A method for analyzing coupled motion of a surface ship and a towed system

Abstract

The application discloses a water surface ship and towing system coupling motion analysis method and belongs to the technical field of ship and ocean engineering. The application constructs a six-degree-of-freedom motion model of a water surface ship, constructs a towing cable motion control model, constructs a six-degree-of-freedom motion model of an underwater towed body, constructs a motion control model of the water surface ship-towing cable-towed body, adopts a three-dimensional panel method to determine the hydrodynamic coefficients in the ship motion model, adopts a fourth-order Runge-Kutta method to determine the six-degree-of-freedom motion of the water surface ship and the towed body, and adopts a finite difference method to determine the tension and oscillation motion of the towing cable. The application quantitatively analyzes the influence of the water surface ship oscillation motion on the towing force of the towing cable and the oscillation motion of the towing cable and the influence of the towing cable on the water surface ship oscillation motion, thereby assisting in optimizing the tail structure of the water surface ship, the shape of the towing cable and the shape of the towed body, improving the navigation performance of the water surface ship and improving the operation safety of the towing system.

Description

Technical Field

[0001] This invention relates to a method for coupled motion analysis of surface vessels and towing systems, belonging to the field of ship and marine engineering technology. Background Technology

[0002] Marine towed systems, as effective underwater detection devices, play a crucial role in marine exploration and underwater acoustic monitoring. A typical marine towed system consists of a towline and a towed body, with the towed body carrying various sensors and detection equipment to perform diverse tasks. The marine towed system is propelled by a surface vessel. While navigating at sea, the surface vessel is affected by wind, waves, and currents, causing it to move. The underwater towline and towed body are also affected by currents and swells, resulting in displacement and oscillations. Since the towed body's power is provided by the towline, the surface vessel's motion is transmitted to the towed body through the towline, causing changes in the towed body's attitude and motion, thus affecting its underwater operations. Conversely, changes in the towed body's attitude and motion not only affect its hydrodynamic performance but are also transmitted to the surface vessel through the towline, influencing its attitude and motion. Therefore, the motions of the surface vessel, towline, and towed body are mutually influential and strongly coupled.

[0003] Currently, hydrodynamic analyses of surface vessels and marine towing systems mainly focus on the impact of surface vessel motion on tow cable motion and tow body motion, as well as the impact of marine towing systems on the maneuverability of surface vessels. There are no analytical methods related to the impact of marine towing systems on the seakeeping of surface vessels or the impact of surface vessel swaying motion in waves on marine towing systems. Summary of the Invention

[0004] The purpose of this invention is to provide a method for analyzing the coupled motion of a surface vessel and a towing system. By analyzing the coupled swaying motion of the surface vessel, towline, and underwater tow body in the marine environment, the method analyzes the tension distribution of the towline, quantifies the influence of the swaying motion of the surface tugboat on the towing force of the towline, the influence of the swaying motion of the surface tugboat on the swaying motion of the towline and tow body, and the influence of the towline and tow body on the swaying motion of the surface tugboat. This method helps to optimize the stern structure of the surface tugboat, the shape of the towline, and the shape of the tow body, thereby improving the operational safety of the towing system.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] The present invention provides a method for coupled motion analysis of a surface vessel and a towing system, comprising the following steps:

[0007] Step 1: Construct a six-degree-of-freedom motion model of the surface vessel based on the three-dimensional time-domain method, as shown in Equation (1):

[0008]

[0009] Where u, v, w, p, q, and r are the ship's six degrees of freedom velocities, respectively. η1, η2, η3, η4, η5, and η6 represent the ship's six degrees of freedom accelerations, and η6 represent the ship's six degrees of freedom motions. For the ship's generalized inertia matrix, These represent the ship's additional mass and damping coefficient when the encounter frequency is infinite. The coefficient matrix is ​​shown in equation (2). This is the static restoring force coefficient of the ship. For delay function, For wave interference force, F tow The tension transmitted from the head end of the tow cable;

[0010]

[0011] Where U is the speed of the ship, M s The displacement of the ship;

[0012] As a preferred method, the surface element method with the Green's function of the three-dimensional moving pulsating source as the kernel is used to determine the additional mass, damping coefficient and wave interference force of the surface vessel at different encounter frequencies.

