# A Hierarchical Sparse Discriminant Autoencoder for Bearing Fault Diagnosis
## 1 Introduction  
It is necessary to monitor the health of rotating parts and diagnose faults in complex working conditions because the working environment of high-speed rotating machinery is usually very harsh and complicated [1, 2]. However, the artificially extracted features of traditional fault diagnosis methods are usually shallow features. Therefore, the research of intelligent fault diagnosis methods based on deep learning methods has received more and more attention. As an important branch of deep learning methods, supervised learning models with powerful feature extraction capabilities and data analysis capabilities have been applied to fault diagnosis [3, 4]. [PERSON] et al. [5] used the strong non-mapping and self-learning ability of the neural network to build a BP neural network model to adapt to the state detection and fault diagnosis of rolling bearings and achieved satisfactory fault classification results. [PERSON] et al. [6] studied the use of the ELM algorithm to classify bearing faults, and experiments show that the performance of the ELM algorithm is better than the BP algorithm. However, many studies have shown that simple supervised models are greatly affected by parameter adjustments and data input. In order to dig deeper into the deep rules of data, unsupervised learning models have begun to be widely studied. Through the transformation of the original data to characterize the deep features of the sample, the common unsupervised learning network is used for feature extraction anddata analysis [7]. In order to obtain good classification performance, the unsupervised model is often combined with the supervised model to form a semi-supervised model to achieve the purpose of adjusting the performance of the unsupervised model with the help of label information to obtain a reliable classification model. [PERSON] et al. [8] proposed an enhanced depth feature extraction method based on Gaussian radial basis kernel function and autoencoder. The advantage of this method is that it can obtain higher test accuracy based on fewer iterations, but the disadvantage is that it requires manual experience to adjust network parameters. [PERSON] et al. [9] proposed a new intelligent fault diagnosis method based on principal component analysis and deep belief network, which can realize reliable fault analysis based on original vibration data, but it is prone to overfitting. As a typical unsupervised learning network, autoencoders have received extensive attention [10; 11]. [PERSON] et al. [12] proposed a frequency domain feature extraction autoencoder network, which uses an asymmetric autoencoder to learn the mapping relationship between time-domain signals and frequency-domain signals and obtains a better clustering effect on bearing data. [PERSON] et al. [13] proposed a rolling bearing fault diagnosis method based on the sparse and nearest neighbor preservation theory deep extreme learning machine, which can unsupervised the deep law of data mining and supervised learning to solve the least square classification diagnosis. The results show that sparsity has a good ability to improve neural network performance. In addition, many studies have also shown that improving the sparsity of the autoencoder can enhance its network performance [14; 15]. Moreover, the introduction of category information into the feature extractor can also enhance the effect of autoencoder feature extraction [16; 17], but most of the existing research still does not consider this approach [18; 19; 20; 21; 22]. Due to the characteristics of deep neural networks, the selection of hyperparameters in the model is still very important [23; 24; 25]. To this end, genetic algorithm [26], cuckoo algorithm [27], gray wolf algorithm [28] and other methods have been used for hyperparameter optimization to improve the performance of neural networks. [PERSON] et al. [29] researched and proposed a GA-SVM rolling bearing intelligent evaluation method based on feature optimization.