双指标阶段性退化建模及可靠性分析

doi:10.12305/j.issn.1001-506X.2021.12.37

系统工程与电子技术 ›› 2021, Vol. 43 ›› Issue (12): 3725-3731.doi: 10.12305/j.issn.1001-506X.2021.12.37

双指标阶段性退化建模及可靠性分析

毛泽龙¹, 王治华^1,*, 吴琼², 刘成瑞³

1. 北京航空航天大学航空科学与工程学院, 北京 100083
2. 北京空间飞行器总体设计部, 北京 100080
3. 北京控制工程研究所研发中心, 北京 100080

收稿日期:2020-12-28 出版日期:2021-11-24 发布日期:2021-11-30
通讯作者: 王治华
作者简介:毛泽龙(1997—), 男, 硕士研究生, 主要研究方向为性能退化可靠性分析|王治华(1981—), 女, 副教授, 博士研究生导师, 博士, 主要研究方向为复杂系统状态监测、性能退化试验优化设计、小样本可靠性分析与寿命预测|吴琼(1981—), 男, 高级工程师, 博士, 主要研究方向为航天器机构设计及可靠性分析与验证|刘成瑞(1978—), 男, 研究员, 硕士研究生导师, 博士, 主要研究方向为航天器故障诊断、容错控制与可靠性
基金资助:
国家自然科学基金(11872085);国家重点研发计划(2018YFF0216004)

Bivariate and two-stage degradation modeling and reliability analysis

Zelong MAO¹, Zhihua WANG^1,*, Qiong WU², Chengrui LIU³

1. School of Aeronautic Science and Engineering, Beihang University, Beijing 100083, China
2. Beijing Institute of Spacecraft System Engineering, Beijing 100080, China
3. Research and Development Center, Beijing Institute of Control Engineering, Beijing 100080, China

Received:2020-12-28 Online:2021-11-24 Published:2021-11-30
Contact: Zhihua WANG

摘要/Abstract

摘要：

高可靠长寿命产品常需同时满足多种功能, 退化机理复杂, 其性能退化过程中多指标、多阶段的问题日益凸显。为此, 考虑退化过程的阶段性特征及不同阶段指标间耦合性规律, 基于Copula函数和Wiener过程建立了双指标阶段性退化模型及可靠性分析方法。同时, 针对产品退化过程中两指标变点不在同一位置的一般性情况, 提出了一种考虑双指标变点的模型参数整体估计方法。最后, 通过舱门锁实例的对比分析, 对所提方法的适用性和有效性进行了验证。结果表明, 同传统双指标模型相比, 所提方法能更为准确地描述退化过程的相关性与阶段性规律, 得到的可靠性评估结果更合理有效。

关键词: 可靠性分析, Wiener退化过程, 双指标, 阶段性, Copula函数

Abstract:

High reliability and long life products often need to meet multiple functions at the same time, and the degradation mechanism is complex. The problem of multi-index and multi-stage in the process of performance degradation is becoming more and more prominent. Therefore, considering the stage characteristics of degradation process and the coupling law between indexes in different stages, a two index stage degradation model and reliability analysis method are established based on Copula function and Wiener process. At the same time, aiming at the general situation that the change points of two indexes are not in the same position in the process of product degradation, a global estimation method of model parameters considering two index change points is proposed. Finally, the applicability and effectiveness of the proposed method are verified by the comparative analysis of an example of cabin door lock. The results show that the proposed simultaneous interpreting method can more accurately describe the correlation and stage rules of degradation process compared with the traditional dual index model, and the reliability evaluation results obtained are more reasonable and effective.

Key words: reliability analysis, Wiener degradation process, bivariate, stage transition, Copula function

中图分类号:

TB114.3

毛泽龙, 王治华, 吴琼, 刘成瑞. 双指标阶段性退化建模及可靠性分析[J]. 系统工程与电子技术, 2021, 43(12): 3725-3731.

Zelong MAO, Zhihua WANG, Qiong WU, Chengrui LIU. Bivariate and two-stage degradation modeling and reliability analysis[J]. Systems Engineering and Electronics, 2021, 43(12): 3725-3731.

