# A Multi-Source Consistency Domain Adaptation Neural Network MCDANN for Fault Diagnosis
## 1 Introduction  
With the increasing complexity and cost of industrial systems, people's tolerance for equipment performance degradation and safety hazards is getting lower and lower, and the requirements for safety and reliability are gradually increasing. Early detection and identification of faults to avoid dangerous situations is crucial [1; 2; 3]. A fault is defined as a phenomenon in which the deviation between one or more parameters of the system and the normal state exceeds a certain threshold, resulting in the inability of the system to perform the specified function. Fault diagnosis is the process of discovering and distinguishing fault types in time according to the state of these parameters. The current fault diagnosis methods mainly carry out fault diagnosis from the three perspectives of signal, model and knowledge [4]. Signal-based methods require certain prior knowledge to transform [5], extract representative features in the time or frequency domain using advanced signal processing techniques [6; 7], and often combined with machine learning methods or neural networks to achieve good results [8; 9]. As mechanical systems become increasingly complex, developing the physical models required for model-based approaches is difficult and expensive [5]. At the same time, the increased availability of data collected from multiple monitoring sensors and the ability of artificial intelligence algorithms to process the data has brought great potential for the development of advanced data-driven approaches [10; 11]. Therefore, data-driven knowledge-based methods have also become one of the current research hotspots. With the development of deep neural networks, in recent years, intelligent fault diagnosis has ushered in a new stage of development. The latest achievements in the field ofdeep learning in the computer field are continuously applied to the field of fault diagnosis, such as convolutional neural networks (CNN) [12; 13; 14], Deep Belief Networks [15; 16; 17], Residual Networks [18], Deep Auto-encoder (DAE) [19] as well as the latest Attention Networks [20; 21; 22]. In practical applications, the training data and the actual running data often come from different distributions, so although deep learning methods have made impressive progress, these practical problems will hinder their application in the industry [23]. Specifically, its main contradiction is as follows: In practical industrial applications, the source domain labeled data and the target domain unlabeled data collected under different working conditions have different distributions, which means that the deep learning model learned on the source domain can not be directly used on the target domain data. It is better to obtain the labeled fault data of the machine on the target domain; At the same time, for rotating machines, the labeled fault data on the source domain can be artificially generated during testing, so that It can be obtained at a small cost; Bnd once it enters the actual industrial production conditions, that is, the target domain, to obtain the labeled fault data, not only requires a high time cost but also may pay huge economic losses even life costs. Therefore, to solve the above contradictions, the development of a domain adaptation model is an important method and is getting more and more attention. Domain adaptation is mainly achieved through discrepancy-based strategies or conducting adversarial learning strategies [24]. Discrepancy-based methods try to enhance the domain similarity by measuring the distance between the source and target domains on the feature layer of the model and reducing this distance using statistical methods or machine learning methods so that the model learned on the source domain can be used on the target domain. For example, [PERSON] et al. combined the maximum variance discrepancy with the MMD for the feature matching [25]. [PERSON] et al. developed an ordered spectrum transfer algorithm to transfer the target data to the source domain [26]. [PERSON] et al. [27] and [PERSON] et al.