[0013] Step 2: Construct the motion control model for the tow cable, as shown in equation (3):

[0014]

[0015] Where t is time, s is the arc length of the tow cable when it is not stretched, M, N and Q are coefficient matrices, and Y is the state variable of the tow cable, as shown in equations (4)-(7).

[0016]

[0017] Y = Y(T,V) t V n V b ,θ,φ) (5)

[0018]

[0019]

[0020] Where T is the tension of the towing cable element, and V t V n V b Let J represent the velocity components of the tow cable element in the local coordinate system of the tow cable, θ and φ be the attitude angles of the tow cable element, and J be the velocity components of the tow cable element in the local coordinate system of the tow cable. n J b The components of water flow velocity in different directions are distinguished. U is the component of the water flow acceleration. t U n and U b C represents the velocity component of the tow cable relative to the water flow. t C n To represent the tangential and normal drag coefficients of the towed cable, let m be the mass per unit length of the towed cable without tension, ρ be the fluid density, g be the acceleration due to gravity, m1 be m + ρA, A be the cross-sectional area of ​​the towed cable without tension, w be the weight per unit length of the towed cable in water, w = (m - ρA)g, d0 be the diameter of the towed cable without tension, and d be the diameter of the towed cable after tension. U is the velocity of the towed cable element relative to the ocean current, e = 1 / EA, E is the Young's modulus of the towed cable, and ε is the strain.

[0021] Step 3: Construct a six-degree-of-freedom motion model of the underwater towed body, as shown in equation (8):

[0022]

[0023] Where, m b Let x be the mass of the towed body. Gb y Gb and z Gb These are the longitudinal, lateral, and vertical coordinates of the drag center of gravity, respectively. xx I yy I zz I xy I xz I yz Let be the moments of inertia of the towed body about the coordinate axes of the towed body's follower coordinate system, u, v, and w be the longitudinal, lateral, and vertical velocities of the towed body's center of gravity in the towed body's follower coordinate system, respectively; p and q be the roll and pitch angular velocities of the towed body's center of gravity, respectively; and r be the yaw angular velocity. Let X, Y, and Z represent the six degrees of freedom accelerations of the towed body, respectively, and let K represent the longitudinal, lateral, and vertical forces acting on the towed body, respectively. b M b N b The torque of the external force about the center of gravity of the dragged object;

[0024] Step 4: Determine the boundary conditions at the bow and stern of the towline, and construct a motion control model of the surface vessel, towline, and towed body by coupling the boundary conditions.

[0025] The boundary condition at the tow cable head is a continuous condition, and the velocity at the tow cable head is the same as the velocity at the towing point of the surface vessel, as shown in equation (9):

[0026] [V s +Ω s ×r CS ] = EDV CS(9)

[0027] Among them, V s Ω represents the translational speed of a surface vessel. s Let r be the angular velocity of the surface vessel. CS Let V be the position coordinates of the towing point in the surface vessel's moving coordinate system G1xyz, E be the transformation matrix between the fixed spatial coordinate system and the surface vessel's moving coordinate system, D be the transformation matrix between the fixed spatial coordinate system and the towing cable's local coordinate system, and V be the position coordinates of the towing point in the surface vessel's moving coordinate system G1xyz. CS The velocity of the tow cable head end in the tow cable local coordinate system;

[0028] When the trailing cable is not carrying the tow body, the trailing cable is a free end with zero tension and zero Euler angle with respect to arc length, as shown in equation (10):

[0029] T CE =0, θ CE '=0,φ CE =0 (10)

[0030] Among them, T CE For the tension at the tail end of the tow cable, θ CE 'and φ CE ' is the rate of change of the Euler angle with respect to the arc length at the trailing end of the cable;

[0031] When the trailing cable pulls the tow body, the speed of the trailing cable is the same as the speed of the tow body, as shown in equation (11):

[0032] [V tb +Ω tb ×r CE ] = EDV CE (11)

[0033] Among them, V tb Ω represents the translational velocity of the towed body. tb Let r be the rotational angular velocity of the towed body. CE Let V be the position coordinates of the tow cable tail end in the tow body's moving coordinate system G2xyz, E be the transformation matrix between the fixed spatial coordinate system and the tow body's moving coordinate system, D be the transformation matrix between the fixed spatial coordinate system and the tow cable's local coordinate system, and V be the position coordinates of the tow cable tail end in the tow body's moving coordinate system G2xyz. CE The velocity of the trailing cable end in the local coordinate system of the tow cable;

[0034] Step 5: Use the three-dimensional surface element method to determine the hydrodynamic coefficients in the ship motion model, use the fourth-order Runge-Kutta method to determine the six degrees of freedom motion of the surface ship in the surface ship motion model, determine the six degrees of freedom motion of the towed body in the towed body motion model, and use the finite difference method to determine the tension and swaying motion of the towed cable in the towed cable motion control model.

