Ship and sea wave interaction visualization method based on sea wave spectrum

Abstract

The invention discloses a ship and sea wave interaction visualization method based on a sea wave spectrum, and the method comprises the steps: S1, building a sea surface model based on an inverse Fourier transform method, and obtaining the circular frequency of any grid point; s2, designing an encounter frequency calculation formula for calculating encounter frequency according to the circular frequency and the obtained encounter angle; s3, designing a calculation model for calculating to obtain the wave disturbance force and moment of the ship on the current sea surface according to the encounter frequency; s4, a six-degree-of-freedom ship motion equation is established, the real-time motion state of the ship on the current sea surface is calculated on the basis of the six-degree-of-freedom ship motion equation and the wave disturbance force and moment borne by the ship on the current sea surface, and the real-time motion state of the ship on the current sea surface is the visual result of ship and sea wave interaction. According to the method, IFFT-based sea surface establishment and the motion model response of the ship in the time domain are coupled, the parallelism of wave modeling and the accuracy of response calculation are both considered, and the method is particularly suitable for a navigation simulator with high real-time performance, multiple degrees of freedom and multi-point output.

Description

Technical Field

[0001] The present invention relates to the technical field of navigation scene simulation, and in particular to a method for visualizing interaction between ships and waves based on wave spectra. Background Art

[0002] As a modern marine engineering tool, navigation simulators are widely used in crew training, ship design optimization, and navigation strategy research. During navigation simulator training, the ship's pilot observes the waves and surrounding vessels mapped in the simulator's visual system, taking appropriate maneuvering measures to perform tasks such as lookout, watchkeeping, and ship maneuvering. The interaction between the ship and waves in navigation simulators not only impacts the ship's safety, performance, and comfort, but also optimizes ship design and improves its performance in adverse sea conditions.

[0003] In the fields of ship motion simulation and ocean environment modeling, wave modeling is a critical step affecting simulation realism and efficiency. Traditional methods often use the linear superposition of regular waves, superimposing several sinusoidal waves of different frequencies and phases to construct sea surface waveforms. Although this method is theoretically mature, it suffers from high computational overhead and difficulty in parallelization in high-precision simulations or multi-point modeling. To improve the efficiency of wave field generation, sea surface modeling methods based on spectrum construction and inverse Fourier transform (IFFT) have been widely adopted in physical simulation and graphics computing in recent years. This method defines the wave spectrum in the frequency domain and uses IFFT to efficiently generate large-scale, temporally and spatially consistent wave fronts. It not only has low computational complexity but also supports parallel processing. In marine simulator applications, however, the urgent challenge is how to couple the wave field constructed based on frequency domain construction with the ship's motion model response in the time domain, while ensuring physical accuracy, in multi-location, real-time dynamic update scenarios, and effectively connect the wave surface disturbance force with the ship's motion model. Summary of the Invention

[0004] The present invention provides a method for visualizing the interaction between ships and waves based on wave spectra, so as to overcome the technical problem that the existing technology cannot effectively couple the wave field constructed based on the frequency domain with the motion model response of the ship in the time domain, and realize the effective connection between the wave surface disturbance force and the ship motion model.

[0005] In order to achieve the above object, the technical solution of the present invention is:

[0006] A method for visualizing the interaction between ships and waves based on wave spectrum, comprising the following steps:

[0007] S1: establishing a sea surface model based on the inverse Fourier transform method, and obtaining the circular frequency of any grid point based on the sea surface model;

[0008] S2: designing an encounter frequency calculation formula for calculating the encounter frequency based on the circular frequency and the obtained encounter angle, and calculating the encounter frequency according to the encounter frequency calculation formula;

[0009] S3: a calculation model is designed to calculate the wave interference force and moment experienced by the ship on the current sea surface according to the encounter frequency, and the wave interference force and moment experienced by the ship on the current sea surface are calculated according to the calculation model;

[0010] S4: Establish a six-degree-of-freedom ship motion equation, and calculate the real-time motion state of the ship on the current sea surface based on the six-degree-of-freedom ship motion equation and the wave interference force and torque applied to the ship on the current sea surface. The real-time motion state of the ship on the current sea surface is the visualization result of the interaction between the ship and the waves.

