Control method for line hanging operation track of unmanned aerial vehicle in complex electromagnetic environment

Abstract

The invention relates to a control method for a line hanging operation track of an unmanned aerial vehicle in a complex electromagnetic environment, and belongs to the technical field of unmanned aerial vehicle track control. The method comprises the following steps: sequentially determining n wire hanging points of the unmanned aerial vehicle for stopping and hanging operation in a transformer substation area according to a wire hanging operation plan of the unmanned aerial vehicle in the transformer substation area, and then carrying out iterative optimization on n initial wire hanging points of the unmanned aerial vehicle determined according to experience along the fastest descending direction of an electric field and a magnetic field by adopting an improved gradient method, n corrected line hanging points are obtained, an inspection route is formed according to connecting lines between the n corrected line hanging points, electromagnetic interference is considered, avoidance is carried out by optimizing a track, and the safety and feasibility of unmanned aerial vehicle inspection are improved to the maximum extent.

Description

Technical Field

[0001] The present invention relates to a method for controlling a line-hanging operation trajectory of a UAV in a complex electromagnetic environment, and belongs to the technical field of UAV trajectory control. Background Art

[0002] Traditional line parameter measurement work often requires the adjacent lines on the same tower (same corridor) to be shut down. The Jiangsu power grid has dense transmission line corridors and many important corridors. As the requirements for power supply and grid safety continue to increase, the contradiction between the demand for parameter measurement and shutdown and the pressure of safe grid operation is becoming increasingly prominent.

[0003] The use of drones to hang lines can reduce the risk of people measuring line parameters falling from heights and the risk of electric shock from induced electricity, and can effectively reduce the probability of power outages in the same tower (same corridor).

[0004] Due to the strong electromagnetic coupling relationship between transmission lines, drones face a more complex electromagnetic environment when hanging on the lines, which greatly exceeds the conventional flight conditions of drones. When the electromagnetic interference to the drone exceeds a certain value, the drone's flight control signal cannot be transmitted normally, and its internal components will become dizzy or arc, causing the drone's performance to degrade. In severe cases, it will cause signal loss and lead to a crash. At the very least, it will affect the measurement effect of the drone's hanging line, and at worst, it will affect the safety of the measurement work.

[0005] Existing drones used for line measurement and line hanging generally lack anti-electromagnetic interference protection. Most rely on lidar, visual, or non-obstacle avoidance methods to avoid direct impact with live objects. In theory, these techniques can limit the impact of electromagnetic interference to a controllable range by setting an appropriate safety distance, reducing its electromagnetic field impact. However, in actual engineering applications, determining the safety distance is influenced by numerous factors, making it difficult to accurately determine. Consequently, the flight paths of existing drones used for line measurement and line hanging often experience significant electromagnetic interference, significantly impacting the drone's line hanging operations. Summary of the Invention

[0006] The technical problem to be solved by the present invention is: how to plan an operation trajectory with minimum electromagnetic interference for the line hanging operation of a UAV.

[0007] To solve the above technical problems, the present invention proposes a technical solution: a method for controlling the trajectory of a UAV line hanging operation in a complex electromagnetic environment, comprising the following steps:

[0008] Step 1: Obtain site information and electrical information of the substation area where the drone needs to perform line hanging operations. The site information includes the number and location information of the lines to be hung within the substation; the electrical information includes the charge density and phase current of the lines to be hung;

[0009] According to the hanging operation plan of the UAV in the substation area, the first initial hanging point g1, the second initial hanging point g2, and the nth initial hanging point g1 are determined in sequence for the UAV to stop and hang in the substation area. n ;

[0010] A three-dimensional coordinate system is established in the substation area where the drone needs to perform the line hanging operation, and the three-dimensional coordinate system takes the empirical point O determined based on experience on the ground of the substation as the origin; the xy plane of the three-dimensional coordinate system is located on the ground; the first initial line hanging point g1, the second initial line hanging point g2, and the nth initial line hanging point g n Coordinates in the three-dimensional coordinate system;

