## 4 Experimental Results  
### Data Collection Environment and Experimental Setup for Leak Detection  
This paper investigated the model transfer across different testbed environments. In Stage 1, the model was pre-trained using leak signals and mechanical noise data collected from a source domain within a controlled testbed environment, as shown in Figure 5[34]. The dataset was obtained using four microphone acoustic sensors, each operating at a sampling frequency of 100 kHz, with a signal measurement duration of 1.5 s per recording. The commercial ICP microphone (Model HT378A06) from PCB Piezotronics, located in Depew, NY, USA, was utilized as the sensor for this study [22]. Leak signals were recorded at 100 distinct locations along the pipeline under 25 unique combinations of leak pressure and leak size. The leak pressure was varied from 1 bar to 5 bar in increments of 1 bar, while the leak diameter ranged from 0.5 mm to 2.5 mm, increasing in intervals of 0.5 mm. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Parameter Definition** \\
**Notation** & \\ \hline \(x_{t}\) & Input data at time step \(t\) \\ \hline \(x_{(d,n)}^{l}\) & 1D feature map \(n\) of domain \(d\) at layer \(l\) \\ \hline \(w_{(d,(m,n))}^{l}\) & Kernel function connecting feature maps \(m\) and \(n\) \\ \hline \(b_{(d,n)}^{l}\) & Bias term for feature map \(n\) \\ \hline \(f_{l}(\cdot)\) & Activation function at layer \(l\) \\ \hline \(N_{d}^{l}\) & Number of output feature maps at layer \(l\) \\ \hline \(L_{d}\) & Total number of convolution layers in domain \(d\) \\ \hline \(R_{n}^{l}\) & List of feature maps at layer \(l-1\) connected to feature map \(n\) \\ \hline \(Z\) & The resulting map obtained by fusing the features derived from the time domain \(x_{T}\) and the frequency domain \(x_{F}\) \\ \hline \(h_{t}^{f}.h_{s}^{b}\) & Forward and backward outputs of the bidirectional LSTM \\ \hline \(a_{t,s}^{i}\) & Attention weight for time steps \(t\) and \(s\) in direction \(i\) \\ \hline \(c_{t}^{i}\) & Context vector summarizing important sequence information \\ \hline \(W_{a}^{i}\) & Weight matrix for calculating attention vectors in direction \(i\) \\ \hline \(y_{a}\) & Attention vector concatenated from forward and backward directions \\ \hline \(f^{concat}(\cdot)\) & Feature fusion function that combines the features from the time and frequency domains \\ \hline \end{tabular}
\end{table} 
Table 4: Nomenclature for the proposed leak detection model. In the target domain, data were collected from 10 leak locations using the same four microphone sensors as employed in the source domain, as shown in Figure 6. The sampling frequency and measurement duration were set to 100 kHz and 5 s, respectively. According to micro-leak detection standards [35], the leak pressure was varied between 1 and 2 bar, and the leak diameter was fixed at 0.5 mm. Both the source and target domains used identical microphone acoustic sensors and applied the same signal preprocessing techniques described in this study. However, the source domain provided a more diverse data collection environment, incorporating additional measurement locations and leakage conditions. In contrast, the target domain focused on conditions specifically tailored to detect low-level leaks. The data collected from the source domain were preprocessed using the methods detailed in Section 2 and converted into 65,985 RMS and frequency features. To assess the performance of the proposed model in detecting leaks, the time- and frequency-domain data were divided into training and test sets using the hold-out method, with a split ratio of 6:4. The source domain included 33,000 leak data points and 32,985 background noise data points, while the target domain comprised 33,000 combined leak and noisy data points. The training procedure involved two stages. In Stage 1, two separate models were trained independently, while in Stage 2, the proposed feature fusion model was developed. For both stages, a batch size of 128 was employed, with training conducted for 30 epochs.