作者：高旭东,胡昌华,杜党波

作者单位：火箭军工程大学，陕西 西安 710025

关键词：剩余寿命；分数布朗运动；记忆效应；极大似然估计；贝叶斯理论；陀螺仪

摘要：

现有文献主要通过马尔科夫过程来描述设备的退化轨迹，鲜有考虑历史状态对未来退化轨迹的影响。鉴于此，为了反映退化轨迹的记忆效应对剩余寿命预测的影响，该文首先基于分数布朗运动建立了一种线性随机退化模型，并通过引入随机效应来反映不同样本间的退化差异性。进一步，基于弱收敛性理论与分数布朗运动的特性推导了剩余寿命分布的近似解析解。其次，基于极大似然算法和贝叶斯理论，完成了模型参数的离线估计与在线更新，进而实现了剩余寿命的在线自适应预测。最后，通过数值仿真与某惯性导航系统中陀螺仪的实测数据对本模型进行实验，结果表明相比于传统线性随机退化模型，该模型能有效的刻画退化轨迹的记忆效应，提高了剩余寿命的预测精度。

Adaptive prediction of remaining useful life for stochastic deteriorating equipment based on linear FBM process

GAO Xudong，HU Changhua，Du Dangbo

（Engineering Rocket Force University of Engineering, Xi’an710025, Shanxi, China）

Abstract：Existing literature mainly describes the degradation trajectory of the equipment through the Markov process, and rarely considers the influence of the historical state on the future degradation trajectory. In view of this, in order to reflect the memory effect of the degradation trajectory, this paper first establishes a linear stochastic degradation model based on the fractional Brownian motion and introduces random effects to reflect the degradation difference between different samples. Furthermore, the approximate analytical solution of the remaining life distribution is derived based on the weak convergence theory and the special effects of fractional Brownian motion. Secondly, based on the maximum likelihood algorithm and Bayesian theory, the offline estimation and online update of the model parameters are completed, and then the online adaptive prediction of the remaining life is realized. Finally, the model is tested by numerical simulation and the measured data of a gyroscope in an inertial navigation system. The results show that compared with the traditional linear stochastic degradation model, the model can effectively describe the memory effect of the degradation trajectory and improve the prediction accuracy of the remaining useful life.

KeyWords: Remaining useful life; fractional Brownian motion; memory effect; Maximum likelihood estimation;  Bayesian theory;  gyroscope

项目基金：国家自然科学基金(61900376, 61833016, 61922089, 61773386, 61673311, 61703244)资助

作者简介：高旭东(1995 - )，男，重庆人，硕士研究生，专业方向为剩余寿命预测与健康管理。

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