A novel failure prediction method of the rotating machinery is presented in this paper. Firstly, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is applied to decompose the vibration signals of the rotating machinery into a number of intrinsic mode functions (IMFs) and a residual (Res), and the metric of maximal information coefficient (MIC) is used to select eligible IMFs to reconstruct signals. Then, the approximate entropy (ApEn)-weighted energy value of the reconstructed signals are calculated to track the degradation process of the rotating machinery. Furthermore, the Chebyshev inequality is introduced to determine the prediction starting time (PST). Finally, the auto regress (AR) model and unscented Kalman filter (UKF) algorithm are used to predict the remaining useful life (RUL) of the rotating machinery. The method is fully evaluated in a test-to-failure experiment. The obtained results show that the proposed method outperforms its counterparts on failure prediction of the rotating machinery.Appl. Sci. 2020, 10, 2056 2 of 18 is confined for the analysis of the stationary signals. Recently, the time-frequency domain analysis method is a hot spot in this field. Empirical mode decomposition (EMD) [7-10], wavelet (WT) [11][12][13][14][15], and neural network (NN) [16][17][18] are common means to extract time-frequency features. Qian et al. used the improved recursive entropy as a health indicator for the performance degradation of bearings [19]. Rai and Upadhyay combined the ensemble empirical mode decomposition (EEMD) with the energy moment entropy to track the degradation process of bearings [20][21][22]. However, the above three types of methods are based on the assumption of linearity. To some extent, vibration signals of the rotating machinery always show a certain degree of non-stationarity and non-linearity because of the constantly changing frictional forces, resistance forces, and loads between components of the rotating machinery.Currently, RUL prediction methods can be categorized into two kinds: model-based and data-driven. The former has to set up a mathematical or physical model which can express the degradation process of the rotating machinery. Liao et al. [23] and Oppenheimer et al.[24] adopted the Paris crack growth model and the Forman crack growth model to predict RUL with the measured data, respectively. Model-based methods can accurately describe the developing trend of damage variables of the rotating machinery according to certain physical laws. However, most mathematical or physical models can't be updated over time, which will result the poor universality. Recently, data-driven methods have become the research focus because they only need the historical data. Therefore, they are quite applicable to the prediction of complex systems for its adjustability. Kalman filter [25,26], Bayesian network [? ], and support vector machine [27] (SVM) are typical data-driven methods used for the RUL prediction of the rotating machinery. However, all above methods a...