# Deep Transfer Learning-Based Fault Diagnosis Using Wavelet Transform for Limited Data
## 1 Introduction  
Fault diagnosis is a crucial component of modern industrial systems since early and accurate fault diagnosis not only ensures operational reliability and safety but also reduces maintenance costs [1, 2, 3]. Recently, the research on data-driven fault diagnostics has grown and developed considerably, thanks to the vast amount of data obtained from the Industrial Internet of Things [4, 5]. In particular, the deep learning-based diagnosis technique is one of the most promising and powerful tools for detecting and diagnosing various industrial faults since it automatically learns the hidden features from historical data [4, 6].  
However, training a deep learning-based fault diagnosis model from scratch is computationally expensive and requires substantial amounts of training data to have a sufficient generalization capacity [7, 8, 9]. In most practical industrial scenarios, the training data are strictly limited, and the generation of realistic training samples is not always feasible, since some critical components of the machines are not allowed to operate even with minor faults. Furthermore, collecting large labeled data is a time-consuming and labor-intensive procedure [10].  
On the other hand, transfer learning (TL) is a fundamental deep learning technique that allows reuse of the trained model, learned from the source domain, with differenttarget domains [7]. Specfically, TL can provide a good performance by overcoming the limited training data of the fault diagnosis [11]. However, leveraging the existing model, trained on large source data to the target domain, is still challenging since the source and target domains are conceptually different tasks in most industrial scenarios. The data distribution of the industrial target domain can be significantly different from one of the well-known existing image classifications of the source domain, such as ImageNet.  
This paper combines wavelet transform and TL to diagnose the industrial faults using limited target samples. The main contributions of the paper are as follows:  
* We adopt a pre-trained model, GoogLeNet, to classify industrial faults where the wavelet transformation converts one-dimensional time-series data into two-dimensional images of the time and frequency domains as the input. To deal with the constraints of the limited target samples, we first partially retrain the pre-trained model using the intermediate data that are conceptually related to the target domain, but less expensive, to collect the samples. We then retrain this relatively small portion of the pre-trained intermediate model using the target data.
* We extensively evaluate the effectiveness of the proposed method and compare it with the state of the art. We use a Simulink model of a triplex reciprocating pump with different fault combinations and severity levels. The proposed method improves the generalization capability to classify the fault types while reducing the dependency on the training data of the source domain. In particular, we show the critical impact of the severity level on the fault classification accuracy.  
The remainder of the paper is organized as follows. Section 2 discusses the related works. Section 3 details the proposed method combining wavelet transform and TL. Section 4 presents the experimental data set and the state-of-the-art methods for a comparative analysis. Section 5 evaluates the performance of the proposed method through an extensive set of experiments. Finally, Section 6 summarizes the overall contributions and discusses the future direction of the research.