基于不完美先验信息的随机系数回归模型剩余寿命预测方法

剩余寿命预测是设备预测与健康管理的核心问题，准确的剩余寿命预测可以在故障发生前进行有效的维护保养，以减小设备故障发生的概率。针对实际剩余寿命预测中先验信息不足或缺乏的问题，提出一种克服不完美先验信息影响的启发式剩余寿命预测方法。首先，利用非线性随机系数回归模型进行退化建模。其次，证明了基于单个设备现场退化数据，期望最大化（EM）算法的参数估计结果收敛于极大似然估计（MLE）算法的参数估计结果，并提出一种合理融合先验信息和现场信息的启发式剩余寿命预测方法。最后，通过数值仿真数据和实际锂电池退化数据对提出的结论和方法进行了验证，结果表明:启发式剩余寿命预测方法相比传统贝叶斯方法能够较好地克服不完美先验信息的影响，更为准确的预测设备地实际剩余寿命。 

Remaining useful life prediction method based on random coefficient regression model with imperfect prior information

Remaining Useful Life (RUL) prediction is a core problem of equipment prognostics and health management. Accurate RUL prediction can make effective maintenance management before the failure occurs to reduce the probability of equipment failure. A heuristic RUL prediction method is proposed to overcome the problem of imperfect prior information or lack of prior information in actual RUL prediction. First, the nonlinear Random Coefficient Regression (RCR) model is used for degradation modelling. Then, the relationship of the parameter estimation results between the Expected Maximization (EM) algorithm and the Maximum Likelihood Estimation (MLE) method based on the field degradation data of single equipment is studied and the conclusion that the result of EM algorithm finally converges to that of MLE method is obtained. Based on this conclusion, a heuristic RUL prediction method is proposed, which fuses both prior information and field information. Finally, the proposed results and algorithm are estimated by the numerical simulation data and practical degradation data of lithium battery. The experimental and simulation results show that, compared to the traditional Bayesian method, the heuristic RUL prediction method can overcome the impact of imperfect prior information and has higher prediction accuracy.