# Generative Oversampling Method for Imbalanced Data on Bearing Fault Detection and Diagnosis
## 1 Introduction  
Fault detection and diagnosis (FDD) in manufacturing facilities is very important for (1) improving productivity by preventing undesired downtime and (2) guaranteeing safe working conditions [1]. Traditional FDD methods were developed using physical models based on mathematics and mechatronics [2; 3; 4; 5; 6]. Those methods require complex analysis steps with domain knowledge. In addition, because physical models are highly dependent on individual specifications, user configuration is needed when the model is used in a specific facility. To overcome the problems of physical models, assorted data-driven FDD methods that use machine learning and statistics, such as support vector machine [7; 8] and fuzzy logic [9], have been proposed. However, these data-driven FDDs still require a complicated pre-processing step before training of the models. Recently, deep neural networks (DNNs) with more powerful fitting abilities have been developed and widely applied to prognostics and health management. In [10; 11; 12; 13; 14; 15], time-domain and frequency-domain features are extracted in data processing, and then an FDD model is applied for motor status classification. In [16; 17; 18], vibration image generation with signal analysis was utilized for feature extractions. The feature extraction method itself can be automated using these approaches, but establishing such models requires complicated signal processing steps. Automatic feature extraction using an auto-encoder has been proposed [19], but the computation cost of the DNN model itself is quite high. To realize wide adoption of data-driven FDD to industry, simpler and more efficient methods are required in both data-processing and DNN models. Furthermore, these data-driven methods have shown great performance with low domain knowledge requirements, but problems related to the quantity and quality of data still remain. Data imbalance is common in FDD because normal condition data are more prevalent than faulty condition data in real manufacturing environments [20]. Such imbalanced conditions degrade data-driven FDD, especially for convolutional neural network (CNN)-based classifiers. Among oversampling [11; 21], down-sampling [22], and ensemble learning [23], all of which have been proposed to solve the data imbalance issue, oversampling is most suitable for industrial FDD because of severe data imbalance ratios. Additionally, oversampling is always the most effective way to deal with class imbalance for the CNN model on image classification [24]. In this study, we investigated the data-driven FDD of bearing faults in an induction motor under data imbalance conditions. Firstly, a CNN based classifier with an imaging method for vibration signals was proposed. We utilized the nested scatter plot (NSP) [25], which is an efficient and scalable image transformation of correlated time-series data. In NSP, the correlated time-series data are represented by a square matrix, similar to a scatter plot, where the elements of density dots are calculated like a heat-map. Experimental evaluation using measured vibration signals from a test bench confirmed that the features of bearing faults are easily extracted using NSP and the CNN-classifier. Secondly, an oversampling method with a generative model was proposed to improve performance when a dataset is imbalanced between normal and faulty conditions. The generative model was developed based on a Wasserstein generative adversarial network with a gradient penalty (WGAN-GP) [26] and deep convolutional generative adversarial networks (DCGAN) [27]. We evaluated the performance improvement of the CNN classifier for various conditions after applying our oversampling method to faulty condition data. The remainder of this paper is organized as follows: Section 2 introduces the proposed data-driven fault detection method. Section 3 presents the generative model based on WGAN-GP and DCGAN. We describe our experiment method and its results in Section 4. The conclusions and future research topics are discussed in Section 5.