[0035] The fourth-order Runge-Kutta method is shown in equations (12) and (13):

[0036]

[0037]

[0038] Where t is time, Δt is time step, y(t) is the state variable at time t, y(t+Δt) is the state variable at time t+Δt, and k1, k2, k3 and k4 are coefficients;

[0039] Equations (12) and (13) are used to determine the six degrees of freedom motion η1, η2, η3, η4, η5, and η6 of the surface vessel in the surface vessel motion model, and to determine the six degrees of freedom motion η of the towed body in the towed body motion model. tb1 η tb2 η tb3 η tb4 η tb5 η tb6 ;

[0040] The finite difference method employs a central difference approach in both time and space, discretizing the tow cable along its length into n infinitesimal length elements Δs, with the tow cable nodes being s0, s1, ..., s2. n Where s0 is the tow cable head, i.e., the tow point, s n For the trailing cable tail end; discretized in time into a series of time steps Δt;

[0041] At tow cable node j, at t i The motion parameters at time t are shown in equation (14):

[0042]

[0043] With tow cable node (t) i+12 ,s j+12 Using ) as the difference base point, the difference form of equation (3) in time and space is shown in equation (15):

[0044]

[0045] In the formula and Let be the coefficient matrix of the cable element in the j-th segment at the i-th time step. Let be the state variable of the cable element in the j-th segment at the i-th time step;

[0046] The tension T and oscillation motion η of the tow cable in the tow cable motion control model are determined by Equation (15) using the Newton-Raphson iteration method. c1 η c2 η c3 η c4 ηc5 η c6 ;

[0047] Furthermore, step 6 is also included: Based on the motion response of the surface vessel, tow cable, and underwater tow body determined in step 5, and the tension distribution of the tow cable, it is possible to quantitatively analyze the influence of the surface vessel's swaying motion on the tow force and swaying motion of the tow cable, as well as the influence of the tow cable on the surface vessel's swaying motion, thereby assisting in optimizing the stern structure of the surface vessel, the shape of the tow cable, and the shape of the tow body, improving the navigation performance of the surface vessel, and enhancing the operational safety of the towing system.

[0048] Beneficial effects:

[0049] This invention provides a method for coupled motion analysis of a surface vessel and a towing system. It employs a six-degree-of-freedom motion model to describe the motion of the surface vessel and the underwater tow body, and a tow cable motion control model to describe the motion of the tow cable. By coupling the boundary conditions at the tow cable's bow and stern ends, a motion model of the surface vessel, tow cable, and underwater tow body is established. Furthermore, the fourth-order Runge-Kutta method and the finite difference method are used to obtain the motion responses of the surface vessel, tow cable, and underwater tow body, and to obtain the tension distribution of the tow cable. This allows for quantitative analysis of the influence of the surface vessel's swaying motion on the tow cable's drag force and the swaying motion of the tow cable and tow body, as well as the influence of the tow cable and tow body on the surface vessel's swaying motion. This, in turn, optimizes the design of the surface vessel's stern structure, the tow cable's shape, and the tow body's shape, thereby improving the surface vessel's navigation performance and enhancing the operational safety of the towing system. Attached Figure Description

[0050] Figure 1 This is a flowchart of a method for coupled motion analysis of a surface vessel and a towing system according to the present invention.

[0051] Figure 2 A schematic diagram of a surface vessel and its towing system;

[0052] Figure 3 A schematic diagram of the motion response time-history curve of a surface vessel;

[0053] Figure 4 This is a schematic diagram of the tension time-history curve at the head of the tow cable;

[0054] Figure 5 This is a schematic diagram of the motion response time history curve at the head end of the tow cable.

