Multi-beam survey line optimization method based on underwater topographic survey
By constructing a line measurement interval and coverage width model and optimization model, combined with a variable step size search algorithm, the problem of insufficient coverage in the multi-beam line measurement optimization is solved, efficient and rapid line measurement optimization is achieved, and the accuracy and fault tolerance of sea area terrain detection are improved.
Patent Information
- Application Number
- CN202510306625.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Priority Date
- 2024-12-20
- Filing Date
- 2025-03-14
- Publication Date
- 2025-07-08
AI Technical Summary
The prior art cannot provide the optimal multi-beam line measurement optimization solution from a full-domain perspective, resulting in insufficient coverage and insufficient accuracy of sea area terrain detection.
Build a basic model of measuring line interval and coverage width in ideal and actual conditions, establish an optimization model for measuring line deployment, and solve it through a variable step length search algorithm. The reference line range of the optimal measuring line can be determined to meet the overlap rate of 10%-20%.
It realizes efficient and rapid determination of optimal measurement lines in the entire region, ensures the integrity and accuracy of all measurement lines coverage, and improves the fault tolerance of sea area terrain detection.
Smart Images
Figure CN120277880A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a multi-beam sounding line optimization method based on underwater topographic survey, belonging to the field of surveying technology. Background Art
[0002] Seafloor terrain exploration has important research value in the field of earth science. The seafloor terrain can be studied through seafloor terrain exploration to understand the evolution process of the earth's natural environment and study the laws of natural disasters such as earthquakes and volcanic eruptions. For crashed airplanes and sunken ships, the location of sediments can also be judged and their volume and shape can be estimated by the changes in the seafloor terrain before and after the accident. Multi-beam sounding is one of the important means of current seafloor terrain exploration. How to achieve high-precision full-coverage exploration of the area to be measured with a reasonable overlap rate, the sounding line optimization method is the key. At present, the ideal approach is to optimize the search for the sounding line interval based on modern optimization algorithms, and use model methods such as the roll motion residual correction model based on the edge wave velocity of multi-beam side-looking data, etc., to find the most ideal sounding line optimization scheme, but it is impossible to give a global perspective. Summary of the Invention
[0003] The purpose of the present invention is to solve the problem that it is impossible to grasp from a global perspective in the prior art, and to provide a multi-beam sounding line optimization method based on underwater topographic survey with strong fault tolerance and capable of obtaining the range where all benchmark sounding lines that meet the optimal sounding lines can be found globally.
[0004] To solve the above problems, the present application is realized through the following technical solutions: A multi-beam sounding line optimization method based on underwater topographic survey, characterized in that it includes the following steps: Step 1, construct a basic model of the sounding line interval and coverage width in an ideal state, and determine the calculation method of basic data under this model; Step 2, construct a basic model of the sounding line interval and coverage width in the actual state, and determine the calculation method of basic data under this model; Step 3, establish an optimization model for sounding line deployment and perform corresponding solutions.
[0005] Further, the specific steps of Step 1 are as follows: Step 1.1, establish a mathematical model based on the basic model of the plane rectangular coordinate system; Step 1.2, in the plane rectangular coordinate system established in Step 1.1, determine the calculation method of the water depth; Step 1.3, in the plane rectangular coordinate system established in Step 1.1, determine the calculation method of the coverage width of the sounding strip of the survey ship; Step 1.4, in the plane rectangular coordinate system established in Step 1.1, determine the calculation method of the overlap rate between adjacent strips.
[0006] Further, the specific steps of Step 1.1 are as follows: Select a certain cross-section perpendicular to the direction of the measurement line. Set the center point of the sea area as the left origin, the vertical downward direction as the positive x-axis, and the straight line where the horizontal plane intersects with this vertical cross-section as the y-axis. According to the right-hand rule, construct a plane rectangular coordinate system. In Step 1.2, when the measurement line direction of the survey ship is along the parallel direction of the intersection line of the slope surface and the horizontal plane, that is, in the ideal state, the water depth is related to the y-axis coordinate of the detection line where the survey ship is located. When the coordinate of the survey ship is y, the water depth height is: ; In the formula: Let represent the depth from the survey ship to the seabed when the survey ship is at point y, that is, when the distance from the survey ship to the center of the sea area is y. When the y-coordinate of the position where the survey ship is located is 0, there is ; represent the slope of the seabed slope, that is, the included angle between the seabed slope and the horizontal plane; In Step 1.3, the coverage width of the sounding strip of the survey ship is related to its depth to the seabed. For the survey ship located at point y, the coverage width of its sounding strip is: ; In the formula: is the width measured along the slope towards the deep water side, is the width measured along the slope towards the shallow water side, , , in the formula: is the opening angle of the multi-beam transducer on the survey ship; In Step 1.4, the spacing between two adjacent measurement lines where the survey ships are located is , and the detection overlap rate between the survey ship located at point y and the survey ship on its shallow water side, that is, the direction where the y-coordinate increases, is: .
[0007] Further, Step 2 specifically includes the following steps: Step 2.1, establish a mathematical model based on the general model of a three-dimensional space rectangular coordinate system; Step 2.2, in the three-dimensional space rectangular coordinate system established in Step 2.1, determine the calculation method for the distance from the survey ship to the seabed; Step 2.3, in the three-dimensional space rectangular coordinate system established in Step 2.1, determine the calculation method for the coverage width of the sounding strip of the survey ship.