[0011] Furthermore, in S1, the specific steps of establishing a sea surface model based on the inverse Fourier transform method and obtaining the circular frequency of any grid point based on the sea surface model include:

[0012] The sea surface coordinate system O'x0y0z0 is defined based on the Cartesian coordinate system. The origin O' is any point on the sea surface. The x0 axis points to the north, the y0 axis points to the east, and the z0 axis points to the center of the earth. The x0O'y0 plane coincides with the still water surface.

[0013] Determine the size of the sea surface to be drawn

[0014] The sea surface to be mapped is divided into M×N spatial grids, and the size of each spatial grid is Δx×Δy.

[0015] The initial ocean wave model is established based on the 3D Gerstner wave model and is expressed as:

[0016]

[0017] The initial wave model is transformed into the inverse Fourier transform form to establish the sea surface model, which is expressed as:

[0018]

[0019] Where x pq is the position vector; η(x pq ,t) is the time at x pq The instantaneous wave height at the location, η(x pq ,t) is obtained by superposition of elementary waves in the form of cosine; A ij is the amplitude of each elementary wave component derived from the ocean wave energy spectrum, i,j represents the i-th elementary wave and the j-th elementary wave; is the phase shift, and The symbol * indicates taking the conjugate complex number; ΔS k is the area of discrete integral domain of wave number vector; ψ ph (k i,j ) is the selected wave spectrum; k ij is the wave number vector, k ij =(k i ,k j )=k(cosθ,sinθ),k=|k ij |, θ is the angle between the wave number vector and the positive x-axis, k i and k j are the wave numbers in the x0 direction and the y0 direction respectively, and the calculation formula is:

[0020]

[0021] Among them, -N / 2≤m≤N / 2, -M / 2≤n≤M / 2;

[0022] ω is the circular frequency, and the calculation formula is:

[0023] ω 2 =gk ij (6)

[0025] Where g is the acceleration due to gravity.

[0026] Furthermore, in S2, an encounter frequency calculation formula is designed for calculating the encounter frequency according to the circular frequency and the obtained encounter angle, and the encounter frequency calculated according to the encounter frequency calculation formula includes:

[0027] The origin O of the ship's coordinate system is defined as the ship's center of gravity G, the positive direction of the x-axis is the bow direction, the positive direction of the y-axis points to the starboard side, and the z-axis points vertically downward to the keel;

[0028] The sea surface coordinate system is converted into the ship coordinate system. The conversion formula is:

[0029]

[0030] Based on the ship coordinate system, the designed encounter frequency calculation formula is:

[0031]

[0032] Where ψ is the heading angle, V is the ship speed, χ is the encounter angle, which is the difference between the heading angle and the absolute wave direction angle; ω e is the encounter frequency, and ω is the circular frequency.

[0033] Furthermore, in S3, the step of designing a calculation model for calculating the wave interference force and torque exerted on the ship on the current sea surface according to the encounter frequency includes:

[0034] Equivalently take the ship as the ship with a square coefficient of C B , Captain The width of the ship is B and the height is d m The box-shaped body; ship_L is the length of the ship;

[0035] Taking x, y, and z as independent variables, the calculation model designed to calculate the wave interference force on the ship on the current sea surface along the x, y, and z axes is:

[0036]

[0037] The calculation model designed to calculate the moments on the x, y, and z axes of the ship at the current sea surface is:

[0038]

[0039] Where a i is the amplitude, i is the i-th elementary wave; ω ei is the encounter frequency corresponding to the i-th elementary wave; ρ is the seawater density; ω i is the circular frequency corresponding to the i-th elementary wave; d is the draft depth.

