2 0.037 5 0.009 4
    FOKELM 0.092 2 0.026 8 4.446 5×10-4 0.012 2 0.031 7 0.008 3
    FF-FOKELM 0.088 6 0.025 9 3.314 5×10-4 0.011 0 0.028 6 0.007 4
    ALD-KOS-ELM 0.146 4 0.011 2 3.716 0×10-4 0.010 9 0.025 0 0.008 1
    NOS-KELM 0.565 0 0.010 4 2.405 9×10-4 0.009 3 0.026 3 0.006 3
    FF-OSKELM 0.045 4 0.003 4 3.512 2×10-4 0.003 3 0.011 0 0.002 3
    注:ELM输入层初始权重的随机性导致ReOS-ELM的实验结果具有很大的随机性,表中只列出了ReOS-ELM一次实验的结果。
    下载: 导出CSV

    表  3  实验2参数设置

    Table  3.   Parameter setup in Experiment 2

    监测项目 正则化
    参数c
    核参数
    σ
    m 阈值δ
    发动机扭矩 2×104 5×104 30 2×10-5
    发动机转速 2×104 1×109 30 2×10-8
    排气温度 2×104 1×107 30 2×10-9
    滑油温度 2×104 2×105 30 2×10-9
    滑油压力 2×104 2×104 30 2×10-9
    燃油瞬时流量 2×103 2×105 30 2×10-6
    注:阈值δ为ALD-KOS-ELM的参数,m为其他3种方法的参数,表示字典规模或时间窗长度。
    下载: 导出CSV

    表  4  实验2预测结果

    Table  4.   Prediction results of Experiment 2

    监测项目 方法 训练 测试
    时间/s RMSE RMSE MAPE MRPE
    发动机扭矩 FOKELM 0.006 8 0.846 3 1.453 8 3.342 7 0.166 5
    ALD-KOS-ELM 0.006 9 0.784 6 1.020 5 2.581 4 0.110 8
    NOS-KELM 0.045 0 0.710 8 1.457 0 3.421 6 0.167 5
    FF-OSKELM 0.005 7 0.653 0 1.304 1 3.062 2 0.150 7
    发动机转速 FOKELM 0.003 1 333.634 4 241.756 6 627.155 1 0.007 2
    ALD-KOS-ELM 0.011 4 91.332 5 167.500 5 451.946 1 0.005 2
    NOS-KELM 0.053 4 156.557 5 276.815 6 684.522 2 0.007 9
    FF-OSKELM 0.004 4 82.935 1 132.873 9 385.796 6 0.004 0
    排气温度 FOKELM 0.005 6 4.859 3 7.474 8 19.777 0 0.012 5
    ALD-KOS-ELM 0.031 0 4.192 1 5.402 7 13.672 6 0.009 3
    NOS-KELM 0.038 8 5.386 8 7.648 3 20.021 0 0.012 8
    FF-OSKELM 0.005 2 3.286 17 3.855 3 9.694 2 0.006 7
    滑油温度 FOKELM 0.004 3 0.183 7 0.321 1 0.511 7 0.008 1
    ALD-KOS-ELM 0.044 4 0.044 7 0.160 4 0.250 0 0.004 2
    NOS-KELM 0.062 6 0.218 9 0.701 0 0.985 9 0.018 5
    FF-OSKELM 0.004 7 0.031 7 0.108 5 0.180 9 0.002 8
    滑油压力 FOKELM 0.004 6 0.111 5 0.105 4 0.140 0 0.030 9
    ALD-KOS-ELM 0.035 0 0.061 4 0.040 7 0.056 3 0.012 5
    NOS-KELM 0.039 1 0.077 5 0.050 4 0.075 7 0.015 2
    FF-OSKELM 0.025 7 0.036 7 0.028 0 0.045 7 0.008 4
    燃油瞬时流量 FOKELM 0.033 5 3.353 4 7.456 0 18.800 3 0.031 7
    ALD-KOS-ELM 0.012 2 2.419 3 6.589 6 23.668 6 0.024 4
    NOS-KELM 0.057 4 2.619 0 7.698 1 18.667 9 0.033 6
    FF-OSKELM 0.007 8 2.163 2 6.508 9 23.396 4 0.024 1
    注:因为方法的测试时间均过于短暂,已能满足绝大部分在线应用需求,此表不再将之作为对比项。
    下载: 导出CSV
  • [1] TIAN Z, QIAN C, GU B, et al.Electric vehicle air conditioning system performance prediction based on artificial neural network[J].Applied Thermal Engineering, 2015, 89:101-104. doi: 10.1016/j.applthermaleng.2015.06.002
    [2] HUANG G B, ZHU Q Y, SIEW C K.Extreme learning machine:Theory and application[J].Neurocomputing, 2006, 70(1-3):489-501. doi: 10.1016/j.neucom.2005.12.126
    [3] YIN G, ZHANG Y T, LI Z N, et al.Online fault diagnosis method based on incremental support vector data description and extreme learning machine with incremental output structure[J].Neurocomputing, 2014, 128:224-231. doi: 10.1016/j.neucom.2013.01.061
    [4] BILAL M, LIN Z P, LIU N.Ensemble of subset online sequential extreme learning machine for class imbalance and concept drift[J].Neurocomputing, 2015, 149:316-329. doi: 10.1016/j.neucom.2014.03.075
    [5] LIANG N Y, HUANG G B, SARATCHANDRAN P, et al.A fast and accurate online sequential learning algorithm for feedforward networks[J].IEEE Transactions on Neural Networks, 2006, 17(6):1411-1423. doi: 10.1109/TNN.2006.880583
    [6] HUANG G B, ZHOU H, DING X, et al.Extreme learning machine for regression and multiclass classification[J].IEEE Transactions on Systems, Man, and Cybernetics-Part B:Cybernetics, 2011, 42(2):513-529. http://cn.bing.com/academic/profile?id=3c625b13139614a7a9cad9abcf0e148b&encoded=0&v=paper_preview&mkt=zh-cn
    [7] SCARDAPANE S, COMMINIELLO D, SCARPINITI M, et al.Online sequential extreme learning machine with kernels[J].IEEE Transactions on Neural Networks and Learning Systems, 2015, 26(9):2214-2220. doi: 10.1109/TNNLS.2014.2382094
    [8] GUO L, HAO J H, LIU M.An incremental extreme learning machine for online sequential learning problems[J].Neurocomputing, 2014, 128:50-58. doi: 10.1016/j.neucom.2013.03.055
    [9] YU X, RASHID M, FENG J, et al.Online glucose prediction using computationally efficient sparse kernel filtering algorithms in type-1 diabetes[J].IEEE Transactions on Control Systems Technology, 2018, 99:1-13. http://cn.bing.com/academic/profile?id=6f9d6f4ef847e5cf224f71777527e2c7&encoded=0&v=paper_preview&mkt=zh-cn
    [10] HAN M, ZHANG S, XU M, et al.Multivariate chaotic time series online prediction based on improved kernel recursive least squares algorithm[J].IEEE Transactions on Cybernetics, 2018, 49(4):1160-1172. http://cn.bing.com/academic/profile?id=e211614187c890abde07fab207026de0&encoded=0&v=paper_preview&mkt=zh-cn
    [11] HONEINE P.Analyzing sparse dictionaries for online learning with kernels[J].IEEE Transactions on Signal Processing, 2015, 63(23):6343-6353. doi: 10.1109/TSP.2015.2457396
    [12] ZHOU X R, LIU Z J, ZHU C X.Online regularized and kernelized extreme learning machines with forgetting mechanism[J].Mathematical Problems in Engineering, 2014, 2014:1-11. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=0621dbc6f0bfa7cab6e5ee747bcb5d83
    [13] ZHOU X R, WANG C S.Cholesky factorization based online regularized and kernelized extreme learning machines with forgetting mechanism[J].Neurocomputing, 2016, 174:1147- 1155. doi: 10.1016/j.neucom.2015.10.033
    [14] RICHARD C, BERMUDEZ J C M, HONEINE P.Online prediction of time series data with kernels[J].IEEE Transactions on Signal Processing, 2009, 57(3):1058-1067. doi: 10.1109/TSP.2008.2009895
    [15] 张伟, 许爱强, 高明哲.基于稀疏核增量超限学习机的机载设备在线状态预测[J].北京航空航天大学学报, 2017, 43(10):2089-2098. http://www.cqvip.com/QK/90750X/201710/673737256.html

