## 6 Conclusions  
This paper mainly proposes an optimized erosion prediction method to predict the erosion effect of the cavitation nozzle under different working conditions. On one hand, a prediction model based on erosion depth is established. On the other hand, an improved optimization algorithm is proposed. Then the improved optimization algorithm MAGA is applied to the prediction model to optimize the BP neural network and improve the prediction performance. Finally, the optimized erosion prediction method is intended to be applied in the formulation and control of the hull underwater cleaning solution, which is an important part of the ship hull underwater cleaning robot project. By this prediction method, the erosion effect of the nozzle under different working conditions can be obtained. Then, in actual operation, for different curved areas on the hull surface and different thicknesses of marine fouling, different schemes are formulated to timely modify the working condition parameters of the nozzle, so as to avoid the water-jet directly damaging the hull surface and anti-corrosion coating. In addition, feedback on the adjustment of the operating condition parameters to the cleaning robot \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Errorsum** & **RMSE** & **APE\({}_{\text{max}}\)** & **MAPE** & \(\mathbf{R^{2}}\) \\ \hline BP & 0.3531 & 0.0738 & 0.1184 & 0.0508 & 0.9848 \\ GA-BP & 0.2862 & 0.0530 & 0.1125 & 0.0457 & 0.9904 \\ MAGA-BP & 0.1860 & 0.0361 & 0.0405 & 0.0223 & 0.9954 \\ \(\Delta_{\text{BP-GABP}}\) & \(-0.1893\) & \(-0.2822\) & \(-0.0496\) & \(-0.0999\) & 0.0057 \\ \(\Delta_{\text{GABP-MAGABP}}\) & \(-0.3501\) & \(-0.3180\) & \(-0.6401\) & \(-0.5114\) & 0.0050 \\ \(\Delta_{\text{BP-MAGABP}}\) & \(-0.4731\) & \(-0.5105\) & \(-0.6579\) & \(-0.5602\) & 0.0107 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Performance evaluation of three prediction models. Figure 12: Absolute percentage error (APE) of different prediction models. can save energy consumption and optimize the control of the robot. For example, the change in jet pressure affects the regulation of the robot's adsorption and propulsion forces. The change in jet angle affects the control angle of the nozzle and the attitude of the underwater robot. The erosion time determines the robot's stay time and moving speed. With the establishment of a large database, the prediction method can also be used to select the appropriate nozzle. In addition, the optimized erosion prediction method of this paper can be summarized as follows:  
1. Refractory brick is a simulated marine fouling, and its erosion depth is used as a test index, which can well reflect the erosion performance of submerged low-pressure water jets produced by angle nozzles under different working conditions. By predicting the erosion effect of water jets to select appropriate nozzles and corresponding optimal working conditions, the application of water jet technology in marine equipment can be promoted, and the efficiency of underwater operations can also be improved. The erosion depth can be controlled by adjusting the operating conditions, to ensure that while removing marine fouling, the hull surface and the anti-corrosion coating cannot be damaged. 2. Since the average error of the prediction result is less than 3%, the prediction model using the three factors of jet pressure, impact time, and jet angle as inputs and erosion depth as output is reliable. This also shows that it is feasible to analyze the primary and secondary factors of the model by using statistical analysis of range and variance based on orthogonal experimental design. The erosion depth increases with the increase of jet pressure and impact time, and decreases with the increase of standoff distance. With the increase of jet angle, the optimal angle appears around 60\({}^{\circ}\). The influence of different experimental factors on the index is jet pressure, impact time, jet angle and target distance in descending order.