[0011] Step 2: Starting from the first initial hanging line point g1, iterate along the direction of the fastest decrease of the electric field and magnetic field to obtain the first corrected hanging line point g1′ where the drone is least affected by electromagnetic interference;

[0012] Step 3: Repeat the principle of step 2 to obtain the second corrected hanging line point g2′, the third corrected hanging line point g3′ of the drone until the nth corrected hanging line point g n ′’s coordinates;

[0013] The UAV operation trajectory control objective function is established with the goal of minimizing the total flight distance of the UAV traversing n correction hanging line points, as shown in the following formula (1):

[0014]

[0015] In formula (1), d ij ′ is the distance between the i-th and j-th correction hanging points among the n correction hanging points; and are the x-axis, y-axis and z-axis coordinates of the i-th correction hanging point among the n correction hanging points; and are the x-axis, y-axis and z-axis coordinates of the j-th correction hanging point among the n correction hanging points; E i ′ is the electric field intensity of the ith correction hanging point among the n correction hanging points; E t is the UAV electric field protection threshold; M i ′ is the magnetic field value of the ith correction hanging point among the n correction hanging points, M t is the drone magnetic field protection threshold, O i ′ is the other physical quantity of the ith correction hanging point among the n correction hanging points, O i It is the protection threshold of other physical quantities of the drone;

[0016] The improved spider bee algorithm is used to solve the UAV operation trajectory control objective function to obtain a UAV line hanging operation trajectory with minimal electromagnetic interference.

[0017] Further, the specific content of step 2 is as follows:

[0018] Step 2.1: Collect the distance d1 between the first initial hanging point g1 and the first line to be hung in the substation and the charge density μ1 of the first line to be hung in real time and substitute them into the following formula (2) to calculate the first electric field intensity E of the first initial hanging point g1 in the substation area: 1 ,

[0019]

[0020] In formula (2), and are the electric field intensity components in three directions of the first initial hanging point g1 in the three-dimensional coordinate system; α1 is the first potential of the first initial hanging point g1 in the first line to be hung in the substation area; ε0 is the dielectric constant of vacuum; c1 is the length of the first line to be hung; λ1 is the local coordinate along the direction of the first line to be hung;

[0021] The first magnetic field strength B of the first initial hanging point g1 in the substation area is calculated according to the following formula (3): 1 ,

[0022]

[0023] In formula (3), and are respectively the magnetic field intensity components of the first initial hanging line point g1 in three directions in the three-dimensional coordinate system; and They are respectively and conjugation of; and are the unit vectors in three directions in the three-dimensional coordinate system; τ0 is the vacuum magnetic permeability; D is the diameter of the first line to be hung; The nth phase current of the first line to be connected; R nx 、R ny and R nz are the components of the spatial distance between the nth sub-conductor and the power point in the x, y, and z directions; dx n is the integral symbol;

[0024] Step 2.2: Initialize the number of iterations k, so that the number of iterations k is equal to 1; set the first electric field strength E 1 and the first magnetic field strength B 1The first iterative electric field strength of the first initial hanging line point g1 when the iteration number k is equal to 1 and the first iteration magnetic field strength The x-axis coordinate x of the first initial hanging line point g1 in the three-dimensional coordinate system is 1 , y-axis coordinate y 1 and the z-axis coordinate z 1 As the first iteration x-axis coordinate of the first initial hanging line point g1 when the iteration number k is equal to 1 First iteration y-axis coordinate and the first iteration z-axis coordinate

[0025] Step 2.3: The first iterative electric field strength and the first iteration magnetic field strength Substitute it into the following formula (4) to make a judgment:

[0026]

[0027] In formula (3), ε1 and ε2 are the first discrimination experience threshold and the second discrimination experience threshold respectively;

[0028] If formula (4) is not satisfied, the first iteration x-axis coordinate of the first initial hanging line point g1 when the iteration number k is equal to 1 is First iteration y-axis coordinate and the first iteration z-axis coordinate As the coordinates of the first corrected hanging line point g1′, and continue to perform the above step 3;

