Ship dynamic stability modeling method and system based on multi-external force coupling

Abstract

The invention provides a ship dynamic stability modeling method and system based on multi-external force coupling, and the method comprises the steps: building a short-peak wave model based on wind wave characteristic parameters under different sea conditions and motion state parameters of a ship, and carrying out the calculation under ground coordinates to obtain a first wave surface equation; a first wave surface equation located in a ground coordinate system is converted into a ship body stable coordinate system through a coordinate and frequency conversion method, a second wave surface equation suitable for the surrounding environment of the ship is obtained, then a fluctuation pressure model caused by sea waves is established, the fluctuation pressure model is corrected through a Smith correction term method, and the ship body stable coordinate system is obtained. A multi-wave superposition fluctuation pressure model is obtained through a harmonic superposition analysis method; then a generalized disturbance force matrix is constructed based on a finite volume method, Archimedes restoring force, inertia hydrodynamic force and viscosity hydrodynamic force are calculated by adopting a specific calculation method, and then a ship motion model is established, so that the accuracy of the model is effectively improved, and the dynamic behavior of the ship can be more accurately predicted under the complex sea condition.

Description

Technical Field

[0001] The present invention relates to the technical field of ship engineering and ocean engineering, and in particular to a ship dynamic stability modeling method and system based on multi-external force coupling. Background Art

[0002] In modern naval warfare, air power has become an indispensable and important support for naval ships. With the continuous development and growth of my country's navy in recent years, its demand for ship-borne aviation power has also gradually increased. At the same time, the maturity of ship-borne helicopter technology and the continuous development of new vertical take-off and landing aircraft have made non-through-deck ships such as frigates and destroyers play an increasingly important role in the field of ship-borne aviation force delivery.

[0003] In the design and operation of modern naval ships, it is crucial to ensure the dynamic stability of ships under various sea conditions. At present, existing technologies mainly rely on traditional static methods to evaluate the stability of ships. Although this method can provide certain reference information, it is insufficient when dealing with complex dynamic environments. Specifically, existing technologies often ignore various dynamic factors encountered by ships in actual operation, such as environmental influences such as waves and wind, resulting in inaccurate evaluation results that cannot fully reflect the true dynamic behavior of ships.

[0004] In addition, traditional modeling methods often simplify too much when dealing with complex motions such as roll, pitch and heave of ships, and do not fully consider the restoring force, interference force and fluid dynamics effects, especially the inertia and viscosity effects in hydrodynamics. This makes the existing models have large errors in predicting the dynamic response of ships in severe sea conditions, making it difficult to meet the needs of modern navies for high-precision dynamic control of ships. Summary of the invention

[0005] The present invention aims at the problems that the evaluation results in the current ship dynamic stability modeling process are not accurate enough, there are large errors, and the real dynamic behavior of the ship cannot be fully reflected. A ship dynamic stability modeling method based on multiple external force coupling is provided. A short-peak wave model is established based on the characteristic parameters of wind and waves and the motion state parameters of the ship, and a generalized interference force matrix, Archimedean restoring force, inertial hydrodynamic force and viscous hydrodynamic force are calculated using a specific calculation method, a coordinate transformation method, a correction method and a finite volume method, and then a ship motion model is established, which effectively improves the accuracy of the model, can more accurately predict the dynamic behavior of the ship under complex sea conditions, and provides a solid foundation for improving the safety and operational performance of the ship. The present invention also relates to a ship dynamic stability modeling system based on multiple external force coupling.

[0006] The technical solution of the present invention is as follows:

[0007] A ship dynamic stability modeling method based on multiple external force coupling, characterized by comprising the following steps:

[0008] Parameter acquisition and coordinate system establishment steps: obtain the wind and wave characteristic parameters and the ship's motion state parameters under different sea conditions, and establish a ground coordinate system with any point on the sea level as the origin, the ship's motion direction as the longitudinal axis, the direction of the starboard side of the ship parallel to the sea level as the transverse axis, and the center of the earth as the vertical axis; establish a hull stable coordinate system with the ship's center of mass as the origin, the ship's motion direction as the longitudinal axis, the direction of the starboard side of the ship parallel to the sea level as the transverse axis, and the center of the earth as the vertical axis; establish a hull stable coordinate system with the ship's center of mass as the origin, the ship's bow direction as the longitudinal axis, and the center of the earth as the vertical axis. The hull coordinate system is established with the direction of the starboard side of the ship as the transverse axis and the direction of the bottom of the ship as the vertical axis; the wind and wave characteristic parameters include wave amplitude, wave number, main propagation direction of wind and waves, propagation direction of wind and wave harmonics, wind and wave angular frequency, time of wind and wave shape transformation, wind and wave natural period and wind and wave natural wave speed; the ship's motion state parameters include ship speed, encounter period, encounter angular frequency, ship displacement, ship length, waterline width, ship waterplane area, draft depth, transverse metacentric height, longitudinal metacentric height, ship mass and moment of inertia;

[0009] The steps of constructing the short-peaked wave wind and wave model are as follows: in the ground coordinate system, a plane wave equation about the wave height is established based on the wave amplitude, wave number, main propagation direction of wind and wave, propagation direction of wind and wave harmonics, and the time of wind and wave shape transformation, and the short-peaked wave wind and wave model is obtained by recursion based on the plane wave equation;

[0010] The wave surface equation and wave height calculation steps are as follows: the directional spectrum of short-peaked waves is calculated according to the propagation direction of wind and wave harmonics, and a first expression about the energy of long-peaked waves is constructed according to the wave amplitude and seawater density under ground coordinates, an angular frequency interval is established according to the wind and wave angular frequency and the bandwidth set based on the wind and wave angular frequency, and then a second expression about the energy of long-peaked waves within the angular frequency interval is obtained, and a third expression about the energy spectrum of long-peaked waves is recursively obtained from the second expression, and then the long-peaked wave energy spectrum is calculated; a short-peaked wave wind and wave spectrum is calculated according to the directional spectrum of short-peaked waves and the energy spectrum of long-peaked waves, a fourth expression about the energy of short-peaked waves is established based on the short-peaked wave wind and wave spectrum, and the fourth expression of the energy of short-peaked waves is calculated by the fourth expression and the short-peaked wave wind and wave model. A wave surface equation is established; then a first relational expression between the encounter period and the encounter angular frequency is established, and the angle between the ship speed direction and the main propagation direction of the wind and waves is taken as the ship encounter angle, and a second relational expression about the encounter period is established based on the ship encounter angle, the natural period of the wind and waves, the natural wave speed of the wind and waves, and the ship speed, and a third relational expression about the encounter angular frequency is established based on the ship encounter angle, the angular frequency of the wind and waves, the natural wave speed of the wind and waves, and the ship speed; based on the first relational expression, the second relational expression and the third relational expression, and using the coordinate and frequency transformation method, the first wave surface equation located in the ground coordinate system is converted into the hull stable coordinate system, and a second wave surface equation applicable to the surrounding environment of the ship is obtained, and the wave height encountered by the ship during navigation is calculated according to the second wave surface equation;

[0011] Steps for obtaining the multi-wave superposition fluctuation pressure model: in the hull stable coordinate system, the sea surface depth of a certain underwater point from the free liquid surface is calculated according to the liquid surface depth under still water conditions and the wave height encountered by the ship during navigation, and a fifth expression for the pressure at a certain underwater point is constructed according to the sea surface depth and the atmospheric pressure; a sixth expression for the pressure at a certain underwater point under short-peak wave and sea wave conditions is calculated according to the fifth expression and the short-peak wave wind and wave model; a fluctuation pressure model caused by sea waves is obtained according to the sixth expression, and the fluctuation pressure model is corrected by the Smith correction term method to obtain a corrected fluctuation pressure model; and the corrected fluctuation pressure model is expressed as a superposition of multiple cosine waves by the harmonic superposition analysis method to obtain a multi-wave superposition fluctuation pressure model;

[0012] The generalized wave disturbance force construction steps are as follows: in a stable hull coordinate system, the ship is divided into multiple triangular face elements based on the finite volume method, and the vector pointing from the ship's center of mass to the centroid of a certain triangular face element is used as the radius vector of the triangular face element, and the wave pressure received by the triangular face element is calculated according to the multi-wave superposition wave pressure model, and the wave force received by the triangular face element is calculated according to the area, normal vector and wave pressure of the triangular face element, and the wave moment received by the triangular face element is calculated according to the radius vector of the triangular face element and the calculated wave force; based on the wave forces and wave moments received by all triangular face elements, the wave forces and wave moments of the entire ship are calculated respectively; and the coordinate and frequency transformation methods are used to convert the wave forces and wave moments of the entire ship in the stable hull coordinate system into the hull coordinate system, and the component arrays of the overall wave forces of the ship and the component arrays of the overall wave moments of the ship are obtained respectively, and then the generalized wave disturbance force matrix is ​​constructed;

[0013] The calculation steps of Archimedean restoring force are as follows: the angle between the line between the center of mass and transverse metacenter of the ship and the horizontal plane is taken as the roll angle; the angle between the line between the center of mass and longitudinal metacenter of the ship and the horizontal plane is taken as the pitch angle; the roll restoring moment of the ship is calculated according to the displacement of the ship, the height of the transverse metacenter and the roll angle, and the pitch restoring moment of the ship is calculated according to the displacement of the ship, the height of the longitudinal metacenter and the pitch angle; the waterplane area of ​​the ship is calculated according to the length and the waterline width, and the heave restoring force of the ship is calculated according to the waterplane area and the draft depth; the Archimedean restoring force is calculated based on the roll restoring moment, the pitch restoring moment and the heave restoring force of the ship;

[0014] The calculation steps of inertial and viscous hydrodynamics are as follows: construct the generalized velocity vector of the ship based on the heave velocity, left-right swing velocity and fore-and-aft swing velocity of the ship, and establish the hydrodynamic equation of the ship based on the generalized velocity vector and its rate of change; and when the ship is in a positive floating state, use the first-order Taylor expansion method to linearly expand the hydrodynamic equation of the ship to obtain the linear hydrodynamic equation of the ship; obtain the fluid inertia matrix and fluid viscosity matrix respectively according to the linear hydrodynamic equation, calculate the inertial hydrodynamics according to the fluid inertia matrix and the generalized velocity vector, and calculate the viscous hydrodynamics according to the fluid viscosity matrix and the generalized velocity vector;

[0015] Steps for establishing the ship motion model: construct the system inertia matrix based on the ship mass and moment of inertia, obtain the first ship motion equation about the resultant external force acting on the ship based on the system inertia matrix and the generalized velocity vector and according to Newton's second law, and establish the second ship motion equation about the resultant external force acting on the ship based on the Archimedean restoring force, inertial hydrodynamic force, viscous hydrodynamic force and generalized wave interference force matrix, and obtain the third ship motion equation recursively based on the first ship motion equation and the second ship motion equation; and under the condition of small-angle motion of the ship, transform the third ship motion equation to obtain the ship motion model, so as to realize the dynamic stability evaluation of the ship under various sea conditions.

