Dynamic covariance reliability analysis and residual life prediction model under the correlation between initial state and degradation rate

WEI Xin; TANG Jiayin; SONG Qingbiao; LI Wenxue

doi:10.16579/j.issn.1001.9669.2026.03.002

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Dynamic covariance reliability analysis and residual life prediction model under the correlation between initial state and degradation rate

·Optimization·Reliability· | 更新时间：2026-03-16

- Dynamic covariance reliability analysis and residual life prediction model under the correlation between initial state and degradation rate
- Journal of Mechanical Strength Vol. 48, Issue 3, Pages: 10-20(2026)
- 作者机构：
  
  西南交通大学数学学院统计系，成都 611756
- 作者简介：
  
  TANG Jiayin, E-mail: jiayintang@163.com
- 基金信息：
  
  National Social Science Fund of China(23BTJ010)
- DOI：10.16579/j.issn.1001.9669.2026.03.002
  CLC： TB114.3;O213.2
- Received：25 April 2024，
  
  Revised：2024-08-24，
  
  Published：15 March 2026
- 稿件说明：
移动端阅览
魏鑫，唐家银，宋庆彪，等. 初始状态与退化率相关下动态协变可靠性分析与剩余寿命预测模型［J］. 机械强度，2026，48（3）：10-20.

WEI Xin，TANG Jiayin，SONG Qingbiao，et al. Dynamic covariance reliability analysis and residual life prediction model under the correlation between initial state and degradation rate［J］. Journal of Mechanical Strength，2026，48（3）：10-20.
魏鑫，唐家银，宋庆彪，等. 初始状态与退化率相关下动态协变可靠性分析与剩余寿命预测模型［J］. 机械强度，2026，48（3）：10-20. DOI： 10.16579/j.issn.1001.9669.2026.03.002.

WEI Xin，TANG Jiayin，SONG Qingbiao，et al. Dynamic covariance reliability analysis and residual life prediction model under the correlation between initial state and degradation rate［J］. Journal of Mechanical Strength，2026，48（3）：10-20. DOI： 10.16579/j.issn.1001.9669.2026.03.002.

摘要

目的

工程技术领域中的系统退化受用户操作、制造工艺、工作环境等多种因素影响，系统初始状态和退化速率之间通常存在相关性（Correlation between the Initial State and the Degradation Rate

CISDR）和动态协变量在退化模型中是需要考虑的关键因素，但同时考虑以上两类随机性的文献鲜见。针对上述问题，基于Gamma退化过程建立了考虑动态协变量及系统初始退化状态与退化率相关的可靠性模型来进行研究、分析。

方法

首先，建立剩余寿命预测模型，基于对系统运行过程中的状态监测数据的统计分析，推断出产品的剩余寿命分布；其次，针对系统退化周期内操作、运行环境的差异，使用奥恩斯坦-乌伦贝克（Ornstein-Uhlenbeck

OU）过程刻画了动态协变量变化，建立了考虑动态协变量的Gamma退化模型；再次，通过指数效应模型建立动态协变量与退化率之间的关联；最后，使用二元正态分布建立系统初始退化状态与退化率相关性模型，推导得到了系统可靠度函数与剩余寿命的概率密度。

结果

结果表明，仿真算例和应用实例验证了所建立的模型能够显著提高剩余寿命预测的准确性，同时考虑两种随机效应后的剩余寿命预测更加客观。

Abstract

Objective

In the field of engineering technology

the degradation of systems is affected by various factors such as user operations

manufacturing processes

and working environments. The correlation between the initial state and the degradation rate (CISDR) and dynamic covariates are key factors to be considered in degradation models; however

there is little literature that takes both types of randomness into account simultaneously. To address the above issue

a reliability model based on the Gamma degradation process

which considers dynamic covariates and the correlation between the initial degradation state of the system and the degradation rate

was established for research and analysis.

Methods

Firstly

a residual life prediction model was established. Based on the statistical analysis of condition monitoring data during system operation

the residual life distribution of the product was further inferred. Secondly

in view of the differences in operation and operating environment during the system degradation cycle

the Ornstein-Uhlenbeck (OU) process was used to characterize the changes in dynamic covariates

and a Gamma degradation model considering dynamic covariates was constructed. Thirdly

the relation between dynamic covariates and degradation rate was established through an exponential effect model. Finally

a bivariate normal distribution was employed to build a correlation model between the initial degradation state of the system and the degradation rate

and the system reliability function and the probability density of residual life were derived.

Results

The results show that both the simulation examples and application cases have verified that the established model can significantly improve the accuracy of residual life prediction. Meanwhile

the residual life prediction that takes two types of random effects into account is more objective.

关键词

Keywords

references

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