[0029] If formula (4) is satisfied, the first iteration x-axis coordinate First iteration y-axis coordinate and the first iteration z-axis coordinate Substitute into the following formula (5) for iterative update and add 1 to the number of iterations k to obtain the second iteration x-axis coordinate of the first initial hanging line point g1 when the number of iterations k is equal to 2: Second iteration y-axis coordinate and the second iteration z-axis coordinate

[0030]

[0031] In formula (5), and are the x-axis, y-axis and z-axis coordinates before iteration; Δx, Δy and Δz are the unit quantities in the x-axis, y-axis and z-axis directions respectively; and They are the x-axis, y-axis and z-axis coordinates after iteration;

[0032] Step 2.4: Set the second iteration x-axis coordinate Second iteration y-axis coordinate and the second iteration z-axis coordinate According to the principles of formulas (2) and (3), the second iterative electric field strength of the first initial hanging line point g1 when the number of iterations k is equal to 2 is calculated as follows: and the second iterative magnetic field strength The second iterative electric field strength and the second iterative magnetic field strength Replace the first iterative electric field strength and the first iteration magnetic field strength Substitute into formula (4) to make a judgment,

[0033] If formula (4) is not satisfied, the x-axis coordinate of the first initial hanging line point g1 when the number of iterations k is equal to 2 is set to Second iteration y-axis coordinate and the second iteration z-axis coordinate As the coordinates of the first corrected hanging line point g1′, and continue to perform the above step 3;

[0034] If formula (4) is satisfied, the x-axis coordinate of the second iteration is Second iteration y-axis coordinate and the second iteration z-axis coordinate Substitute into formula (5) for iterative update and add 1 to the number of iterations k to obtain the third iteration x-axis coordinate of the first initial hanging line point g1 when the number of iterations k is equal to 3 The third iteration y-axis coordinate and the third iteration z-axis coordinate

[0035] Step 2.5: Repeat the principles of steps 2.3 and 2.4 until formula (4) is satisfied. The iterative x-axis coordinates, iterative and iterative z-axis coordinates of the first initial hanging line point g1 when formula (4) is satisfied are used as the coordinates of the first revised hanging line point g1′, and continue to execute the above step 3.

[0036] The beneficial effects of the present invention are as follows: the present invention adopts an improved gradient method to iteratively optimize the n initial hanging points of the drone determined according to experience along the direction where the electric field and the magnetic field drop fastest, and obtains n corrected hanging points. The inspection route is formed according to the lines between the n corrected hanging points, and electromagnetic interference is taken into consideration and avoided by optimizing the trajectory to maximize the safety and feasibility of drone inspections. DETAILED DESCRIPTION

[0037] The following is a further explanation of the trajectory control method of the UAV hanging line operation in a complex electromagnetic environment in combination with the specific embodiment of the present invention.

[0038] Example

[0039] The trajectory control method for a UAV wire-hanging operation in a complex electromagnetic environment in this embodiment includes the following steps:

[0040] Step 1: Obtain site information and electrical information of the substation area where the drone needs to perform line hanging operations. The site information includes the number and location of the lines to be hung within the substation; the electrical information includes the charge density and phase current of the lines to be hung.

[0041] According to the UAV hanging line operation plan in the substation area, the first initial hanging line point g1, the second initial hanging line point g2, and the nth initial hanging line point g1 are determined in sequence. n ;

[0042] A three-dimensional coordinate system is established in the substation area where the drone needs to perform the line hanging operation. The three-dimensional coordinate system takes the empirical point O determined based on experience on the ground of the substation as the origin; the xy plane of the three-dimensional coordinate system is located on the ground; the first initial line hanging point g1, the second initial line hanging point g2, and so on until the nth initial line hanging point g n Coordinates in a three-dimensional coordinate system;

[0043] Step 2: Starting from the first initial hanging line point g1, iterate along the direction of the fastest decrease in electric and magnetic fields to obtain the first corrected hanging line point g1′ where the drone is least affected by electromagnetic interference. The details are as follows:

