###### Abstract
The RUL prediction sequence is always ignored in this way. In order to get the sufficient data for deep learning model, several data augmentation techniques have been applied in fault diagnosis [28] and RUL prediction [29]. Generative Adversarial Networks (GANs) have been widely used to solve the problem of data imbalance in fault diagnosis [30; 31]. [PERSON] et al. [32] proposed a RUL prediction method based on conditional generative adversarial network (CGAN) and deep gated recurrent unit (DGRU) network. Hundreds of run-to-failure data were used to train the CGAN to generate more data. Then, the DGRU was applied to predict the RUL. However, GAN models still require enough data to train, which is not suitable when only several run-to-failure samples are offered. The RUL prediction sequence is rarely considered in the existing DL-based models. Thus, the uncertainty between the predicted result at different times is always ignored [33]. The accuracy of the predicted result is the only object in the training process. Both the uncertainty and accuracy of the predicted result are important for maintaining the health of the machine. In the existing literature, limited research about the uncertainty of the predicted RUL was offered. In [34], Recurrent Convolutional Neural Network (RCNN) was used for RUL prediction and the variational inference was used to quantify the uncertainty of the RCNN model in RUL prediction. However, only quantifying the uncertainty is not enough. Large fluctuations of the predicted RUL would appear unless uncertainty is controlled. Thus, the uncertainty of the predicted RUL should not only be quantified but also controlled in the actual application to get a reliable and stable prognosis. This paper proposes a RUL prediction method based on data augmentation strategy and Wiener-LSTM network to solve these two problems. During the data augmentation process, the RMS of the monitored vibration signal is calculated to fit the degradation model. Then, the range of parameters in the degradation model can be acquired when fitting different data. Sobol sampling is implemented in each range to reconstruct different combinations of the parameters. Finally, these different combinations of the parameters are substituted into the degradation model to get more generated run-to-failure data. During the process of the RUL prediction by Wiener-LSTM network optimized by PSO algorithm, the Wiener process is used to model the predicted RUL, which can control the uncertainty propagation. Then the LSTM is applied to fit the assumed Wiener process during the iterations. After the training of the Wiener-LSTM model, the predicted RUL is closed to the assumed Wiener process. Thus, a smooth curve without large fluctuations of the predicted RUL can be acquired by the proposed model. In order to embed the Wiener process into the LSTM, a joint optimization strategy is implemented to derive a new loss function. Meanwhile, the PSO algorithm is used here to optimize the hyperparameters in the Wiener-LSTM model. The main contributions of this paper are described as follows:  
1. A data augmentation method based on degradation process modeling and Sobol sampling augments the run-to failure training data;
2. A new loss function for the Wiener-LSTM model is proposed, and the Wiener process is introduced into the LSTM network to control the uncertainty. The rest of this paper is organized as follows: In Section 2, the problem of the RUL prediction methods based on conventional LSTM is proposed. In Section 3, the framework of the proposed method is introduced in detail. In Section 4, the proposed methods are validated on a rolling bearing dataset. In Section 5, the paper is sealed with a conclusion.