## 1 Introduction  
Rolling bearings are widely used in industrial installations and are one of the most important parts of rotating machinery. The running state of rolling bearings is vital for reliable operation of the whole mechanical equipment, as bearing faults represent 41% of all mechanical fault occurrences [1; 2; 3], Mostly equipment faults are caused by rolling bearing faults [4]. Bearing faults account for about 20% among all kinds of gear-box faults [5]. Bearing faults are responsible for 40 to 90% of unexpected induction motor shutdowns [6]. Monitoring and diagnosis bearings faults can reduce the accident percentage by about 75%, according to statistical data, and the corresponding maintenance cost is cut down by 25-50% [7]. Predicting the residual life and performance degradation trend of rolling bearings have become a research hotspot. It is also a very important part of Prognostics and Health Management (PHM) [8; 9]. Much of the literature has employed a variety of techniques for predicting bearings' residual life. There are many data-driven technologies; traditional prediction methods include regression-based models [10] such as the Wiener process [11], Gamma process [12], random filtering model [13], Hidden Markov model and semi-hidden Markov model [14; 15]. For nonlinear systems, there is pattern recognition and machine-learning technology. In recent years, artificial neural networks and machine learning have been applied to the rolling bearings research field. In [6], Artificial Neural Networks models were proposed to estimate the remaining useful life of a defective bearing. In References [16; 17], the authors proposed variation mode decomposition and a deep belief network to diagnosis rolling bearing faults. In [18], the authors proposed using high-orderdifferential mathematical morphology gradient spectrum entropy and an extreme learning machine to predict bearing performance. Reference [19] used artificial intelligence and machine-learning approaches to design a classifier. The wavelet decomposition and support vector data description (SVDD) were introduced to train and predict health prediction index of rolling bearings in the whole life-cycle in [20]. In [21], the authors proposed the prediction residual life model of rolling bearings based on an optimized support vector machine (SVM), and parameters of the SVM model were optimized using phase-space reconstruction and the nearest point of neighbor domain method. Reference [22] put forward Principal Component Analysis (PCA) and Least Squares Support Vector Machines (LS-SVM); the LS-SVM model was built and trained for bearing degradation process prediction, and the multi-features fusion technique PCA was used to merge the original features and reduce the dimension. In [23], proportional risk model and logarithmic regression model were introduced to predict bearing residual life. The residual life of rolling bearings in helicopters was predicted using mainstream approaches and their basic framework in [24]. Reference [25] used feature spectrum and SVM classifier to predict the residual life of rolling bearings; the whole life-cycle of the monitored bearing was divided into different stages by a SVM classifier. The degradation state of the rolling bearing can be assessed by comparing distance between the newly measured data and the trained dataset. [PERSON] et al. [26] proposed using SVR based on a soft computing model to predict the residual life of rolling bearings. In short, research on the residual life of bearings has become a hotspot, and many related research literatures have appeared in this field. This paper presents a new method to predict the residual life of rolling bearings, based on the WCDPSO-KELM and Ensemble Empirical Mode Decomposition (EEMD) method.