[0044] Step 2.1: Collect the distance d1 between the first initial hanging point g1 and the first line to be hung in the substation and the charge density μ1 of the first line to be hung in real time and substitute them into the following formula (1) to calculate the first electric field intensity E of the first initial hanging point g1 in the substation area: 1 ,

[0045]

[0046] In formula (1), and are the electric field intensity components of the first initial hanging point g1 in the three directions in the three-dimensional coordinate system; α1 is the first potential of the first initial hanging point g1 in the first line to be hung in the substation area; ε0 is the vacuum dielectric constant; c1 is the line length of the first line to be hung; λ1 is the local coordinate along the direction of the first line to be hung;

[0047] The first magnetic field strength B of the first initial hanging point g1 in the substation area is calculated according to the following formula (2):1 ,

[0048]

[0049] In formula (2), and are the magnetic field intensity components of the first initial hanging line point g1 in three directions in the three-dimensional coordinate system; and They are and conjugation of; and are the unit vectors in three directions in the three-dimensional coordinate system; τ0 is the magnetic permeability of vacuum; D is the diameter of the first line to be hung; The nth phase current of the first line to be connected is R nx 、R ny and R nz They are; dx n yes;

[0050] Step 2.2: Initialize the number of iterations k, so that the number of iterations k is equal to 1; set the first electric field strength E 1 and the first magnetic field strength B 1 As the first iterative electric field strength of the first initial hanging line point g1 when the iteration number k is equal to 1 and the first iteration magnetic field strength Set the x-axis coordinate x of the first initial hanging line point g1 in the three-dimensional coordinate system 1 , y-axis coordinate y 1 and the z-axis coordinate z 1 As the first iteration x-axis coordinate of the first initial hanging line point g1 when the iteration number k is equal to 1 First iteration y-axis coordinate and the first iteration z-axis coordinate

[0051] Step 2.3: Set the first iteration electric field strength and the first iteration magnetic field strength Substitute it into the following formula (3) to make a judgment:

[0052]

[0053] In formula (3), ε1 and ε2 are the first discrimination experience threshold and the second discrimination experience threshold respectively;

[0054] If formula (3) is not satisfied, the first iteration x-axis coordinate of the first initial hanging line point g1 when the iteration number k is equal to 1 is First iteration y-axis coordinate and the first iteration z-axis coordinate As the coordinates of the first corrected hanging line point g1′, and continue to perform the above step 3;

[0055] If formula (3) is satisfied, the x-axis coordinate of the first iteration First iteration y-axis coordinate and the first iteration z-axis coordinate Substitute into the following formula (4) for iterative update and add 1 to the number of iterations k to obtain the second iteration x-axis coordinate of the first initial hanging line point g1 when the number of iterations k is equal to 2: Second iteration y-axis coordinate and the second iteration z-axis coordinate

[0056]

[0057] In formula (4), and are the x-axis, y-axis and z-axis coordinates before iteration; Δx, Δy and Δz are the unit quantities in the x-axis, y-axis and z-axis directions respectively; and They are the x-axis, y-axis and z-axis coordinates after iteration;

[0058] Step 2.4: Set the second iteration x-axis coordinate Second iteration y-axis coordinate and the second iteration z-axis coordinate According to the principles of formulas (1) and (2), the second iteration electric field strength of the first initial hanging point g1 when the iteration number k is equal to 2 is calculated as follows: and the second iterative magnetic field strength The second iterative electric field strength and the second iterative magnetic field strength Replace the first iteration electric field strength and the first iteration magnetic field strength Substitute into formula (3) to make a judgment,

[0059] If formula (3) is not satisfied, the x-axis coordinate of the first initial hanging line point g1 at the second iteration when the number of iterations k is equal to 2 is Second iteration y-axis coordinate and the second iteration z-axis coordinate As the coordinates of the first corrected hanging line point g1′, and continue to perform the above step 3;