[0008] Further, the specific steps of Step 2.1 are as follows: The measurement line direction of the survey ship may be in any direction. Generally, take the intersection point of the straight line passing through the center of the sea area and perpendicular to the horizontal plane and the slope surface as the coordinate origin, the projection of the slope surface normal vector on the horizontal plane as the positive x-axis, the vertical upward direction as the positive z-axis. Looking from top to bottom, the positive x-axis direction vector rotates counterclockwise by 90 degrees to be the positive y-axis direction, and construct a three-dimensional space rectangular coordinate system that satisfies the right-hand rule; Vector is the unit projection vector of the survey line direction on the horizontal xoy plane, then The included angle with the positive x-axis is , , and the unit vector in the opposite direction of the normal vector of the seabed slope is: , is the slope of the seabed slope; The vector projects onto the seabed slope, and the projection vector is the vector , and the included angle between the two vectors is the vector and the included angle with the horizontal plane , that is the included angle between the vector and the slope surface, The vector and The included angle is , then: , we get: , and the unit vector in the same direction as is: , The beam is intercepted by a cross-section perpendicular to the survey line direction. The intersection line of the cross-section and the seabed slope, that is, the straight line where the vector is located, is perpendicular to the survey line direction. Therefore, the vector , the vector is the vector rotated counterclockwise by around the unit normal vector on the slope surface; Given the vector , the direction vector , if , then rotates counterclockwise around (right-hand rule) by an angle to get the vector: , If it rotates in the clockwise direction, the angle is taken as negative, and the vector is: , Written in row vector form: , The included angle between the vector and the xoy plane is , and the coordinates of point A where the survey ship is located in the central sea area are , the included angle between the vector and the vector is , the cosine of the included angle between the vector and the vector is: , since is a vector obtained by rotation is a unit vector, so is also a unit vector , then .
[0009] Furthermore, the specific steps of step 2.2 are as follows: When the survey ship sails along the survey line direction, the included angle between the survey line direction and the positive x-axis is , the distance from the position of the survey ship to the seabed will change, and its height changes with the distance from the survey ship to the center of the sea area , and the angle as follows: The specific steps of step 2.3 are as follows: The coverage width on the deep-water side of the sounding strip is: ; The coverage width on the shallow-water side is: , Coverage width: , In the formula: s represents the distance from the survey ship to the center point of the sea area
[0010] Furthermore, the survey line optimization deployment model in step 3 includes the following steps: Step 3.1, under the condition that the overlap rate is 10%-20%, determine the survey line angle with the largest interval between survey lines; Step 3.2, under the condition that the overlap rate is 10%, determine the shortest survey line length; Step 3.3, determine the optimal reference survey line
[0011] Furthermore, the specific steps of step 3.1 are as follows: Step 3.1.1, calculate the seawater depth, coverage width and the overlap rate of two survey lines of the reference survey line and the adjacent survey line on the deep-water side of the reference survey line respectively according to the mathematical model in step 1; Step 3.1.2, according to the overlap rate calculated in step 3.1.1, with as the decision variable, construct the following optimization model: ; Step 3.1.3, use the variable step size search algorithm to solve the optimization model in step 3.1.2 to obtain the survey line angle with the largest interval between survey lines
[0012] Furthermore, the specific calculation process of step 3.1.1 is as follows: Draw a north-south straight line through the center of the sea area, which intersects the east-west boundary perpendicularly at point O. Take point O as the origin, the due west direction of the east-west boundary as the positive x-axis direction, and the due south direction as the positive y-axis direction, and construct a plane rectangular coordinate system that satisfies the right-hand rule; The reference survey line intersects the east-west boundary at point , the water depth at the origin O is the same as the water depth at the center of the sea area, both are D, and the slope of the seabed slope is , the direction vector of the reference survey line is: , The coordinates of the center of the sea area in this coordinate system are (0, y0), where y0 represents the distance from the center of the sea area to the x-axis. The linear equation of the reference survey line is: , then The coordinates at the point are: , the water depth at this point is: , the point on the line The distance to point O: , Point The water depth of the seawater at the place is: , the coverage width on the deep-water side of the reference survey line is: , The coverage width on the shallow-water side is: , where: is a function of; The adjacent survey line on its deep-water side intersects the east-west boundary at point , this survey line is equivalent to the reference survey line translated to the deep-water side, and its linear equation is: , then The coordinates of are: , The water depth at this point is: , This survey line is parallel to the reference survey line and is obtained by translating the reference survey line to the left. The distance from the point on this survey line to is: , point The water depth of the seawater at the place is: , The coverage width on the deep-water side of this reference survey line is: , the coverage width on the shallow-water side is: , where: is a function of; The interval between the reference survey line and its adjacent survey line on the deep-water side is , then there is , the overlap rate of the two survey lines is: .