[0016] Preferably, in the wave surface equation and wave height calculation step, when the bandwidth in the third expression tends to zero, the integral expression of the long-peak wave energy is calculated according to the first expression and the third expression, and the relationship between the wave harmonic amplitude and the spectral density function is calculated according to the integral expression.

[0017] Preferably, in the parameter acquisition and coordinate system establishment steps, the wind and wave characteristic parameters also include wavelength, and the wave number is calculated based on the wavelength.

[0018] Preferably, the coordinate and frequency transformation method includes coordinate transformation based on rotation matrix and transformation of wave frequency to encounter frequency.

[0019] A ship dynamic stability modeling system based on multi-external force coupling is characterized by comprising a parameter acquisition and coordinate system establishment module, a short-peak wave wind and wave model construction module, a wave surface equation and sea wave height calculation module, a multi-wave superposition fluctuation pressure model acquisition module, a generalized wave interference force calculation module, an Archimedean restoring force calculation module, an inertial and viscous hydrodynamic calculation module and a ship motion model establishment module, which are connected in sequence.

[0020] The parameter acquisition and coordinate system establishment module acquires the wind and wave characteristic parameters and the motion state parameters of the ship under different sea conditions, and establishes a ground coordinate system with any point on the sea level as the origin, the ship's motion direction as the longitudinal axis, the direction of the starboard side of the ship and parallel to the sea level as the transverse axis, and the center of the earth as the vertical axis; establishes a hull stable coordinate system with the ship's center of mass as the origin, the ship's motion direction as the longitudinal axis, the direction of the starboard side of the ship and parallel to the sea level as the transverse axis, and the center of the earth as the vertical axis; establishes a hull stable coordinate system with the ship's center of mass as the origin, the ship's bow direction as the longitudinal axis, The hull coordinate system is established with the direction of the starboard side of the ship as the transverse axis and the direction of the bottom of the ship as the vertical axis; the wind and wave characteristic parameters include wave amplitude, wave number, main propagation direction of wind and waves, propagation direction of wind and wave harmonics, wind and wave angular frequency, time of wind and wave shape transformation, wind and wave natural period and wind and wave natural wave speed; the motion state parameters of the ship include ship speed, encounter period, encounter angular frequency, ship displacement, ship length, waterline width, ship waterplane area, draft depth, transverse metacentric height, longitudinal metacentric height, ship mass and moment of inertia;

[0021] The short-peaked wave wind and wave model construction module establishes a plane wave equation about the wave height in the ground coordinate system based on the wave amplitude, wave number, main propagation direction of wind and waves, propagation direction of wind and wave harmonics, and time of wind and wave shape transformation, and recursively obtains the short-peaked wave wind and wave model according to the plane wave equation;

[0022] The wave surface equation and wave height calculation module calculates the directional spectrum of short-peaked waves according to the propagation direction of wind and wave harmonics, and constructs a first expression for the energy of long-peaked waves according to the wave amplitude and seawater density under ground coordinates, establishes an angular frequency interval according to the wind and wave angular frequency and the frequency band width set based on the wind and wave angular frequency, and then obtains a second expression for the energy of long-peaked waves within the angular frequency interval, and recursively obtains a third expression for the energy spectrum of long-peaked waves from the second expression, and then calculates the energy spectrum of long-peaked waves; calculates the short-peaked wave wind and wave spectrum according to the directional spectrum of short-peaked waves and the long-peaked wave energy spectrum, establishes a fourth expression for the energy of short-peaked waves based on the short-peaked wave wind and wave spectrum, and calculates the short-peaked wave wind and wave model by the fourth expression. The first wave surface equation; then establish a first relationship between the encounter period and the encounter angular frequency, and take the angle between the ship speed direction and the main propagation direction of the wind and waves as the ship encounter angle, and establish a second relationship about the encounter period based on the ship encounter angle, the natural period of wind and waves, the natural wave speed of wind and waves, and the ship speed, and establish a third relationship about the encounter angular frequency based on the ship encounter angle, the angular frequency of wind and waves, the natural wave speed of wind and waves, and the ship speed; based on the first relationship, the second relationship, and the third relationship, and using the coordinate and frequency transformation method, the first wave surface equation located in the ground coordinate system is converted into the hull stable coordinate system, and the second wave surface equation applicable to the surrounding environment of the ship is obtained, and the wave height encountered by the ship during navigation is calculated according to the second wave surface equation;

[0023] The multi-wave superposition fluctuation pressure model acquisition module calculates the sea surface depth of a certain underwater point from the free liquid surface according to the liquid surface depth under calm water conditions and the wave height encountered by the ship during navigation in a stable coordinate system of the hull, and constructs a fifth expression for the pressure of a certain underwater point according to the sea surface depth and the atmospheric pressure; calculates a sixth expression for the pressure of a certain underwater point under short-peak wave and sea wave conditions according to the fifth expression and the short-peak wave wind and wave model; obtains the fluctuation pressure model caused by the sea waves according to the sixth expression, and corrects the fluctuation pressure model by using the Smith correction term method to obtain the corrected fluctuation pressure model; and expresses the corrected fluctuation pressure model as the superposition of multiple cosine waves by using the harmonic superposition analysis method to obtain the multi-wave superposition fluctuation pressure model;

[0024] The generalized wave disturbance force calculation module divides the ship into multiple triangular face elements based on the finite volume method in a stable hull coordinate system, and uses the vector from the ship's center of mass to the centroid of a certain triangular face element as the radius vector of the triangular face element, calculates the wave pressure on the triangular face element according to the multi-wave superposition wave pressure model, calculates the wave force on the triangular face element according to the area, normal vector and wave pressure of the triangular face element, and calculates the wave moment on the triangular face element according to the radius vector of the triangular face element and the calculated wave force; calculates the wave force and wave moment of the entire ship based on the wave force and wave moment on all triangular face elements; and uses the coordinate and frequency transformation method to convert the wave force and wave moment of the entire ship in the stable hull coordinate system into the hull coordinate system, and obtains the component array of the entire ship's wave force and the component array of the entire ship's wave moment, thereby constructing a generalized wave disturbance force matrix;

[0025] The Archimedean restoring force calculation module uses the angle between the line between the ship's center of mass and transverse metacenter and the horizontal plane as the roll angle; uses the angle between the line between the ship's center of mass and longitudinal metacenter and the horizontal plane as the pitch angle; calculates the ship's roll restoring moment according to the ship's displacement, transverse metacenter height and roll angle, and calculates the ship's pitch restoring moment according to the ship's displacement, longitudinal metacenter height and pitch angle; calculates the ship's waterplane area according to the ship's length and waterline width, and calculates the ship's heave restoring force according to the ship's waterplane area and draft; calculates the Archimedean restoring force based on the roll restoring moment, pitch restoring moment and the ship's heave restoring force;

[0026] The inertial and viscous hydrodynamic calculation module constructs a generalized velocity vector of the ship based on the heave velocity, left-right swing velocity and fore-and-aft swing velocity of the ship, and establishes a hydrodynamic equation of the ship according to the generalized velocity vector and its rate of change; and when the ship is in a positive floating state, a first-order Taylor expansion method is used to linearly expand the hydrodynamic equation of the ship to obtain a linear hydrodynamic equation of the ship; a fluid inertia matrix and a fluid viscosity matrix are obtained according to the linear hydrodynamic equation, the inertial hydrodynamic force is calculated according to the fluid inertia matrix and the generalized velocity vector, and the viscous hydrodynamic force is calculated according to the fluid viscosity matrix and the generalized velocity vector;

[0027] The ship motion model establishment module constructs a system inertia matrix based on the ship mass and moment of inertia, obtains a first ship motion equation about the resultant external force acting on the ship based on the system inertia matrix and the generalized velocity vector and according to Newton's second law, and establishes a second ship motion equation about the resultant external force acting on the ship based on Archimedean restoring force, inertial hydrodynamic force, viscous hydrodynamic force and generalized wave interference force matrix, and obtains a third ship motion equation recursively based on the first ship motion equation and the second ship motion equation; and under the condition of small-angle motion of the ship, the third ship motion equation is transformed to obtain a ship motion model, so as to realize dynamic stability evaluation of the ship under various sea conditions.

[0028] Preferably, in the wave surface equation and wave height calculation module, when the bandwidth in the third expression tends to zero, the integral expression of the long-peak wave energy is calculated according to the first expression and the third expression, and the relationship between the wave harmonic amplitude and the spectral density function is calculated according to the integral expression.

[0029] Preferably, in the parameter acquisition and coordinate system establishment step module, the wind and wave characteristic parameters also include wavelength, and the wave number is calculated based on the wavelength.

[0030] Preferably, the coordinate and frequency transformation method includes coordinate transformation based on rotation matrix and transformation of wave frequency to encounter frequency.