[0040] Furthermore, in S4, the specific steps of establishing a six-degree-of-freedom ship motion equation and calculating the real-time motion state of the ship on the current sea surface based on the six-degree-of-freedom ship motion equation and the wave interference force and torque exerted on the ship on the current sea surface include:

[0041] Based on the Froude-Krenov hypothesis, the calculation is carried out, ignoring the mutual coupling between heave and heave and the other four degrees of freedom, and the six-degree-of-freedom ship motion equation MMG is established, which is expressed as:

[0042]

[0043] Where, X H 、Y H , Z H , K H 、M H With N H are the forces and moments of the bare hull in the corresponding six degrees of freedom directions; X P 、Y P , Z P , K P 、M P 、N P are the propeller force and torque respectively; X R 、Y R , Z R , K R 、M R 、NR are the rudder force and moment respectively; X wind 、Y wind , Z wind , K wind 、M wind 、N wind are the wind force and torque respectively; X wave 、Y wave , Z wave , K wave 、M wave 、N wave are the force and moment of the wave respectively; m is the mass of the ship; m x 、m y 、m z are the additional mass of the ship in the longitudinal, transverse and vertical directions respectively; I xx , I yy , I zz are the moments of inertia around the Ox, Oy, and Oz axes respectively; J xx 、J yy 、J zz are the additional moments of inertia around the Ox, Oy, and Oz axes respectively; u, v, and w are the longitudinal, transverse, and vertical velocities respectively; p, q, and r are the angular velocities around the Ox, Oy, and Oz axes respectively;

[0044] Use formula (9) to formula (14) to obtain the wave interference force and moment of the ship at different circular frequencies, and sum them according to the set weights to obtain the wave interference force and moment at the current moment;

[0045] The wave interference force and torque at the current moment are assigned to the right side of the equation (15) respectively, and the Runge-Kutta method is used to solve the problem to obtain the real-time motion state of the ship on the current sea surface.

[0046] Furthermore, the selected wave spectrum is any one of Phillips spectrum, Pierson-Moskowitz spectrum, and JONSWAP spectrum.

[0047] Beneficial effects: The present invention uses the inverse Fourier transform (IFFT) method to replace the traditional regular wave linear superposition method to establish a sea surface model. Since IFFT has a high degree of parallelism in the frequency domain to time domain conversion process, it not only significantly reduces the computational complexity of wave field construction, but also improves the execution efficiency of the overall algorithm on multi-core processors. At the same time, the method designs an encounter frequency calculation formula for calculating the encounter frequency based on the circular frequency and the obtained encounter angle to calculate the encounter frequency, and designs a calculation model for calculating the wave interference force and torque on the current sea surface based on the encounter frequency, and calculates the interference force and torque of waves of different frequencies on the current sea surface based on the calculation model, and performs real-time superposition in the time domain, so that the attitude response of the ship on the virtual sea surface is more realistic and has stronger dynamic consistency. The present invention couples the sea surface establishment based on IFFT with the motion model response of the ship in the time domain, taking into account the parallelism of wave modeling and the accuracy of response calculation, and is particularly suitable for high real-time, multi-degree-of-freedom, and multi-point output navigation simulators. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0049] Figure 1 The figure is a flow chart of a method for visualizing the interaction between ships and waves based on wave spectrum in the present invention. DETAILED DESCRIPTION

[0050] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0051] This embodiment provides a method for visualizing the interaction between ships and waves based on wave spectrum. Figure 1 As shown, the specific steps include:

[0052] S1: establishing a sea surface model based on the inverse Fourier transform method, and obtaining the circular frequency of any grid point based on the sea surface model;

[0053] S2: designing an encounter frequency calculation formula for calculating the encounter frequency based on the circular frequency and the obtained encounter angle, and calculating the encounter frequency according to the encounter frequency calculation formula;

[0054] S3: a calculation model is designed to calculate the wave interference force and moment experienced by the ship on the current sea surface according to the encounter frequency, and the wave interference force and moment experienced by the ship on the current sea surface are calculated according to the calculation model;

[0055] S4: Establish a six-degree-of-freedom ship motion equation, and calculate the real-time motion state of the ship on the current sea surface based on the six-degree-of-freedom ship motion equation and the wave interference force and torque applied to the ship on the current sea surface. The real-time motion state of the ship on the current sea surface is the visualization result of the interaction between the ship and the waves.

[0056] In the specific embodiment S1, the specific steps of establishing a sea surface model based on the inverse Fourier transform method and obtaining the circular frequency of any grid point based on the sea surface model include:

[0057] The sea surface coordinate system O'x0y0z0 is defined based on the Cartesian coordinate system. The origin O' is any point on the sea surface. The x0 axis points to the north, the y0 axis points to the east, and the z0 axis points to the center of the earth. The x0O'y0 plane coincides with the still water surface.