[0013] Furthermore, step 3.2 specifically includes the following steps: Step 3.2.1, determine the recurrence formula for the distance between the survey line on the deep-water side and the reference survey line: The distance between the k-th survey line on the deep-water side of the reference survey line and the reference survey line is , under the condition that the overlap rate of the (k - 1)-th survey line satisfies 10%, , where , , the specific derivation process is as follows: The abscissa of the reference survey line is x. Since the positive direction of the horizontal axis points to the deep - water direction, the depth of the survey line at point x is: , The width measured on the deep - water side of the reference survey line is: , and the width detected on the shallow - water side: , Let , , then the width measured on the deep - water side is: , and the width measured on the shallow - water side is: ; For the first survey line on the deep - water side of the reference survey line, that is, the distance between the adjacent survey line on the deep - water side and the reference survey line is , so the abscissa of this survey line is , and the depth of the survey line is: , Then the width measured on the deep - water side of the first survey line is: , and the width detected on the shallow - water side: , The coincidence rate between the reference survey line and the first survey line on the deep - water side is: , let , then: , Let , then: , the interval between the second survey line on the deep - water side of the reference survey line and the reference survey line is , and the depth of this survey line is: , Then the width measured on the deep - water side of the second survey line is: , and the width detected on the shallow - water side: , The coincidence rate between the first survey line and the second survey line on the deep - water side is: , Let , then: , let , then: ; Similarly, the distance between the k - th survey line on the deep - water side of the reference survey line and the reference survey line can be obtained as , under the condition that the overlap rate of the (k - 1)-th survey line satisfies 10%, there is ; Step 3.2.2. Determine the recurrence formula for the distance between the sounding lines on the shallow water side and the reference sounding line: The distance between the s-th sounding line on the shallow water side of the reference sounding line and the reference sounding line is , under the condition that the overlap rate of the (s - 1)-th sounding line is 10%, , where, , , and the specific derivation process is as follows: The abscissa of the reference sounding line is x. Since the positive direction of the horizontal axis points to the deep water direction, the depth of the sounding line at point x is: , The width measured on the deep water side of the reference sounding line is: , and the width detected on the shallow water side: , Let , , then the width measured on the deep water side is: , and the width measured on the shallow water side is: ; For the 1st sounding line on the shallow water side of the reference sounding line, that is, the distance between the adjacent sounding line on the shallow side and the reference sounding line is , so the abscissa of this sounding line is , and the depth of the sounding line is: , Then the width measured on the deep water side of the 1st sounding line is: , and the width detected on the shallow water side: , The coincidence rate between the reference sounding line and the 1st sounding line on the shallow water side is: , let , then: , Let , then: , and the interval between the 2nd sounding line on the shallow water side of the reference sounding line and the reference sounding line is , and the depth of this sounding line is: , the width measured on the deep water side of the 2nd sounding line is: , and the width detected on the shallow water side: , The coincidence rate between the 1st sounding line and the 2nd sounding line on the shallow water side is: , Let , then: , let , then: ; Similarly, it can be obtained that the distance between the s-th sounding line on the shallow water side of the reference sounding line and the reference sounding line is , under the condition that the overlap rate of the (s - 1)-th sounding line is 10%, there is .
[0014] Further, the specific steps of step 3.3 are as follows: After the benchmark survey line is deployed, in order to cover the entire rectangular area, u survey lines are required on the deep-water side and v survey lines are required on the shallow-water side. The total width of the coverage should exceed the length of the measurement area in the east-west direction , that is , that is , After simplification, we get: , The optimal deployment position of the benchmark survey line is the position where the sum of u + v + 1 numbers is the smallest under the above conditions. Therefore, the following optimization model is constructed: , Traverse and solve the above model, and select from all and the minimum value of the sum of the values, that is is the smallest, , and the total number of survey lines required is lines.
[0015] This application designs a certain survey line as the benchmark, deduces the recurrence formula for the survey line spacing on both the deep and shallow sides to meet the 10% overlap rate, and constructs an optimal survey line deployment optimization model based on this. This model is easy to solve, has a fast solution rate, and can obtain the range where all benchmark survey lines that meet the optimal survey lines can be found in the entire domain, rather than a single optimal solution, with a strong fault tolerance rate. BRIEF DESCRIPTION OF THE DRAWINGS
[0016] Figure 1 is the flow chart of the present invention; Figure 2 is the schematic diagram for constructing a plane rectangular coordinate system; Figure 3 is the schematic diagram of water depth change; Figure 4 is the schematic diagram for calculating the coverage width of the sounding strip; Figure 5 is the schematic diagram for constructing a three-dimensional space rectangular coordinate system; Figure 6 is the schematic diagram of the survey line; Figure 7 is the schematic diagram of the benchmark survey line with a survey line angle of 90 degrees; Figure 8 is the horizontal axis coordinate of the benchmark survey line for searching the next part of the optimal solution; Figure 9 is the horizontal axis coordinate of the benchmark survey line of the partial optimal solution. DETAILED DESCRIPTION OF THE INVENTION
[0017] The following refers to the accompanying drawings to give specific embodiments of the present invention for further explaining the composition of the present invention.
[0018] Embodiment 1. A multi-beam sounding line optimization method based on underwater topographic survey, and its process is as Figure 1 shown, including the following steps: Step 1, construct a basic model of sounding line interval and coverage width under ideal conditions, and determine the calculation method of basic data under this model; Step 2, construct a basic model of sounding line interval and coverage width under actual conditions, and determine the calculation method of basic data under this model; Step 3, establish an optimization model for sounding line deployment and perform corresponding solutions.
[0019] Further, the specific steps of Step 1 include the following steps: Step 1.1, establish a mathematical model based on the basic model of the plane rectangular coordinate system; Step 1.2, in the plane rectangular coordinate system established in Step 1.1, determine the calculation method of water depth; Step 1.3, in the plane rectangular coordinate system established in Step 1.1, determine the calculation method of the coverage width of the sounding strip of the survey ship; Step 1.4, in the plane rectangular coordinate system established in Step 1.1, determine the calculation method of the overlap rate between adjacent strips.