图/表 6

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参考文献 30

1	张彬, 章立军, 罗久飞, 等. 基于函数主元分析的多阶段退化过程建模与预测[J]. 仪器仪表学报, 2019, 40 (7): 30- 38.
	ZHANG B , ZHANG L J , LUO J F , et al. Multi-phase degradation process modeling and prediction based on functional principal component analysis[J]. Chinese Journal of Scientific Instrument, 2019, 40 (7): 30- 38.
2	黄金波, 孔德景, 崔利荣. 多阶段可校正系统退化建模与可靠性评估[J]. 系统工程与电子技术, 2016, 38 (4): 965- 969.
	HUANG J B , KONG D J , CUI L R . Degradation modeling and reliability assessment of multi-stage system with calibrations[J]. Systems Engineering and Electronics, 2016, 38 (4): 965- 969.
3	LIU K , ZOU T J , DANG W , et al. Misspecification analysis of two-phase Gamma-Wiener degradation models[J]. Quality and Reliability Engineering International, 2020, 36 (6): 2066- 2084. doi: 10.1002/qre.2674
4	XU D , WEI Q D , ELSAYED E A , et al. Multivariate degradation modeling of smart electricity meter with multiple performance characteristics via vine Copulas[J]. Quality and Reliability Engineering International, 2017, 33 (4): 803- 821. doi: 10.1002/qre.2058
5	SONG S , COIT D W , FENG Q , et al. Reliability analysis for multi-component systems subject to multiple dependent competing failure processes[J]. IEEE Trans.on Reliability, 2014, 63, 331- 345. doi: 10.1109/TR.2014.2299693
6	杨志远, 赵建民, 李俐莹, 等. 二元相关退化系统可靠性分析及剩余寿命预测[J]. 系统工程与电子技术, 2020, 42 (11): 2661- 2668. doi: 10.3969/j.issn.1001-506X.2020.11.31
	YANG Z Y , ZHAO J M , LI L Y , et al. Reliability analysis and residual life estimation of bivariate dependent degradation system[J]. Systems Engineering and Electronics, 2020, 42 (11): 2661- 2668. doi: 10.3969/j.issn.1001-506X.2020.11.31
7	PANDEY M D , YUAN X X , VAN N J M , et al. The influence of temporal uncertainty of deterioration on life-cycle management of structures[J]. Structure and Infrastructure Engineering, 2009, 5 (2): 145- 156. doi: 10.1080/15732470601012154
8	YE Z S , XIE M . Stochastic modelling and analysis of degradation for highly reliable products[J]. Applied Stochastic Models in Business and Industry, 2015, 31 (1): 16- 32. doi: 10.1002/asmb.2063
9	ZHANG Z X , SI X S , HU C H , et al. Degradation data analysis and remaining useful life estimation: a review on Wiener-process-based methods[J]. European Journal of Operational Research, 2018, 271 (3): 775- 796. doi: 10.1016/j.ejor.2018.02.033
10	鄢伟安, 宋保维, 段桂林, 等. 基于两阶段维纳退化过程的液力耦合器可靠性评估[J]. 系统工程与电子技术, 2014, 36 (9): 1882- 1886.
	YAN W A , SONG B W , DUAN G L , et al. Reliability evaluation of LCD based on two-phase Wiener degradation process[J]. Systems Engineering and Electronics, 2014, 36 (9): 1882- 1886.
11	WANG X L , JIANG P , GUO B , et al. Real-time reliability evaluation for an individual product based on change-point Gamma and Wiener process[J]. Quality and Reliability Engineering International, 2014, 30 (4): 513- 525. doi: 10.1002/qre.1504
12	FENG J , SUN Q , JIN T D . Storage life prediction for a high-performance capacitor using multi-phase Wiener degradation model[J]. Communications in Statistics-Simulation and Computation, 2012, 41 (8): 1317- 1335. doi: 10.1080/03610918.2011.624241
13	张奡, 王治华, 赵振平, 等. 两阶段非线性Wiener过程退化建模与可靠性分析[J]. 系统工程与电子技术, 2020, 42 (4): 954- 959.
	ZHANG A , WANG Z H , ZHAO Z P , et al. Two-phase nonlinear Wiener process for degradation modeling and reliability[J]. Systems Engineering and Electronics, 2020, 42 (4): 954- 959.
14	黄亮, 刘君强, 贡英杰. 基于Wiener过程的发动机多阶段剩余寿命预测[J]. 北京航空航天大学学报, 2018, 44 (5): 1081- 1087.
	HUANG L , LIU J Q , GONG Y J . Multi-phase residual life prediction of engines based on Wiener process[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44 (5): 1081- 1087.
15	王小林. 基于非线性Wiener过程的产品退化建模与剩余寿命预测研究[D]. 长沙: 国防科学技术大学, 2014.
	WANG X L. Research of degradation modeling and residual life estimation for deteriorate products based on nonlinear Wiener process[D]. Changsha: National University of Defense Technology, 2014.
16	王耀冬, 宣兆龙, 朱宏, 等. 破坏性测量与非破坏性测量相结合的火工品二元Wiener过程退化失效建模[J]. 弹箭与制导学报, 2017, 37 (5): 139- 142.
	WANG Y D , XUAN Z L , ZHU H , et al. The degradation failure modeling of the initiating explosive device binary Wiener which combined with destructive measurement and non-destructive measurement[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2017, 37 (5): 139- 142.
17	XU A C , SHEN L J , WANG B X , et al. On modeling bivariate Wiener degradation process[J]. IEEE Trans.on Reliability, 2018, 67 (3): 897- 906. doi: 10.1109/TR.2018.2791616
18	DONG Q L , CUI L R , SI S B . Reliability and availability analysis of stochastic degradation systems based on bivariate Wiener processes[J]. Applied Mathematical Modelling, 2020, 79, 414- 433. doi: 10.1016/j.apm.2019.10.044
19	任子强, 司小胜, 胡昌华, 等. 融合多传感器数据的发动机剩余寿命预测方法[J]. 航空学报, 2019, 40 (12): 134- 145.
	REN Z Q , SI X S , HU C H , et al. Remaining useful life prediction method for engine combining multi-sensors data[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40 (12): 134- 145.
20	牛一凡, 邵景峰. 基于非线性数据融合的设备多阶段寿命预测[J]. 信息与控制, 2019, 48 (6): 729- 737.
	NIU Y F , SHAO J F . Multi-stage lifetime estimation for equipment based on nonlinear data fusion[J]. Information and Control, 2019, 48 (6): 729- 737.
21	PAN Z Q , BALAKRISHNAN N , SUN Q , et al. Bivariate degradation analysis of products based on Wiener process and Copulas[J]. Journal of Statistical Computation and Simulation, 2013, 83 (7): 1316- 1329. doi: 10.1080/00949655.2012.658805
22	HAO H B , SU C . Bivariate nonlinear diffusion degradation process modeling via copula and MCMC[J]. Mathematical Problems in Engineering, 2014, 510929.
23	周源, 吕卫民, 王少蕾, 等. 基于Copula函数耦合性建模的二元加速退化数据统计分析方法[J]. 兵器装备工程学报, 2018, 39 (5): 160- 165.
	ZHOU Y , LYU W M , WANG S L , et al. Statistical analysis method of bivariate degradation data based on dependency modeling via Copula function[J]. Journal of Ordnance Equipment Engineering, 2018, 39 (5): 160- 165.
24	PENG W W , LI Y F , MI J H , et al. Reliability of complex systems under dynamic conditions: a Bayesian multivariate degradation perspective[J]. Reliability Engineering & System Safety, 2016, 153, 75- 87.
25	SUN F Q , FU F Y , LIAO H T , et al. Analysis of multivariate dependent accelerated degradation data using a random-effect general Wiener process and D-vine Copula[J]. Reliability Engineering and System Safety, 2020, 204, 107168.
26	RUIZ C , LIAO H T , POHL E A . Analysis of correlated multivariate degradation data in accelerated reliability growth[J]. Quality and Reliability Engineering International, 2021, 37 (7): 3125- 3144.
27	PENG W W , LI Y F , YANG Y J , et al. Bivariate analysis of incomplete degradation observations based on inverse Gaussian processes and Copulas[J]. IEEE Trans.on Reliability, 2016, 65 (2): 624- 639.
28	LIU Z Y , MA X B , YANG J , et al. Reliability modeling for systems with multiple degradation processes using inverse Gaussian process and Copulas[J]. Mathematical Problems in Engineering, 2014, 829597.
29	SHEN L S , ZHANG Y G , SONG K L , et al. Failure analysis of a lock mechanism with multiple dependent components based on two-phase degradation model[J]. Engineering Failure Analysis, 2019, 104, 1076- 1093.
30	李霞. Copula方法及其应用[M]. 北京: 经济管理出版社, 2014.
	LI X . Copula method and its application[M]. Beijing: Econo-mic Management Press, 2014.