[0031] The beneficial effects of the present invention are:

[0032] The present invention provides a ship dynamic stability modeling method based on multi-external force coupling. Based on the characteristic parameters of wind and waves under different sea conditions and the motion state parameters of the ship, a short-peak wave wind and wave model including multiple characteristic parameters such as amplitude, wave number, main propagation direction of wind and waves, propagation direction of wind and wave harmonics is established, so that the behavior of wind and waves and their influence on the ship can be described more accurately and quickly, thereby improving the accuracy of the model. Based on the established ground coordinate system and hull stable coordinate system, the wind and wave model is converted from the ground coordinate system to the hull coordinate system through the coordinate and frequency transformation method, so that the actual motion state of the ship in the waves can be more accurately reflected. Then, a second wave surface equation suitable for the surrounding environment of the ship is calculated by adopting a specific calculation method and constructed expressions and relations, and the wave height encountered by the ship during navigation is calculated according to the second wave surface equation, so that the actual wave conditions can be reflected more accurately, especially for accurate wave height prediction under complex sea conditions, thereby reducing the risk of the ship encountering extreme sea conditions. And protect the safety of the ship and its crew; then use the Smith correction term method to correct the wave pressure model obtained by establishing various expressions to obtain a corrected wave pressure model to improve the calculation accuracy, which can effectively and accurately evaluate the force situation of the ship in wind and waves; and obtain a multi-wave superposition wave pressure model through the harmonic superposition analysis method. The multi-wave superposition wave pressure model takes into account the pressure change at a certain point underwater, the interaction between wind and waves and the nonlinear effect, effectively improves the accuracy and reliability of the wave pressure calculation, and makes the prediction of the dynamic response of the ship more accurate; then based on the finite volume method and using a specific calculation method, a generalized wave interference force is constructed, which can more accurately predict the dynamic response of the ship in wind and waves, and can effectively model and simulate the wave force on the complex hull, effectively improve the calculation accuracy, and can more accurately evaluate the safety of take-off and landing of ship-borne helicopters under high sea conditions, which is of great significance to ensuring the safe take-off and landing of ship-borne helicopters under high sea conditions. Finally, a specific calculation method is used to calculate the Archimedean restoring force, inertial hydrodynamic force, viscous hydrodynamic force and wave interference force, and then a ship motion model is established, which can accurately predict the dynamic response of the ship in wind and waves. The present invention takes into account various dynamic factors encountered by ships in actual operation, such as environmental influences such as waves and wind, as well as restoring force, interference force and fluid dynamic effects, especially inertial and viscous effects in hydrodynamics. The evaluation results are accurate, can fully reflect the real dynamic behavior of the ship, and can effectively improve the take-off and landing capabilities and safety of carrier-based aircraft under complex sea conditions, thereby enhancing the overall combat effectiveness of carrier-based aviation forces.

[0033] The present invention also relates to a ship dynamic stability modeling system based on multiple external force coupling, which corresponds to the above-mentioned ship dynamic stability modeling method based on multiple external force coupling, and can be understood as a system that implements the above-mentioned ship dynamic stability modeling method based on multiple external force coupling, including a parameter acquisition and coordinate system establishment module, a short-peak wave wind and wave model construction module, a wave surface equation and wave height calculation module, a multi-wave superposition fluctuation pressure model acquisition module, a generalized wave interference force calculation module, an Archimedean restoring force calculation module, an inertial and viscous hydrodynamic calculation module and a ship motion model establishment module, which are connected in sequence. The modules cooperate with each other to establish a short-peak wave model based on the characteristic parameters of wind and waves and the motion state parameters of the ship, and use specific calculation methods, coordinate transformation methods, correction methods and finite volume methods to calculate the generalized interference force matrix, Archimedean restoring force, inertial hydrodynamic force and viscous hydrodynamic force, and then establish a ship motion model, which effectively improves the accuracy of the model, can more accurately predict the dynamic behavior of the ship under complex sea conditions, and provides a solid foundation for improving the safety and operational performance of the ship. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a flow chart of the ship dynamic stability modeling method based on multiple external force coupling of the present invention.

[0035] Figure 2 It is a schematic diagram of the ground coordinate system of the present invention.

[0036] Figure 3 It is a schematic diagram of the hull stability coordinate system of the present invention.

[0037] Figure 4 It is a schematic diagram of the hull coordinate system of the present invention.

[0038] Figure 5 It is a schematic diagram of the conversion relationship between the hull stable coordinate system and the hull coordinate system of the present invention.

[0039] Figure 6 It is a schematic diagram of the plane wave shape of the present invention.

[0040] Figure 7 It is a schematic diagram of the ship of the present invention sailing in wind and waves.

[0041] Figure 8 It is a schematic diagram of dividing a ship based on the finite volume method according to the present invention.

[0042] Fig. 9 It is a schematic diagram of the external forces and moments acting on the ship of the present invention.

[0043] Fig.10 is the ship roll restoring moment K of the present invention P Schematic diagram. DETAILED DESCRIPTION

[0044] The present invention will be described below in conjunction with the accompanying drawings.

[0045] The present invention relates to a ship dynamic stability modeling method based on multiple external force coupling. The flow chart of the method is as follows: Figure 1 As shown, the following steps are included in sequence:

[0046] Parameter acquisition and coordinate system establishment steps: obtain the wind and wave characteristic parameters and the ship's motion state parameters under different sea conditions, and establish a ground coordinate system with any point on the sea level as the origin, the ship's motion direction as the longitudinal axis, the direction of the starboard side of the ship parallel to the sea level as the transverse axis, and the center of the earth as the vertical axis; establish a hull stable coordinate system with the ship's center of mass as the origin, the ship's motion direction as the longitudinal axis, the direction of the starboard side of the ship parallel to the sea level as the transverse axis, and the center of the earth as the vertical axis; establish a hull stable coordinate system with the ship's center of mass as the origin, the ship's bow direction as the longitudinal axis, and the center of the earth as the vertical axis. A hull coordinate system is established with the direction of the starboard side of the ship as the transverse axis and the direction of the bottom of the ship as the vertical axis; the wind and wave characteristic parameters include wave amplitude, wave number, main propagation direction of wind and waves, propagation direction of wind and wave harmonics, wind and wave angular frequency, time of wind and wave shape transformation, wind and wave natural period and wind and wave natural wave speed; the ship's motion state parameters include ship speed, encounter period, encounter angular frequency, ship displacement, ship length, waterline width, ship waterplane area, draft, transverse metacentric height, longitudinal metacentric height, ship mass and moment of inertia.

[0047] Specifically, the ground coordinate system E-ξηζ is Figure 2 As shown in the figure, it is a fixed inertial coordinate system fixed to the earth, which is used to describe the motion state of the waves. Among them, the origin E of the coordinate system can be taken as any point on the sea level, the center of the earth is the vertical axis, that is, the Eζ axis points to the center of the earth, the direction of the ship's motion is the longitudinal axis, that is, the Eξ axis points to the direction of the ship's motion, the direction to the starboard of the ship and parallel to the sea level is the transverse axis, that is, the Eη axis points to the starboard of the ship and parallel to the sea level, the Eξ axis and the Eη axis are located in the sea level and are perpendicular to each other, and the distribution of the three coordinate axes conforms to the right-hand rule. The hull stable coordinate system Ox s y s z s like Figure 3 As shown in Figure 1, it is a coordinate system that moves with the ship and is used to describe the motion of the ship hull in a stable state. The origin of the coordinate system O is the center of mass of the ship, and the direction of motion of the ship is the longitudinal axis, that is, Ox s The axis points to the direction of the ship's motion, and the direction to the starboard side of the ship and parallel to the sea level is the transverse axis, that is, Oy s Pointing to the starboard side of the ship and parallel to the sea level, with the center of the earth as the vertical axis, i.e. Oz s The axis points to the center of the earth, Ox s y s The plane is parallel to the sea level, and the distribution of the three coordinate axes conforms to the right-hand rule.b y b z b ,like Figure 4 As shown in FIG. 1 , it is a motion coordinate system fixed to the hull, used to describe the motion state of the ship hull. The origin of the coordinate system O is the center of mass of the ship, and the direction of the bow of the ship is the longitudinal axis, that is, Ox b The axis coincides with the ship's roll axis and points to the bow, and the direction of the starboard side of the ship is the transverse axis, that is, Oy b The axis coincides with the pitch axis of the ship and points to the starboard side of the ship. The direction of the bottom of the ship is the vertical axis, i.e. Oz b The axis coincides with the bow axis of the ship and points to the bottom of the ship. The selection and definition of the above variables, that is, the symbols of the ship motion and force variables are shown in Table 1.

[0048] Table 1

[0049]

[0050] The three translational position quantities are swell x, swell y and heave (heave) z. The three translational position quantities are swell x, swell y and heave (heave) z. The hull coordinate system can be obtained by three simple rotations of the hull stable coordinate system, such as Figure 5 As shown, the three rotations are: around z s The yaw angle ψ is rotated by the axis, and O-x1y1z is obtained s ; Rotate the pitch angle θ around the y1 axis to get Ox b y1z1; around x b Axis rotation roll angle Get Ox b y b z b .

[0051] The steps for constructing the short-peaked wave wind and wave model are as follows: In the ground coordinate system, a plane wave equation about the wave height is established based on the wave amplitude, wave number, the main propagation direction of wind and waves, the propagation direction of wind and wave harmonics, and the time of wind and wave shape transformation, and the short-peaked wave wind and wave model is obtained by recursively deducing the plane wave equation.

[0052] When a ship is sailing under high sea conditions, it will be disturbed by various marine environments such as waves, sea breezes, and ocean currents. Among them, random waves are the most important disturbance factor. Therefore, before analyzing the motion state of the ship under high sea conditions, it is very necessary to understand the distribution of random waves under high sea conditions. Specifically, wave simulation has always been a very complex problem. In real situations, the wind and waves on the sea surface are extremely complex irregular random three-dimensional waves, so it is very difficult to accurately model the waves. However, in the process of studying the problem of ship motion, it is considered that the wind and waves generally propagate in one direction along the wind direction, that is, the wind and waves only propagate along their main propagation direction (that is, the ξ axis of the ground coordinate system). Therefore, it can be assumed that the crests and troughs of the waves are parallel to each other and perpendicular to the wave propagation direction. At this time, assuming that the main propagation direction of the wind and waves is the ξ axis, the wave height (wave surface height) ζ at a fixed point on the sea surface is expressed as a binary function of ξ and time t ζ = ζ(ξ,t). According to the Longuet-Higgins model, the long-peak wave model of irregular wind waves can be regarded as the superposition of countless waves with different amplitudes (amplitudes), wavelengths and initial phases in the vertical plane of the main propagation direction of the wind waves. According to the following fluid mechanics assumptions:

[0053] a) The fluid is incompressible;

[0054] b) The fluid has only potential velocity;

[0055] c) The wind and waves are slight.

