针对比例风险退化系统健康评估的迭代算法

doi:10.3901/JME.2023.10.366

机械工程学报 ›› 2023, Vol. 59 ›› Issue (10): 366-373.doi: 10.3901/JME.2023.10.366

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针对比例风险退化系统健康评估的迭代算法

郑锐^1,2, 周一帆¹

1. 东南大学机械工程学院南京 211189;
2. 合肥工业大学管理学院合肥 230009

收稿日期:2022-04-27 修回日期:2022-10-15 出版日期:2023-05-20 发布日期:2023-07-19
通讯作者: 周一帆(通信作者),男,1981年出生,博士,副教授,博士研究生导师。主要研究方向为可靠性与设备维修决策优化、统计质量控制和制造业企业信息化。E-mail:yifan.zhou@seu.edu.cn E-mail:yifan.zhou@seu.edu.cn
作者简介:郑锐,男,1985年出生,博士,讲师。主要研究方向为可靠性工程、质保决策和维修优化。E-mail:rui_zheng@mail.sina.cn
基金资助:
国家自然科学基金资助项目(72071044，71671041)。

Iteration Algorithm for the Health Assessment of Proportional-hazards Deterioration System

ZHENG Rui^1,2, ZHOU Yifan¹

1. School of Mechanical Engineering, Southeast University, Nanjing 211189;
2. School of Management, Hefei University of Technology, Hefei 230009

Received:2022-04-27 Revised:2022-10-15 Online:2023-05-20 Published:2023-07-19

摘要/Abstract

摘要： 系统的健康状态评估是故障预测和健康管理的关键环节,其前提是对故障机理的准确刻画。比例风险模型在可靠性工程中广泛用于描述寿命和协变量对故障时间的影响。工程实际中的协变量过程大多具有随机性,给评估比例风险退化系统的健康状态带来极大的挑战。针对协变量过程具有马尔可夫性质的比例风险模型,提出一种迭代算法近似评估系统的健康状态。该方法首先基于离散化思想构建寿命和协变量状态在单位时间内的联合一步转移概率矩阵,然后通过相邻单位时间的状态转移规律推导条件可靠性和平均剩余寿命等关键健康指标的迭代计算公式。通过两个实际案例验证该迭代算法的有效性:案例一通过与解析法的对比表明迭代算法的评估结果随着离散化水平的提高不断趋于解析值,并由此给出离散化水平的设置准则;案例二通过与转移矩阵近似法的对比表明迭代算法具有计算速度快和内存需求小等优点。

关键词: 比例风险模型, 健康评估, 条件可靠性, 平均剩余寿命, 迭代算法

Abstract: Health assessment is of crucial significance for prognostics and health management. Its accuracy relies heavily on the failure mechanism of the system under consideration. Proportional hazards models are widely adopted in reliability engineering for describing the joint effects of age and covariates on failure time. In many practical situations, the covariate progress is stochastic, making it of great challenge to assess the health state of a system in the proportional hazards model. An iteration method is developed to approximately address the problem of health assessment in the proportional hazards model with a Markovian covariate process. First, the one-step transition probability matrix for the joint process of age and covariate is constructed. Based on the state-transition properties of consecutive time units, the calculation formulas of some health indices such as conditional reliability and remaining useful time are provided with proof. The effectiveness of the proposed approach is verified by two practical examples. In example 1, the comparison with the analytical method shows that the accuracy is increasing with the increase of discretization level, and a recommendation for determining a discretization level is provided. In example 2, the comparison with the transition matrix method shows that the proposed recursive method can produce accurate estimations efficiently with low memory requirements.

Key words: proportional hazards model, health assessment, conditional reliability, mean residual life, recursive algorithm

中图分类号:

TH17

郑锐, 周一帆. 针对比例风险退化系统健康评估的迭代算法[J]. 机械工程学报, 2023, 59(10): 366-373.

ZHENG Rui, ZHOU Yifan. Iteration Algorithm for the Health Assessment of Proportional-hazards Deterioration System[J]. Journal of Mechanical Engineering, 2023, 59(10): 366-373.

