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基于Copula相似性的航空发动机RUL预测

许先鑫 李娟 孙秀慧 戴洪德

许先鑫, 李娟, 孙秀慧, 等. 基于Copula相似性的航空发动机RUL预测[J]. 航空动力学报, 2023, 39(X):20220576 doi: 10.13224/j.cnki.jasp.20220576
引用本文: 许先鑫, 李娟, 孙秀慧, 等. 基于Copula相似性的航空发动机RUL预测[J]. 航空动力学报, 2023, 39(X):20220576 doi: 10.13224/j.cnki.jasp.20220576
XU Xianxin, LI Juan, SUN Xiuhui, et al. RUL prediction for aero-engines based on Copula similarity[J]. Journal of Aerospace Power, 2023, 39(X):20220576 doi: 10.13224/j.cnki.jasp.20220576
Citation: XU Xianxin, LI Juan, SUN Xiuhui, et al. RUL prediction for aero-engines based on Copula similarity[J]. Journal of Aerospace Power, 2023, 39(X):20220576 doi: 10.13224/j.cnki.jasp.20220576

基于Copula相似性的航空发动机RUL预测

doi: 10.13224/j.cnki.jasp.20220576
基金项目: 科技项目基金(F062102009)
详细信息
    作者简介:

    许先鑫(1999-),女,主要从事预测与健康管理研究

    通讯作者:

    李娟(1981-),女,副教授、硕士生导师,博士,主要从事预测与健康管理研究。E-mail:daidaiquanquan123@126.com

  • 中图分类号: V263.6

RUL prediction for aero-engines based on Copula similarity

  • 摘要:

    针对航空发动机性能退化特征众多,以及特征相互影响等问题,考虑退化特征间的非线性相关关系,提出了基于Copula相似性的航空发动机RUL(remaining useful life)预测方法。通过K-means聚类将航空发动机的工作状态分类,建立退化模型,选取退化性能趋势最明显的3组传感器。基于Copula函数对选取的3组传感器进行相关性建模分析,构建发动机传感器之间的Copula结构。基于Copula相似性实现对航空发动机的剩余寿命预测。结果表明:基于Copula相似性的航空发动机RUL预测方法相较传统方法,在发动机运行周期的50%、70%、90%预测误差分别减少13.053%、31.328%、74.602%,预测精度得到提高。

     

  • 图 1  预测框架图

    Figure 1.  Chart of predictive framework

    图 2  发动机剩余寿命对比图

    Figure 2.  Comparison chart of engine remaining life

    图 3  发动机主要部件简图

    Figure 3.  Sketch of engine main components

    图 4  操作设置聚类结果图

    Figure 4.  Clustering graph of operation settings

    图 5  已选传感器退化趋势图

    Figure 5.  Degradation trend graph of the selected sensors

    表  1  二元Copula函数简介

    Table  1.   Introduction to binary Copula functions

    函数

    类型
    分布函数表达式 特性
    Clayton

    Copula
    $ C_\delta ^{\text{Cl}} = {\left( {{\mu ^{ - \delta }} + {v^{ - \delta }} - 1} \right)^{\tfrac{{ - 1}}{\delta }}} $ 上尾
    相关
    Gumbel

    Copula
    $ C_\theta ^{\text{Gu}} = \exp \left\{ {-\Bigg\{\bigg[(-{\text{ln}}\;\mu)^{\theta }+(-{\text{ln}}\;v)^{\theta }\bigg]\Bigg\}^{\tfrac{1}{\theta }}} \right\} $ 下尾
    相关
    Frank

    Copula
    $ C_\lambda ^{\rm{Fr}} = - \dfrac{1}{\lambda }\ln \left\{ {1 - \left[{\dfrac{{\left( {1 - {{\text{e}}^{ - \lambda \mu }}} \right)\left( {1 - {{\text{e}}^{ - \lambda v}}} \right)}}{{\left( {1 - {{\text{e}}^{ - \lambda }}} \right)}}} \right]} \right\} $ 不反映尾部

    相关性
    下载: 导出CSV

    表  2  传感器变量介绍[24]

    Table  2.   Introduction of sensor variables[24]

