## 2 Background
Another alternative is the data-driven approach, which uses statistical methods, such as random coefficient models [42; 43], Wiener process models [44; 45], or proportional hazards models [46], as well as those that use machine learning models, such as artificial neural networks (ANNs) [47; 48], gated recurrent units (GRUs) [49; 50], long short-term memory (LSTM) [51; 52; 53], or CNNs [32]. These approaches can be effective without requiring expert knowledge in cases where there are large amounts of data available. However, they do not provide a detailed understanding of the underlying physical processes. There are also hybrid approaches that combine elements of both physics-based and data-driven approaches, using physical models to provide a detailed understanding of the monitored machinery, but also using data-driven techniques to simplify the model development. These approaches are effective in cases where there are limited amounts of data but a detailed understanding of the monitored machinery is required [54; 55]. In general, physics-based approaches offer a deeper understanding of physical processes, but they are more complex for model development and validation. On the other hand, data-driven approaches are simpler and more effective with large amounts of data, but they do not offer insight into the underlying physical processes. Hybrid approaches offer a compromise between accuracy and simplicity. Most of the works using data-driven approaches for RUL prediction use the same bearing dataset for both training and testing. [PERSON] et al. (2016) developed a health prognostics technique that uses the Hilbert-Huang transform to extract failure signals based on Spearman's coefficient, and fuses them into a single feature by means of normalized partial derivative weights. The HI curve is then estimated using a recursive likelihood estimation model (RMLE). In the work presented by [PERSON] and [PERSON] (2016), images obtained after applying the wavelet transform are used as input features. A 2D convolutional neural network is used to combine them and a Gaussian process regression (GPR) model is then used to predict the RUL. The Laplacian score (LS) with the LSTM network is used in the work presented by [PERSON] and [PERSON] (2018), using LS to select the best time-domain features and LSTM to predict RUL. [PERSON] et al. (2018) used six time-frequency domain features that were fused using RNNs into a single one. RUL prediction was carried out by using a double exponential model. In the work presented by [PERSON] et al. (2018), convolutional autoencoder (CAE) networks were used to extract features, and a subsequent status degradation model was used to predict the RUL. The robustness of these works was not tested, as they used the FEMTO dataset for both training and testing. Similarly, the same issue is present in the work by [PERSON] and [PERSON] (2018), where time-domain features were extracted manually and then used to predict the RUL by means of a stacked bidirectional LSTM neural network using the JYTU-SY dataset. To cover this gap, this work proposes a health prognostics technique that identifies outer race bearing failures and predicts the RUL of electric motor bearings. The proposed model identifies an unambiguous signature of the outer race bearing failures regardless of the motor-working conditions, which provides it with the necessary robustness to correctly predict the RUL, obtaining accurate results on other datasets where the motor used is different or works under different conditions than the one used for training, without the need for retraining the model. This is a significant contribution as it allows the model to be applied to a wider range of electric motors working at different conditions and potentially improves maintenance schedules for electric motors. Additionally, the ability to predict RUL and identify bearing failures can help prevent unexpected breakdowns and improve the overall reliability and efficiency of the electric motors.