# An Ensemble Learning and RUL Prediction Method Based on Bearings Degradation Indicator Construction
## 1 Introduction  
Rolling bearings are one of the key components supporting rotating shafts in rotating mechanical equipment. Bearing failure is often considered one of the most common causes of mechanical equipment failure [1; 2]. Bearing reliability is critical for the reliability, durability, and efficiency of mechanical equipment. Any accidental failure of a bearing may cause have various negative effects [3; 4] ranging from production downtime to casualties or even catastrophic environmental pollution. To address these issues, online detection of bearing health is urgently required to effectively enhance the safety of mechanical equipment operation [5; 6; 7], predict bearing remaining useful life (RUL), and to implement an action plan to prevent catastrophic events and extend the bearing life cycle [7]. Advances in bearing RUL prediction technology have provided increasingly powerful technical support for intelligent bearing RUL prediction and health management [8; 9; 10]. In the past few decades, the research has achieved theoretical results that have been widely applied. Most bearing RUL prediction methods apply a model-based or data-driven approach [11; 12]. The model-based method mainly relies on an accurate mathematical model of bearing degradation, but bearing degradation is a complicated and difficult problem [13]. The data-driven approach uses data mining and artificial intelligence [14] to explore the potential relationship between current bearingstate data and RUL. Data-driven methods have become a promising approach. Data-driven analysis methods can be used as objective and rational tools to understand the data and make decisions [15; 16]. For example, in the field of life sciences [17], the data-driven approach was used to conduct diagnosis [18; 19]. In the field of engineering applications, the data-driven method has been used to obtain information on road lighting infrastructure. Based on the feature selection technology of supervised and unsupervised filters, the dimension of feature space was reduced to classify and identify lamps, which was ultimately used to evaluate and optimize the performance of the street lighting at night [20]. Some experts used ensemble data-driven statistical models to map comparative shallow landslide susceptibility to obtain the relationship between heavy rain and shallow landslides [21]. The deep learning approach [22] has advantages for bearing RUL prediction [6], providing new opportunities for this research field [10; 23]. A typical deep learning framework consists of four phases: data acquisition and processing, feature extraction and calculation, learning model building, and prediction. In today's big data era, the premise of accurate bearing RUL prediction is to extract as much effective information as possible from massive amounts of monitoring data [24]. However, the data are increasingly complicated and high-dimensional. The irrelevant and redundant features in these high-dimensional data increase the complexity of the learning model, and can even reduce the prediction accuracy, which creates the problem known as \"dimensional disaster\" [25]. In the feature extraction and calculation stage, deep learning has some shortcomings: the time-domain features are less able to reflect the bearing degradation process details, the frequency-domain features are not sensitive to medium-term bearing degradation, and the time frequency-domain characteristics of wavelets can cause information loss. These three problems usually lead to information redundancy and increases the neural network nodes, which in turn leads to difficult training and over-fitting of the mode [6]. In this process, the traditional algorithm mainly finds a set of features with high contribution rate. Some authors [26; 27; 28] defined different feature types based on the contribution of features to degradation information (DI). In this case, feature correlation is a measure of the degradation-stage-related information.