[0020] Further, the specific content of Step 1.1 is as follows: The specific content of Step 1.1 is as follows: Select a certain cross-section perpendicular to the direction of the measurement line. Let the center point of the sea area be the left origin, the vertical downward direction be the positive direction of the x-axis, and the straight line where the horizontal plane intersects the vertical cross-section be the y-axis. According to the right-hand rule, construct a plane rectangular coordinate system, as Figure 2 shown; In Step 1.2, when the sounding line direction of the survey ship is along the parallel direction of the intersection line of the slope surface and the horizontal plane, that is, under ideal conditions, the water depth is related to the y-axis coordinate of the detection line where the survey ship is located. When the coordinate of the survey ship is y, the water depth is: ; In the formula: Let represent the depth from the survey ship to the seabed when the survey ship is at point y, that is, when the distance from the survey ship to the center of the sea area is y. When the y-coordinate of the position where the survey ship is located is 0, there is ; represent the slope of the seabed slope, that is, the included angle between the seabed slope and the horizontal plane; The specific derivation process is as follows: When the sounding line direction of the survey ship is along the parallel direction of the intersection line of the slope surface and the horizontal plane, that is, under ideal conditions, let the distance between two adjacent sounding lines of the survey ship be d. The schematic diagram of the change in the depth from the survey ship to the seabed is as Figure 3 shown, When the distance between two adjacent sounding lines is d, the change in water depth is: , if it is the deep - water side, the coordinate of the survey ship is -d, and the water depth at this time is: , , if it is the shallow - water side, the coordinate of the survey ship is d, and the water depth at this time is: ; The coverage width of the sounding strip of the survey ship in step 1.3 is related to its depth from the seabed. For the survey ship located at point y, the coverage width of its sounding strip is: ; In the formula: is the width measured along the slope towards the deep - water side, is the width measured along the slope towards the shallow - water side, , , in the formula: is the opening angle of the multi - beam transducer on the survey ship; The specific derivation process is as follows: Taking the survey ship at the center point as an example for derivation. At this time, the coordinate of the survey ship is the origin, and the y - axis coordinate is 0, as Figure 4 shown. According to the known conditions and the sine theorem, , calculate the length of AB, that is, the width of detection along the slope towards the deep - water side is: , In the formula: The length of OB is the depth of the survey ship from the seabed , when the survey ship is at the center position, the depth is , the width of detection along the slope towards the deep - water side is: , similarly, , calculate the length of BC, that is, the width of detection along the slope towards the shallow - water side: ; In step 1.4, the distance between two adjacent survey lines where the survey ships are located is , and the detection overlap rate of the survey ship at point y and the survey ship on its shallow - water side (the direction where the y - coordinate increases) is: .
[0021] Furthermore, step 2 specifically includes the following steps: Step 2.1, establish a mathematical model based on the general model of the three - dimensional space rectangular coordinate system; Step 2.2, in the three - dimensional space rectangular coordinate system established in step 2.1, determine the calculation method of the distance from the survey ship to the seabed; Step 2.3, in the three - dimensional space rectangular coordinate system established in step 2.1, determine the calculation method of the coverage width of the sounding strip of the survey ship.
[0022] Further, the specific steps of step 2.1 are as follows: The survey line direction of the survey ship may be in any direction. Generally, taking the intersection point of the straight line passing through the center of the sea area and perpendicular to the horizontal plane and the slope surface as the coordinate origin, taking the projection of the slope surface normal vector on the horizontal plane as the positive x-axis direction, and the vertically upward direction as the positive z-axis direction. Looking down from above, the positive x-axis direction vector is rotated counterclockwise by 90 degrees to obtain the positive y-axis direction, and a three-dimensional space rectangular coordinate system is constructed, as shown in Figure 5. vector is the unit projection vector of the survey line direction on the horizontal xoy plane, then The included angle with the positive x-axis direction is , , and the unit vector in the opposite direction of the seabed slope surface normal vector is: , is the slope of the seabed slope surface; The vector is projected onto the seabed slope surface, and the projection vector is the vector , and the included angle between the two vectors is the vector and the included angle with the horizontal plane, that is The included angle between the vector and the slope surface, The included angle between the vector and is , then: , we get: , and the unit vector in the same direction as is: , The beam is intercepted by a cross-section perpendicular to the survey line direction. The cross-section intersects the seabed slope surface, that is, the straight line where the vector is located. Therefore, the vector , the vector is the vector rotated counterclockwise by around the unit normal vector on the slope surface; Given the vector , the direction vector , if , then rotated around (right-hand rule) counterclockwise by the angle to obtain the vector: , If it is rotated clockwise, the angle is taken as a negative value, and the vector can be obtained as: , Written in row vector form: , vector The included angle with the xoy plane is , and the coordinates of point A where the survey ship is located in the central sea area are , vector and vector have an included angle of , vector and vector 's cosine of the included angle is: , since is obtained by rotating vector , and is a unit vector, so is also a unit vector, , then .
[0023] Furthermore, the specific steps of step 2.2 are as follows: When the survey ship sails along the survey line direction, when the survey ship sails along the survey line direction, the included angle between the survey line direction and the positive x-axis is , the distance from the position of the survey ship to the seabed will change, and its height changes with the distance of the survey ship to the center of the sea area, and the angle as: ; Furthermore, the specific steps of step 2.3 are as follows: The coverage width on the deep-water side of the sounding strip is: ; The coverage width on the shallow-water side is: , Coverage width: , In the formula: s represents the distance of the survey ship from the center point of the sea area.