    序号 符号 描述
    1 T2 风扇入口总温
    3 T30 高压压气机出口总温
    4 T50 低压涡轮出口总温
    5 P2 风扇入口压力
    6 P15 外涵总压
    7 P30 高压压气机出口总压
    8 Nf 风扇物理转速
    9 Ne 核心机物理转速
    10 epr 发动机压比
    11 Ps30 高压压气机出口静压
    12 Phi 燃油流量与高压压气机出口总压比值
    13 NRf 风扇换算转速
    14 Nre 核心机换算转速
    15 BPR 涵道比
    16 farB 燃烧室燃气比
    17 htBleed 引气焓值
    18 Nf_dmd 设定风扇转速
    19 PCNfR_dmd 设定核心机换算转速
    20 W31 高压涡轮冷却引气流量
    21 W32 低压涡轮冷却引气流量
    注:发动机压比为高压压气机出口总压和风扇入口压力之比。
    下载: 导出CSV

    表  3  某发动机运行数据

    Table  3.   Operating data of an engine

    $ t $ $ {{\boldsymbol{y}}_1} (t) $ $\cdots$ $ {\boldsymbol{x}}_1^l (t) $ $ {\boldsymbol{x}}_2^l (t) $ $\cdots$ $ {\boldsymbol{x}}_{_{21}}^l (t) $
    1 10.0047 489.05 604.13 17.1735
    2 0.0015 518.67 642.13 23.3619
    3 34.9986 449.44 555.42 8.8555
    $ \vdots$ $ \vdots$ $ \vdots$ $ \vdots$ $ \vdots$
    223 34.9992 $\cdots$ 449.44 556.6 $\cdots$ 8.6695
    下载: 导出CSV

    表  4  聚类操作设置参数表

    Table  4.   Clustering parameters table of operation setting

    类别 $ {{\boldsymbol{Y}}_1} (t) $ $ {{\boldsymbol{Y}}_2} (t) $ $ {{\boldsymbol{Y}}_3} (t) $
    1 10.003 0.251 20
    2 0.0012 0.001 100
    3 25.003 0.621 80
    4 42.003 0.841 40
    5 20.003 0.701 0
    6 35.003 0.841 60
    下载: 导出CSV

    表  5  历史样本Copula参数值

    Table  5.   Copula parameter values of historical sample

    $ {L_{\rm{ru}}} $ $ Q_1^1 $ $ Q_2^1 $ $ Q_3^1 $ $ \tau _1^1 $ $ \tau _2^1 $ $ \tau _3^1 $
    223 Fra Cla Cla 0.479 0.454 0.495
    181 Fra Joe Joe 0.531 0.460 0.524
    209 Joe Joe Joe 0.472 0.332 0.333
    $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $
    220 Cla Cla Cla 0.420 0.390 0.418
    255 Fra Fra Fra 0.512 0.492 0.536
    156 Joe Fra Fra 0.513 0.450 0.514
    注:表中Fra表示Frank Copula,Cla表示Clayton Copula,Joe 表示Joe Copula。
    下载: 导出CSV

    表  6  现役发动机参数值

    Table  6.   Parameter values of in-service engine

    传感器组合 Copula $ {\boldsymbol{\tau}} $
    (4,11) Clayton 0.474
    (4,15) Frank 0.458
    (11,15) Frank 0.519
    下载: 导出CSV

    表  7  现役发动机寿命预测值

    Table  7.   Life prediction of in-service engine

    相似样本 $ {L_{\rm{ru}}} $ 50%cycle 70%cycle 90%cycle
    178 255 127.500 76.500 25.500
    60 300 150 90 30
    151 317 158.500 95.100 31.700
    $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $
    108 230 115 69 23
    35 188 94 56.4 18.8
    16 172 86 51.600 17.200
    预测结果 217.86 108.930 65.358 21.786
    真实寿命 210 105 63 21
    预测误差 7.860 3.930 2.358 0.786
    下载: 导出CSV

    表  8  方法对比误差表

    Table  8.   Error comparison table of two methods

    方法 估计误差
    50%cycle 70%cycle 90%cycle
    传统方法[25] 26.346 20.014 18.037
    基于Copula
    相似性
    22.907 13.744 4.581
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-08-08
  • 网络出版日期:  2023-11-20

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