[0060] If formula (3) is satisfied, the x-axis coordinate of the second iteration Second iteration y-axis coordinate and the second iteration z-axis coordinate Substitute into formula (4) for iterative update and add 1 to the number of iterations k to obtain the third iteration x-axis coordinate of the first initial hanging line point g1 when the number of iterations k is equal to 3 The third iteration y-axis coordinate and the third iteration z-axis coordinate

[0061] Step 2.5: Repeat the principles of steps 2.3 and 2.4 until formula (3) is satisfied. The iterative x-axis coordinates, iterative and iterative z-axis coordinates of the first initial hanging line point g1 when formula (3) is satisfied are used as the coordinates of the first revised hanging line point g1′, and continue to perform the above step 3;

[0062] Step 3: Repeat the principle of step 2 to obtain the second corrected hanging line point g2′, the third corrected hanging line point g3′ of the drone until the nth corrected hanging line point g n ′’s coordinates;

[0063] The UAV operation trajectory control objective function is established with the goal of minimizing the total flight distance of the UAV traversing n correction hanging line points, as shown in the following formula (5):

[0064]

[0065] In formula (5), d ij ′ is the distance between the i-th and j-th correction hanging points among the n correction hanging points; and are the x-axis, y-axis and z-axis coordinates of the i-th correction hanging point among the n correction hanging points; and are the x-axis, y-axis and z-axis coordinates of the j-th correction hanging point among the n correction hanging points; E i ′ is the electric field intensity of the ith correction hanging point among the n correction hanging points; E t is the UAV electric field protection threshold; M i ′ is the magnetic field value of the ith correction hanging point among the n correction hanging points, M t is the drone magnetic field protection threshold, O i ′ is the other physical quantity of the ith correction hanging point among the n correction hanging points, O i It is the protection threshold of other physical quantities of the drone;

[0066] The improved spider bee algorithm is used to solve the UAV operation trajectory control objective function to obtain a UAV line hanging operation trajectory with minimal electromagnetic interference.

[0067] The improved spider bee algorithm includes the following:

[0068] 1) Search behavior

[0069] The spider bee randomly explores the search space with a constant step size or explores the area around the spider's drop point to find more suitable prey. The spider bee's position update formula is as follows (6):

[0070]

[0071] In formula (6): W i t+1 and W i t are the positions of spider bee i at the t-th iteration and the t+1-th iteration, respectively. and are all individuals randomly selected from the population at the tth iteration. μ1 and μ2 are used to determine the direction of the spider bee's movement. r2, r3 and r4 are random numbers in (0,1). UB and LB are the upper and lower bounds of the spider bee's position, respectively.

[0072] 2) Pursuit

[0073] When the prey is found, the spider bee will initiate a trapping attack on the prey. However, the spider will escape from the spider bee, and the distance between the two will gradually increase. The pursuit behavior turns into exploration behavior, and the position update formula is as follows (7):

[0074]

[0075] In formula (7), C is the distance control factor that determines the speed of the spider bee. When C>0.5, the spider bee is fast, and vice versa, the prey is fast; r5 is a random number in (0,1); v is a vector between [-k,k] that follows a normal distribution.

[0076] 3) Nesting behavior

[0077] The spider wasp drags the captured prey to a nest of suitable size or randomly selects a female spider's location to build a nest. The two calculation formulas are shown in the following formula (8):

[0078]

[0079] In formula (8), W 0 is the optimal position of the current spider bee, γ is the data generated by levy's flight, and U is a random vector of all 0s or 1s.

[0080] 4) Mating behavior

[0081] Offspring are produced through a crossover operation between male and female spider bees, which has a specific probability, as shown in the following formula:

[0082]

[0083] Where Crossover is the uniform crossover operator between male and female bees, is the drone vector, C R is the crossover rate of the crossover operator.

[0084] Since the Spider Bee Algorithm has the disadvantages of being easily trapped in local optimality and slow early convergence when dealing with complex problems, an improved Spider Bee optimization algorithm is proposed to improve it. The specific improvement strategies are as follows:

[0085] 1.1) In order to improve the convergence speed and accuracy of the algorithm, the early stage of the algorithm should focus on global exploration, and the later stage should focus on refining the search for the current optimal solution. Therefore, a dynamic weight factor as shown in formula (9) is introduced in the search stage to improve the efficiency of the early search of the algorithm.

