In recent years, a notable development for predicting the remaining useful life (RUL) of components is prognostics that use data-driven approaches based on deep learning. In particular, long shortterm memory networks (LSTMNs) have been successfully applied in RUL prediction. However, to the best of our knowledge, these deep learning-based prognostics do not take into account uncertainty, and their prediction performance needs improvement. Bayesian model averaging (BMA) is a very useful ensemble

more »

... method because it can quantify uncertainty. In this paper we propose a deep learning ensembled prediction approach based on BMA and LSTMNs. We constructed multiple LSTMN models with different subdatasets derived from the degradation of training data. Then, BMA was used to integrate the LSTMN submodels into one framework for a reliable prognostic. The main advantages of this method are that it 1) provides uncertainty management by postprocess forecast ensembles to create predictive probability density functions (PDFs) and generate probabilistic predictions with uncertainty intervals using BMA and 2) it improves prediction performance by ensemble multiple deep learning submodels (trained with different subdatasets) with corresponding weights calculated by the posterior model probability of the BMA. Finally, we introduced an online iterated training strategy for the BMA algorithm to realize higher prediction performance than that of an offline training strategy. In the experiments, we used lithium-ion battery data sets from the Center for Advanced Life Cycle Engineering at the University of Maryland. The results demonstrate the effectiveness and reliability of our proposed ensemble prognostic approach. INDEX TERMS Deep learning, LSTMN, BMA, ensemble approach, prognostic. II. RELATED WORK A. LONG SHORT-TERM MEMORY NETWORKS LSTMNs belong to the family of (deep) RNNs and are capable of addressing the RNN vanishing gradient problem [37] .