[0024] Furthermore, the survey line optimization deployment model in step 3 includes the following steps: Step 3.1, under the condition that the overlap rate is 10%-20%, determine the maximum included angle between survey lines with the largest interval; Step 3.2, under the condition that the overlap rate is 10%, determine the shortest survey line length; According to step 3.1, the maximum included angle between survey lines with the largest interval is determined to be 90°, the depth at each point on the survey line is equal, and the overlap rate at any position between adjacent survey lines is equal. In the plane rectangular coordinate system constructed above, let the abscissa of the reference survey line be x, and taking the overlap rate of 10% as the constraint condition, calculate the coordinates where the survey lines are located successively from the deep and shallow sides until the entire rectangular sea area can be covered. With the goal of the shortest sum of the lengths of the survey lines in all rectangular areas, the abscissa x of the reference survey line is the decision variable, as Figure 7 shown.
[0025] The abscissa of the reference survey line is x. Since the positive direction of the horizontal axis points towards the deep water, the depth of the survey line at point x is: , and the width measured on the deep water side of the reference survey line is: , The width detected on the shallow water side: . Let , , then the width measured on the deep water side is: , and the width measured on the shallow water side is: .
[0026] Step 3.3: Determine the optimal reference survey line.
[0027] Furthermore, the specific steps of Step 3.1 are as follows: Step 3.1.1: Calculate the seawater depth, coverage width, and overlap rate of the two survey lines of the reference survey line and the adjacent survey line on the deep water side of the reference survey line respectively according to the mathematical model in Step 1; Since the seabed forms a slope and is in an ideal state, with the angle of the slope determined, the change in the interval d between the survey lines has a similar pattern. Let the survey line passing through the center of the sea area be the reference, and the angle between the projection vector of the survey line direction on the xoy plane and the positive x-axis be . According to the mathematical model in Step 2, when is determined, the coverage width is related to the distance of the survey ship along the survey line direction to the center of the sea area: with different survey line angles, under the condition that the overlap rate is between 10% - 20%, the intervals between the survey lines are different; Step 3.1.2: Taking as the decision variable, construct the following optimization model according to the overlap rate calculated in Step 3.1.1: ; Step 3.1.3: Use the variable step - size search algorithm to solve the optimization model in Step 3.1.2 to obtain the survey line angle with the largest interval between the survey lines.
[0028] In this embodiment, first, with a step size of 5 degrees for the survey line angle and a step size of 0.1 nautical mile for the survey line interval , conduct a rough search and find that there is a situation where the overlap rate is between 10% - 20% between 85° - 95°. Then, within the range of 85° - 95°, with a step size of 1 degree for the survey line angle and a step size of 0.001 nautical mile for the survey line interval, conduct a fine search. When the reference survey line passes through the center of the sea area, the optimal result appears at the survey line angle , and the maximum interval from the survey line on the deep water side is m.
[0029] Furthermore, the specific calculation process of step 3.1.1 is as follows: Draw a north-south straight line through the center of the sea area, which perpendicularly intersects the east-west boundary at point O. As Figure 6 shown, taking point O as the origin and the due west direction of the east-west boundary as the positive direction of the x-axis, a plane rectangular coordinate system is constructed according to the right-hand rule; the reference survey line intersects the east-west boundary at point , the water depth at the origin O is the same as that at the center of the sea area, both being D, and the angle between the slope and the horizontal plane is , and the direction vector of the reference survey line is: , The coordinates of the center of the sea area in this coordinate system are (0, y0), where y0 represents the distance from the center of the sea area to the x-axis. The straight-line equation of the reference survey line is: , then The coordinates of point are: , and the water depth at this point is: , for a point on the straight line The distance to point O is: , The water depth of point is: , The coverage width on the deep-water side of this reference survey line is: , and the coverage width on the shallow-water side is: , where: is a function of; The adjacent survey line on its deep-water side intersects the east-west boundary at point , and this survey line is equivalent to the reference survey line being translated towards the deep-water side. Its straight-line equation is: , then The coordinates of are: , The water depth at this point is: , This survey line is parallel to the reference survey line and is obtained by translating the reference survey line to the left. The distance from a point on this survey line to is: , the water depth of point is: , the coverage width on the deep-water side of this reference survey line is: , and the coverage width on the shallow-water side is: , where: is a function of; The interval between the reference survey line and its adjacent survey line on the deep-water side is , then there is , and the overlap rate of the two survey lines is: .
[0030] Furthermore, step 3.2 specifically includes the following steps: Step 3.2.1: Determine the recurrence formula for the distance between the sounding lines on the deep-water side and the reference sounding line. The distance between the k-th sounding line on the deep-water side of the reference sounding line and the reference sounding line is , under the condition that the overlap rate of the (k - 1)-th sounding line is 10%, , where , , and the specific derivation process is as follows: The abscissa of the reference sounding line is x. Since the positive direction of the horizontal axis points to the deep-water direction, the depth of the sounding line at point x is: , The width measured on the deep-water side of the reference sounding line is: , and the width detected on the shallow-water side: , Let , , then the width measured on the deep-water side is: , and the width measured on the shallow-water side is: .