[0055] Figure 6 This is a schematic diagram of the motion response time history curve of the towed body. Detailed Implementation

[0056] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0057] Example 1:

[0058] This embodiment applies a coupled motion analysis method for surface vessels and towing systems according to the present invention. By analyzing the coupled swaying motion of the surface vessel, towline, and underwater tow body in a marine environment, as well as the tension distribution of the towline, it quantifies the influence of the surface tug's swaying motion on the towline's drag force and the towline's swaying motion, and the influence of the towline on the surface tug's swaying motion. Figure 1 As shown, it includes the following steps:

[0059] Step 1: Construct a six-degree-of-freedom motion model of the surface vessel based on the three-dimensional time-domain method, as shown in Equation (1):

[0060]

[0061] Where u, v, w, p, q, and r are the ship's six degrees of freedom velocities, respectively. η1, η2, η3, η4, η5, and η6 represent the ship's six degrees of freedom accelerations, and η6 represent the ship's six degrees of freedom motions. For the ship's generalized inertia matrix, These represent the ship's additional mass and damping coefficient when the encounter frequency is infinite. The coefficient matrix is ​​shown in equation (2). For the static restoring force coefficient of the ship, For delay function, For wave interference force, F tow The tension transmitted from the head end of the tow cable;

[0062]

[0063] Where U is the speed of the ship, M s The displacement of the ship;

[0064] In the embodiment, the surface element method with the Green's function of a three-dimensional moving pulsating source as the kernel is used to determine the additional mass, damping coefficient and wave interference force of the surface vessel at different encounter frequencies.

[0065] In the embodiment, the surface vessel, towline, and tow body are as follows: Figure 2 As shown, the surface vessel's speed U is 6 knots, and its displacement M is... s It is 5,000 tons;

[0066] Step 2: Construct the motion control model for the tow cable, as shown in equation (3):

[0067]

[0068] Where t is time, s is the arc length of the tow cable when it is not stretched, M, N and Q are coefficient matrices, and Y is the state variable of the tow cable, as shown in equations (4)-(7).

[0069]

[0070] Y = Y(T,V) t V n V b ,θ,φ) (5)

[0071]

[0072]

[0073] Where T is the tension of the towing cable element, and V t V n V b Let J represent the velocity components of the tow cable element in the local coordinate system of the tow cable, θ and φ be the attitude angles of the tow cable element, and J be the velocity components of the tow cable element in the local coordinate system of the tow cable. n J b The components of water flow velocity in different directions are distinguished. U is the component of the water flow acceleration. t U n and U b C represents the velocity component of the tow cable relative to the water flow. t C n To represent the tangential and normal drag coefficients of the towed cable, let m be the mass per unit length of the towed cable without tension, ρ be the fluid density, g be the acceleration due to gravity, m1 be m + ρA, A be the cross-sectional area of ​​the towed cable without tension, w be the weight per unit length of the towed cable in water, w = (m - ρA)g, d0 be the diameter of the towed cable without tension, and d be the diameter of the towed cable after tension. U is the velocity of the towed cable element relative to the ocean current, e = 1 / EA, E is the Young's modulus of the towed cable, and ε is the strain.

[0074] In this embodiment, the tow cable is 2000m long, 0.05m in diameter, weighs 2.335N / m in water (w), and has a tangential drag coefficient C. t The normal drag coefficient C is 0.015. n It is 2.0;

[0075] Step 3: Construct a six-degree-of-freedom motion model of the underwater towed body, as shown in equation (8):

[0076]

[0077] Where, m b Let x be the mass of the towed body. Gb y Gb and zGb These are the longitudinal, lateral, and vertical coordinates of the drag center of gravity, respectively. xx I yy I zz I xy I xz I yz Let be the moments of inertia of the towed body about the coordinate axes of the towed body's follower coordinate system, u, v, and w be the longitudinal, lateral, and vertical velocities of the towed body's center of gravity in the towed body's follower coordinate system, respectively; p and q be the roll and pitch angular velocities of the towed body's center of gravity, respectively; and r be the yaw angular velocity. Let X, Y, and Z represent the six degrees of freedom accelerations of the towed body, respectively, and let K represent the longitudinal, lateral, and vertical forces acting on the towed body, respectively. b M b N b The torque of the external force about the center of gravity of the dragged object;

[0078] In the embodiment, the drainage volume m of the towing body b It is 1.5 tons;

[0079] Step 4: Determine the boundary conditions at the bow and stern of the towline, and construct a motion control model of the surface vessel, towline, and towed body by coupling the boundary conditions.

