# Latent Dimensions of Auto-Encoder as Robust Features for Inter-Conditional Bearing Fault Diagnosis
## 2 Problem Description and Related Work  
Before describing the problem, some notations and definitions regarding the problem are introduced. _Transfer Learning:_ The process of learning the information from the data of one condition and transferring the knowledge to a new condition. _Source Domain:_ The condition of the machine from which the data are collected and is used to train the fault diagnosis model. _Target Domain:_ The condition of the machine from which the data are collected and is used to test the knowledge transfer. Transfer of class knowledge in Transfer Learning (TL) tasks can be classified into two methods. This is based on what is available during the training process:  
_Robust Learning:_ Refers to how to appropriately predict class label \(Y_{j}^{t}\) of the \(j\)th observation \(X_{j}^{t}\) of the target domain when there is an available set of observations from the source domain \(D_{s}=(X_{i}^{s},Y_{i})_{i=0}^{n_{s}-1}\)  
_Domain adaptation:_ In some cases, a few observations from the target domain \(D_{t}=(X_{i}^{t},Y_{i}^{t})_{i=0}^{n_{t}-1}\) are also available, and the model is adapted to the target domain. This is called domain adaptation. Here, \(X_{i}^{s}=(x_{0}^{i},x_{1}^{i},\ldots,x_{m}^{i})\) is the sample set of the \(i\)th observation from the source domain, and \(Y_{i}^{s}\) is the corresponding label of that observation. In addition, \(X_{i}^{t}\) and \(Y_{i}^{t}\) stand for the sample set and corresponding label in the target domain, respectively. While applying this to an industrial machine, the domains represent different conditions. There are various TL tasks from the literature that learn the distribution of the \(D_{s}\) and tries to adapt to the distribution of \(D_{t}\). As represented in Figure 1, some methods train using information from the target domain, which can be considered as Domain Adaptation methods, and some do not; these can be considered as Robust Learners. The problem considered in this work is robust learning as, most of the time, the target domain data are scarce and infeasible to collect. From the investigated literature, there are many transfer learning methodologies between machine conditions which have achieved high accuracies. The majority of these methods are domain-adaptation-based transfers of learning. The following are the state-of-the-art articles in the domain adaptation for bearing fault diagnosis. [PERSON] et al. [8] proposed one such domain adaptation method named MDIAN. In [8], the authors use a modified ResNet-50 structure to extract multiple scale features and to try to reduce the conditional maximum mean discrepancy using the so extracted features of source and target domain observations. As reported in their work, MDIAN outperforms several SOTA approaches, such as Convolutional Neural Network (CNN) and CNN + Maximum Mean Discrepancy, for various transfer learning tasks of fault diagnosis. In another domain adaptation work, [PERSON] et al. [16] proposed a methodology where features from vibration data are extracted using a Convolutional Neural Network. Along with the general prediction loss of the source domain data, this CNN parallelly trains to minimize the central moment discrepancy between the source and target distributions. They have achieved great transfer learning accuracies across conditions for various datasets. To the knowledge of the authors,it has been the best performing algorithm yet for the task of transfer learning given some target domain data. Furthermore, [PERSON] et al. [16] also described their implementation of several algorithms such as CNN-NAP (Nuisance Attribute Projection) [17] and MCNN (Multitask Convolutional Neural Network) [18] from the literature for transfer learning of machine faults. The uniqueness of these implementations (CNN-NAP, MCNN) is that they use a source-only dataset to train the classifier, similar to the consideration in this work.