Nonlinear hydrodynamic calculation method for shallow water floating body based on limited water depth Green function

Abstract

The application discloses a shallow water floating body nonlinear hydrodynamic calculation method based on a limited water depth Green function, and realizes double breakthroughs in precision and efficiency. The limited water depth Green function strictly satisfies the water bottom boundary condition, and is combined with instantaneous wet surface dynamic iteration to accurately capture the shallow water nonlinear wave body interaction. The steady phase method is used to analyze the far field Green function and recursive convolution dimension reduction technology, and the calculation efficiency is greatly improved. The influence of shallow water on the diffraction force, radiation force and motion attitude of the floating body is studied, the position, motion speed and motion attitude of the floating body are obtained according to the nonlinear hydrodynamic force suffered by the floating body, the floating body motion differential equation is solved, the balance between precision and efficiency is realized, the shallow water nonlinear calculation bottleneck is broken through, and high-precision calculation is realized.

Description

Technical Field

[0001] This invention relates to the field of numerical calculation technology of marine engineering hydrodynamics, and more specifically, to a nonlinear hydrodynamic calculation method for shallow-water floating bodies based on the Green's function for finite water depth. Background Technology

[0002] As marine development expands into shallower waters, such as offshore wind power and offshore oil and gas development, the application of floating structures in shallow water environments is increasing. Shallow water environments possess unique hydrodynamic characteristics. Compared to deep water environments, shallow-water floating bodies experience more complex hydrodynamic forces, and their motion response and structural safety are influenced by various factors, including wave-seabed interaction and nonlinear effects. Therefore, accurately calculating the hydrodynamic characteristics of shallow-water floating bodies is crucial for the design, operation, and maintenance of these floating structures.

[0003] Traditional deep-water Green's functions do not consider the influence of the bottom boundary, leading to the following defects in hydrodynamic calculations of shallow-water floating bodies: 1. Insufficient applicability of linear theory: Potential flow theory underestimates the amplitude operator of heave / roll response in shallow water, resulting in large errors; 2. Contradiction between computational efficiency and accuracy: Fully viscous CFD models have excessively high computational costs for mesh reconstruction and free surface tracking, making them difficult to use for iterative engineering design; 3. Distortion of shallow-water effects: Deep-water Green's functions ignore the interaction between waves and the bottom, failing to reflect characteristics such as increased wave height, shortened wavelength, and enhanced nonlinearity in shallow water areas. Summary of the Invention

[0004] This invention aims to provide a nonlinear hydrodynamic calculation method for shallow-water floating bodies, considering the influence of shallow water on the motion and forces acting on the floating body through a finite-depth Green's function. A hydrodynamic model is constructed using an improved finite-depth Green's function, combined with a nonlinear iterative solution framework. The influence of shallow water on the nonlinear hydrodynamics of the floating body is considered, studying the effects of shallow water on the diffraction force, radiation force, and motion attitude of the floating body. Based on the nonlinear hydrodynamic forces acting on the floating body, the differential equations of motion are solved to obtain the floating body's position, velocity, and motion attitude, achieving a balance between accuracy and efficiency.

[0005] To achieve the above objectives, the present invention proposes the following technical solutions.

[0006] A nonlinear hydrodynamic calculation method for shallow-water floating bodies based on the Green's function for finite water depth is provided, including the following steps: S1. Real-time acquisition of multi-source data is carried out using a sensor network deployed around the floating body. The wave surface elevation spatiotemporal sequence is obtained by wave radar, and the direction spectrum of the incident wave is obtained by spectral analysis. The vertical distribution of current velocity at the location of the floating body is obtained by acoustic Doppler current profiler. The pressure distribution of the wetted surface of the floating body is obtained by pressure sensor array. The time history of the six degrees of freedom motion of the floating body is obtained by motion sensor. The multi-source data is preprocessed to form a standardized dataset. S2. Construct the floating body state vector based on the standardized dataset, use the velocity potential Green's function that satisfies the bottom boundary conditions of finite water depth as the basic solution, and use the steady phase method to analytically approximate the far-field wave effect to calculate the acceleration integral; use the singularity stripping technique to ensure the accuracy of the near-field integral and reduce the complexity of the Green's function convolution. S3, decompose the total wave force, and at each time step, dynamically trim and update the wetted surface mesh of the floating body according to the instantaneous motion attitude of the floating body to establish the motion equation of the floating body; S4 defines the convergence criterion as a weighted combination of three indicators and performs multi-objective convergence criterion. If the convergence condition is not met, the relaxation factor is adjusted and the time step is reduced, and the calculation is re-iterated until convergence. S5, after convergence, outputs the floating body motion time history, wave load time history, and key spectrum analysis results, obtaining the floating body's position, motion velocity, and motion attitude, and obtaining the nonlinear hydrodynamic calculation results of the shallow water floating body, which can be used for motion response prediction and safety assessment of floating structures in shallow water environments.