[0080] The boundary condition at the tow cable head is a continuous condition, and the velocity at the tow cable head is the same as the velocity at the towing point of the surface vessel, as shown in equation (9):

[0081] [V s +Ω s ×r CS ] = EDV CS (9)

[0082] Among them, V s Ω represents the translational speed of a surface vessel. s Let r be the angular velocity of the surface vessel. CS Let V be the position coordinates of the towing point in the surface vessel's moving coordinate system G1xyz, E be the transformation matrix between the fixed spatial coordinate system and the surface vessel's moving coordinate system, D be the transformation matrix between the fixed spatial coordinate system and the towing cable's local coordinate system, and V be the position coordinates of the towing point in the surface vessel's moving coordinate system G1xyz. CS The velocity of the tow cable head end in the tow cable local coordinate system;

[0083] When the trailing cable is not carrying the tow body, the trailing cable is a free end with zero tension and zero Euler angle with respect to arc length, as shown in equation (10):

[0084] T CE =0, θ CE '=0,φ CE =0 (10)

[0085] Among them, T CE For the tension at the tail end of the tow cable, θ CE 'and φ CE ' is the rate of change of the Euler angle with respect to the arc length at the trailing end of the cable;

[0086] When the trailing cable pulls the tow body, the speed of the trailing cable is the same as the speed of the tow body, as shown in equation (11):

[0087] [V tb +Ω tb ×r CE ] = EDV CE (11)

[0088] Among them, V tb Ω represents the translational velocity of the towed body. tb Let r be the rotational angular velocity of the towed body. CE Let V be the position coordinates of the tow cable tail end in the tow body's moving coordinate system G2xyz, E be the transformation matrix between the fixed spatial coordinate system and the tow body's moving coordinate system, D be the transformation matrix between the fixed spatial coordinate system and the tow cable's local coordinate system, and V be the position coordinates of the tow cable tail end in the tow body's moving coordinate system G2xyz. CE The velocity of the trailing cable end in the local coordinate system of the tow cable;

[0089] In the embodiment, the tail end of the tow cable tows the tow body, and the boundary condition of the head end of the tow cable is a continuity condition, that is, the speed of the head end of the tow cable is the same as the speed of the towing point at the stern of the vessel on the water surface, and the boundary condition of the tail end of the tow cable is that the speed of the tail end of the tow cable is the same as the speed of the tow body.

[0090] Step 5: Use the three-dimensional surface element method to determine the hydrodynamic coefficients in the ship motion model, use the fourth-order Runge-Kutta method to determine the six degrees of freedom motion of the surface ship in the surface ship motion model, determine the six degrees of freedom motion of the towed body in the towed body motion model, and use the finite difference method to determine the tension and swaying motion of the towed cable in the towed cable motion control model.

[0091] The fourth-order Runge-Kutta method is shown in equations (12) and (13):

[0092]

[0093]

[0094] Where t is time, Δt is time step, y(t) is the state variable at time t, y(t+Δt) is the state variable at time t+Δt, and k1, k2, k3 and k4 are coefficients;

[0095] Equations (12) and (13) are used to determine the six degrees of freedom motion η1, η2, η3, η4, η5, and η6 of the surface vessel in the surface vessel motion model, and to determine the six degrees of freedom motion η of the towed body in the towed body motion model.tb1 η tb2 η tb3 η tb4 η tb5 η tb6 ;

[0096] The finite difference method employs a central difference approach in both time and space, discretizing the tow cable along its length into n infinitesimal length elements Δs, with the tow cable nodes being s0, s1, ..., s2. n Where s0 is the tow cable head, i.e., the tow point, s n For the trailing cable tail end; discretized in time into a series of time steps Δt;

[0097] At tow cable node j, at t i The motion parameters at time t are shown in equation (14):

[0098]

[0099] With tow cable node (t) i+12 ,s j+12 Using ) as the difference base point, the difference form of equation (3) in time and space is shown in equation (15):

[0100]

