## 1 Introduction
Workers rely on their working experience to adjust the working conditions at will, which is not reliable and causes a lot of undesired damage. This manual method has a high cost and low efficiency, which will cause a considerable waste. In addition, divers are very difficult to work underwater, and there are great safety risks. Therefore, the ship hull underwater cleaning robot technology has greater advantages [1]. This paper is a part of the research on cleaning technology in the ship hull underwater cleaning robot project based on our patent. In the project, submerged cavitation water jet technology is adopted as the cleaning method. The cleaning equipment is mounted on the robot, and a hybrid adsorption method based on thrust adsorption is used to keep the robot staying on the hull surface for underwater operations [32]. Because this process depends on hydrodynamic performance, adsorption force and hovering attitude of an underwater robot, higher jet pressure will increase the complexity of hydrodynamic performance, make the adsorption of the robot on ship hull more difficult, cause the robot's unstable attitude by excessive reaction forces, increase energy consumption and improve the difficulty of control. Therefore, low-pressure conditions are selected for this research. The submerged water jet is a cavitation water jet. Although the cavitation water jet is at low pressure, the impact pressure of the cavitation water jet is 8.6-124 times that of the continuous water jet [33]. So even when the pressure is lower, the damaging effect of higher pressure can be achieved. In underwater cleaning, higher pressure water jets may not get good erosion results. Due to the large damage ability of cavitation and lack of effective erosion control, this cleaning method is difficult to control cleaning effect, and can cause certain damage to hull surface and anticorrosion coating during the process of removing marine fouling [1,7,8]. This damage can cause the steel layer of ship hull to be directly exposed to seawater, which will accelerate the corrosion process of steel, promote hull aging, increase maintenance costs, and reduce operating life of the ship. In addition, when the anticorrosion coating is damaged, toxic copper compounds will be released [7] and pollute the marine environment, which is prohibited in many countries. Therefore, the cleaning operation must be accurately controlled by the optimized erosion prediction to ensure that while removing marine fouling, the hull and anticorrosion coating are not damaged. However, there is almost no comprehensive consideration of erosion control of underwater cleaning in the existing research works. Only a few studies [7; 8; 34] have analyzed the erosion effect of underwater cleaning for a particular situation under one or several working conditions, and selected a constant working condition for cleaning. Considering that the situations in underwater cleaning areas are variable, the hull surface is not flat and the thickness of marine fouling is different, as shown in Figure 1, a single constant working condition in these existing studies cannot always be appropriate. The unsuitable erosion will waste power consumption of robots, affect the cleaning effect, and even damage the anticorrosion coating and hull surface. Therefore, the erosion prediction under different working conditions in this paper can be better used to achieve real-time erosion control of underwater cleaning robots. One of the essential factors to the successful application of underwater cleaning robot technology in actual cleaning operation is to control erosion to avoid the damage to anticorrosion coating and hull surface. Although this erosion control will slightly increase the development cost of robots, when the underwater cleaning robot is successfully applied in the ship underwater cleaning, the benefits will far outweigh the increased development costs. The underwater cleaning of the ship hull has been approved by several classification societies to extend the dock repair interval to two cycles [1].