[0007] The velocity potential Green's function in S2 is:

[0008] Where G(x,y,z,ξ,ψ,ε) represents the velocity potential generated at the field point (x,y,z) after placing a unit point source at the source point (ξ,ψ,ε); r is the actual distance from the source point to the field point. ; Distance to the underwater mirror image point The integral term characterizes the shallow water wave propagation effect; Let k be the zeroth-order Bessel function, d be the water depth, and R be the horizontal distance between the source and field points. z represents the vertical coordinate of the field point.

[0009] S2 further includes: Calculate the horizontal distance R between the source point and the field point. If R > 5λ, where λ is the wavelength corresponding to the peak frequency, mark it as the far field; otherwise, mark it as the near field. When marked as far field, the phase function is solved to obtain the steady-state point. At the steady-state point, the magnitude function and phase function are expanded by Taylor series and retained to the second-order terms to calculate the accelerated integral. When labeled as near field, singularity stripping technique is used to identify singular terms, calculate the analytic singular part, perform numerical integration on the regularized part, and add the singular and regularized parts together.

[0010] S3 includes: The total wave force is decomposed as follows:

[0011] Among them, F FK Represents the Froude-Krylov force, F D F represents diffraction force. R F represents radiation force. wave Represents the total wave force; F FK The expression is , The incident potential is generated by nonlinear wave theory; F D The expression is , For the diffraction potential solved based on the Green's function, F R The expression is In the formula The diffraction and radiation potentials are solved based on the Green's function; ρ represents the fluid density; S B Represents the mesh of the wetted surface of an object; n i This represents the i-th component of the unit normal vector on the surface of the floating body.

[0012] S3 further includes: Dynamically trimming the wet surface mesh of the floating body S B Furthermore, by stabilizing the numerical process through relaxation iteration, an instantaneous wet surface update S is introduced into the boundary conditions of the object surface. B The iteration format is: ,in, This represents the wetted surface mesh of the object at the q-th iteration step, where q represents the iteration number and p... q denoted as the displacement of the floating body calculated in the q-th iteration, and β as the relaxation factor, a coefficient between 0 and 1 used to control and stabilize the iteration process.

[0013] S3 further includes: Solve the equations of motion for the floating body to establish the equations of motion for the floating body:

[0014] Among them, A ∞ B ∞ Mass and damping are added to the infinite frequency; K(t) is the time delay function kernel, obtained through the Fourier transform of the Green's function; X represents the displacement vector of the floating body. This represents the velocity vector of the floating body. Let G represent the acceleration vector of the floating body, G represent the structural mass matrix of the floating body, and C represent the restoring force coefficient matrix. Let F represent the convolution integral term, t represent the current time, τ represent the time integration variable, K() be the time delay function, and F be the time integral term. wave (t) represents the total wave force at the current time, Fmoor (t) represents the translational force acting on the floating body at the current time; To accelerate the computation of convolution terms, the integral term is transformed using the exponential basis recursive convolution method:

[0015] Among them, a m Let q represent the m-th weight coefficient. m (t) represents the m-th state variable, and M represents the number of variables used for convolution integration.

[0016] Memory variables Updated to

[0017] Among them, b m This represents the attenuation coefficient corresponding to the m-th state. Indicates the time step.

[0018] S4 includes: The convergence criterion is:

[0019] Where α1, α2, α3 are weight coefficients, and satisfy α1+α2+α3=1; To account for the convergence tolerance, let X represent the displacement vector of the floating body, ΔX represent the increment of the displacement vector, and F wave Represents the total wave force, ΔF wave η represents the increment of the total wave force. max Indicates the maximum wavefront elevation, Δη max χ represents the increment of the maximum wavefront elevation; χ represents the comprehensive convergence index.