[0056] The plane wave propagating along the ξ axis can be expressed as:

[0057] ζ=ζ a cos(kξ-ωt) (1)

[0058] Where ζ is the wave height (also known as the distance the wave surface deviates from the sea level, or the height of the wave surface relative to the mean sea level); ζ a is the amplitude; k is the wave number; λ is the wavelength, and the wave number is related to the wavelength: k = 2π / λ; ω is the angular frequency of wind waves. t is the time when the angular frequency of wind waves and the shape of wind waves change, describing the change of wind waves over time. When t = 0, its plane wave shape is as follows Figure 6 shown.

[0059] According to the plane wave formula, the long crest wave model (also called the Longuet-Higgins model of long crest waves) can be derived, as shown below:

[0060]

[0061] Among them, k i ,ω i , aiare the wave number, wind wave angular frequency and amplitude of the i-th harmonic respectively; ε i is the random initial phase of the i-th harmonic between 0 and 2π.

[0062] However, the above long-peak wave model still has problems such as being unable to accurately capture the propagation characteristics of waves and slow calculation speed because it only considers the main propagation direction of wind waves as the ξ axis. Therefore, the short-peak wave model of wind waves is introduced. This model considers that the propagation direction of different harmonics of wind waves will propagate along different propagation angles μ. It is defined that μ=0 when propagating along the ξ axis, and the angle μ is positive when rotating positively around the ζ axis according to the right-hand rule. Therefore, in the short-peak wave model of wind waves, the wave height ζ at a fixed point on the sea surface should be expressed as a three-variable function of ξ, η and time t ζ=ζ(ξ,η,t). The wave equation of the plane propagating at the propagation angle μ is re-described in the three-dimensional ground coordinate system E-ξηζ as follows:

[0063] ζ=ζ a cos[k(ξcosμ j -ηsinμ j )-ωt] (3)

[0064] Among them, a is the amplitude, k is the wave number, ζ is the wave height, μ represents the propagation angle, the propagation direction of different harmonics of wind and waves is along different propagation angles μ, the main propagation direction of wind and waves along the ξ axis, the main propagation direction of wind and waves along the η axis, ω is the angular frequency of wind and waves.

[0065] The short-peaked wave model (also called the Longuet-Higgins model of short-peaked wave) derived from the plane wave equation is as follows:

[0066]

[0067] The short-peaked wave model takes into account the main propagation direction of wind and waves along the ξ-axis and η-axis, and introduces the propagation direction of wind and wave harmonics as propagation along different propagation angles μ, so that the short-peaked wave model can more accurately capture the propagation characteristics of waves (including the propagation direction and energy distribution of wind and waves). And because the short-peaked wave model contains more degrees of freedom, it can more carefully characterize the irregularity of waves, thereby improving the accuracy of prediction, which is crucial for studying wave dynamics, marine engineering design and safety assessment. At the same time, the short-peaked wave model is also applicable to various complex marine environments, including wave conditions in different sea areas, seasons and weather conditions, and can better simulate the wind and wave behavior in the real world, providing a more reliable foundation for scientific research and engineering practice in related fields.

[0068] The wave surface equation and wave height calculation steps are as follows: the directional spectrum of short-peaked waves is calculated according to the propagation direction of wind and wave harmonics, and a first expression about the energy of long-peaked waves is constructed according to the wave amplitude and seawater density under ground coordinates, an angular frequency interval is established according to the wind and wave angular frequency and the bandwidth set based on the wind and wave angular frequency, and then a second expression about the wave energy in the angular frequency interval is obtained, and a third expression about the long-peaked wave energy spectrum is recursively obtained from the second expression, and then the long-peaked wave energy spectrum is calculated; a short-peaked wave wind and wave spectrum is calculated according to the directional spectrum of short-peaked waves and the long-peaked wave energy spectrum, a fourth expression about the short-peaked wave energy is established based on the short-peaked wave wind and wave spectrum, and the first expression of short-peaked waves is calculated by the fourth expression and the short-peaked wave wind and wave model. wave surface equation; then, a first relationship is established based on the encounter period and the encounter angular frequency, and the angle between the ship speed direction and the main propagation direction of the wind and waves is taken as the ship encounter angle, and a second relationship is established based on the encounter period, the ship encounter angle, the inherent period of wind and waves, the inherent wave speed of wind and waves and the ship speed, and a third relationship is established based on the encounter angular frequency, the ship encounter angle, the inherent angular frequency of wind and waves, the inherent wave speed of wind and waves and the ship speed; based on the first relationship, the second relationship and the third relationship, the coordinate and frequency transformation method is used to transform the first wave surface equation located in the ground coordinate system into the stable coordinate system of the hull, and the second wave surface equation applicable to the surrounding environment of the ship is obtained, and the wave height encountered by the ship during navigation is calculated according to the second wave surface equation.

[0069] Specifically, the directional spectrum of short-peaked waves is first calculated according to the propagation direction of wind wave harmonics, and the calculation is performed according to the following formula:

[0070]

[0071] The 12th ITTC suggested that n in M(μ) be temporarily set to 1, then:

[0072]

[0073] Then, according to the knowledge of fluid mechanics, long-crest waves have energy. Therefore, in the ground coordinates, the first expression of the energy E of long-crest waves is constructed according to the wave amplitude and seawater density, which is expressed as follows:

[0074]

[0075] Where i is the harmonic order, ζ ai is the amplitude of the ith harmonic, ρ is the seawater density, and g is the gravitational acceleration.

[0076] According to the angular frequency ω of the wind and waves and the bandwidth dω set based on the angular frequency of the wind and waves, an angular frequency interval (ω, ω+dω) is established, and then a second expression for the energy of long-peak waves in the angular frequency interval is obtained, which is expressed as follows:

[0077]

[0078] The third expression about the long-peak wave energy spectrum is derived from the second expression, that is, equation (8), which is defined as: ζ (ω) is shown in the following formula:

[0079]

[0080] According to formula 9, the long peak wave energy spectrum S can be calculated ζ (ω).

[0081] Preferably, when the bandwidth in the third expression tends to zero, that is, when dω→0, the integral expression of the long crest wave energy is calculated according to the first expression and the third expression, as shown below:

[0082]

[0083] According to the integral expression of long crest wave energy, the wave harmonic amplitude ζ can be obtained: ai With the spectral density function S ζ (ω) is related to:

[0084]

[0085] The short-peak wave wind wave spectrum is in the long-peak wave energy spectrum S ζ The directional spectrum of short-peaked waves M(μ) is added to the basis of (ω). Therefore, the short-peaked wave wind wave spectrum is calculated according to the directional spectrum of short-peaked waves and the energy spectrum of long-peaked waves, which is expressed as follows:

[0086] S ζ (ω,μ)=S ζ (ω)M(μ) (10)

[0087] The fourth expression for the energy of short-peaked waves is established based on the short-peaked wave spectrum, which is expressed as follows:

[0088]

[0089] Discretizing the above equation 11 and substituting it into the short crest wave wind wave model can obtain the first wave surface equation of the short crest wave wind wave, which is expressed as follows:

[0090]

[0091] In summary, the state of the waves at a certain moment can be obtained (the state includes wave height, energy distribution, waveform and phase distribution).

[0092] When a ship is sailing on the sea, due to its certain speed, the wave frequency encountered by the ship is not the same as the wave frequency at a fixed point on the sea. When the ship is sailing against the waves, the wave frequency it encounters is higher than the wave frequency at a fixed point on the sea; conversely, when the ship is sailing with the waves, the wave frequency it encounters is lower than the wave frequency at a fixed point on the sea. Therefore, when studying the problem of ships sailing in wind and waves, we first define the wave period encountered by the ship as the encounter period T e , the corresponding angular frequency is called the encounter angular frequency ω e , which is related to the encounter period, establish the first relationship between the encounter period and the encounter angular frequency, that is, In addition, if Figure 7 As shown, the encounter period of the ship is T e and the encounter angular frequency ω e The natural period of the sea wave T, the angular frequency of the wind and wave ω (also called the natural angular frequency ω), the ship speed V, and the ship encounter angle μ e (the angle between the ship speed V and the wind and wave propagation direction) and the inherent wave speed C of the wind and waves, and the relationship can be expressed as:

[0093]

[0094] According to the above equations (13), (14) and the encounter period T e and the encounter angular frequency ω e The geometric relationship between the wave surface and the wave frequency is obtained by converting the first wave surface equation in the ground coordinate system, that is, equation (12), into the stable coordinate system of the hull through the coordinate and frequency transformation method (coordinate transformation based on the rotation matrix and the transformation from wave frequency to encounter frequency). The second wave surface equation suitable for the short-peaked waves around the ship is obtained, which is expressed as follows:

[0095]

[0096] According to the second wave surface equation of short-peaked wind waves, that is, according to formula (15), the wave height ζ encountered by the ship during navigation can be calculated: e , which indicates the shape of the wave surface encountered by the ship during navigation, can more accurately reflect the actual wave conditions, especially for the accurate prediction of wave height under complex sea conditions, reducing the risk of ships encountering extreme sea conditions, thereby protecting the safety of the ship and its crew.

[0097] Steps for obtaining a multi-wave superposition fluctuation pressure model: in a stable coordinate system of the hull, calculate the sea surface depth of a certain underwater point from the free liquid surface according to the liquid surface depth under still water conditions and the wave height encountered by the ship during navigation, and construct a fifth expression for the pressure at a certain underwater point according to the sea surface depth and the atmospheric pressure; calculate a sixth expression for the pressure at a certain underwater point under short-peak wave and sea wave conditions according to the fifth expression and the short-peak wave wind and wave model; obtain a fluctuation pressure model caused by sea waves according to the sixth expression, and use the Smith correction term method to correct the fluctuation pressure model to obtain a corrected fluctuation pressure model; and express the corrected fluctuation pressure model as a superposition of multiple cosine waves through the harmonic superposition analysis method to obtain a multi-wave superposition fluctuation pressure model.

