Research on multibeam line layout based on geometric mathematical model and regression analysis

Abstract

A multibeam sounding system is a system that emits acoustic pulse waves through a mechanical device to map the seafloor topography in real time. It can accurately and rapidly measure the size, shape and elevation changes of underwater targets. In this study, the mathematical model of the multibeam sounding system is proposed, and the optimized design of the survey line is carried out according to different seabed geomorphology. Firstly, relevant formulas are deduced by mathematical geometry and trigonometric functions in plane space, then a spatial right-angled coordinate system is established and the direction of the survey line is projected to the x-axis, which transforms the survey line problem in three-dimensional space into a planar type, and finally, according to the mathematical definitions, the shape of the multibeam irradiation on the sloping surface is judged to be an ellipse and the projection model is constructed. The bivariate model is constructed using regression analysis, and the line measurement that meets the requirements is determined by solving the optimal solution. The conclusion shows that the optimal solution for the angle between the direction of the survey line and the projection of the normal direction of the seabed slope on the horizontal plane is 45°, and the survey line that meets the requirements of the shortest measurement length, covering the entire sea area to be surveyed, and the overlap rate of 10-20% can be obtained.