A typical way to predict the remaining useful life (RUL) of bearings is to predict certain health indicators (HIs) according to the historical HI series and forecast the end of life (EOL). The autoregressive neural network (ARNN) is an early idea to combine the artificial neural network (ANN) and the autoregressive (AR) model for forecasting, but the model is limited to linear terms. To overcome the limitation, this paper proposes an improved autoregressive integrated moving average with the recurrent process (ARIMA-R) method. The proposed method adds moving average (MA) components to the framework of ARNN, adding the long-range dependence and nonlinear factors. To deal with the recursive characteristics of the MA term, a process of MA component estimating is constructed based on the expectation-maximum method. In the concrete realization of the method, the rotation tree (RTF) is introduced in place of ANN to improve the prediction performance. The experiment on FEMTO datasets reveals that the proposed ARIMA-R method outperforms the ARNN method in terms of predictive performance evaluation indicators.

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Prediction of the effective number of full charging-discharging cycle is valuable for lithium-ion battery (LIB) replacement and recycling. This paper proposes to construct a cumulative degradation indicator (CDI) to work as a more predictable indicator. The proposed CDI is better than the original degradation indicator (DI) in multiple criteria. In the stage of determining the end-of-life (EoL) threshold, a relevance vector machine (RVM) is introduced to screen a small number of available samples, and to reduce the prediction error. In the experimental verification stage, this paper uses LIB full-life data from NASA to verify the early and long-term prediction performance of RCDC using a small sample. The experimental results show that when the proportion of training data approaches 50%, the prediction error gradually converges to the actual value.

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