[0098] Specifically, this step can also be understood as a step for studying the distribution of the seawater pressure field under the sea surface. During the research process, it is generally believed that the interference force and torque of the waves on the hull are caused by the fluctuation of the pressure field distribution under the liquid surface. Therefore, before analyzing the wind and wave forces and torques on the ship, the distribution of the seawater pressure field under the sea surface is first studied. From the basic water pressure formula, it can be seen that the fifth expression, that is, the pressure P at a certain point underwater, can be expressed as:

[0099] P=P0+ρgh (16)

[0100] Where P0 is the atmospheric pressure; ρ is the density of seawater; g is the acceleration of gravity; and h is the depth of a certain point underwater (also called a research point) from the free surface of the liquid. Under wave conditions, the sea surface depth h can be expressed as the liquid surface depth z under still water conditions and the wave height ζ encountered by the ship during navigation. e The sum is expressed as follows:

[0101] h=z+ζ e (17)

[0102] According to the fifth expression and the short-peak wave wind wave model, the sixth expression of the pressure at a certain point underwater under the condition of short-peak wave sea waves is calculated. That is, the sixth expression of the pressure at a certain point underwater under the condition of long-peak wave sea waves is obtained by substituting equation (4) into equation (16), as shown in the following equation:

[0103] P=P0+ρgz+ρgζ a cos(kξ-ωt) (18)

[0104] Based on the sixth expression, the fluctuating pressure model caused by the waves is defined as ΔP, then:

[0105] ΔP=ρgζ a cos(kξ-ωt) (19)

[0106] According to the Smith effect, the amplitude of the wave surface fluctuation is affected by the depth, so the Smith correction term is used to correct the fluctuation pressure model to obtain the corrected fluctuation pressure model, as shown in the following formula:

[0107]

[0108]

[0109] ΔP=e -kz ρgζ a cos(kξ-ωt) (22)

[0110] Expanded in the hull stable coordinate system, we have:

[0111] ΔP=e -kz ρgζ a cos(kx s cosμ e +ky s sinμ e -ω e t) (23)

[0112] The modified fluctuating pressure model is expressed as the superposition of multiple cosine waves through the harmonic superposition analysis method, and the multi-wave superposition fluctuating pressure model is obtained, that is, formula (23) is expressed as the cosine wave superposition form, as shown in the following formula:

[0113]

[0114] The generalized wave disturbance force construction step can also be understood as the disturbance force and moment analysis step of the ship. By dividing the complex hull into surface meshes (triangular face elements), and by solving and superimposing the wave forces on each triangular face element, the wave forces acting on the complex hull can be effectively modeled and simulated. In the stable coordinate system of the hull, the ship is divided into multiple triangular face elements based on the finite volume method, and the vector pointing from the ship's center of mass to the centroid of a certain triangular face element is taken as the radius vector of the triangular face element. The wave pressure exerted on the triangular face element is calculated according to the multi-wave superposition wave pressure model, and the wave force exerted on the triangular face element is calculated according to the area, normal vector and wave pressure of the triangular face element. The wave moment exerted on the triangular face element is calculated according to the radius vector of the triangular face element and the calculated wave force. Based on the wave forces and wave moments exerted on all triangular face elements, the wave force and wave moment of the entire ship are calculated respectively. The coordinate and frequency transformation method is used to transform the wave force and wave moment of the entire ship in the stable coordinate system of the hull into the hull coordinate system, and the component arrays of the overall wave force of the ship and the component arrays of the overall wave moment of the ship are obtained respectively, thereby constructing the generalized wave interference force.

[0115] Specifically, Figure 8 As shown in the figure, in the stable coordinate system of the hull, the ship is divided into N triangular face elements based on the finite volume method, and the vector pointing from the ship's center of mass O to the centroid of the i-th triangular face element is taken as the radius vector r of the triangular face element. i , then the wave pressure and wave force can be calculated at the centroid of each face element through the multi-wave superposition wave pressure model. Among them, the wave pressure ΔP of the triangular face element is calculated according to the multi-wave superposition wave pressure model. i , and calculate the wave force on the i-th triangular surface element according to the area, normal vector and wave pressure of the triangular surface element, and calculate according to the following formula:

[0116] ΔF i =ΔP i n i S i (25)

[0117] In the above formula, the subscript i represents the i-th triangle face element; n i is the normal vector of the i-th triangle face; S i is the area of ​​the i-th triangle face; ΔP i is the fluctuating pressure ΔP on the i-th triangle element i , which is x s ,y s ,z,t constitutes the quaternion function ΔP(x s ,y s ,z,t), where x s ,y s ,z three parameters can be directly obtained from the ship's surface mesh file.

[0118] Among them, the symbol e is used ij represents the jth endpoint of the ith triangular face element, each triangular face element consists of e i1 ,e i2 ,e i3 It consists of three endpoints, and the coordinate x of each endpoint ij ,y ij ,z ij All of them can be directly obtained from the surface mesh file. In each small triangular face element, the edge vector v can be constructed using the endpoints, and in the small triangular face element i, it is recorded by e i1 Point to e i2 The edge vector is v i21 , by e i1 Point to e i3 The edge vector is v i31 , then the area of ​​triangle face i is S i for:

[0119]

[0120] The normal vector n of triangle face element i i Then it is parallel to v i21 ×v i31 , which is calculated as follows:

[0121]

[0122] The vector pointing from the ship's mass center O to the centroid of the i-th triangle element is defined as the radius r of the triangle element. i , then according to the radius vector of the i-th triangle element and the calculated wave force ΔF i The wave moment on the i-th triangular surface element can be calculated according to the following formula:

[0123] ΔM i =r i ×ΔF i (28)

[0124] Then, based on the wave forces and wave moments on all triangular face elements, the wave force F and wave moment M of the entire ship can be calculated respectively. That is, the wave force (moment) of the entire ship can be expressed as the sum of the wave forces (moments) on each triangular face element as shown below:

[0125]

[0126] The coordinate and frequency transformation method is used to transform the wave force F and wave moment M of the whole ship in the stable coordinate system of the hull into the hull coordinate system, and the component arrays (F) of the whole wave force in the coordinate system of the ship body are obtained respectively. b , and the component array of the overall wave moment in the ship body coordinate system (F) b , and then through (F) b and (M) b The generalized wave interference force matrix w is constructed and expressed as follows:

[0127]

[0128] Among them, (F) zb For (F) b The third term of is the force in the z-axis direction in the ship's coordinate system, and (M) xb ,(M) xb For (M) b The first and second items in the equation are the moments in the x- and y-axis directions in the coordinate system of the ship. In the subsequent six-degree-of-freedom dynamics study, the wave disturbance force w is recorded as follows:

[0129]

[0130] The calculation steps of Archimedean restoring force are as follows: the angle between the line between the center of mass and transverse metacenter of the ship and the horizontal plane is taken as the roll angle; the angle between the line between the center of mass and longitudinal metacenter of the ship and the horizontal plane is taken as the pitch angle; the roll restoring moment of the ship is calculated according to the ship displacement, transverse metacenter height and roll angle, and the pitch restoring moment of the ship is calculated according to the ship displacement, longitudinal metacenter height and pitch angle; the waterplane area of ​​the ship is calculated according to the ship length and waterline width, and the heave restoring force of the ship is calculated according to the waterplane area and draft of the ship; the Archimedean restoring force is calculated based on the roll restoring moment, pitch restoring moment and heave restoring force of the ship.

[0131] The main external forces and moments acting on the ship are as follows: Fig. 9 As shown in Figure 1, it can be divided into four parts: gravity, fluid dynamics, ocean environment force and main force. Among them, the combined force of gravity and buoyancy in fluid dynamics is defined as the Archimedean restoring force τ P , also known as static force; hydrodynamic force τ in fluid dynamics H It can be further divided into inertial hydrodynamic force τ I and viscous hydrodynamic force τ v ; The main ocean environment forces are wave force w (i.e. wave interference force), wind force and flow force. Considering that wind force and flow force have less influence on the movement of ships than wave force, this application only considers wave force w as one ocean environment force in the research process; Since this application only studies the movement state of ships in the process of straight-line navigation at a constant speed, it can be considered that the thrust and resistance of the ship are equal in magnitude and opposite in direction and can offset each other, and the rudder control force is zero, that is, there is no need to consider the main force in the research process. Specifically, first, the angle between the line between the center of mass and the transverse metacenter of the ship and the horizontal plane is taken as the roll angle The angle between the line between the center of mass and the longitudinal metacenter of the ship and the horizontal plane is taken as the pitch angle θ; then the ship's roll restoring moment is calculated according to the ship's displacement, transverse metacenter height and roll angle. The ship's roll restoring moment K P Analysis Fig.10 It can be expressed as:

[0132]

[0133] Among them, Δ is the displacement of the ship; h is the transverse metacentric height, that is, Fig.10 The distance from the mid-transverse metacenter M to the center of mass G. The definition of the transverse metacenter is: when the ship is in equilibrium, the line of action of the buoyancy and the ship have a roll angle The intersection of the lines of action of the buoyancy force.

[0134] Then, the pitch restoring moment of the ship is calculated according to the ship displacement Δ, the longitudinal metacentric height H and the pitch angle θ. The pitch restoring moment of the ship M is P It can be expressed as:

[0135] M P =ΔHθ (31)

[0136] Among them, H is the longitudinal metacentric height, that is, the longitudinal metacentric height of the ship M l (Not shown in the figure) The distance to the center of mass G.

[0137] The waterline area of ​​the ship is calculated based on the ship length and waterline width, and is calculated according to the following formula:

[0138] A w =C WP LB (32)

[0139] Among them, L is the length of the ship, B is the width of the waterline, and C is the WP is the waterplane coefficient of the ship.

[0140] The ship heave restoring force is calculated based on the ship's waterline area and draft. The ship heave restoring force is the change in buoyancy caused by the ship's heave motion and is calculated according to the following formula:

[0141] Z P =ρgzA w (33)

[0142] Among them, A w is the waterplane area of ​​the ship, z is the draft, which can also be called the ship's vertical swing, indicating the distance the ship deviates from the equilibrium position in the vertical direction, ρ is the seawater density, and g is the acceleration of gravity.

[0143] The Archimedean restoring force τ is calculated based on the roll restoring moment, pitch restoring moment and heave restoring force of the ship. P It is the combined force of gravity and buoyancy on the ship, which can be expressed as:

[0144]

[0145] Among them, F P is the restoring force, which includes the heave restoring force Z P ; T P is the restoring moment, which includes the roll restoring moment K P and pitch restoring moment M P .

