###### Abstract
Statistical methods use models with various assumptions to probabilistically predict the RUL [6]. Statistical techniques, such as the Wiener process [13] and gamma process [14] are used for degradation modeling, and Markovian-based models [15] are used as an RUL prediction model for turbofan engines. Artificial intelligence utilizes machine learning methods, mainly deep learning techniques [16]. For supervised learning, signal data needs target values that indicate the degradation process. The PwL function is mainly used to construct a degradation model [17]. This model assumes that the RUL is constant until a certain point of failure. After this point of failure, it decreases linearly. For generalization and reducing the complexity of RUL prediction problems, all engines use the same constant RUL value during the normal/healthy operation of the engines [7; 9; 18; 19]. Deep-learning-based RUL prediction methods have produced significant results for turbofan engines. Several studies on turbofan engines used deep learning techniques, such as recurrent neural networks (RNNs) to analyze time series data. An RNN, which is a deep learning technique for time series data, can successfully obtain short-term dependencies but has problems learning long-term dependencies. A long short-term memory (LSTM) network controls the flow of time-dependent information through gates to overcome the long-term dependency problem. [PERSON] et al. [11] proposed an LSTM model to make RUL predictions using the time-sequence data from the sensors. They achieved better RUL prediction accuracy compared with the hidden Markov and traditional RNN models. [PERSON] et al. [20] used sensor data sequence with the bidirectional long short-term memory (BiLSTM) network for RUL prediction and stated that the BiLSTM network outperformed the traditional machine learning approaches. [PERSON] et al. [21] used sensor smoothing and selection and proposed a deep LSTM network for RUL prediction. They tested the proposed approach using the C-MAPSS sub-datasets FD001 and FD003 [22]. To solve the high-dimensionality problem of C-MAPSS data, an autoencoder (AE) was used to compress the sensor measurements, and a BiLSTM model was proposed with the aim of better prediction [6]. Dual-channel LSTM [19] was used with the first-order difference of sensor measurements and extracted more information about the degradation process of the engines. By classifying the degradation phases, multi-scale LSTM was applied to predict the RULafter the constant value degradation phase [23]. They achieved a 40% reduction in the root-mean-square error (RMSE) for the FD001 dataset. Another deep learning technique, namely, CNN, has been broadly used in turbofan RUL prediction due to its superiority in feature extraction. A deep CNN approach with a time window [9] was applied to normalized raw C-MAPSS data. [PERSON] et al. [24] combined deep CNN with an attention mechanism to extract highly abstract degradation and trend features. Temporal convolution expanded the receptive field for long sequences to improve the prediction performance [25]. [PERSON] et al. [26] also used temporal convolution with an attention mechanism for selecting relevant information from a series of sensor measurements. The multi-scale deep CNN method with different-sized filters was proposed to achieve complex features for the degradation process and had a high prognostic performance [27]. Also, the spatio-temporal attention mechanism with position encoding was applied to capture the temporal relation between features [28]. Various types of CNNs and RNNs have been used in the literature in a hybrid fashion to improve generalization and consider temporal and spatial features of sensor measurements. A CNN and LSTM were combined within a deep network in a parallel manner for complicated prognostic scenarios [29]. The health index (HI), which was calculated from raw sensor measurements, was used as a new time series and fed to the network, which consisted of serial CNN-LSTM layers [30].