## 1 Introduction
The results demonstrated that the strategy generated clear, clean fused images, without the noise caused by up-sampling of infrared information. In the GAN approach, the joint distribution of latent representations was sought by adversarial layers [21; 22]. After adversarial learning, the trained latent representations were well-aligned to explain the co-occurrence configurations of the fused images. [PERSON] et al. [23] presented a multichannel GAN for generating traffic signs. In contrast to other existing approaches, the proposed method processed multiple channels with different textures and resolutions. Similarly, the principle of GAN has been applied to fault diagnosis. Usually, the testing data from different machine-fault conditions are unavailable for training; however, deep generative neural networks can provide reliable diagnoses by artificially generating training samples [24]. In practical working conditions with data-acquisition equipment, the achievable fault data are really limited. Furthermore, the problem of fault types being unevenly distributed also restricts the diagnostic accuracy. To solve these problems, [PERSON] et al. [25] presented an imbalanced fault diagnosis method using GAN. Moreover, a detailed comparative study is provided in this paper. Considering the mode collapse of GAN, [PERSON] et al. [26] presented a deep learning method to identify different failure modes of gears. However, the study did not consider the robustness of the model under different operating  
Figure 1: The relationship between performance and data volume. and faulty conditions, such as different workloads and fault sizes. In addition, the quality of the generated data needs to be analyzed. Mode collapse is another challenge of the GAN model [27]. A novel GAN model with a gradient penalty term was designed to avoid model collapse, thereby ensuring model performance. This paper combines the results of deep learning network applications in other fields with the characteristics of a vibration signal. The SDAE [28] was used to mine implied feature information from complex vibration signals. Compared to the prime deep learning for complex fault diagnosis, the superiority of SDAE is that it uses the depth structure to mine the essential information. In addition, SDAE is robust, which reduces the influence of noise on the recognition results to enhance their accuracy. Furthermore, GAN solves the problem of insufficient SDAE training samples. We built a novel deep learning system with data augmentation called GAN-SDAE based on waterfall model fusion. For fault diagnosis of complex vibration signals, a single method is not continuously accurate or effective in considering the limitation of the fault samples. Model fusion includes the combination of models that realize different functions and has been widely used in different fault diagnosis fields [29; 30]. The fault diagnosis method based on model fusion can complement the advantages of different models and make up for the shortcomings. The GAN model solves the limited fault samples and the SDAE model analyzes the fault types. So, the GAN and SDAE models are integrated and optimized. The GAN-SDAE system for fault diagnosis can greatly improve the ability and accuracy of fault diagnosis. Moreover, the uncertainty of the GAN-SDAE system is analyzed to assure the system stability. In this paper, we first review the fault diagnosis, which is the basis for building a new model. Secondly, we introduce the GAN data augmentation, and the generated training data are used in the SDAE model training. This process actually constructs the GAN-SDAE system. The accuracy of the GAN-SDAE system is then analyzed and the system is repetitively tested to analyze the system uncertainty. Finally, the usefulness of the proposed system is demonstrated using two examples of bearings and gears. Based on the above introductions, the novelties and highlights of this paper are as follows:  
1. The existing GAN model is improved, by designing a gradient penalty term to avoid model collapse. 2.