[0146] Archimedean restoring force τ P It can also be expressed as follows:

[0147]

[0148] The restoring force matrix P is defined as:

[0149]

[0150] And define the ship's generalized position vector x as:

[0151]

[0152] Then the Archimedean restoring force τ P It can be expressed as:

[0153] τ P =-Px (38)

[0154] The calculation steps of inertial and viscous hydrodynamics are as follows: construct the generalized velocity vector of the ship based on the heave velocity, left and right swing velocity and fore and aft swing velocity, and establish the hydrodynamic equation of the ship according to the generalized velocity vector and its rate of change; and when the ship is in a positive floating state, use the first-order Taylor expansion method to linearly expand the hydrodynamic equation of the ship to obtain the linear hydrodynamic equation of the ship; obtain the fluid inertia matrix and fluid viscosity matrix according to the linear hydrodynamic equation, calculate the inertial hydrodynamic force according to the fluid inertia matrix and the generalized velocity vector, and calculate the viscous hydrodynamic force according to the fluid viscosity matrix and the generalized velocity vector.

[0155] Specifically, firstly, the generalized velocity vector v of the ship is constructed based on the heave velocity w, left and right swing velocity p and fore and aft swing velocity q of the ship, which is expressed as follows:

[0156]

[0157] According to the generalized velocity vector v and the rate of change of the generalized velocity vector Establish the hydrodynamic equation of the ship τ H , which is expressed as follows:

[0158]

[0159] When the ship is in a positive floating state (which can also be understood as being in a balanced position), the first-order Taylor expansion method is used to calculate the ship hydrodynamic equation τ H After linear expansion, the linear hydrodynamic equation of the ship is obtained, which is expressed as follows:

[0160]

[0161] Among them, τ I is the inertial hydrodynamic force, τ v Viscous water dynamics.

[0162] According to the linear hydrodynamic equation, the fluid inertia matrix M is obtained A and the fluid viscosity matrix D, expressed as follows:

[0163]

[0164] The hydrodynamic force τ of the ship isH It can be expressed as

[0165]

[0166] Among them, the fluid inertia matrix M A It consists of nine hydrodynamic derivatives:

[0167]

[0168] in, represents the inertial hydrodynamic derivative of the heave force with respect to the heave acceleration, represents the inertial hydrodynamic derivative of the rolling moment with respect to the rolling angular acceleration, It represents the inertial hydrodynamic derivative of the pitching moment with respect to the pitching angular acceleration, w is the component of the ship velocity on the z-axis of the ship body coordinate system, p is the component of the ship angular velocity on the x-axis of the ship body coordinate system, and q is the component of the ship angular velocity on the y-axis of the ship body coordinate system.

[0169] When the ship moves at a small angle, the inertial hydrodynamic force is calculated based on the fluid inertia matrix and the generalized velocity vector, and the three degrees of freedom motion can be decoupled. Therefore, the inertial hydrodynamic force τ I It can be expressed as:

[0170]

[0171] In addition, due to the inertial hydrodynamic force τ I The effect on the hull is the same as increasing the generalized mass of the ship by a certain value Δm, so the inertial hydrodynamic derivative is often expressed in the form of additional mass (moment of inertia):

[0172]

[0173] The viscosity matrix D also consists of nine hydrodynamic derivatives:

[0174]

[0175] When the ship moves at a small angle, the viscous hydrodynamic force is calculated based on the fluid viscosity matrix and the generalized velocity vector. In other words, the three degrees of freedom can be decoupled in the same way. Therefore, the viscous hydrodynamic force τ v It can be expressed as:

[0176]

[0177] Steps for establishing the ship motion model: construct the system inertia matrix based on the ship mass and moment of inertia, obtain the first ship motion equation about the resultant external force acting on the ship based on the system inertia matrix and the generalized velocity vector and according to Newton's second law, and establish the second ship motion equation about the resultant external force acting on the ship based on the Archimedean restoring force, inertial hydrodynamic force, viscous hydrodynamic force and generalized wave interference force matrix, and obtain the third ship motion equation recursively based on the first ship motion equation and the second ship motion equation; and under the condition of small-angle motion of the ship, transform the third ship motion equation to obtain the ship motion model, so as to realize the dynamic stability evaluation of the ship under various sea conditions.

[0178] Specifically, the system inertia matrix M is first constructed based on the ship mass m and the moment of inertia J: RB ,

[0179] M RB =diag(m,m,m,J x ,J y ,J z )

[0180] Where m is the mass of the ship, J x ,J y ,J z are the moments of inertia of the ship relative to the x, y, and z axes of the hull coordinate system.

[0181] Then based on the system inertia matrix M RB The generalized velocity vector and Newton's second law give the first ship motion equation about the resultant external force on the ship, expressed in the following vector form:

[0182]

[0183] And based on the Archimedean restoring force τ P , inertial hydrodynamic force τ I , viscous hydrodynamic force τ v The generalized wave disturbance force matrix w is used to establish the second ship motion equation regarding the resultant external force on the ship, which is expressed as follows:

[0184] τ RB =τ I +τ v +τ P +w

[0185] According to the first ship motion equation and the second ship motion equation, the third ship motion equation is obtained recursively, which can be expressed as:

[0186]

[0187] The above formula can be rearranged as follows:

[0188]

[0189] Under the condition of small-angle motion of the ship, Therefore, the above formula is transformed to obtain the ship motion model, which is expressed as follows:

[0190]

[0191] make

[0192] Based on the above formula, the dynamic stability evaluation of ships under various sea conditions can be realized.

[0193] The present invention also relates to a ship dynamic stability modeling system based on multiple external force coupling, which corresponds to the ship dynamic stability modeling method based on multiple external force coupling, and can be understood as a system for implementing the above method. The system includes a parameter acquisition and coordinate system establishment module, a short-peak wave wind and wave model construction module, a wave surface equation and sea wave height calculation module, a multi-wave superposition fluctuation pressure model acquisition module, a generalized wave interference force calculation module, an Archimedean restoring force calculation module, an inertial and viscous hydrodynamic calculation module, and a ship motion model establishment module, which are connected in sequence. Specifically,

[0194] The parameter acquisition and coordinate system establishment module acquires the wind and wave characteristic parameters and the motion state parameters of the ship under different sea conditions, and establishes a ground coordinate system with any point on the sea level as the origin, the ship's motion direction as the longitudinal axis, the direction of the starboard side of the ship and parallel to the sea level as the transverse axis, and the center of the earth as the vertical axis; establishes a hull stable coordinate system with the ship's center of mass as the origin, the ship's motion direction as the longitudinal axis, the direction of the starboard side of the ship and parallel to the sea level as the transverse axis, and the center of the earth as the vertical axis; establishes a hull stable coordinate system with the ship's center of mass as the origin, the ship's bow direction as the longitudinal axis, The hull coordinate system is established with the direction of the starboard side of the ship as the transverse axis and the direction of the bottom of the ship as the vertical axis; the wind and wave characteristic parameters include wave amplitude, wave number, main propagation direction of wind and waves, propagation direction of wind and wave harmonics, wind and wave angular frequency, time of wind and wave shape transformation, wind and wave natural period and wind and wave natural wave speed; the motion state parameters of the ship include ship speed, encounter period, encounter angular frequency, ship displacement, ship length, waterline width, ship waterplane area, draft depth, transverse metacentric height, longitudinal metacentric height, ship mass and moment of inertia;

[0195] The short-peaked wave wind and wave model construction module establishes a plane wave equation about the wave height in the ground coordinate system based on the wave amplitude, wave number, main propagation direction of wind and waves, propagation direction of wind and wave harmonics, and time of wind and wave shape transformation, and recursively obtains the short-peaked wave wind and wave model according to the plane wave equation;

[0196] The wave surface equation and wave height calculation module calculates the directional spectrum of short-peaked waves according to the propagation direction of wind and wave harmonics, and constructs a first expression for the energy of long-peaked waves according to the wave amplitude and seawater density under ground coordinates, establishes an angular frequency interval according to the wind and wave angular frequency and the frequency band width set based on the wind and wave angular frequency, and then obtains a second expression for the energy of long-peaked waves within the angular frequency interval, and recursively obtains a third expression for the energy spectrum of long-peaked waves from the second expression, and then calculates the energy spectrum of long-peaked waves; calculates the short-peaked wave wind and wave spectrum according to the directional spectrum of short-peaked waves and the long-peaked wave energy spectrum, establishes a fourth expression for the energy of short-peaked waves based on the short-peaked wave wind and wave spectrum, and calculates the short-peaked wave wind and wave model by the fourth expression. The first wave surface equation; then establish a first relationship between the encounter period and the encounter angular frequency, and take the angle between the ship speed direction and the main propagation direction of the wind and waves as the ship encounter angle, and establish a second relationship about the encounter period based on the ship encounter angle, the natural period of wind and waves, the natural wave speed of wind and waves, and the ship speed, and establish a third relationship about the encounter angular frequency based on the ship encounter angle, the angular frequency of wind and waves, the natural wave speed of wind and waves, and the ship speed; based on the first relationship, the second relationship, and the third relationship, and using the coordinate and frequency transformation method, the first wave surface equation located in the ground coordinate system is converted into the hull stable coordinate system, and the second wave surface equation applicable to the surrounding environment of the ship is obtained, and the wave height encountered by the ship during navigation is calculated according to the second wave surface equation;

[0197] The multi-wave superposition fluctuation pressure model acquisition module calculates the sea surface depth of a certain underwater point from the free liquid surface according to the liquid surface depth under calm water conditions and the wave height encountered by the ship during navigation in a stable coordinate system of the hull, and constructs a fifth expression for the pressure of a certain underwater point according to the sea surface depth and the atmospheric pressure; calculates a sixth expression for the pressure of a certain underwater point under short-peak wave and sea wave conditions according to the fifth expression and the short-peak wave wind and wave model; obtains the fluctuation pressure model caused by the sea waves according to the sixth expression, and corrects the fluctuation pressure model by using the Smith correction term method to obtain the corrected fluctuation pressure model; and expresses the corrected fluctuation pressure model as the superposition of multiple cosine waves by using the harmonic superposition analysis method to obtain the multi-wave superposition fluctuation pressure model;

