Study of Multibeam Line Measurement Problem Based on Exhaustive Method and Approximate Differentiation

Based on the principle of multibeam bathymetry and its application in measuring the depth of water bodies, this paper explores the optimal design of the line under different circumstances. Firstly, a two-dimensional Cartesian coordinate system is established, and a mathematical model describing the change of multibeam bathymetry coverage width with seawater depth by the motion of the survey vessel is established through the geometrical relationship of the graphs. Then, a three-dimensional spatial coordinate system is established, and a mathematical model describing the variation of the multibeam bathymetric coverage width with the seawater depth and the motion direction angle in terms of the coordinates of the position of the survey vessel is built by using the geometric relationship of the graph, the three-cosine theorem and the two-dimensional motion decomposition. Then, the problem of finding the optimal survey line in a small-scale sea area is solved by an exhaustive method, which is to find the optimal initial survey line from the south side of the sea area through a loop, and then iteratively traverse all the distributions of the optimal survey line, and then use a genetic algorithm to check the convergence of the results obtained by the exhaustive method in order to make sure that the results are the global optimal solution. Finally, the transducer opening angle is calculated as a function of the total length of the line, the overlap ratio of the missed sea area to the total area to be measured, and the sum of the coverage widths, and optimized using the least-squares method to reduce the range of each parameter, and then a more accurate differential model is used to continue to approximate the optimal solution. The proposed model can ensure the global optimization of the solution.