参考文献

[1] Wang Z Q,Hu C H,Si X S,et al. Remaining useful life prediction of degrading systems subjected to imperfect maintenance:Application to draught fans[J]. Mechanical Systems and Signal Processing,2018,100:802-813.
[2] 雷亚国,杨彬,杜兆钧,等. 大数据下机械装备故障的深度潜移诊断方法[J]. 机械工程学报,2019,55(7):1-8. LEI Yaguo,YANG Bin,DU Zhaojun,et al. Deep transfer diagnosis method for machinery in big data era[J]. Journal of Mechanical Engineering,2019,55(7):1-8.
[3] Wu X,Ryan S M. Value of condition monitoring for optimal replacement in the proportional hazards model with continuous degradation[J]. IIE Transactions,2010,42:553-563.
[4] Mousavi S M,Shams H,Ahmadi S. Simultaneous optimization of repair and control limit policy in condition-based maintenance[J]. Journal of Intelligent Manufacturing,2017,28:245-254.
[5] Zhao H,Xu F,Liang B,et al. A condition-based opportunistic maintenance strategy for multi-component system[J]. Structural Health Monitoring,2019,18:270-283.
[6] Yahyatabar A,Najafi A A. Condition based maintenance policy for series-parallel systems through proportional hazards model:A multi-stage stochastic programming approach[J]. Computers and Industrial Engineering,2018,126:30-46.
[7] Tang D,Yu J,Chen X,et al. An optimal condition-based maintenance policy for a degrading system subject to the competing risks of soft and hard failure[J]. Computers and Industrial Engineering,2015,83:100-110.
[8] LIU B,LIANG Z,PARLIKAD A K,et al. Condition-based maintenance for systems with aging and cumulative damage based on proportional hazards model[J]. Reliability Engineering and System Safety,2017,168:200-209.
[9] Jafari L,Naderkhani F,Makis V. Joint optimization of maintenance policy and inspection interval for a multi-unit series system using proportional hazards model[J]. Journal of the Operational Research Society,2018,69:36-48.
[10] Jafari L,Makis V. Joint optimal lot sizing and preventive maintenance policy for a production facility subject to condition monitoring[J]. International Journal of Production Economics,2015,169:156-168.
[11] Duan C,Makis V,Deng C. An integrated framework for health measures prediction and optimal maintenance policy for mechanical systems using a proportional hazards model[J]. Mechanical Systems and Signal Processing,2018,111:285-302.
[12] Zhao S,Makis V,Chen S,et al. Evaluation of reliability function and mean residual life for degrading systems subject to condition monitoring and random failure[J]. IEEE Transactions on Reliability,2018,67:13-25.
[13] Zheng R,Makis V. Optimal condition-based maintenance with general repair and two dependent failure modes[J]. Computers & Industrial Engineering,2020,141:106322.
[14] ZHAO S,MAKIS V,CHEN S,et al. Health assessment method for electronic components subject to condition monitoring and hard failure[J]. IEEE Transactions on Instrumentation and Measurement,2019,68:138-150.
[15] Cox D R. Regression models and life-tables[J]. Journal of the Royal Statistical Society Series B (Methodological),1972,34:187-220.
[16] Kim M J,Jiang R,Makis V,et al. Optimal bayesian fault prediction scheme for a partially observable system subject to random failure[J]. European Journal of Operational Research,2011,214:331-339.
[17] Ghasemi A,Yacout S,Ouali M S. Optimal condition based maintenance with imperfect information and the proportional hazards model[J]. International Journal of Production Research,2007,45:989-1012.
[18] MAKIS V,WU J,GAO Y. An application of DPCA to oil data for CBM modeling[J]. European Journal of Operational Research,2006,174:112-123.
[19] Tijms H C. A first course in stochastic models[M]. Chichester:John Wiley & Sons,Ltd,2003.
[20] van Noortwijk J M. A survey of the application of gamma processes in maintenance[J]. Reliability Engineering and System Safety,2009,94:2-21.
[21] Tang D,Yu J. Optimal replacement policy for a periodically inspected system subject to the competing soft and sudden failures[J]. Eksploatacja i Niezawodnosc- Maintenance and Reliability,2015,17:228-235.
[22] Wang J,Qiu Q,Wang H. Joint optimization of condition-based and age-based replacement policy and inventory policy for a two-unit series system[J]. Reliability Engineering and System Safety,2021,205:107251.

针对比例风险退化系统健康评估的迭代算法

Iteration Algorithm for the Health Assessment of Proportional-hazards Deterioration System

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