## 1 Introduction  
Mechanical big data has the characteristics of large volume, diversity, and high velocity. The prediction of remaining useful life (RUL) has been used as an important parameter for condition-based maintenance decision making [1]. Traditional data-driven prognostic methods have their limitations for processing mechanical big data. Many prognostic methods are developed based on explicit model equations [2]. Therefore, they are largely dependent on human expertise and knowledge in model building and signal processing, and hence are difficult to implement for automatic processing of massive data. These prognostic methods include recurrent neural networks [3; 4], Kalman filters [5; 6; 7], dynamic Bayesian networks [8], \(k\)-reliable decentralized prognosis [9], particle filter-based [10; 11; 12; 13], and combined particle filter and neural networks [14]. In addition, some fuzzy systems-based approaches for prediction have been developed [15]. However, in comparison with fuzzy systems, particle filters take a probabilistic approach, in that the posterior distribution is modeled by sampling from a set of distributions, whereas in fuzzy systems the model output is based on the input variables of fuzzy set membership and an implication of rules. Among all the approaches, particle filters [16] have emerged in recent years as a comparatively good RUL prediction method and are becoming more and more widespread, mainly due to their capability of dealing with dynamic systems characterized with nonlinear and non-Gaussian natures. For example, [PERSON] and [PERSON] [17] showed the superior RUL prediction performance of a particle filter-based approach using the gear data provided by the NASA Glenn Spiral Bevel Gear Test Facility. However, all of the above mentioned methods require either complicated signal processing techniques to extract features from the sensor data, or knowledge of system dynamics to build the explicit model equations. This type of requirement involves manual processing and analysis of data by human experts, and therefore makes these methods unsuitable for automatic data processing and feature extraction for big data. There also may be situations in which these models are unavailable, such as in offshore well drilling and wind turbines, or for some bearings in which online measurements of the damage may not be available, in which the traditional particle filter approach cannot be used [11]. To effectively extract features from massive bearing condition monitoring data and accurately predict bearing RUL, new effective methods are needed. The recent developments in deep learning have provided an attractive opportunity to build advanced RUL prediction methods for big data. Since the introduction of a deep belief network [18], deep belief networks and other deep learning methods have become widely used for big data processing and analysis. Deep learning is capable of extracting useful and important features from data to improve the power of prediction [19]. Equipped with multiple layers of structure, deep learning is also capable of processing massive data and extracting hidden information. One recent successful story of deep learning is AlphaGo by Google Deepmind [20]. AlphaGo has demonstrated the power of deep learning for massive data processing and feature learning by defeating the best human Go player in the world. Deep neural network architectures have been successfully built in various domains such as image recognition, automatic speech recognition, and natural language processing [21]. Recently [22; 23] applied deep learning on raw vibration signals and time-domain features for machine fault diagnostics. In addition to classification problems, deep learning also has promising capability to solve prediction problems. These prediction problems include predicting car traffic [24], weather [25], wind speed [26], and internet traffic [27]. A number of deep learning algorithms have been used for solving prediction problems.