# A Hierarchical Decision Fusion Diagnosis Method for Rolling Bearings
## 1 Introduction  
The rolling bearing is one of the most frequently used parts in all kinds of mechanical equipment. About 30% of the faults in rotating machinery are caused by bearing faults, and the operating state of them will directly affect the machine's performance [1, 2]. Periodic load and impact are the main causes of rolling bearing wear, cracking, spalling and other failures [3]. Therefore, the importance of rolling bearing condition monitoring and fault diagnosis has been increasingly recognized and has drawn extensive attention in the past decades [4, 5]. As the vibration signals contain abundant bearing state information, vibration-based methods have been widely used in the past few decades. Common vibration signal feature extraction methods include time-domain analysis [6], frequency domain analysis [7], time-frequency analysis [8, 9] and other nonlinear analysis methods [10, 11, 12]. Conventional time-domain or frequency-domain methods have difficulty extracting minor fault information from rolling bearing vibration signals with background noise [13]. Therefore, the vibration signal processing methods came into being, such as sparse decomposition [14], empirical mode decomposition (EMD) [15], ensemble local mean decomposition (ELMD) [16], short time Fourier transform (STFT) [17], wavelet transform (WT) [18], wavelet packet transform (WPT) [19], spectral kurtosis (SK) [20], fast spectral kurtosis (FK) [21], etc. A number of cases have shown that wavelet packet decomposition combined with time-domain analysis is an effective feature extraction method [22]. However, time-domain features are diverse; thus, the selection of time-domain features has become the focus of research. The traditional fault diagnosis method of rolling bearings is based on a classifier for pattern recognition of rolling bearings, while fault detection, isolation and degree estimation are realized [23, 24, 25]. However, this kind of method requires a large number of training samples and high representative features, which can easily lead to misdiagnosis. Inorder to reduce the risk of misdiagnosis caused by the complexity of the diagnosis system, [PERSON] [26] proposed a hierarchical diagnosis network based on deep learning to identify the fault mode of rolling bearings using a two-layer diagnosis network. The fault location and fault degree were evaluated respectively. The results showed that the method has high reliability. However, most bearings are running in normal condition. The contingency of fault occurrence makes it very difficult to collect fault data and establish complete diagnosis knowledge, so the double-layer diagnosis network will face the problem of sample imbalance [27]. In addition, the key step of rolling bearing fault diagnosis is to extract the appropriate eigenvalue from the bearing signal as the diagnostic index and to realize the fault diagnosis of the rolling bearing by setting the threshold of the diagnostic index [28]. However, feature extraction and selection mainly depend on human experience, and fault diagnosis based on a single feature will be affected by external environmental factors or human factors and the result of classification will be unstable [29]. How to obtain fault diagnosis results with strong reliability and high stability and minimize the influence of sample imbalance on bearing fault diagnosis is one of the challenges of rolling bearing fault diagnosis. Aiming at the above problems, a hierarchical back propagation neural networks (BPNNs) diagnosis method of rolling bearings based on decision fusion is proposed. The first layer is the fault detection decision fusion network, the second layer is the fault isolation decision fusion network and the third layer is the fault degree estimation decision fusion network. When the bearing is in normal condition, only the first layer is activated and the calculation cost is low, which overcomes the problems in the literature [26]. Hierarchical diagnosis architecture avoids the difficulty of neural networks training caused by incomplete raw data.