Journal of Zhejiang University-SCIENCE A

, Volume 20, Issue 4, pp 272–289 | Cite as

Condition-based scheduled maintenance optimization of structures based on reliability requirements under continuous degradation and random shocks

  • Xiao-sheng Zhang
  • Jian-qiao ChenEmail author
  • Jun-hong Wei


In this paper, a condition-based scheduled maintenance model with aperiodic inspections of structures is developed. The structures are experiencing both a gradual degradation process and a random shock process. The former is characterized by a stationary gamma process (SGP), and the latter is assumed to be a homogeneous Poisson process (HPP). Two typical common failure modes are considered in the reliability and the condition-based maintenance model, namely: (1) soft failures caused by the continuous degradation process, together with sudden damage increments due to shocks with moderate impacts, and (2) hard failures caused by the same shock process when a severe shock occurs. A remaining useful lifetime-based (RUL-based) inspection policy is utilized to determine the inspection schedule. Thereafter, at each inspection point, different maintenance actions are to be determined to minimize the average cost rate for either an infinite or a finite time span. The developed models are demonstrated by a numerical example. Sensitivity analyses of the optimal solution with various model parameters are also performed. It is illustrated that, as compared with the pure continuous degradation process, the additional shock loads exert notable impacts on the optimal maintenance strategies.

Key words

Soft failure Hard failure Remaining useful lifetime (RUL) Reliability Maintenance Cost rate Finite horizon 






1. 在连续退化和冲击荷载的共同影响下,建立结构时变可靠度计算模型。2. 在前述可靠度分析的基础上,建立基于状态维修的非周期检测模型;基于剩余使用寿命检测策略,确定检测时间,并确定系统的最优维护策略,旨在将平均维护成本率降至最低。3. 针对无限时间域和有限时间域,分别确定对应的最佳维修策略。


1. 通过理论推导,构建结构时变可靠度计算公式(公式(13)),分析各参数与可靠度之间的变化关系(图4)。2. 通过仿真模拟,运用蒙特卡洛法确定结构在使用过程中的最佳维修策略(图5和6)。


1. 与仅考虑连续退化的情况相比,随机冲击荷载的存在,使得系统的可靠度降低,更容易发生失效。2. 冲击载荷的存在,对最佳维修策略具有显著影响。3. 有限时间域的最优解与无限时间域的最优解之间存在很大的不同,因此,有必要对这两种情况分别进行研究。


软失效 硬失效 剩余寿命 可靠度 维修 成本率 有限时域 

CLC number

TU607 TH17 


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Copyright information

© Zhejiang University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Department of MechanicsHuazhong University of Science and TechnologyWuhanChina

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