考虑不完美维修的随机退化设备剩余寿命自适应预测方法

在现有考虑不完美维修的随机退化设备剩余寿命预测研究中，通常仅考虑维修活动对退化状态或退化速率的单一影响，仅有考虑二者双重影响的研究，忽略了退化设备的个体差异性。鉴于此，提出一种基于多阶段扩散过程的自适应剩余寿命预测方法，同时考虑不完美维修活动对设备退化状态和退化速率的影响，并利用随机游走模型描述退化速率随观测数据的更新过程以表征设备的个体差异性。基于历史退化数据，利用极大似然估计法得到退化模型参数的初值；基于状态观测数据，利用卡尔曼滤波算法和期望最大化算法自适应的更新模型参数。利用卷积算子和蒙特卡洛方法推导得到了首达时间意义下设备剩余寿命的概率密度函数。最后，通过仿真算例和陀螺仪的实例研究验证了所提方法的有效性和优越性。

Remaining Useful Lifetime Prognostic Approach for Stochastic Degradation Equipment Considering Imperfect Maintenance Activities

In the existing research on the remaining useful life prediction of stochastic degradation equipment with imperfect maintenance, only the single influence of maintenance activities on the degradation state or degradation rate is usually considered,while the research that considers both two influences ignores the unit-to-unit variability of degradation equipment. In view of this, an adaptive remaining useful life prognostic approach based on a multi-stage diffusion process is proposed, which takes into account the influence of imperfect maintenance activities on the degradation state and degradation rate, and describes the update process of degradation rate with observation data by using a random walk model to characterize the unit-to-unit variability of equipment. Based on the historical degradation data, the initial values of degradation model parameters are obtained by the maximum likelihood estimation method. Based on the state observation data, the Kalman filtering and expectation-maximization algorithm are used to adaptively update the model parameters. The probability density function of the remaining useful life in the sense of the first hitting time is derived by the convolution operator and the Monte Carlo method. Finally, the effectiveness and superiority of the proposed approach are verified by the simulation example and the case study of gyroscopes.