[0086]

[0087] In formula (9), ω max 、ω min are the maximum and minimum values of the weight, respectively, t max is the maximum number of iterations, and t is the current number of iterations.

[0088] After the dynamic weight factor is introduced, the spider bee position update formula in the exploration phase is shown in formula (10).

[0089]

[0090] 1.2) To prevent the spider bee algorithm from falling into a local optimal solution during the optimization process, a Gaussian mutation operator is introduced during the spider bee mating phase. The standard Gaussian distribution is shown in Equation (11). Gaussian mutation uses a Gaussian distribution to generate mutation vectors, performing precise searches near the current optimal solution, enhancing the algorithm's local search capabilities and balancing global and local searches.

[0091]

[0092] After introducing the Gaussian mutation operator, the spider bee position update formula is shown in formula (12).

[0093]

Claims

1. A method for controlling the trajectory of a drone's line-hanging operation in a complex electromagnetic environment, characterized by: The following steps are involved: Step 1: Obtain site information and electrical information of the substation area where the drone needs to perform line hanging operations. The site information includes the number and location information of the lines to be hung within the substation; the electrical information includes the charge density and phase current of the lines to be hung; According to the hanging operation plan of the UAV in the substation area, the first initial hanging point g1, the second initial hanging point g2, and the nth initial hanging point g1 are determined in sequence for the UAV to stop and hang in the substation area. n ; A three-dimensional coordinate system is established in the substation area where the drone needs to perform the line hanging operation, and the three-dimensional coordinate system takes the empirical point O determined based on experience on the ground of the substation as the origin; the xy plane of the three-dimensional coordinate system is located on the ground; the first initial line hanging point g1, the second initial line hanging point g2, and the nth initial line hanging point g n Coordinates in the three-dimensional coordinate system; Step 2: Starting from the first initial hanging line point g1, iterate along the direction of the fastest decrease of the electric field and magnetic field to obtain the first corrected hanging line point g1′ where the drone is least affected by electromagnetic interference; Step 3: Repeat the principle of step 2 to obtain the second corrected hanging line point g2′, the third corrected hanging line point g3′ of the drone until the nth corrected hanging line point g n ′’s coordinates; The UAV operation trajectory control objective function is established with the goal of minimizing the total flight distance of the UAV traversing n correction hanging line points, as shown in the following formula (1): In formula (1), d ij ′ is the distance between the i-th and j-th correction hanging points among the n correction hanging points; and are the x-axis, y-axis and z-axis coordinates of the i-th correction hanging point among the n correction hanging points; and are the x-axis, y-axis and z-axis coordinates of the j-th correction hanging point among the n correction hanging points; E i ′ is the electric field intensity of the ith correction hanging point among the n correction hanging points; E t is the UAV electric field protection threshold; M i ′ is the magnetic field value of the ith correction hanging point among the n correction hanging points, M t is the drone magnetic field protection threshold, O i ′ is the other physical quantity of the ith correction hanging point among the n correction hanging points, O i It is the protection threshold of other physical quantities of the drone; The improved spider bee algorithm is used to solve the UAV operation trajectory control objective function to obtain a UAV line hanging operation trajectory with minimal electromagnetic interference.

