# Study on EEMD-Based KICA and Its Application in Fault-Feature Extraction of Rotating Machinery
## 1 Introduction  
The faults of gears, rolling bearings and shafts of rotating machinery are disastrous for the whole machinery. Many studies on fault diagnosis of rotating machinery have been published [1; 2; 3]. However, due to cost issues and limited monitoring environments, multiple sensors cannot be installed on rotating machinery, and sometimes it is even single-channel monitoring. In order to acquire more fault information of single-channel vibration signals of rotating machinery and improve the efficiency of fault diagnosis, many feature extraction methods have been proposed, such as wavelets [4; 5], empirical mode decomposition (EMD) [6; 7], ensemble empirical mode decomposition (EEMD) [8; 9], variational mode decomposition (VMD) [10; 11] and so on. However, these methods have the problem that the extracted features sometimes are not clear enough, they cannot estimate the number of fault signals, and they need to be searched artificially from all component signals. In recent years, blind source separation (BSS) has been applied more and more to diagnose the faults of rotating machinery [12; 13]. The goal of BSS is to estimate latent signals from the mixed signals without any knowledge of the mixing process. Kernel-independent component analysis (KICA) is one of the most famous algorithms of BSS [14; 15]. The vibration signal of large rotating machinery often mixes several signals and shows a strong nonlinear characteristic. The advantage of KICA is that both linear signals and nonlinear signals can be separated.  
Estimating the number of latent signals accurately is an important prerequisite for an effective separation of a blind signal. The typical methods are spatial smoothing rank (SSR) [16; 17] and information theory [18; 19], but they all have some limitations, such as signal-to-noise ratio (SNR).  
Singular-value decomposition (SVD) is a nonparametric technique [20; 21]. Listing the singular values in descending order first, the sequence number of the maximum ratio of neighboring singular values (NSVR) can be applied to estimate the number of source signals, and it has a good estimation effect under a large number of coherent signals, as well as low SNR.  
In this paper, a fault-feature extraction method of single-channel vibration signals based on EEMD-based KICA is proposed, and the number of fault signals is estimated by SVD. The three experimental analyses show that this method has a better performance than wavelets, EMD, VMD and EEMD to extract the fault features of rotating machinery. Its advantage is that the number of fault signals of a single-channel vibration signal can be estimated and the extracted fault features are obvious. This method only needs to input a single-channel vibration signal, and the outputs are fault signals and number, without artificial selection, which improves the efficiency of fault-feature extraction.  
The structure of this paper is as follows: The theory of EEMD, correlation coefficients, SVD and KICA are introduced in Section 2. The mathematical model of the proposed method is in Section 3. The performance of the proposed method with faulty gear is evaluated by an experimental analysis in Section 4.1, and the performance of the proposed method with a faulty rolling bearing is evaluated in Section 4.2. In Section 4.3, a faulty shaft experiment proves the effectiveness of the proposed method. The conclusion of this paper is presented in Section 5.