[0058] Determine the size of the sea surface to be drawn

[0059] The sea surface to be mapped is divided into M×N spatial grids, and the size of each spatial grid is Δx×Δy.

[0060] The initial ocean wave model is established based on the 3D Gerstner wave model and is expressed as:

[0061]

[0062] When there are a large number of elementary waves, the amount of calculation for direct superposition will be very large. Therefore, this embodiment uses IFFT instead of direct superposition to reduce the amount of calculation. In addition, IFFT can be accelerated by GPU, which has little impact on the rendering frame rate. This embodiment performs inverse Fourier transform on the initial wave model of formula (1) to establish a sea surface model, which is expressed as:

[0063]

[0064] Where x pq is the position vector; η(x pq ,t) is the time at x pq The instantaneous wave height at the location, η(x pq ,t) is obtained by superposition of elementary waves in the form of cosine; A ijis the amplitude of each elementary wave component derived from the ocean wave energy spectrum, i, j represent the i-th elementary wave and the j-th elementary wave. In this embodiment, the numbers of i and j are both limited to positive integer powers of 2; is the phase shift, and The symbol * indicates taking the conjugate complex number; ΔS k is the area of discrete integral domain of wave number vector; ψ ph (k i,j ) is the selected wave spectrum; k ij is the wave number vector, k ij =(k i ,k j )=k(cosθ,sinθ),k=|k ij |, θ is the angle between the wave number vector and the positive x-axis, k i and k j are the wave numbers in the x0 direction and the y0 direction respectively, and the calculation formula is:

[0065]

[0066] Among them, -N / 2≤m≤N / 2, -M / 2≤n≤M / 2;

[0067] ω is the circular frequency. In deep water, the calculation formula of ω is:

[0068] ω 2 =gk ij (6)

[0070] Where g is the acceleration due to gravity.

[0071] In a specific embodiment, in S2, an encounter frequency calculation formula is designed for calculating the encounter frequency based on the circular frequency and the obtained encounter angle, and the encounter frequency calculated according to the encounter frequency calculation formula includes:

[0072] The origin O of the ship's coordinate system is defined as the ship's center of gravity G. The positive direction of the x-axis is the bow direction, the positive direction of the y-axis points to the starboard side, and the z-axis points vertically downward to the keel.

[0073] In order to describe the motion of a ship in waves, it is necessary to convert the sea surface coordinate system into the ship coordinate system. The conversion formula is:

[0074]

[0075] Based on the ship coordinate system, the designed encounter frequency calculation formula is:

[0076]

[0077] Where ψ is the heading angle, V is the ship speed, χ is the encounter angle, which is the difference between the heading angle and the absolute wave direction angle; ω e is the encounter frequency, and ω is the circular frequency.

[0078] In a specific embodiment, in S3, the calculation model designed to calculate the wave interference force and torque on the ship on the current sea surface based on the encounter frequency includes:

[0079] Equivalently take the ship as the ship with a square coefficient of C B , Captain The width of the ship is B and the height is d m The box-shaped body; ship_L is the length of the ship;

[0080] Considering x, y, and z as independent variables, the calculation model designed to calculate the wave interference force on the ship on the current sea surface along the x, y, and z axes is:

[0081]

[0082] The calculation model designed to calculate the moments on the x, y, and z axes of the ship at the current sea surface is:

[0083]

[0084]

[0085] Where a i is the amplitude, i is the i-th elementary wave; ω ei is the encounter frequency corresponding to the i-th elementary wave; ρ is the seawater density; ω i is the circular frequency corresponding to the i-th elementary wave; d is the draft depth.

