# Flow Velocity Computation in Solid-Liquid Two-Phase Flow by a Hybrid Network CNN-RKSVM
## 3 The Hybrid Network for Flow Velocity Computation
### The Sample Dataset  
The sample dataset consists of ERT measurements and the corresponding real flow velocities, which were obtained from the Tianjin Dredging Co., Ltd., Tianjin, China. The ERT measurements are obtained by the ERT system, and the real flow velocities are obtained by the electromagnetic flowmeter. Moreover, the ERT system in this paper used the single electrode measurement after single electrode excitation. Thus, for the 16-electrode ERT system, 240 measurements can be obtained as the input of the CNN-RKSVM.  
The pipeline of the dredging transportation experimental platform has a diameter of 0.8 m and a length of 358 m. The horizontal pipe section is installed with measuring devices such as an electromagnetic flowmeter, a densitometer, and an ERT system. The flow direction of solid-liquid two-phase flow is shown in Figure 4. The distance between the electromagnetic flowmeter and the ERT system is 5 m. The difference in flow velocity  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & **Kernel Size** & **Step Size** & **Output Dimension** \\ \hline Input & — & — & \(240\times 1\times 1\) \\ Conv1 & 7\(\times\)1 & 1 & \(240\times 1\times 16\) \\ Conv2 & 5\(\times\)1 & 1 & \(240\times 1\times 32\) \\ Pool1 & 2\(\times\)1 & 2 & \(120\times 1\times 32\) \\ Conv3 & 3\(\times\)1 & 1 & \(120\times 1\times 32\) \\ Conv  
between the two locations of the electromagnetic flowmeter and the ERT system is negligible under the experimentally set working conditions. In addition, the distance between the two adjacent ERT sensors is 0.3 m.  
As shown in Figure 4, the solid phase and liquid phase were mixed into a solid-liquid two-phase flow in a mixing tank, which was further transferred into a transporting pipeline by the dredge pump. The solid phase included coarse sand and gravel (with a conductivity of approximately 0 mS/cm). Different types of solid-phase objects were employed to evaluate the applicability of various methods for flow velocity along different flow patterns. Meanwhile, the liquid phase consisted of water (with a conductivity of 1.3 mS/cm). The flow velocities and solid phase fractions (SPFs) were adjustable by means of a dredge pump in the pipeline. The inlet solid-liquid two-phase flow velocity was 1-6 m/s, and the SPF ranged between 5% and 40%.  
The accuracy and generalization of the CNN-RKSVM are strongly dependent on the quality of the sample dataset. Therefore, simulating actual working conditions is crucial for obtaining ERT measurements under different SPFs and flow velocities.  
The solid phase used in the experiments included coarse sand and gravel. For coarse sand, the experiments involved eight SPFs: 5%, 10%, 15%, 20%, 25%, 30%, 35%, and 40%. For gravel, the experiments involved six SPFs: 5%, 10%, 15%, 20%, 25%, and 30%. The flow velocity ranged from 0 m/s to 6 m/s for both types of solid phases under different SPFs. To enhance the generalization ability of the CNN-RKSVM, ERT measurements from two types of solid-phase objects were combined to form the sample dataset. The sample dataset was grouped to training and testing datasets according to the 10-fold cross-validation method. The data distribution of the datasets and their sample sizes are shown in Table 2.