# Improved Hierarchical Adaptive Deep Belief Network for Bearing Fault Diagnosis
## 1 Introduction  
Mechanical equipment failures in rotating machinery, such as aircraft engines, are usually caused by damage and malfunction of critical components. Although regular maintenance and forced retirement can improve the safety and reliability of equipment operation, these solutions result in a heavy economic burden and waste of resources. According to statistics, in rotating machinery that uses rolling bearings, approximately 40% of the mechanical failures are due to bearing damage [1]. Therefore, effective fault diagnosis of these key components can provide a strong basis for the evaluation of the operational status of mechanical equipment, thereby reducing maintenance costs [2]. The traditional methods based on signal processing mainly use related expertise to extract faulty components from initial noisy signals. Currently, signal processing methods based on time-frequency analysis have caught the attention of scholars, including empirical mode decomposition, wavelet packet transform, short-time Fourier transform, and so forth [3; 4; 5]. [PERSON] et al. [6] diagnosed the rubbing fault by extending variational mode decomposition method. [PERSON] et al. [7] combined independent component analysis with empirical model decomposition to separate the bearing fault components in wind turbine gearboxes. [PERSON] et al. [8] used the square envelope analysis to study the performance degradation evaluation under Gaussian noise. [PERSON] et al. [9] advanced a strategy that combines intrinsic characteristic-scale decomposition and turntable Q-factor wavelet transform to detect the early bearingfault. Improved Local Mean Decomposition (LMD) can effectively diagnose bearing fault types by expanding the sides of the vibration signal to suppress edge effects [10]. Fault-related features have been revealed successfully in the aforementioned applications. However, satisfactory performance is achieved on the basis of professional knowledge, a requirement that is sometimes difficult for field maintenance personnel to meet. On the basis of these considerations, the machine-learning-based approaches tailored for fault diagnosis, such as artificial neural network (ANN) [11], decision tree [12], and support vector machine (SVM) [13] have been gradually developed. The goal is to reduce human intervention as much as possible and move toward an intelligent direction. As a result, deep learning methods are proposed, inspired by the artificial intelligence and machine learning [14], which correspond to traditional shallow machine-learning methods. Since its introduction, deep learning has shown strong capabilities in speech recognition, image processing, and other fields. Especially, some classic networks such as deep belief network (DBN) [15] and convolutional neural network (CNN) [16] have been successfully ameliorated for fault detection. [PERSON] et al. [17] presented a new model based on DBNs, with improved logistic sigmoid units for fault identification of wind turbine gearboxes. [PERSON] et al. [18] used CNN to analyze the raw bearing vibration signal, thereby achieving fault recognition successfully. The diagnosis result was considerably better than that of the traditional ANN. Moreover, a two-layer hierarchical detection network based on CNN was proposed in [19], for the classification of bearing fault types and the detection of the fault severity. [PERSON] et al. [20] suggested an unsupervised feature learning procedure using deep denoising autoencoder for diagnosing rotating mechanical components, as well as discussed the influence of input dimensions and hidden layer numbers on diagnostic results. To improve the reliability of fault detection, [PERSON] et al. [21] presented a novel multisensor data-fusion method optimized by Sparse Autoencoder (SAE) and DBN. [PERSON] et al. [22] proposed a new deep learning model to realize intelligent fault identification of bearings under a strong noise environment. [PERSON] et al.