# Dynamic Simulation Model-Driven Fault Diagnosis Method for Bearing under Missing Fault-Type Samples
## 1 Introduction  
In modern industrial production, one of the most important parts of rotating machinery is bearing. Its health status is critical to maintaining the stable operation and safe use of the rotating machinery [1], therefore it is important to develop advance condition monitoring and accurate fault identification of bearings [2]. Due to advances in computer technology, data-driven algorithms based on an increasing number of computer vision and artificial intelligence fields, such as transfer learning [3], support matrix machine [4], graph convolution [5] and convolutional autoencoder [6] have greatly enriched the fault diagnosis methods of rotating machinery. Deep learning-based approaches have strong feature learning capability and can imitate the learning process of the brain by creating deep networks to depict the rich internal information of the data and ultimately achieve accurate fault diagnosis [7; 8; 9; 10].  
[PERSON] et al. [11] firstly proposed the generative adversarial network (GAN) that can generate new samples in an unsupervised learning way to extract the distribution properties of data. GAN is also widely used in the field of fault diagnosis. [PERSON] et al. [12] developed a novel framework for imbalanced fault classification based on Wasserstein generative adversarial networks with gradient penalties (WGAN-GP). [PERSON] et al. [13] developed a new ACGAN framework by adding an independent classifier. They introduced the Wasserstein distance and spectral normalization (SN) in the loss functions of GAN. [PERSON] et al. [14] introduced the attention module to guide WGAN-GP to enhance the learning ability. It can be seen that GAN-like models have significant advantages in fault identification and diagnosis due to their characteristics.  
It is observed that the above studies are aimed at generating more trustworthy sample data and enhancing training datasets by optimizing and improving the structure of the GAN when all fault-type samples are available for training. However, several types of fault signal data may occasionally be missing, leading to a failure to identify rare fault categories in practical engineering applications. Hence it is essential to build a model to replace and complement the missing fault samples.  
To resolve the above deficiencies, a new model-based GAN and dynamic simulation model of fault bearing is proposed in this paper for rotating machinery under missing fault samples. Firstly, to obtain vibration responses of bearings in various states and get the missing fault samples, a rotor-bearing system simulation model is developed. Secondly, gradient normalization (GN) [15; 16] is adopted to enhance the feature learning ability of the Wasserstein generative adversarial network (WGAN). The proposed WGAN-GN is used to generate samples for the fault types, and then the generated samples are combined with the original samples into a complete dataset. Next, a stacked autoencoders (SAE) model is employed to extract advanced features from the complete dataset and achieve accurate fault classification. Finally, the viability and robustness of the proposed method are confirmed by several experimental instances. The following is a summary of the main contributions:  
1. A rotor-bearing system simulation model is built to obtain simulation signal of the missing fault type samples.
2. A novel WGAN-GN method is proposed to generate replaced data under missing sample conditions.
3. The generated simulated data is joined with the raw data to create a complete dataset for SAE network training to achieve the extraction of features and fault classification.  
This paper is organized as follows. The theoretical foundation is explained in Section 2. The framework and steps involved in the proposed method are described in Section 3 in detail. To demonstrate the efficacy of the method, two case studies are applied in Section 4. Finally, the findings are condensed in Section 5.