# Failure Prediction of the Rotating Machinery Based on CEEMDAN-ApEn Feature and AR-UKF Model
## 1 Introduction  
With the development of material science and ultra-micro fabrication techniques, the rotating machinery plays an more and more vital role in modern industry. However, the performance of the rotating machinery would always deteriorate with time, which results in the potential for failure occurrence. Once the failure occurs, it will not only cause huge economic losses but also lead to catastrophic casualties and severe social impacts [1; 2]. Consequently, it is important and significant to address the failure prediction issue of the rotating machinery. Generally speaking, the failure prediction process of the rotating machinery is commonly divided into the two stages: the fault feature extraction stage and the remaining useful life (RUL) prediction stage. Theoretically, the main methods for extracting fault features of the rotating machinery can be classified into three types: time domain, frequency domain, and time-frequency domain. Root mean square (RMS), skewness, and kurtosis are common features of time domain methods [3]. Kurtosis is commonly used to identify early fault because of its high sensitivity [4]. RMS is insensitive to early fault, but it shows strong stability on describing the degradation process of the rotating machinery [5]. [PERSON] et al. first tracked the degradation of the rotating machinery with kurtosis and skewness [6]. Features of time domain possess many merits, such as simple in computation and clear in conception, but they are susceptible to noises. Frequency domain methods are mainly based on Fast Fourier Transform (FFT); thus, center frequency and RMS of frequency are frequently used features. FFT is an averaged chirp frequency feature representation of the signals over the entire time period. Therefore, it cannot reflect frequency domain features of the signals in the local time region, so itis 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; 8; 9; 10], wavelet (WT) [11; 12; 13; 14; 15], and neural network (NN) [16; 17; 18] are common means to extract time-frequency features. [PERSON] et al. used the improved recursive entropy as a health indicator for the performance degradation of bearings [19]. [PERSON] and [PERSON] 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. [PERSON] et al. [23] and [PERSON] 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 [7], and support vector machine [27] (SVM) are typical data-driven methods used for the RUL prediction of the rotating machinery. However, all above methods are still suffering from the deficiencies of low accuracy and the requirements of numerous historical data for training.