[0086] In S4, the specific steps of establishing a six-degree-of-freedom ship motion equation and calculating the real-time motion state of the ship on the current sea surface based on the six-degree-of-freedom ship motion equation and the wave interference force and torque exerted on the ship on the current sea surface include:

[0087] Based on the Froude-Krenov hypothesis, the calculation is carried out, ignoring the mutual coupling between heave and heave and the other four degrees of freedom, and the six-degree-of-freedom ship motion equation MMG is established, which is expressed as:

[0088]

[0089] Where, X H 、Y H , Z H , K H 、M H With N H are the forces and moments of the bare hull in the corresponding six degrees of freedom directions; XP 、Y P , Z P , K P 、M P 、N P are the propeller force and torque respectively; X R 、Y R , Z R , K R 、M R 、N R are the rudder force and moment respectively; X wind 、Y wind , Z wind , K wind 、M wind 、N wind are the wind force and torque respectively; X wave 、Y wave , Z wave , K wave 、M wave 、N wave are the force and moment of the wave respectively; m is the mass of the ship; m x 、m y 、m z are the additional mass of the ship in the longitudinal, transverse and vertical directions respectively; I xx , I yy , I zz are the moments of inertia around the Ox, Oy, and Oz axes respectively; J xx 、J yy 、J zz are the additional moments of inertia around the Ox, Oy, and Oz axes respectively; u, v, and w are the longitudinal, transverse, and vertical velocities respectively; p, q, and r are the angular velocities around the Ox, Oy, and Oz axes respectively;

[0090] Use formula (9) to formula (14) to obtain the wave interference force and moment of the ship at different circular frequencies, and sum them according to the set weights to obtain the wave interference force and moment at the current moment;

[0091] The wave interference force and torque at the current moment are assigned to the right side of the equation (15) respectively, and the Runge-Kutta method is used to solve the problem to obtain the real-time motion state of the ship on the current sea surface.

[0092] Specifically, the process of solving the problem using the Runge-Kutta method is an existing technology and will not be described in detail here.

[0093] In a specific embodiment, the selected wave spectrum is any one of the Phillips spectrum, the Pierson-Moskowitz spectrum, and the JONSWAP spectrum.

[0094]

[0095] u=(u x ,u y )=(Ucosα,Usinα), α is the wind direction.

[0096] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for visualizing ship-wave interaction based on wave spectrum, characterized in that: The specific steps include: S1: establishing a sea surface model based on the inverse Fourier transform method, and obtaining the circular frequency of any grid point based on the sea surface model; S2: designing an encounter frequency calculation formula for calculating the encounter frequency based on the circular frequency and the obtained encounter angle, and calculating the encounter frequency according to the encounter frequency calculation formula; S3: a calculation model is designed to calculate the wave interference force and moment experienced by the ship on the current sea surface according to the encounter frequency, and the wave interference force and moment experienced by the ship on the current sea surface are calculated according to the calculation model; S4: Establish a six-degree-of-freedom ship motion equation, and calculate the real-time motion state of the ship on the current sea surface based on the six-degree-of-freedom ship motion equation and the wave interference force and torque applied to the ship on the current sea surface. The real-time motion state of the ship on the current sea surface is the visualization result of the interaction between the ship and the waves.

2. The ship and wave interactive visualization method based on wave spectrum according to claim 1 is characterized in that: In S1, the specific steps of establishing a sea surface model based on the inverse Fourier transform method and obtaining the circular frequency of any grid point based on the sea surface model include: The sea surface coordinate system O'x0y0z0 is defined based on the Cartesian coordinate system. The origin O' is any point on the sea surface. The x0 axis points to the north, the y0 axis points to the east, and the z0 axis points to the center of the earth. The x0O'y0 plane coincides with the still water surface. Determine the size of the sea surface to be drawn The sea surface to be mapped is divided into M×N spatial grids, and the size of each spatial grid is Δx×Δy. The initial ocean wave model is established based on the 3D Gerstner wave model and is expressed as: The initial wave model is transformed into the inverse Fourier transform form to establish the sea surface model, which is expressed as: Where x pq is the position vector; η(x pq ,t) is the time at x pq The instantaneous wave height at the location, η(x pq ,t) is obtained by superposition of elementary waves in the form of cosine; A ij is the amplitude of each elementary wave component derived from the ocean wave energy spectrum, i,j represents the i-th elementary wave and the j-th elementary wave; is the phase shift, and The symbol * indicates taking the conjugate complex number; ΔS k is the area of discrete integral domain of wave number vector; ψ ph (k i,j ) is the selected wave spectrum; k ij is the wave number vector, k ij =(k i ,k j )=k(cosθ,sinθ),k=|k ij |, θ is the angle between the wave number vector and the positive x-axis, k i and k j are the wave numbers in the x0 direction and the y0 direction respectively, and the calculation formula is: Among them, -N / 2≤m≤N / 2, -M / 2≤n≤M / 2; ω is the circular frequency, and the calculation formula is: ω 2 =gk ij (6) Where g is the acceleration due to gravity.