[0198] The generalized wave disturbance force calculation module divides the ship into multiple triangular face elements based on the finite volume method in a stable hull coordinate system, and uses the vector from the ship's center of mass to the centroid of a certain triangular face element as the radius vector of the triangular face element, calculates the wave pressure on the triangular face element according to the multi-wave superposition wave pressure model, calculates the wave force on the triangular face element according to the area, normal vector and wave pressure of the triangular face element, and calculates the wave moment on the triangular face element according to the radius vector of the triangular face element and the calculated wave force; calculates the wave force and wave moment of the entire ship based on the wave force and wave moment on all triangular face elements; and uses the coordinate and frequency transformation method to convert the wave force and wave moment of the entire ship in the stable hull coordinate system into the hull coordinate system, and obtains the component array of the entire ship's wave force and the component array of the entire ship's wave moment, thereby constructing a generalized wave disturbance force matrix;

[0199] The Archimedean restoring force calculation module uses the angle between the line between the ship's center of mass and transverse metacenter and the horizontal plane as the roll angle; uses the angle between the line between the ship's center of mass and longitudinal metacenter and the horizontal plane as the pitch angle; calculates the ship's roll restoring moment according to the ship's displacement, transverse metacenter height and roll angle, and calculates the ship's pitch restoring moment according to the ship's displacement, longitudinal metacenter height and pitch angle; calculates the ship's waterplane area according to the ship's length and waterline width, and calculates the ship's heave restoring force according to the ship's waterplane area and draft; calculates the Archimedean restoring force based on the roll restoring moment, pitch restoring moment and the ship's heave restoring force;

[0200] The inertial and viscous hydrodynamic calculation module constructs a generalized velocity vector of the ship based on the heave velocity, left-right swing velocity and fore-and-aft swing velocity of the ship, and establishes a hydrodynamic equation of the ship according to the generalized velocity vector and its rate of change; and when the ship is in a positive floating state, a first-order Taylor expansion method is used to linearly expand the hydrodynamic equation of the ship to obtain a linear hydrodynamic equation of the ship; a fluid inertia matrix and a fluid viscosity matrix are obtained according to the linear hydrodynamic equation, the inertial hydrodynamic force is calculated according to the fluid inertia matrix and the generalized velocity vector, and the viscous hydrodynamic force is calculated according to the fluid viscosity matrix and the generalized velocity vector;

[0201] The ship motion model establishment module constructs a system inertia matrix based on the ship mass and moment of inertia, obtains a first ship motion equation about the resultant external force acting on the ship based on the system inertia matrix and the generalized velocity vector and according to Newton's second law, and establishes a second ship motion equation about the resultant external force acting on the ship based on Archimedean restoring force, inertial hydrodynamic force, viscous hydrodynamic force and generalized wave interference force matrix, and obtains a third ship motion equation recursively based on the first ship motion equation and the second ship motion equation; and under the condition of small-angle motion of the ship, the third ship motion equation is transformed to obtain a ship motion model, so as to realize dynamic stability evaluation of the ship under various sea conditions.

[0202] Preferably, in the wave surface equation and wave height calculation module, when the bandwidth in the third expression tends to zero, the integral expression of the long-peak wave energy is calculated according to the first expression and the third expression, and the relationship between the wave harmonic amplitude and the spectral density function is calculated according to the integral expression.

[0203] Preferably, in the parameter acquisition and coordinate system establishment step module, the wind and wave characteristic parameters also include wavelength, and the wave number is calculated based on the wavelength.

[0204] Preferably, the coordinate and frequency transformation method is based on the coordinate transformation of the rotation matrix and the transformation of the wave frequency to the encounter frequency.

[0205] The present invention provides an objective and scientific method and system for modeling the dynamic stability of a ship based on multiple external forces coupling. A short-peak wave model is established based on the characteristic parameters of wind and waves and the motion state parameters of the ship, and a generalized interference force matrix, Archimedean restoring force, inertial hydrodynamic force and viscous hydrodynamic force are calculated using specific calculation methods, coordinate transformation methods, correction methods and finite volume methods. Then, a ship motion model is established, which effectively improves the accuracy of the model, can more accurately predict the dynamic behavior of the ship under complex sea conditions, and provides a solid foundation for improving the safety and operational performance of the ship.

[0206] It should be noted that the above-described specific implementations can enable those skilled in the art to more fully understand the invention, but do not limit the invention in any way. Therefore, although this specification has described the invention in detail with reference to the drawings and embodiments, those skilled in the art should understand that the invention can still be modified or replaced by equivalents. In short, all technical solutions and improvements that do not deviate from the spirit and scope of the invention should be included in the protection scope of the patent for the invention.

Claims

1. A ship dynamic stability modeling method based on multi-external force coupling, characterized in that: The following steps are involved: Parameter acquisition and coordinate system establishment steps: obtain wind and wave characteristic parameters and ship motion state parameters under different sea conditions, and establish a ground coordinate system with any point on the sea level as the origin, the ship motion direction as the longitudinal axis, the starboard side of the ship and parallel to the sea level as the transverse axis, and the center of the earth as the vertical axis; establish a hull stable coordinate system with the ship's center of mass as the origin, the ship motion direction as the longitudinal axis, the starboard side of the ship and parallel to the sea level as the transverse axis, and the center of the earth as the vertical axis; A hull coordinate system is established with the ship's center of mass as the origin, the direction of the ship's bow as the longitudinal axis, the direction of the ship's starboard side as the transverse axis, and the direction of the ship's bottom as the vertical axis; the wind and wave characteristic parameters include amplitude, wave number, main propagation direction of wind and waves, propagation direction of wind and wave harmonics, wind and wave angular frequency, time of wind and wave shape transformation, wind and wave natural period, and wind and wave natural wave speed; the ship's motion state parameters include ship speed, encounter period, encounter angular frequency, ship displacement, ship length, waterline width, ship waterplane area, draft, transverse metacentric height, longitudinal metacentric height, ship mass, and moment of inertia; The steps of constructing the short-peaked wave wind and wave model are as follows: in the ground coordinate system, a plane wave equation about the wave height is established based on the wave amplitude, wave number, main propagation direction of wind and wave, propagation direction of wind and wave harmonics, and the time of wind and wave shape transformation, and the short-peaked wave wind and wave model is obtained by recursion based on the plane wave equation; The wave surface equation and wave height calculation steps are as follows: the directional spectrum of short-peaked waves is calculated according to the propagation direction of wind and wave harmonics, and a first expression about the energy of long-peaked waves is constructed according to the wave amplitude and seawater density under ground coordinates, an angular frequency interval is established according to the wind and wave angular frequency and the bandwidth set based on the wind and wave angular frequency, and then a second expression about the energy of long-peaked waves within the angular frequency interval is obtained, and a third expression about the energy spectrum of long-peaked waves is recursively obtained from the second expression, and then the long-peaked wave energy spectrum is calculated; a short-peaked wave wind and wave spectrum is calculated according to the directional spectrum of short-peaked waves and the energy spectrum of long-peaked waves, a fourth expression about the energy of short-peaked waves is established based on the short-peaked wave wind and wave spectrum, and the fourth expression of the energy of short-peaked waves is calculated by the fourth expression and the short-peaked wave wind and wave model. A wave surface equation is established; then a first relational expression between the encounter period and the encounter angular frequency is established, and the angle between the ship speed direction and the main propagation direction of the wind and waves is taken as the ship encounter angle, and a second relational expression about the encounter period is established based on the ship encounter angle, the natural period of the wind and waves, the natural wave speed of the wind and waves, and the ship speed, and a third relational expression about the encounter angular frequency is established based on the ship encounter angle, the angular frequency of the wind and waves, the natural wave speed of the wind and waves, and the ship speed; based on the first relational expression, the second relational expression and the third relational expression, and using the coordinate and frequency transformation method, the first wave surface equation located in the ground coordinate system is converted into the hull stable coordinate system, and a second wave surface equation applicable to the surrounding environment of the ship is obtained, and the wave height encountered by the ship during navigation is calculated according to the second wave surface equation; The steps of obtaining the multi-wave superposition fluctuation pressure model are as follows: in the hull stable coordinate system, the sea surface depth of a certain underwater point from the free liquid surface is calculated according to the liquid surface depth under calm water conditions and the wave height encountered by the ship during navigation, and the fifth expression about the pressure of a certain underwater point is constructed according to the sea surface depth and the atmospheric pressure; the sixth expression of the pressure of a certain underwater point under the short-peak wave and sea wave conditions is calculated according to the fifth expression and the short-peak wave wind and wave model; The fluctuating pressure model caused by the ocean waves is obtained according to the sixth expression, and the fluctuating pressure model is corrected by using the Smith correction term method to obtain the corrected fluctuating pressure model; and the corrected fluctuating pressure model is expressed as the superposition of multiple cosine waves by using the harmonic superposition analysis method to obtain the multi-wave superposition fluctuating pressure model; The generalized wave disturbance force construction steps are as follows: in a stable hull coordinate system, the ship is divided into multiple triangular face elements based on the finite volume method, and the vector pointing from the ship's center of mass to the centroid of a certain triangular face element is used as the radius vector of the triangular face element, and the wave pressure received by the triangular face element is calculated according to the multi-wave superposition wave pressure model, and the wave force received by the triangular face element is calculated according to the area, normal vector and wave pressure of the triangular face element, and the wave moment received by the triangular face element is calculated according to the radius vector of the triangular face element and the calculated wave force; based on the wave forces and wave moments received by all triangular face elements, the wave forces and wave moments of the entire ship are calculated respectively; and the coordinate and frequency transformation methods are used to convert the wave forces and wave moments of the entire ship in the stable hull coordinate system into the hull coordinate system, and the component arrays of the overall wave forces of the ship and the component arrays of the overall wave moments of the ship are obtained respectively, and then the generalized wave disturbance force matrix is ​​constructed; The calculation steps of Archimedean restoring force are as follows: the angle between the line between the center of mass and transverse metacenter of the ship and the horizontal plane is taken as the roll angle; the angle between the line between the center of mass and longitudinal metacenter of the ship and the horizontal plane is taken as the pitch angle; the roll restoring moment of the ship is calculated according to the displacement of the ship, the height of the transverse metacenter and the roll angle, and the pitch restoring moment of the ship is calculated according to the displacement of the ship, the height of the longitudinal metacenter and the pitch angle; the waterplane area of ​​the ship is calculated according to the length and the waterline width, and the heave restoring force of the ship is calculated according to the waterplane area and the draft depth; the Archimedean restoring force is calculated based on the roll restoring moment, the pitch restoring moment and the heave restoring force of the ship; The calculation steps of inertial and viscous hydrodynamics are as follows: construct the generalized velocity vector of the ship based on the heave velocity, left-right swing velocity and fore-and-aft swing velocity of the ship, and establish the hydrodynamic equation of the ship based on the generalized velocity vector and its rate of change; and when the ship is in a positive floating state, use the first-order Taylor expansion method to linearly expand the hydrodynamic equation of the ship to obtain the linear hydrodynamic equation of the ship; obtain the fluid inertia matrix and fluid viscosity matrix respectively according to the linear hydrodynamic equation, calculate the inertial hydrodynamics according to the fluid inertia matrix and the generalized velocity vector, and calculate the viscous hydrodynamics according to the fluid viscosity matrix and the generalized velocity vector; Steps for establishing the ship motion model: construct the system inertia matrix based on the ship mass and moment of inertia, obtain the first ship motion equation about the resultant external force acting on the ship based on the system inertia matrix and the generalized velocity vector and according to Newton's second law, and establish the second ship motion equation about the resultant external force acting on the ship based on the Archimedean restoring force, inertial hydrodynamic force, viscous hydrodynamic force and generalized wave interference force matrix, and obtain the third ship motion equation recursively based on the first ship motion equation and the second ship motion equation; and under the condition of small-angle motion of the ship, transform the third ship motion equation to obtain the ship motion model, so as to realize the dynamic stability evaluation of the ship under various sea conditions.