[0031] For the 1st sounding line on the deep-water side of the reference sounding line, that is, the distance between the adjacent sounding line on the deep-water side and the reference sounding line is , so the abscissa of this sounding line is , and the depth of the sounding line is: , Then the width measured on the deep-water side of the 1st sounding line is: , and the width detected on the shallow-water side: , The overlap rate between the reference sounding line and the 1st sounding line on the deep-water side is: , Let , then: , let , then: , The interval between the 2nd sounding line on the deep-water side of the reference sounding line and the reference sounding line is , and the depth of this sounding line is: , Then the width measured on the deep-water side of the 2nd sounding line is: , and the width detected on the shallow-water side: , The overlap rate between the 1st and 2nd sounding lines on the deep-water side is: , Let , then: , let , then: ; Similarly, the distance from the k-th survey line on the deep-water side of the reference survey line to the reference survey line can be obtained as , when the overlap rate of the (k - 1)-th survey line meets the condition of 10%, there is ; Step 3.2.2. Determine the recurrence formula for the distance from the survey line on the shallow-water side to the reference survey line: The distance from the s-th survey line on the shallow-water side of the reference survey line to the reference survey line is , when the overlap rate of the (s - 1)-th survey line meets the condition of 10%, , where, , , the specific derivation process is as follows: The abscissa of the reference survey line is x. Since the positive direction of the horizontal axis points to the deep-water direction, the depth of the survey line at the x point is: , The width measured on the deep-water side of the reference survey line is: , and the width detected on the shallow-water side: , let , , then the width measured on the deep-water side is: , and the width measured on the shallow-water side is: .
[0032] For the 1st survey line on the shallow-water side of the reference survey line, that is, the distance between the adjacent survey line on the shallow side and the reference survey line is , so the abscissa where this survey line is located is , and the depth of the survey line is: , Then the width measured on the deep-water side of the 1st survey line is: , and the width detected on the shallow-water side: , The coincidence rate between the reference survey line and the 1st survey line on the shallow-water side is: , Let , then: , let , then: , The interval between the 2nd survey line and the reference survey line on the shallow-water side of the reference survey line in sequence is , and the depth of this survey line is: , The width measured on the deep-water side of the 2nd survey line is: , and the width detected on the shallow-water side: , The coincidence rate between the 1st survey line and the 2nd survey line on the shallow-water side is: , let , then: , let , then: .
[0033] Similarly, it can be obtained that the distance from the s-th survey line on the shallow water side of the reference survey line to the reference survey line is . Under the condition that the overlap rate of the (s - 1)-th survey line satisfies 10%, there is .
[0034] Furthermore, the specific steps of step 3.3 are as follows: After the reference survey line is deployed, in order to cover the entire rectangular area, u survey lines are required on the deep water side and v survey lines are required on the shallow water side. The total width they cover should exceed the length of the measurement area in the east-west direction , that is , that is , After simplification, it is obtained that , The optimal deployment position of the reference survey line is the position where the sum of u + v + 1 numbers is the smallest under the above conditions. Therefore, the following optimization model is constructed: , The above model is solved by traversal. Select from all and the minimum value of the sum of the values, that is is the smallest, , and the total number of survey lines required is lines.
[0035] Example 2. A. General model simulation experiment of survey line interval and coverage width Given the data of the distance of the survey ship from the center point of the sea area and the included angle of the survey line direction, according to the constructed general model of survey line interval and coverage width, after calculation, the results are shown in Table 2. Table 1 Calculation results of Problem 2 , B. Optimal survey line deployment optimization model simulation experiment The given area is a rectangular area, 2 nautical miles long in the north-south direction and 4 nautical miles wide in the east-west direction. It can be understood that the center point of the sea area is the center point of the rectangle. When the included angle of the survey line is different, the coverage width is different and is related to the depth of the survey ship to the seabed. The shallower the depth to the seabed, the smaller the coverage width. The survey ship usually adopts a Z-shaped route to search in the search area. In order to achieve full coverage of the area and with simple operation, Z-shaped survey lines are usually selected to be parallelly distributed. When the depth of the survey ship from the seabed is deeper, the distance d between the parallel survey lines can be larger. When the depth of the survey ship from the seabed is shallower, the distance between the survey lines is smaller. The distance between the survey lines is variable, and its variation law is related to the included angle Regarding, according to the requirements of the problem, the minimum overlap rate between two survey lines should exceed 10%, and the maximum overlap rate should not exceed 20%.
[0036] The reference survey line is usually located at the center of the area, that is, the number of survey lines on the deep-water side and the shallow-water side is not much different. Starting from 2, Starting from 2, the difference between the two does not exceed 2. Solve by traversing. First, verify and Whether the values of meet the constraint conditions. When the constraint conditions are met, select The minimum value of the sum of the values, that is is the smallest. At this time , the total number of survey lines required is lines. After solving, at least 34 survey lines are required to achieve full coverage of the entire rectangular area, and the overlap rate between adjacent survey lines is 10%. The total length of the 34 survey lines is: ; and there are many such schemes. Search and solve the horizontal axis coordinate of the reference survey line, and search in steps of 50 meters. The search range is from the deep water to the center of the sea area. The results are as Figure 8 shown.
[0037] An arbitrary set of solutions is selected from them. Search in steps of 10 near 3450. The search results are as Figure 9 shown.
[0038] Select the scheme with the horizontal axis coordinate of the reference survey line being 3490, and use the mathematical model and algorithm in step 1 to verify the results. The calculation results are shown in . From It can be seen that the overlap rate between any two survey lines is 10%. The coverage width on the deep-water side of the survey line with the deepest water is 365.39 meters, and the coverage width on the shallow-water side of the survey line with the shallowest water is 22.51 meters. Both cover the north-south boundaries on both sides of the rectangular area. This scheme can achieve full coverage of the entire sea area with the least number of survey lines.
[0039] Table 2 Verification of the search scheme for 34 survey lines , In this scheme, the total navigation route of the survey ship is: (nautical miles).
[0040] The specific embodiments described in this article are only examples to illustrate the spirit of the present invention. Those skilled in the technical field to which the present invention belongs can make various modifications or supplements to the described specific embodiments or use similar methods to replace them, but will not deviate from the spirit of the present invention or exceed the defined scope.
