## 1 Introduction  
Fault diagnosis is necessary for mechanical equipment in modern industries [1; 2; 3]. Through condition monitoring, the signals of various sensors are extracted and analyzed for fault diagnosis. Because of the inconstancy and enrichment of the response signals under harsh operating conditions, it is difficult to identify the failure mode of mechanical systems. Deep learning algorithms for diagnosing machinery faults have become prevalent owing to their robustness and capacity for adaptation. Deep architectures of computational layers and neurons are the foundation of deep learning. [PERSON] et al. [4] proposed a semi-supervised and deep ladder network (SSDLN); with few labeled samples, the model is trained through a high-dimensional feature space to diagnose gear failures. [PERSON] et al. [5] presented a novel unsupervised learning algorithm based on the generalized norm of the feature matrix for intelligent fault diagnosis. The feature sparsity was successfully measured by optimizing the objective function. However, in real engineering scenarios, it is difficult to identify useful details in the recorded fault signal. Therefore, it is necessary to reduce the feature dimensions. [PERSON] et al. [6] proposed a spider monkey optimization (SMO)-based deep neural network (DNN) model. Compared to the classic DNN model, the SMO-DNN achieved a dimensionality reduction and accurate classification. As another classic deep learning model, the deep belief network conducts information fusion through data reduction [7]. [PERSON] et al. [8] presented an unsupervised fault-diagnosis model using the sparse-filtering algorithm. The model uses the learned fault features to classify different fault types. Current deep learning is inherently challenged by an unstable network structure. It is necessary to analyze the robust stability of deep neural networks [9]. Compared to other deep learning methods,the sparse denoising auto-encode (SDAE) model is established by a series of auto-encoders and has a stable deep network structure with a layer-by-layer nature [10]. The SDAE is widely used in fault diagnosis of rotating machinery. Typical examples are gears and bearings [11; 12]. Another problem of deep learning is that many training samples are required. Deep learning models are traditionally big data driven and an obvious lack of sufficient training affects the accuracy of the model [13]. Based on a relatively small dataset, [PERSON] et al. [14] presented a deep learning-enhanced framework that had a satisfactory accuracy. However, in practice, there are very few fault samples affected by cost. In traditional mathematical statistics, the definition of small sample data is that of samples of size \(n\leq 30\)[15]. Obviously, most of the fault samples are small sample data, which lead to limitations in the data [16]. This data limitation results in poor model performance, as shown in Figure 1[17]. The deep learning model of fault diagnosis is trained by a few training samples. Given the limited fault data, the model training is often insufficient, resulting in an inaccurate fault diagnosis. Therefore, data limitation is a huge challenge for deep-learning model training. So, we propose the generative adversarial network (GAN) data-augmentation to effectively solve the data-limitation problem. In the current era of fierce artificial intelligence, GAN can productively solve the problem of small-sample data with insufficient data volumes. Based on artificial intelligence theory, GAN provides enough data for deep learning training. The GAN is a data-augmentation model proposed by [PERSON] [18]. It has been proverbially applicable to image processing. [PERSON] et al. [19] proposed a new method called 3D GAN to calculate the full-dose images with low-dose ones. The conclusion showed that the 3D GAN method outperformed the benchmark methods. Similarly, [PERSON] et al. [20] presented a GAN method to fuse the images with different resolutions.