[0101] In the formula and Let be the coefficient matrix of the cable element in the j-th segment at the i-th time step. Let be the state variable of the cable element in the j-th segment at the i-th time step;

[0102] The tension T and oscillation motion η of the tow cable in the tow cable motion control model are determined by Equation (15) using the Newton-Raphson iteration method. c1 η c2 η c3 η c4 η c5 η c6 ;

[0103] In the embodiment, through simulation, the heave motion response time-history curve of the surface vessel is as follows: Figure 3 As shown in the figure, the horizontal axis represents time t, and the vertical axis represents the dimensionless heave response of the surface vessel. The amplitude of the heave response of the surface vessel is greater than the wave amplitude, approximately 1.55 times the wave amplitude. The tension-time history curve at the towline tip is shown in the figure. Figure 4 As shown in the figure, the horizontal axis represents time t, and the vertical axis represents the tension at the tow cable head, which varies between 119 kN and 121 kN. The pitch angle time-history curve at the tow cable head is shown in the figure. Figure 5As shown in the figure, the horizontal axis represents time t, and the vertical axis represents the pitch angle at the tow cable tip, which ranges from -1.5° to 4.5°. The motion response time-history curve of the towed body is shown in the figure. Figure 6 As shown in the figure, the horizontal axis represents time t, and the vertical axis represents the heave motion response of the towed body. The amplitude of the heave motion response of the towed body is much smaller than the wave amplitude, approximately 0.062 times the wave amplitude.

[0104] Furthermore, step 6 is also included: Based on the motion response of the surface vessel, tow cable, and underwater tow body determined in step 5, and the tension distribution of the tow cable, it is possible to quantitatively analyze the influence of the surface vessel's swaying motion on the tow force and swaying motion of the tow cable, as well as the influence of the tow cable on the surface vessel's swaying motion, thereby assisting in optimizing the stern structure of the surface vessel, the shape of the tow cable, and the shape of the tow body, improving the navigation performance of the surface vessel, and enhancing the operational safety of the towing system.