Claims
1. A multi-beam survey line optimization method based on underwater topographic survey, characterized in that: It includes the following steps: Step 1: Construct a basic model of the sounding line interval and coverage width under ideal conditions, and determine the calculation method of basic data under this model; Step 2: Construct a basic model of the sounding line interval and coverage width under actual conditions, and determine the calculation method of basic data under this model, which specifically includes the following steps: Step 2.1: Establish a mathematical model based on the general model of a three-dimensional space rectangular coordinate system, specifically as follows: The sounding line direction of the survey ship is in any direction. Generally, the intersection point of the straight line passing through the center of the sea area and perpendicular to the horizontal plane and the slope surface is used as the coordinate origin, the projection of the slope surface normal vector on the horizontal plane is used as the positive x-axis direction, and the vertically upward direction is used as the positive z-axis direction. Looking from top to bottom, the positive x-axis direction vector is rotated counterclockwise by 90 degrees to be the positive y-axis direction, and a three-dimensional space rectangular coordinate system is constructed to satisfy the right-hand rule; Vector is the unit projection vector of the survey line direction on the horizontal xoy plane, then The included angle with the positive x-axis is , , The unit vector in the direction opposite to the normal vector of the seabed slope is: , being the slope of the seabed slope; The vector projects onto the seabed slope, and the projection vector is the vector , and the included angle between the two vectors is the vector and the included angle with the horizontal plane , that is the included angle between the vector and the slope, the included angle between the vector and is , then: , we get: , And The unit vector in the same direction is: , Intercept the beam with a cross-section perpendicular to the survey line. The intersection line of the cross-section and the seabed slope, that is, the vector The straight line where it is located is perpendicular to the survey line direction. Therefore, the vector , the vector is the vector rotated counterclockwise by around the unit normal vector on the slope; Known vector , direction vector , if , then rotates counterclockwise around (right-hand rule) by an angle to obtain the vector: , If it rotates in the clockwise direction, the angle takes a negative value, and the vector is: , Written in row vector form: , vector The included angle with the xoy plane is , and the coordinates of point A where the survey ship is located in the central sea area are , vector The included angle with vector is , vector The cosine of the included angle with vector is: ， Since is obtained by rotating the vector , and is a unit vector, so is also a unit vector, , then ; Step 2.2: In the three-dimensional space rectangular coordinate system established in Step 2.1, determine the calculation method of the distance from the survey ship to the seabed; Step 2.3: In the three-dimensional space rectangular coordinate system established in Step 2.1, determine the calculation method of the coverage width of the sounding strip of the survey ship; Step 3: Establish an optimized model for sounding line deployment and perform corresponding solutions.
2. The multi-beam sounding line optimization method based on underwater topographic survey according to claim 1, wherein: The specific content of Step 1 includes the following steps: Step 1.1: Establish a mathematical model based on the basic model of a plane rectangular coordinate system; Step 1.2: In the plane rectangular coordinate system established in Step 1.1, determine the calculation method of the water depth; Step 1.3: In the plane rectangular coordinate system established in Step 1.1, determine the calculation method of the coverage width of the sounding strip of the survey ship; Step 1.4: In the plane rectangular coordinate system established in Step 1.1, determine the calculation method of the overlap rate between adjacent strips.
3. A multi-beam survey line optimization method based on underwater topographic survey according to claim 2, characterized in that: The specific content of Step 1.1 is as follows: Select a certain cross-section perpendicular to the sounding line direction. Let the center point of the sea area be the left origin, the vertically downward direction be the positive x-axis direction, and the straight line where the horizontal plane intersects the vertical cross-section be the y-axis. According to the right-hand rule, a plane rectangular coordinate system is constructed; In step 1.2, when the survey line direction of the survey ship is along the parallel direction of the intersection line of the slope surface and the horizontal plane, that is, in the ideal state, the water depth is related to the y-axis coordinate of the detection line where the survey ship is located. When the coordinate of the survey ship is y, the water depth is: ; In the formula: Let represent the depth from the survey ship to the seabed when the survey ship is at point y, that is, when the distance from the survey ship to the center of the sea area is y, ; The coverage width of the sounding strip of the survey ship in step 1.3 is related to its depth to the seabed. For the survey ship located at point y, the coverage width of its sounding strip is: ; In the formula: is the width measured along the slope towards the deep water side, is the width measured along the slope towards the shallow water side, ， ， In the formula: is the opening angle of the multi-beam transducer on the survey ship; The distance between the measurement lines where two adjacent survey vessels are located in step 1.4 is , and the detection overlap rate of the survey vessel located at point y and the survey vessel on its shallow water side, that is, the direction in which the y coordinate increases, is: .
4. A multi-beam survey line optimization method based on underwater topographic survey according to claim 1, characterized in that: The specific content of step 2.2 is as follows: When the survey ship sails along the survey line direction and always keeps the included angle of the survey line direction unchanged, the distance from the position of the survey ship to the seabed will change, and its height changes with the distance from the survey ship to the center of the sea area , the included angle between the survey line direction and the positive direction of the x-axis is . The variation relationship is as follows: ; The specific content of step 2.3 is as follows: The coverage width on the deep-water side of the sounding strip is: ; The coverage width on the shallow water side is: , Coverage width: , In the formula: s represents the distance from the survey ship to the center point of the sea area.