2. The ship dynamic stability modeling method based on multiple external force coupling according to claim 1 is characterized in that: In the wave surface equation and wave height calculation steps, when the bandwidth in the third expression tends to zero, the integral expression of the long-peak wave energy is calculated according to the first expression and the third expression, and the relationship between the wave harmonic amplitude and the spectral density function is calculated according to the integral expression.

3. The ship dynamic stability modeling method based on multiple external force coupling according to claim 1 is characterized in that: In the parameter acquisition and coordinate system establishment steps, the wind and wave characteristic parameters also include wavelength, and the wave number is calculated based on the wavelength.

4. The ship dynamic stability modeling method based on multiple external force coupling according to claim 1 is characterized in that: The coordinate and frequency transformation method includes coordinate transformation based on rotation matrix and transformation from wave frequency to encounter frequency.

5. A ship dynamic stability modeling system based on multi-external force coupling, characterized in that: It includes a parameter acquisition and coordinate system establishment module, a short-peak wave wind and wave model construction module, a wave surface equation and wave height calculation module, a multi-wave superposition wave pressure model acquisition module, a generalized wave interference force calculation module, an Archimedean restoring force calculation module, an inertial and viscous hydrodynamic calculation module, and a ship motion model establishment module. The parameter acquisition and coordinate system establishment module acquires the wind and wave characteristic parameters and the motion state parameters of the ship under different sea conditions, and establishes a ground coordinate system with any point on the sea level as the origin, the ship's motion direction as the longitudinal axis, the direction to the starboard side of the ship and parallel to the sea level as the transverse axis, and the center of the earth as the vertical axis; establishes a hull stable coordinate system with the ship's center of mass as the origin, the ship's motion direction as the longitudinal axis, the direction to the starboard side of the ship and parallel to the sea level as the transverse axis, and the center of the earth as the vertical axis; A hull coordinate system is established with the ship's center of mass as the origin, the direction of the ship's bow as the longitudinal axis, the direction of the ship's starboard side as the transverse axis, and the direction of the ship's bottom as the vertical axis; the wind and wave characteristic parameters include amplitude, wave number, main propagation direction of wind and waves, propagation direction of wind and wave harmonics, wind and wave angular frequency, time of wind and wave shape transformation, wind and wave natural period, and wind and wave natural wave speed; the ship's motion state parameters include ship speed, encounter period, encounter angular frequency, ship displacement, ship length, waterline width, ship waterplane area, draft, transverse metacentric height, longitudinal metacentric height, ship mass, and moment of inertia; The short-peaked wave wind and wave model construction module establishes a plane wave equation about the wave height in the ground coordinate system based on the wave amplitude, wave number, main propagation direction of wind and waves, propagation direction of wind and wave harmonics, and time of wind and wave shape transformation, and recursively obtains the short-peaked wave wind and wave model according to the plane wave equation; The wave surface equation and wave height calculation module calculates the directional spectrum of short-peaked waves according to the propagation direction of wind and wave harmonics, and constructs a first expression for the energy of long-peaked waves according to the wave amplitude and seawater density under ground coordinates, establishes an angular frequency interval according to the wind and wave angular frequency and the frequency band width set based on the wind and wave angular frequency, and then obtains a second expression for the energy of long-peaked waves within the angular frequency interval, and recursively obtains a third expression for the energy spectrum of long-peaked waves from the second expression, and then calculates the energy spectrum of long-peaked waves; calculates the short-peaked wave wind and wave spectrum according to the directional spectrum of short-peaked waves and the long-peaked wave energy spectrum, establishes a fourth expression for the energy of short-peaked waves based on the short-peaked wave wind and wave spectrum, and calculates the short-peaked wave wind and wave model by the fourth expression. The first wave surface equation; then establish a first relationship between the encounter period and the encounter angular frequency, and take the angle between the ship speed direction and the main propagation direction of the wind and waves as the ship encounter angle, and establish a second relationship about the encounter period based on the ship encounter angle, the natural period of wind and waves, the natural wave speed of wind and waves, and the ship speed, and establish a third relationship about the encounter angular frequency based on the ship encounter angle, the angular frequency of wind and waves, the natural wave speed of wind and waves, and the ship speed; based on the first relationship, the second relationship, and the third relationship, and using the coordinate and frequency transformation method, the first wave surface equation located in the ground coordinate system is converted into the hull stable coordinate system, and the second wave surface equation applicable to the surrounding environment of the ship is obtained, and the wave height encountered by the ship during navigation is calculated according to the second wave surface equation; The multi-wave superposition fluctuation pressure model acquisition module calculates the sea surface depth of a certain underwater point from the free liquid surface according to the liquid surface depth under calm water conditions and the wave height encountered by the ship during navigation in the hull stable coordinate system, and constructs a fifth expression for the pressure of a certain underwater point according to the sea surface depth and the atmospheric pressure; calculates a sixth expression for the pressure of a certain underwater point under short-peak wave conditions according to the fifth expression and the short-peak wave wind and wave model; The fluctuating pressure model caused by the ocean waves is obtained according to the sixth expression, and the fluctuating pressure model is corrected by using the Smith correction term method to obtain the corrected fluctuating pressure model; and the corrected fluctuating pressure model is expressed as the superposition of multiple cosine waves by using the harmonic superposition analysis method to obtain the multi-wave superposition fluctuating pressure model; The generalized wave disturbance force calculation module divides the ship into multiple triangular face elements based on the finite volume method in a stable hull coordinate system, and uses the vector from the ship's center of mass to the centroid of a certain triangular face element as the radius vector of the triangular face element, calculates the wave pressure on the triangular face element according to the multi-wave superposition wave pressure model, calculates the wave force on the triangular face element according to the area, normal vector and wave pressure of the triangular face element, and calculates the wave moment on the triangular face element according to the radius vector of the triangular face element and the calculated wave force; calculates the wave force and wave moment of the entire ship based on the wave force and wave moment on all triangular face elements; and uses the coordinate and frequency transformation method to convert the wave force and wave moment of the entire ship in the stable hull coordinate system into the hull coordinate system, and obtains the component array of the entire ship's wave force and the component array of the entire ship's wave moment, thereby constructing a generalized wave disturbance force matrix; The Archimedean restoring force calculation module uses the angle between the line between the ship's center of mass and transverse metacenter and the horizontal plane as the roll angle; uses the angle between the line between the ship's center of mass and longitudinal metacenter and the horizontal plane as the pitch angle; calculates the ship's roll restoring moment according to the ship's displacement, transverse metacenter height and roll angle, and calculates the ship's pitch restoring moment according to the ship's displacement, longitudinal metacenter height and pitch angle; calculates the ship's waterplane area according to the ship's length and waterline width, and calculates the ship's heave restoring force according to the ship's waterplane area and draft; calculates the Archimedean restoring force based on the roll restoring moment, pitch restoring moment and the ship's heave restoring force; The inertial and viscous hydrodynamic calculation module constructs a generalized velocity vector of the ship based on the heave velocity, left-right swing velocity and fore-and-aft swing velocity of the ship, and establishes a hydrodynamic equation of the ship according to the generalized velocity vector and its rate of change; and when the ship is in a positive floating state, a first-order Taylor expansion method is used to linearly expand the hydrodynamic equation of the ship to obtain a linear hydrodynamic equation of the ship; a fluid inertia matrix and a fluid viscosity matrix are obtained according to the linear hydrodynamic equation, the inertial hydrodynamic force is calculated according to the fluid inertia matrix and the generalized velocity vector, and the viscous hydrodynamic force is calculated according to the fluid viscosity matrix and the generalized velocity vector; The ship motion model establishment module constructs a system inertia matrix based on the ship mass and moment of inertia, obtains a first ship motion equation about the resultant external force acting on the ship based on the system inertia matrix and the generalized velocity vector and according to Newton's second law, and establishes a second ship motion equation about the resultant external force acting on the ship based on Archimedean restoring force, inertial hydrodynamic force, viscous hydrodynamic force and generalized wave interference force matrix, and obtains a third ship motion equation recursively based on the first ship motion equation and the second ship motion equation; and under the condition of small-angle motion of the ship, the third ship motion equation is transformed to obtain a ship motion model, so as to realize dynamic stability evaluation of the ship under various sea conditions.

6. The ship dynamic stability modeling system based on multiple external force coupling according to claim 5 is characterized in that: In the wave surface equation and wave height calculation module, when the bandwidth in the third expression tends to zero, the integral expression of the long-peak wave energy is calculated according to the first expression and the third expression, and the relationship between the wave harmonic amplitude and the spectral density function is calculated according to the integral expression.

7. The ship dynamic stability modeling system based on multiple external force coupling according to claim 5 is characterized in that: In the parameter acquisition and coordinate system establishment step module, the wind and wave characteristic parameters also include wavelength, and the wave number is calculated based on the wavelength.

8. The ship dynamic stability modeling system based on multiple external force coupling according to claim 5 is characterized in that: The coordinate and frequency transformation method includes coordinate transformation based on rotation matrix and transformation from wave frequency to encounter frequency.

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