2. The control method according to claim 1, wherein: The specific content of step 2 is as follows: Step 2.1: Collect the distance d1 between the first initial hanging point g1 and the first line to be hung in the substation and the charge density μ1 of the first line to be hung in real time and substitute them into the following formula (2) to calculate the first electric field intensity E of the first initial hanging point g1 in the substation area: 1 , In formula (2), and are the electric field intensity components in three directions of the first initial hanging point g1 in the three-dimensional coordinate system; α1 is the first potential of the first initial hanging point g1 in the first line to be hung in the substation area; ε0 is the dielectric constant of vacuum; c1 is the length of the first line to be hung; λ1 is the local coordinate along the direction of the first line to be hung; The first magnetic field strength B of the first initial hanging point g1 in the substation area is calculated according to the following formula (3): 1 , In formula (3), and are respectively the magnetic field intensity components of the first initial hanging line point g1 in three directions in the three-dimensional coordinate system; and They are respectively and conjugation of; and are the unit vectors in the three directions of the three-dimensional coordinate system respectively; τ0 is the magnetic permeability of vacuum; D is the diameter of the first line to be hung; The nth phase current of the first line to be connected; R nx 、R ny and R nz are the components of the spatial distance between the nth sub-conductor and the power point in the x, y, and z directions; dx n is the integral symbol; Step 2.2: Initialize the number of iterations k, so that the number of iterations k is equal to 1; set the first electric field strength E 1 and the first magnetic field strength B 1 The first iterative electric field strength of the first initial hanging line point g1 when the iteration number k is equal to 1 and the first iteration magnetic field strength The x-axis coordinate x of the first initial hanging line point g1 in the three-dimensional coordinate system is 1 , y-axis coordinate y 1 and the z-axis coordinate z 1 As the first iteration x-axis coordinate of the first initial hanging line point g1 when the iteration number k is equal to 1 First iteration y-axis coordinate and the first iteration z-axis coordinate Step 2.3: The first iterative electric field strength and the first iteration magnetic field strength Substitute it into the following formula (4) to make a judgment: In formula (3), ε1 and ε2 are the first discrimination experience threshold and the second discrimination experience threshold respectively; If formula (4) is not satisfied, the first iteration x-axis coordinate of the first initial hanging line point g1 when the iteration number k is equal to 1 is First iteration y-axis coordinate and the first iteration z-axis coordinate As the coordinates of the first corrected hanging line point g1′, and continue to perform the above step 3; If formula (4) is satisfied, the first iteration x-axis coordinate First iteration y-axis coordinate and the first iteration z-axis coordinate Substitute into the following formula (5) for iterative update and add 1 to the number of iterations k to obtain the second iteration x-axis coordinate of the first initial hanging line point g1 when the number of iterations k is equal to 2: Second iteration y-axis coordinate and the second iteration z-axis coordinate In formula (5), and are the x-axis, y-axis and z-axis coordinates before iteration; Δx, Δy and Δz are the unit quantities in the x-axis, y-axis and z-axis directions respectively; and They are the x-axis, y-axis and z-axis coordinates after iteration; Step 2.4: Set the second iteration x-axis coordinate Second iteration y-axis coordinate and the second iteration z-axis coordinate According to the principles of formulas (2) and (3), the second iterative electric field strength of the first initial hanging line point g1 when the number of iterations k is equal to 2 is calculated as follows: and the second iterative magnetic field strength The second iterative electric field strength and the second iterative magnetic field strength Replace the first iterative electric field strength and the first iteration magnetic field strength Substitute into formula (4) to make a judgment, If formula (4) is not satisfied, the x-axis coordinate of the first initial hanging line point g1 when the number of iterations k is equal to 2 is set to Second iteration y-axis coordinate and the second iteration z-axis coordinate As the coordinates of the first corrected hanging line point g1′, and continue to perform the above step 3; If formula (4) is satisfied, the x-axis coordinate of the second iteration is Second iteration y-axis coordinate and the second iteration z-axis coordinate Substitute into formula (5) for iterative update and add 1 to the number of iterations k to obtain the third iteration x-axis coordinate of the first initial hanging line point g1 when the number of iterations k is equal to 3 The third iteration y-axis coordinate and the third iteration z-axis coordinate Step 2.5: Repeat the principles of steps 2.3 and 2.4 until formula (4) is satisfied. The iterative x-axis coordinates, iterative and iterative z-axis coordinates of the first initial hanging line point g1 when formula (4) is satisfied are used as the coordinates of the first revised hanging line point g1′, and continue to execute the above step 3.

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