# Deep Transfer Learning-Based Fault Diagnosis Using Wavelet Transform for Limited Data
## 2 Related Works  
Due to the significant advantage of automatic feature extraction, various deep learning models, such as auto-encoder [10], the Recurrent Neural Network (RNN) [12], and the Convolutional Neural Network (CNN) [13, 14], have been investigated for fault detection and diagnosis problems. [PERSON] et al. [13] adopted a CNN model to automatically extract features and enable classification of the bearing fault. However, various operating conditions of industrial environments seriously degrade the effectiveness of the deep learning-based fault detection and diagnosis method [1, 3]. [PERSON] et al. [14] integrated a CNN model with training interference and varying kernel dropout using the raw time-series signal as the input. The data augmentation further improves the classification accuracy of the extended CNN model under various operating conditions. [PERSON] et al. [15] developed a two-dimensional CNN model, which uses the frequency spectrum obtained from multiple sensors as the input for the bearing fault diagnosis.  
Most deep learning models need a large amount of training data in order to train [7, 8]. However, faulty industrial data are costly to collect because crucial components or equipment in manufacturing systems are not permitted to operate in faulty states. Further, the distribution of sensor measurements, even for the same equipment, varies depending on the operating conditions. Moreover, conventional augmentation methods make generating realistic training samples difficult due to the complex non-linear operations of industrial machines [16].  
As one of the most promising techniques, TL leverages the rich capability of the source domain to facilitate the industrial target model using the fine-tuning or adaptation for the fault detection and diagnosis problem [17]. [PERSON] et al. [9] proposed a fusion method for bearing fault classification without having a strong knowledge of feature engineering or the large training samples of deep learning models. The XGBoost classifier is trained with two types of features, namely, predetermined empirical features and adaptive featuresprovided by LiftingNet. LiftingNet adaptively extracts the hidden features for the target task that depend on noise and working conditions. To enhance the sparsity and the adaptive feature's learning of limited data, [PERSON] et al. [10] adopted the parameter TF to construct their model of the multiple stacked non-negativity constraint sparse autoencoders for the rolling bearing fault diagnosis. [PERSON] et al. [18] developed a few-shot learning method in which the pre-trained Siamese neural network is extended with wide first-layer kernels to conduct the rolling bearing fault diagnosis. [PERSON] et al. [19] proposed a sparse autoencoder-based fault diagnosis method in which the particle swarm optimization method provides the optimal hyperparameters of the architecture. Kurtogram images are used to train the proposed model to implement fault diagnosis.  
However, the TL model may only provide a low prediction accuracy of the target domain due to the significant domain discrepancy between the source and target domains in practical fault diagnosis scenarios. In our work, we introduce the intermediate domain, which is conceptually similar to the target domain, to partially retrain the pre-trained network model. Moreover, the wavelet transform provides the frequency spectrum characteristics of the time-varying measurements. Further, we extensively evaluate the effectiveness of the proposed method using various fault combinations and severity levels of the complex reciprocating pump model, while most existing studies use relatively simple bearing faults.