[0105] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for coupled motion analysis of a surface vessel and its towing system, characterized in that: Includes the following steps: Step 1: Construct a six-degree-of-freedom motion model of the surface vessel based on the three-dimensional time-domain method, as shown in equation (1): （1） in, These represent the ship's six degrees of freedom speeds. These are the six degrees of freedom accelerations of the ship. These represent the six degrees of freedom motion of a ship. For the ship's generalized inertia matrix, These represent the ship's additional mass and damping coefficient when the encounter frequency is infinite. The coefficient matrix is ​​shown in equation (2). This is the static restoring force coefficient of the ship; For delay function, For wave interference force, The tension transmitted from the head end of the tow cable; （2） in, U For the speed of the ship, The displacement of the ship; Step 2: Construct the towing cable motion control model, as shown in equation (3): （3） Where t is time, s is the arc length of the tow cable when it is not stretched, M, N and Q are coefficient matrices, and Y is the state variable of the tow cable, as shown in equations (4)-(7); （4） （5） （6） （7） Where T is the tension of the towing cable element. These are the velocity components of the tow cable element in the tow cable's local coordinate system. as well as Let be the attitude angle of the tow cable element. The components of water flow velocity in different directions are distinguished. The component of the water flow acceleration, and The velocity component of the tow cable relative to the water flow. To represent the tangential and normal drag coefficients of the tow cable, respectively, where m is the mass per unit length of the tow cable when unstretched. For fluid density, It is the acceleration due to gravity. for A is the cross-sectional area of ​​the tow cable when it is not stretched. The weight of a unit length of tow cable in water. , This is the diameter of the tow cable after stretching. , , E The Young's modulus of the towing cable. In response to the situation; Step 3: Construct a six-degree-of-freedom motion model of the underwater towed body, as shown in equation (8): （8） in, For the mass of the towing body, as well as These are the longitudinal, lateral, and vertical coordinates of the drag center of gravity. These are the moments of inertia of the towed body about the coordinate axes of the towed body's following coordinate system. These represent the longitudinal velocity, lateral velocity, and vertical velocity of the towed body's center of gravity in the towed body's servo coordinate system, respectively. These are the roll and pitch angular velocities of the drag center, respectively, where r is the bow roll angular velocity. These are the six degrees of freedom accelerations of the towed body. These represent the longitudinal force, lateral force, and vertical force acting on the towing body, respectively. The torque of the external force about the center of gravity of the dragged object; Step 4: Determine the boundary conditions at the bow and stern of the towline, and construct a motion control model of the surface vessel, towline, and towed body by coupling the boundary conditions. The boundary condition at the tow cable head is a continuous condition, and the velocity at the tow cable head is the same as the velocity at the towing point of the surface vessel, as shown in equation (9): （9） in, The translational speed of the vessel on the water. The rotational angular velocity of the surface vessel. For the towing point in the ship's moving coordinate system on the water surface The following position coordinates, This is the transformation matrix between the fixed spatial coordinate system and the moving coordinate system of the ship on the water surface. D This is the transformation matrix between the fixed spatial coordinate system and the local coordinate system of the towing cable. The velocity of the tow cable head end in the tow cable local coordinate system; When the trailing cable is not carrying the trailing body, the trailing cable is a free end, the tension at the trailing cable is zero, and the rate of change of the Euler angle with respect to the arc length is zero, as shown in equation (10): （10） in, For the tension at the tail end of the tow cable, as well as The rate of change of the Euler angle with respect to the arc length at the trailing end of the cable; When the trailing cable pulls the tow body, the speed of the trailing cable is the same as the speed of the tow body, as shown in equation (11): (11) in, The translational velocity of the towed body, Let be the rotational angular velocity of the towed body. For the trailing end of the tow cable in the moving coordinate system of the tow body The following position coordinates, This is the transformation matrix between the fixed spatial coordinate system and the moving coordinate system of the dragged body. D This is the transformation matrix between the fixed spatial coordinate system and the local coordinate system of the towing cable. The velocity of the trailing cable end in the local coordinate system of the tow cable; Step 5: Use the three-dimensional surface element method to determine the hydrodynamic coefficients in the ship motion model, use the fourth-order Runge-Kutta method to determine the six degrees of freedom motion of the surface ship in the surface ship motion model, determine the six degrees of freedom motion of the towed body in the towed body motion model, and use the finite difference method to determine the tension and six degrees of freedom motion of the towed cable in the towed cable motion control model. The fourth-order Runge-Kutta method is shown in equations (12) and (13): （12） （13） in, t For time, For time step, Let be the state variable at time t. for The state variable at time t, as well as For coefficients; The six degrees of freedom motion of the surface vessel in the surface vessel motion model are determined using equations (12) and (13). Determine the six degrees of freedom motion of the towed body in the towed body motion model. ; The finite difference method employs a central difference approach in both time and space to discretize the tow cable along its length. n A length microelement The tow cable nodes are respectively ,in This refers to the beginning of the tow cable, i.e., the towing point. For the trailing end of the cable; discretized in time into a series of time steps. ; At the tow cable node j At, The motion parameters at time t are shown in equation (14): （14） With tow cable node As the difference base point, the difference form of equation (3) in time and space is shown in equation (15): （15） In the formula and In the first j Segment drag cable micro element, first The coefficient matrix of the time step, In the first j Segment drag cable micro element, first The state variables at each time step; The tension of the towing cable in the towing cable motion control model is determined by Equation (15) using the Newton-Raphson iteration method. T and six degrees of freedom motion .

2. The method for coupled motion analysis of a surface vessel and a towing system as described in claim 1, characterized in that: The process includes the following steps: Step 6: Based on the motion response of the surface vessel, tow cable, and underwater tow body determined in Step 5, and the tension distribution of the tow cable, it is possible to quantitatively analyze the influence of the six degrees of freedom motion of the surface vessel on the tow force and the six degrees of freedom motion of the tow cable, as well as the influence of the tow cable on the six degrees of freedom motion of the surface vessel, further optimizing the stern structure of the surface vessel, the shape of the tow cable, and the shape of the tow body, improving the navigation performance of the surface vessel, and enhancing the operational safety of the towing system.

3. The method for coupled motion analysis of a surface vessel and a towing system as described in claim 1, characterized in that: In step 1, the surface element method with the Green's function of the three-dimensional moving pulsating source as the kernel is used to determine the additional mass, damping coefficient and wave interference force of the surface vessel at different encounter frequencies.

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