3. The ship and wave interactive visualization method based on wave spectrum according to claim 2 is characterized in that: In S2, an encounter frequency calculation formula is designed for calculating the encounter frequency based on the circular frequency and the obtained encounter angle, and the encounter frequency calculated according to the encounter frequency calculation formula includes: The origin O of the ship's coordinate system is defined as the ship's center of gravity G, the positive direction of the x-axis is the bow direction, the positive direction of the y-axis points to the starboard side, and the z-axis points vertically downward to the keel; The sea surface coordinate system is converted into the ship coordinate system. The conversion formula is: x0=xcosψ-ysinψ+Vt y0=xsinψ+ycosψ+Vt z0=z (7) Based on the ship coordinate system, the designed encounter frequency calculation formula is: Where ψ is the heading angle, V is the ship speed, χ is the encounter angle, which is the difference between the heading angle and the absolute wave direction angle; ω e is the encounter frequency, and ω is the circular frequency.

4. The ship and wave interactive visualization method based on wave spectrum according to claim 3 is characterized in that: In S3, the step of designing a calculation model for calculating the wave interference force and moment experienced by the ship on the current sea surface based on the encounter frequency includes: Equivalently take the ship as the ship with a square coefficient of C B , Captain The width of the ship is B and the height is d m The box-shaped body; ship_L is the length of the ship; Taking x, y, and z as independent variables, the calculation model designed to calculate the wave interference force on the ship on the current sea surface along the x, y, and z axes is: The calculation model designed to calculate the moments on the x, y, and z axes of the ship at the current sea surface is: Where a i is the amplitude, i is the i-th elementary wave; ω ei is the encounter frequency corresponding to the i-th elementary wave; ρ is the seawater density; ω i is the circular frequency corresponding to the i-th elementary wave; d is the draft depth.

5. The ship and wave interactive visualization method based on wave spectrum according to claim 4 is characterized in that: In S4, the specific steps of establishing a six-degree-of-freedom ship motion equation and calculating the real-time motion state of the ship on the current sea surface based on the six-degree-of-freedom ship motion equation and the wave interference force and torque exerted on the ship on the current sea surface include: Based on the Froude-Krenov hypothesis, the calculation is carried out, ignoring the mutual coupling between heave and heave and the other four degrees of freedom, and the six-degree-of-freedom ship motion equation MMG is established, which is expressed as: Where, X H 、Y H , Z H , K H 、M H With N H are the forces and moments of the bare hull in the corresponding six degrees of freedom directions; X P 、Y P , Z P , K P 、M P 、N P are the propeller force and torque respectively; X R 、Y R , Z R , K R 、M R 、N R are the rudder force and moment respectively; X wind 、Y wind , Z wind , K wind 、M wind 、N wind are the wind force and torque respectively; X wave 、Y wave , Z wave , K wave 、M wave 、N wave are the force and moment of the wave respectively; m is the mass of the ship; m x 、m y 、m z are the additional mass of the ship in the longitudinal, transverse and vertical directions respectively; I xx , I yy , I zz are the moments of inertia around the Ox, Oy, and Oz axes respectively; J xx 、J yy 、J zz are the additional moments of inertia around the Ox, Oy, and Oz axes respectively; u, v, and w are the longitudinal, transverse, and vertical velocities respectively; p, q, and r are the angular velocities around the Ox, Oy, and Oz axes respectively; Use formula (9) to formula (14) to obtain the wave interference force and moment of the ship at different circular frequencies, and sum them according to the set weights to obtain the wave interference force and moment at the current moment; The wave interference force and torque at the current moment are assigned to the right side of the equation (15) respectively, and the Runge-Kutta method is used to solve the problem to obtain the real-time motion state of the ship on the current sea surface.

6. The ship and wave interactive visualization method based on wave spectrum according to claim 5 is characterized in that: The selected wave spectrum is any one of the Phillips spectrum, Pierson-Moskowitz spectrum, and JONSWAP spectrum.

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