###### Abstract
[21] adopted deep convolutional neural networks to extract information from the input data and then used a strong classifier-light gradient boosting machine (LightGBM) to replace the fully connected layer of deep convolutional neural networks to improve the accuracy of RUL prediction. [PERSON] et al. [22] proposed a convolutional neural network-based multi-task learning method for RUL prediction considering the influence of the health status detection process on RUL estimation. Unfortunately, the CNN-based methods mentioned above lack time memory ability. As such, these methods cannot extract the temporal dependence in the degradation data. In recent years, approaches based on the recurrent neural network (RNN) and its variants have become dominant in RUL prediction. In ref. [23], [PERSON] et al. presented an improved multi-stage long short-term memory network with a clustering method for the RUL prediction of aero-engines, which integrated clustering analysis and long short-term memory (LSTM) to improve the low prediction accuracy of traditional single-parameter and single-stage models. [PERSON] et al. [24] researched an LSTM method with a multi-layer self-attention (MLSA) mechanism for aero-engine RUL estimation. The degradation data characteristics and time step characteristics were extracted simultaneously by the MLSA mechanism, where LSTM was used to capture the degradation process of the system. To suppress the raw signal noise and improve the quality of input data, [PERSON] et al. [25] provided a novel bidirectional LSTM-based two-stream network. One stream came from the raw data and the other from a series of new handcrafted feature flows (HFFs). Then, bidirectional LSTM (BiLSTM) was used to estimate the RUL of aero-engines based on these processed data. Moreover, [PERSON] et al. [26] constructed an integrated deep multiscale feature fusion network (IDMFFN) for aero-engine RUL prediction. Different scale features were firstly extracted by convolutional filters with different sizes, and then a gate recurrent unit (GRU) layer was built to replace the traditional, fully connected layer to obtain more accurate prediction results. [PERSON] et al. [27] put forward a hierarchical scheme with LSTM networks to regard RUL prediction as a bi-level optimization problem; the lower level was used to predict the time series in the near future, and the upper level was used to estimate the RUL by merging the measurement data and the predicted ones obtained by the lower level. Despite the advancement of the above deep learning models, most of them only provide point values of RUL and neglect the prediction uncertainties. In reality, RUL prediction is often impacted by many uncertain factors including data uncertainty imported by noise from the data themselves or the measurement errors of the sensors, changes in operating conditions (also called aleatoric uncertainty) [28; 29], and model uncertainty introduced by limited access to monitoring data (also called epistemic uncertainty) [30; 31]. Therefore, it is necessary to analyze these uncertainties in deep learning to avoid making incorrect decisions. However, these kinds of uncertainties were rarely considered in the existing deep learning-based aero-engine RUL prediction methods [32]. To shorten this gap, in this paper, we construct a novel RUL probability prediction method for aero-engine based on a bidirectional gate recurrent unit (BiGRU) and improved variational Bayesian inference (IVBI) technology to achieve RUL prediction with its confidence interval (CI) as well. Finally, the proposed method is verified using a commercial modular aeropopulsion system simulation (CMAPSS) data set and compared with five other existing models. Experimental studies show the feasibility and effectiveness of our model.