    ZHANG W, XU A Q, GAO M Z.Online condition prediction of avionic devices based on sparse kernel incremental extreme learning machine[J].Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(10):2089-2098(in Chinese). http://www.cqvip.com/QK/90750X/201710/673737256.html
    [16] 张伟, 许爱强, 高明哲.一种基于积累一致性测量的在线状态预测算法[J].上海交通大学学报, 2017, 51(11):1391-1398. http://d.old.wanfangdata.com.cn/Periodical/shjtdxxb201711016

    ZHANG W, XU A Q, GAO M Z.An online condition prediction algorithm based on cumulative coherence measurement[J].Journal of Shanghai Jiaotong University, 2017, 51(11):1391-1398(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/shjtdxxb201711016
    [17] ZHANG W, XU A Q, PING D F, et al.An improved kernel-based incremental extreme learning machine with fixed budget for nonstationary time series prediction[J].Neural Computing & Applications, 2019, 31(3):637-652. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=ab5cb05588d91facb1cde1abec547d0f
    [18] LIM J S, LEE S, PANG H S, et al.Low complexity adaptive forgetting factor for online sequential extreme learning machine (OS-ELM) for application to nonstationary system estimations[J].Neural Computing & Applications, 2013, 22(3-4):569- 576. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=3f9ad96fbcac7e97fb7c8d6338a519e2
    [19] 郭威, 徐涛, 于建江, 等.基于M-estimator与可变遗忘因子的在线贯序超限学习机[J].电子与信息学报, 2018, 40(6):94-101. http://d.old.wanfangdata.com.cn/Periodical/dzkxxk201806013

    GUO W, XU T, YU J J, et al.Online sequential extreme learning machine based on m-estimator and variable forgetting factor[J].Journal of Electronics & Information Technology, 2018, 40(6):94-101(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/dzkxxk201806013
    [20] 张英堂, 马超, 李志宁, 等.基于快速留一交叉验证的核极限学习机在线建模[J].上海交通大学学报, 2014, 48(5):641-646. http://d.old.wanfangdata.com.cn/Periodical/shjtdxxb201405011

    ZHANG Y T, MA C, LI Z N, et al.Online modeling of kernel extreme learning machine based on fast leave-one-out cross-validation[J].Journal of Shanghai Jiaotong University, 2014, 48(5):641-646(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/shjtdxxb201405011
    [21] HUYNH H T, WON Y.Regularized online sequential learning algorithm for single-hidden layer feedforward neural networks[J].Pattern Recognition Letters, 2011, 32(14):1930-1935. doi: 10.1016/j.patrec.2011.07.016
  • 加载中
图(8) / 表(4)
计量
  • 文章访问数:  449
  • HTML全文浏览量:  2
  • PDF下载量:  550
  • 被引次数: 0
出版历程
  • 收稿日期:  2018-11-22
  • 录用日期:  2018-12-28
  • 刊出日期:  2019-07-20

目录

    /

    返回文章
    返回
    常见问答