# Intra-Domain Transfer Learning for Fault Diagnosis with Small Samples
## 1 Introduction  
Fault diagnosis is a crucial aspect of system safety and dependability [1], as it can pinpoint fault locations, identify fault types, and even gauge the severity of certain faults [2]. Existing approaches to fault diagnosis can generally be categorized as either model-based or data-driven [3]. The former approach necessitates a deep understanding of the subject matter since it builds a mathematical model of the subject of interest based on its first principles. The latter employs machine learning, statistics, signal processing, and other techniques to perform pattern recognition on monitoring data. Data-driven approaches are becoming more popular since they have a lower barrier to entry [4, 5]. Data-driven approaches typically rely on a large amount of training samples to learn patterns that can be generalized to testing instances [6, 7]. However, samples of faulty types are insufficient in many real-world applications, leading to an imbalanced classification problem [8]. Oversampling and down-sampling techniques may be used to create a more balanced dataset [9], but this introduces a bias, wherein more samples are selected from one class than another. Another workaround is data augmentation by learning the underlying generating mechanisms of scarce classes using generative models, such as a Variational Auto-Encoder (VAE) [10] or a Generative Adversarial Network (GAN) [11, 12]. Though some success has been reported, it is a paradox to learn from data that are rare to synthesize more data. Deep transfer learning has been adopted to address the issue of small samples in fault diagnosis, with the hope of reutilizing the knowledge learned from a source task in a targettask [13]. Importantly, the number of samples required for training in the target task can be greatly reduced. In one study, an enhanced deep auto-encoder model was proposed to transfer the knowledge learned from a data-abundant source domain to a data-scarce target domain for the purpose of fault diagnosis [14]. Elsewhere, deep transfer learning was applied to transfer knowledge among various operating modes of rotating machinery, including rotational speed [15] and working load [16; 17]. However, negative transfer may occur if source and target domains have significant differences; i.e., if domain-specific samples have large discrepancies in their probability distributions [18]. In other words, bringing source domain knowledge into the target task does not help, but rather hinders performance. The effect of negative transfer has been noted in several transfer-learning-enabled fault diagnosis applications [15; 18; 19], inspiring researchers to examine the causes of negative transfer. A review can be found in [20; 21]. Although the factors contributing to negative transfer are multifaceted, the primary cause is rooted in a covariate shift between source and target domains [21; 22]. Therefore, domain adaptation measures have been proposed to prevent negative transfer or mitigate its adverse impact, including source data filtering using an adversarial approach [22], new architectural design [23; 24; 25], the use of transitive transfer strategy [26], etc. Although many negative transfer countermeasures have been developed, transferring a pretrained model directly from a distant inter-domain to the target domain still poses problems [27; 28]. More specifically, there is a knowledge gap on how to mitigate negative transfer in transfer learning with small samples in fault diagnosis tasks. This gap constitutes the major motivation of this study. Inspired by the work in [26], where intermediate domains were implanted to bridge the gap between distant source and target domains, we propose an intra-domain learning strategy to explicitly utilize the knowledge of a distribution-alike source domain for the purpose of fault diagnosis with small samples. Concretely, we conduct a vanilla transfer from an off-the-shelf inter-domain deep learning model to a data-abundant source domain.