基于非线性分数布朗运动的光电设备剩余寿命自适应预测

Adaptive Prediction of Remaining Useful Life for Optoelectronic Equipment Based on Nonlinear Fractional Brownian Motion

在现有研究中,通常采用无记忆效应的马尔可夫过程模型来描述光电设备的随机退化,忽略了其退化过程中状态之间的长期相关性。鉴于此,首先,基于非线性分数布朗运动提出了一种具有记忆效应的随机退化模型,用于描述测量误差与随机效应影响下的光电设备退化过程;在此基础上,基于弱收敛理论推导得到了首达时间意义下设备剩余寿命的近似解析式。其次,分别采用极大似然估计算法与贝叶斯推理完成了模型参数的离线估计与实时更新,进而实现剩余寿命的自适应预测。最后,将所提方法应用于GaAs激光器的性能监测数据中,实验结果表明所提方法能有效提高光电设备剩余寿命的预测精度。

In the existing studies, the Markov process model without memory effects is usually used to describe the random degradation of optoelectronic equipment, ignoring the long-term correlation of states in the degradation process. In view of this, we firstly proposed a random degradation model with memory effects based on nonlinear fractional Brownian motion to describe the degradation process of optoelectronic equipment under the influence of measurement errors and random effects. On this basis, we employed the weak convergence theory to derive the approximate analytical formula of the remaining useful life of equipment in the sense of the first hitting time. Secondly, we adopted the maximum likelihood estimation algorithm and Bayesian inference to complete the offline estimation and real-time update of the model parameters, thus realizing the adaptive prediction of the remaining useful life. Finally, the proposed method was applied to the performance monitoring data of GaAs lasers. The experimental results show that the proposed method can effectively improve the prediction accuracy of the remaining useful life of optoelectronic equipment.