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

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

许先鑫¹,
李娟^1,*, ,,
孙秀慧¹,
戴洪德²

1.
鲁东大学数学与统计科学学院统计系，山东烟台 264025
2.
中国人民解放军海军航空大学航空基础学院，山东烟台 264001

基金项目: 国防科技项目基金（F062102009）

详细信息

作者简介:
许先鑫（1999-），女，学士，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：daidaiquan quan123@126.com

中图分类号: V263.6
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出版历程
- 收稿日期: 2022-08-08
- 网络出版日期: 2023-11-20

RUL prediction for aero-engines based on Copula similarity

XU Xianxin¹,
LI Juan^{1,*
, ,},
SUN Xiuhui¹,
DAI Hongde²

1.
Department of Statistics，School of Mathematics and Statistics，Lu Dong University，Yantai Shandong 264025，China
2.
School of Basic Sciences for Aviation，Naval Aviation University，Yantai Shandong 264001，China

摘要

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。
- 预测与健康管理 /
- 特征退化 /
- 剩余使用寿命 /
- Copula /
- 非线性 /
- 相似性
Abstract:
In view of many degradation features of aero-engine performance and their mutual influence, the RUL prediction method of aero-engine based on Copula similarity was proposed considering the nonlinear correlations of the degradation features. The working state of the aero-engine was classified through K-means clustering, and a degradation model was established to select three sets of sensors with the most obvious degradation performance trend. Based on the Copula function, the correlation modeling and analysis of the selected three sets of sensors were carried out to build the Copula structure between engine sensors. The prediction of the remaining life of aero-engine was realized based on Copula similarity. The results showed that, compared with the traditional method, the Copula similarity-based aero-engine RUL prediction method reduces the prediction errors by 13.053%, 31.328%, and 74.602% at 50%, 70%, and 90% of the engine operating cycle, respectively, and the prediction accuracy is improved.
- prediction and health management /
- performance degradation /
- remaining useful life /
- Copula /
- nonlinearity /
- similarity

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图 1 预测框架图

Figure 1. Chart of predictive framework

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图 2 发动机剩余寿命对比图

Figure 2. Comparison chart of engine remaining life

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图 3 发动机主要部件简图

Figure 3. Sketch of engine main components

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图 4 操作设置聚类结果图

Figure 4. Clustering graph of operation settings

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图 5 已选传感器退化趋势图

Figure 5. Degradation trend graph of the selected sensor

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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

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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 9	Nf Ne	风扇物理转速核心机物理转速
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。

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表 3 某发动机运行数据

Table 3. Operating data of an engine

$ t $	$ {y_1} （t） $	$\cdots$	$ x_1^l （t） $	$ x_2^l （t） $	$\cdots$	$ 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

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表 4 聚类操作设置参数表

Table 4. Clustering parameters table of operation setting

类别	$ {Y_1} （t） $	$ {Y_2} （t） $	$ {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

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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
┇	┇	┇	┇	┇	┇	┇
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。

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表 6 现役发动机参数值

Table 6. parameter values of in-service engine

传感器组合	Copula		$ \tau $
（4,11）	Clayton	0.474
（4,15）	Frank	0.458
（11,15）	Frank	0.519

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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
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
┇	┇	┇	┇	┇
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

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表 8 方法对比误差表

Table 8. Error comparison table of two method

方法	估计误差
方法	50%Cycle	70%Cycle	90%Cycle
传统方法^[25]	26.346	20.014	18.037
传统方法^[25]	26.346	20.014	18.037	基于Copula 相似性	22.907	13.744	4.581

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