5. The multi-beam survey line optimization method based on underwater topographic survey according to claim 4, characterized in that: The optimized sounding line deployment model in Step 3 includes the following steps: Step 3.1: Under the condition that the overlap rate is between 10% and 20%, determine the sounding line angle with the largest interval between sounding lines; Step 3.2: Under the condition that the overlap rate is 10%, determine the shortest sounding line length; Step 3.3: Determine the optimal reference sounding line.
6. The multi-beam survey line optimization method based on underwater topographic survey according to claim 5, wherein: The specific content of Step 3.1 includes the following steps: Step 3.1.1: Calculate the sea water depth, coverage width and the overlap rate of the two sounding lines of the reference sounding line and the adjacent sounding line on the deep water side of the reference sounding line respectively according to the mathematical model in Step 1. The specific calculation process is as follows: Draw a north-south straight line through the center of the sea area, which perpendicularly intersects the east-west boundary at point O. Taking point O as the origin, the due west direction of the east-west boundary as the positive direction of the x-axis, and the due south direction as the positive direction of the y-axis, construct a plane rectangular coordinate system that satisfies the right-hand rule; the reference survey line intersects the east-west boundary at point , the water depth at the origin O is the same as the water depth at the center of the sea area, both are D, and the slope of the seabed slope is , the direction vector of the reference survey line is: , The coordinates of the sea area center in this coordinate system are (0, y0), where y0 represents the distance from the sea area center to the x-axis. The linear equation of the reference survey line is: , Then The coordinates at the point are: , and the water depth at this point is:
7. Points on a straight line Distance to point O: ， Point The water depth at the is: The coverage width on the deep-water side of this reference survey line is: , The coverage width on the shallow water side is: , In the formula: is a function of; The adjacent sounding line on its deep - water side intersects the east - west boundary at point , and this sounding line is equivalent to the reference sounding line translated towards the deep - water side. Its straight - line equation is: , Then The coordinates are: , The water depth at this point is: , This survey line is parallel to the reference survey line and is obtained by shifting the reference survey line to the left by The distance from a point on this survey line to is: , Point The seawater depth at the is: The coverage width on the deep-water side of this reference survey line is: , The coverage width on the shallow water side is: , In the formula: is a function of; The interval between the reference survey line and the adjacent survey line on its deep-water side is , then there is , The overlapping rate of the two survey lines is: ; Step 3.1.
2. Based on the overlap rate calculated in Step 3.1.1, with as the decision variable, construct the following optimization model: ; Step 3.1.3: Use the variable step size search algorithm to solve the optimization model in Step 3.1.2 to obtain the sounding line angle with the largest interval between sounding lines.
8. A multi-beam sounding line optimization method based on underwater topographic survey according to claim 6, characterized in that: The specific content of Step 3.2 includes the following steps: Step 3.2.
1. Determine the recurrence formula for the distance between the sounding lines on the deep-water side and the reference sounding line: The distance between the k-th sounding line on the deep-water side of the reference sounding line and the reference sounding line is , under the condition that the overlap rate of the (k - 1)-th sounding line meets 10%, . The specific derivation process is as follows: The first survey line on the deep-water side of the reference survey line, that is, the distance between the adjacent survey lines on the deep-water side and the reference survey line is , so the abscissa of this survey line is , and the depth of the survey line is: , Then the width measured on the deep-water side of the first survey line is: , Width of detection on the shallow water side: , Among them, , , The coincidence rate between the reference survey line and the first survey line on the deep water side is: , Let , then: , Let , then: , The deep water of the reference survey line successively has an interval between the second survey line and the reference survey line of , and the depth of this survey line is: , Then the width measured on the deep-water side of the second survey line is: , Width of detection on the shallow water side: , The coincidence rate between the first survey line and the second survey line on the deep water side is: , Let , then: , Let , then: ; Step 3.2.
2. Determine the recurrence formula for the distance between the sounding line on the shallow side and the reference sounding line: The distance between the s-th sounding line on the shallow side of the reference sounding line and the reference sounding line is , under the condition that the overlap rate of the (s - 1)-th sounding line meets 10%, , the specific derivation process is as follows: The first sounding line on the deep side of the reference sounding line, that is, the distance between the adjacent sounding line on the shallow side and the reference sounding line is , so the abscissa where this sounding line is located is , and the depth of the sounding line is: , Then the width measured on the deep-water side of the first survey line is: , Width of detection on the shallow water side: , The coincidence rate between the reference survey line and the first survey line on the shallow water side is: , Let , then: , Let , then: , The interval between the second survey line on the shallow side of the reference survey line and the reference survey line in sequence is , and the depth of this survey line is: , The width measured on the deep-water side of the second survey line is: , Width of detection on the shallow side: , The coincidence rate between the first survey line and the second survey line on the shallow water side is: , Let , then: , Let , then: ; Among them, the abscissa of the reference survey line is x. Since the positive direction of the horizontal axis points towards the deep water direction, the depth of the survey line at point x is: , The width measured on the deep water side of the reference survey line is: , Width of detection on the shallow water side: , Let , , then the width measured on the deep water side is: , The width measured on the shallow side is: .
9. A multi-beam survey line optimization method based on underwater topographic survey according to claim 7, characterized in that: The specific steps of step 3.3 are as follows: u survey lines are required on the deep-water side and v survey lines are required on the shallow-water side, and the total coverage width should exceed the east-west length of the measurement area , that is , namely , After simplification, we get: , The optimal deployment position of the reference sounding line is the position with the smallest number of u + v + 1 under the above conditions. Therefore, the following optimization model is constructed: , Traverse and solve the above model, and select from all and the minimum value of the sum of the values, that is, is the smallest, , and the total number of survey lines required is lines.