Relevance Vector Machine Based Remaining Useful Life Prediction for Traction Systems of High-speed Trains
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摘要: 高速列车牵引系统在运行过程中总是受到诸多不确定因素的影响, 例如, 由于列车的负载、运行环境及元器件的老化引起的不确定性, 不确定因素不可避免地影响牵引系统剩余寿命的预测精度. 为了提高不确定情景下剩余寿命预测的准确性, 本文首先采用改进的相关向量机(Relevance vector machine, RVM)方法, 建立鲁棒性能良好的多步回归模型, 由于t分布比常用的高斯分布更具有鲁棒性, 通过权重和随机误差服从t分布而非高斯分布, 改进了相关向量机回归模型, 随后将超参数的先验一并融入似然函数, 通过最大化似然函数估计未知的超参数, 此外, 利用首达时间方法从概率角度对剩余寿命进行了预测, 最后通过牵引系统中电容器退化的案例, 与传统的相关向量机方法、自回归方法和支持向量机方法进行对比, 验证了所提算法的有效性.Abstract: Traction systems often suffer from many uncertainties during their running processes, such as the inevitable uncertainties caused by the change of loading, operation and usage conditions. In order to improve the accuracy of remaining useful life (RUL) prediction under the uncertain scenario, a robust multi-step regression model is established by the improved relevance vector machine (RVM) method, in which weights and random errors are t distributed rather than Gaussian distributed. Then, unknown hyperparameters are estimated by taking priors of the hyperparameters into consideration. Moreover, the RUL is predicted by the first hitting time (FHT) method in probability perspective. The proposed method is demonstrated by a case study of capacitors degradation in traction systems. The results show the effectiveness of the proposed method.
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图 2 上下端电压从平稳过程到退化过程直至停机的演变趋势
Fig. 2 The voltages evolution from the stationary process to the degradation process
图 3 上下端电压在支撑电容器退化过程中的平均幅值
Fig. 3 The mean amplitude of the upper and lower voltages during the capacitors' degradation
图 4 建模过程中的预测值与真实值进行比较
Fig. 4 The comparison between predicted values and the actual values in the modeling process
图 5 剩余寿命预测值与真实值对比图
Fig. 5 The RUL comparison between the predicted values and the actual values
图 6 高斯分布与
$ t $ 分布拟合效果对比图Fig. 6 The fitting comparison between the Gaussian distribution and the
$ t $ distribution表 1 退化趋势模型中的参数取值
Table 1 The parameter values in the degradation model
SVM RVM 改进RVM 核函数 径向基 高斯 高斯 $ \alpha_i $ / $ 1.0\times 10^{12} $ $ 1.2\times 10^{-6} $ $ \beta $ / $ 2.47\times 10^{-4} $ $ 6.62\times 10^{-4} $ 
下载: 导出CSV
表 2 剩余寿命均方根误差(RMSE)及相对平均偏差(RAD)比较
Table 2 The RMSE and RAD comparison of RUL between different methods
AR SVM RVM 改进RVM RMSE (min) 1.6860 3.5654 2.3905 1.4586 RAD (%) 29.6802 35.8900 20.3468 11.3533
下载: 导出CSV
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