# A Collaborative Domain Adversarial Network for Unlabeled Bearing Fault Diagnosis
## 1 Introduction  
Bearings are a critical support component in mechanical transmission systems, and their fault diagnosis is key to ensuring the safe operation of equipment and avoiding economic losses. Numerous intelligent fault diagnosis methods have emerged in the research of bearing fault diagnosis [1; 2]. In the early stages of intelligent fault diagnosis for bearings, scholars proposed diagnostic methods based on shallow machine learning, including extreme learning machines, support vector machines, and Bayesian methods [3; 4]. In recent years, the accuracy of traditional unsupervised learning methods such as clustering, feature statistics, and random forests in identifying mechanical faults has been significantly lower than that of supervised learning neural networks in fault diagnosis [5; 6; 7], attracting widespread attention from both industry and academia. Particularly, deep learning, as a representative data-driven method, has been successfully applied to the field of mechanical equipment fault diagnosis. However, supervised deep learning methods have certain limitations, such as the need for sufficient and complete labeled fault samples and the requirement that the distribution of fault sample features used for training is consistentwith the distribution of real fault sample features [8; 9]. In actual industrial production, due to the variable operating states of equipment such as load, speed, and torque, as well as the impact of mechanical wear and external noise variations, the original vibration signals exhibit different feature distributions. Moreover, most of the collected data are unlabeled, and obtaining a complete labeled fault dataset is very difficult and requires significant human and material resources [10]. Many scholars have conducted extensive research in solving the problem of unlabeled equipment fault diagnosis [11; 12; 13]. The domain adversarial adaptive method is a transfer learning approach that has made significant contributions to solving the problem of fault recognition with few training samples and missing labels [14]. [PERSON] et al. [15] proposed an adversarial adaptive network with periodic feature alignment to facilitate transferable feature learning. Additionally, numerous researchers have integrated both approaches to enhance diagnostic performance [16; 17]. [PERSON] et al. [18] proposed transfer learning by adding domain discriminators on the basis of Adversarial Generative Networks (GANs). For various types of transfer tasks, the transfer learning can be divided into subdomain transfer learning [19], closed domain transfer learning [20], multi-source domain transfer learning, etc. [PERSON] et al. [21] proposed an unsupervised transfer learning model for multi-source domains by transferring multiple sets of source domain data to the target domain. In order to solve the problem of insufficient fault samples that prevent the practical application of intelligent fault diagnosis methods, [PERSON] et al. [22] proposed a Cyclic Consistent Generative Adversarial Network (Cycle GAN). [PERSON] et al. [23] introduced a novel approach called Adversarial Multiple-Target Domains Adaptation (AMDA), which utilizes adversarial learning to ensure that the distribution of sample features in multiple target domains is similar to that in the source domain. While these earlier methods have enhanced diagnostic performance, they primarily rely on adversarial learning for feature distribution alignment and do not address fault class-wise alignment [24]. Most domain adversarial fault identification models focus only on the effect of cross-domain fault identification, paying little attention to the structural issues of network models when the source and target domain distributions cannot strictly coincide. This makes the features prone to defects such as information unidirectionality and focal flattening, leading to bottlenecks in model performance improvement. To address the issue of training with unlabeled data, [PERSON] et al.