参数	取值	参数	取值	参数	取值
μ₁₁	0.502	μ₂₁	0.307	τ₁	0.22
μ₁₂	3.09	μ₂₂	1.73	τ₂	0.27
σ₁₁	7.48e-2	σ₂₁	3.96e-2	θ₁	1.26
σ₁₂	0.101	σ₂₂	5.04e-2	θ₂	1.40
γ₁₁	1.31	γ₂₁	1.16	θ₃	3.94
γ₁₂	1.29	γ₂₂	1.14	-	-

模型	log-LF	AIC
M₀	2 726	-5 418
M₁	2 512	-5 017
M₂	2 490	-4 944

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[7]	兰杰, 袁宏杰, 夏静. 基于离散时间贝叶斯网络的动态故障树分析的改良方法[J]. 系统工程与电子技术, 2018, 40(4): 948-953.
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[9]	闫华, 武小悦. 航天测控通信系统可靠性分析的改进Krylov投影算法[J]. Journal of Systems Engineering and Electronics, 2012, 34(10): 2180-2186.
[10]	胡涛，俞建. n/k(G)表决冗余多阶段任务系统可靠性优化模型[J]. Journal of Systems Engineering and Electronics, 2012, 34(1): 217-220.
[11]	蒋英杰，孙志强，谢红卫，宫二玲. 基于Bayes信息融合的人为差错概率计算方法[J]. Journal of Systems Engineering and Electronics, 2011, 33(4): 949-953.
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双指标阶段性退化建模及可靠性分析

Bivariate and two-stage degradation modeling and reliability analysis

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