## 1 Introduction  
In recent years, interest in prognostics and health management (PHM) has rapidly increased across industry. PHM includes machine maintenance and prognostics, and aims to maximize machine availability and reliability. Unexpected machine breakdown can result increased production downtime and maintenance costs and reduced productivity. Therefore, remaining useful lifetime (RUL) prediction is crucial for determining the condition of machines and establishing a maintenance strategy [1; 2; 3; 4]. Vibration sensors are widely used to monitor the condition of the machine. Therefore, RUL prediction methods using vibration signals are actively studied in the industry and academia. RUL prediction is divided into two major categories: model-based (i.e., physics-based) methods and data-driven methods. The model-based methods derive mathematical or physical models to estimate the degradation process of the machine. The commonly used models include Markov process, Wiener process, and Gaussian mixture model [3]. These methods rely on the expert's domain knowledge of the failure mechanism. However, in practice, creating a robust mathematical model is difficult because of the complex and noisy working environments [5]. On the contrary, data-driven methods derive their health indicators (HIs) from measured data, e.g., vibration signals, using signal processing and machine learning techniques. Data-driven methods can be limited when the collected data is insufficient or uncertain. However, if massive data are available, degradation trends can be estimated without physical domain knowledge. Data-driven methods are more flexible and easier to apply to the system than model-based methods. Particularly, with the development of advanced sensors and computing technologies, data-driven prognostics methods have become much more popular in recent years [6]. In this study, we focus on data-driven methods to predict the RUL from vibration signals. The general framework of data-driven prognostics methods comprises three steps: data acquisition, HI construction, and RUL prediction [7]. The performance of RUL prediction relies on the HI construction step. Therefore, the most important challenge is to extract representative features from the measured signals. A HI that is properly designed by using high-quality features can efficiently monitor the degradation of bearings [8]. Many studies related to feature extraction for prognostics have been conducted [8; 9; 10]. Time domain and frequency domain analyses are traditional methods for extracting features from vibration signals. [PERSON] et al. [11] extracted 14 time domain features using statistics such as root mean square, mean, variance, and crest factor to denoise the raw signal and capture the degradation trend. Time domain features are suitable for stationary signals. However, they may be sensitive to changes in the signal and could inherit nonlinearity [12]. Frequency domain features can describe additional information that cannot be observed in the time domain because of their superior ability to identify and isolate frequency components [13]. Time-frequency domain features consider both time and frequency domains. Generally, the vibration signal of a bearing is nonstationary and has a weak defect signal within a strong background of noise. Time-frequency analysis is a powerful and effective way to analyze nonstationary and transient vibration signals. Short-time Fourier transform, wavelet transform, wavelet packet decomposition (WPD), and empirical mode decomposition (EMD) have been extensively used to extract features from raw signals [14; 15; 16; 17; 18]. The HI is constructed using comprehensive multi-domain feature information, including time domain, frequency domain, and time-frequency domain. Therefore, researchers have proposed suitable HIs by selecting, extracting, and fusing multiple features. [PERSON] et al. [4] extracted time-frequency features using WPD and EMD techniques. Then, they used self-organizing maps (SOM) to construct a HI confidence value (CV).