# Flow Velocity Computation in Solid-Liquid Two-Phase Flow by a Hybrid Network CNN-RKSVM
## 5 Conclusions  
Flow velocity detection plays an increasingly important role in dredging engineering. In this paper, a method combining a CNN and a RKSVM was used to calculate the flow velocity. The proposed method was designed in two stages. In the first stage, the ERT measurements of different types of solid phases, various SPFs, and distinct flow velocities were obtained from the dredging engineering experimental platform, which constituted the sample dataset. Then, the feature data of the sample dataset were extracted through the CNN block. Accordingly, the feature data were transformed to the FC block and consisted of a new learning dataset for the second stage. In the second stage, the RKSVM was built by the new learning dataset. After the RKSVM was trained well, it replaced the FC block in the CNN block in the first stage. Consequently, the CNN-RKSVM was created for the flow velocity calculation. Our experiments showed that the CNN-RKSVM method overcame problems such as low accuracy and poor generalization compared to existing flow velocity detection methods. Therefore, the CNN-RKSVM method proposed in this paper provides a new method for flow velocity detection in dredging engineering.  
However, the sample dataset used in this paper was obtained by the Tianjin Dredging Co., Ltd., and parameters such as viscosity coefficient and conductivity of the solid-liquid  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**V** & \multicolumn{4}{c}{**V \(<\) V\({}_{0}\)**} & \multicolumn{4}{c}{**V \(>\) V\({}_{0}\)**} \\ \hline
**Method** & **CC** & **RKSVM** & **CNN** & **CNN–RKSVM** & **CC** & **RKSVM** & **CNN** & **CNN–RKSVM** \\ \hline RMSE & 0.883 & 0.395 & 0.340 & 0.319 & 0.952 & 0.362 & 0.328 & 0.281 \\ MAPE & 0.252 & 0.152 & 0.136 & 0.124 & 0.265 & 0.182 & 0.151 & 0.135 \\ Runtime(s) & 0.007 & 0.564 & 0.295 & 0.903 & 0.006 & 0.529 & 0.312 & 0.835 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Evaluation parameters for the four methods.  
two-phase flow were fixed. Therefore, the sample dataset did not contain all the working conditions in dredging engineering. In addition, the input of the CNN-RKSVM method was the 1D ERT measurements, which lose some of the neighborhood information during the feature extraction by the CNN block. In the future, ERT-reconstructed images will be used as the input of the CNN-RKSVM method to improve accuracy. Nevertheless, the quality of ERT reconstruction images plays a key role, so it is important to choose a suitable image reconstruction algorithm.  
Conceptualization, K.L. and S.Y.; methodology, K.L. and S.Y.; software, K.L. and L.L.; validation, K.L., S.Y. and L.L.; writing--original draft preparation, K.L. All authors have read and agreed to the published version of the manuscript.  
The authors are grateful for financial support from the National Natural Science Foundation of China (grant no. 61973232) and the Tianjin Research Innovation Project for Postgraduate Students (grant no. 2022 BKY102).  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.  
We would like to acknowledge Engineer [PERSON] from Tianjin Dredging Co., Ltd., for his technical and equipment support.  
The authors declare no conflicts of interest.