# Deep Transfer Learning-Based Fault Diagnosis Using Wavelet Transform for Limited Data
## 4 Evaluation Setup
### Fault Data  
We consider the sufficient samples of the bearing fault data as the intermediate domain, and the limited samples of the pump model are used as the target domain. We use the triplex reciprocating pump model of the Simulink since it allows us to run different fault combinations and severity levels with detailed working conditions [28]. We refer to the detailed description of the bearing fault data of the intermediate domain in [25].  
This section describes the experimental data generated using the reciprocating pump model to evaluate the effectiveness and feasibility of the proposed method under limited target data [28]. The triplex reciprocating pump consists of the pump housing, crank, and plungers. The pump model is configured to generate three common types of faults, namely, cylinder leaks, blocked inlet, and increased bearing friction. Thus, the number of possible fault types is eight, including one healthy state without any faults, three of a single fault, three combinations of two faults, and one with three simultaneous faults. Table 1 describes the details of these eight classes, labeled as \(f_{0},\dots,f_{7}\) of the target domain used in this study. Due to the noise of the model, we obtain different simulation outputs even with the same fault parameters. Each sample of the pump model comprises 1201 output flow data values at the sampling rate of 1000 Hz.  
We consider different severity ranges of cylinder leaks \(10^{-6}<s_{c}\leq 3.6\times 10^{-6}\), blocked inlet \(0.53\leq s_{b}<0.8\), and bearing friction \(0<s_{f}\leq 6\times 10^{-4}\) based on the specifications of the pump model. Each range of the fault types \(f_{1},\dots,f_{7}\) is divided into nine severity levels. We set \(s_{c}=10^{-6},s_{b}=0.8,s_{f}=0\) as the healthy state \(f_{0}\). We obtain 400 samples for the given fault type and the severity level. Thus, the total number of samples per fault types  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Label** & **Classes** & **Number of Samples** &
\begin{tabular}{c} **Number of Samples** \\ **per Severity Level** \\ \end{tabular} \\ \hline \(f_{0}\) & healthy state & 3600 & – \\ \(f_{1}\) & cylinder leak & 3600 & 400 \\ \(f_{2}\) & blocked inlet & 3600 & 400 \\ \(f_{3}\) & cylinder leak and blocked inlet & 3600 & 400 \\ \(f_{4}\) & bearing friction & 3600 & 400 \\ \(f_{5}\) & cylinder leak and bearing friction & 3600 & 400 \\ \(f_{6}\) & blocked inlet and bearing friction & 3600 & 400 \\ \(f_{7}\) & cylinder leak and blocked inlet and bearing friction & 3600 & 400 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Description of 8 different classes of the triplex reciprocating pump model.  
\(f_{1},\ldots,f_{7}\) is equal to \(9\times 400\) where 9 corresponds to the number of severity levels of each fault type. We also generate the equal number of samples as the healthy state \(f_{0}\).  
The data sets are split into the ratio of \(r:0.1:0.1\) as training, validation, and testing sets. We randomly shuffle and select the samples of each class to build each data set. We vary the ratio of the training data set \(r=0.1,\ldots,0.8\) in order to evaluate the impact of the size of the training data.