[0020] S5 includes: After the convergence criterion is satisfied, the floating body motion time history and wave load time history are extracted, and key spectrum analysis results are generated simultaneously. The floating body motion time history is sampled at intervals to form a data block containing displacement and velocity, and a dual timestamp index structure is adopted. The wave load time history is decomposed into four force vectors: first-order excitation, second-order difference frequency excitation, second-order sum frequency excitation, and slamming pulse excitation, and written into independent storage space respectively. The power spectral density of the floating body's motion and the stress at key structural points is calculated based on the floating body's motion time history to obtain the motion response power spectral density and tension power spectral density. Based on the above time history and spectral results, the real-time position, motion velocity, and motion attitude of the floating body are output for quantitative extraction of shallow water nonlinear hydrodynamic characteristics, and for prediction and safety assessment of the motion response of floating structures.

[0021] The process of predicting and assessing the motion response of floating structures includes: using a neural network model driven by the nonlinear hydrodynamic characteristics of shallow water to predict the extreme values ​​of the floating body's motion in advance; setting response thresholds; determining the response level based on the predicted values ​​and real-time fatigue damage; setting different colored warning lights to remind workers: green light to continue, yellow light to remind workers, and red light to stop work; and thus completing the prediction and assessment of the motion response of floating structures.

[0022] Compared with the prior art, the embodiments of the present invention achieve the following beneficial effects: 1. This invention fully considers nonlinear problems. To address the issue that linear potential flow theory cannot capture high-order wave forces in shallow water and the distortion of wet surface boundary treatment, it introduces an instantaneous wet surface dynamic iteration mechanism to update the wave rise boundary in real time, establishes a nonlinear load decomposition model, accurately characterizes the slamming effect, and fully considers nonlinear problems.

[0023] 2. This invention significantly improves computational efficiency. To address the problem of exponential memory growth caused by storing historical Green's functions in the traditional boundary element method, a hybrid acceleration algorithm for Green's functions with finite depth is proposed. The stable phase method is used for analytical solutions in the far field, and singularity stripping technology is used in the near field to further reduce the complexity of integral terms, reduce memory consumption, and significantly improve computational efficiency.

[0024] 3. The deep-water Green's function of this invention ignores bottom reflection, resulting in significant errors in shallow-water wave height and motion response. By introducing a finite-depth Green's function that strictly satisfies the bottom boundary conditions, and correcting the hydrodynamic coefficients in shallow water through Green's function frequency domain transformation, the problem of calculation in shallow water areas is solved. Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating the nonlinear hydrodynamic calculation method for shallow-water floating bodies based on the Green's function for finite water depth provided in an embodiment of the present invention. Detailed Implementation

[0026] The present invention will now be described in detail with reference to the accompanying drawings.

[0027] Example 1

[0028] To meet the urgent need for the safe and economical development of marine resources in areas with limited water depth, efficient computational tools capable of accurately capturing shallow water effects are required. This invention provides an indispensable method for the refined design and safety assessment of shallow-water floating structures. Figure 1 As shown, this invention provides a nonlinear hydrodynamic calculation method for shallow-water floating bodies based on the Green's function for finite water depth, characterized by comprising the following steps: S1. Real-time acquisition of multi-source data is carried out using a sensor network deployed around the floating body. The wave surface elevation spatiotemporal sequence is obtained by wave radar, and the direction spectrum of the incident wave is obtained by spectral analysis. The vertical distribution of current velocity at the location of the floating body is obtained by acoustic Doppler current profiler. The pressure distribution of the wetted surface of the floating body is obtained by pressure sensor array. The time history of the six degrees of freedom motion of the floating body is obtained by motion sensor. The multi-source data is preprocessed to form a standardized dataset. S2. Construct the floating body state vector based on the standardized dataset, use the velocity potential Green's function that satisfies the bottom boundary conditions of finite water depth as the basic solution, and use the steady phase method to analytically approximate the far-field wave effect to calculate the acceleration integral; use the singularity stripping technique to ensure the accuracy of the near-field integral and reduce the complexity of the Green's function convolution. S3, decompose the total wave force, and at each time step, dynamically trim and update the wetted surface mesh of the floating body according to the instantaneous motion attitude of the floating body to establish the motion equation of the floating body; S4 defines the convergence criterion as a weighted combination of three indicators and performs multi-objective convergence criterion. If the convergence condition is not met, the relaxation factor is adjusted and the time step is reduced, and the calculation is re-iterated until convergence. S5, after the calculation converges, outputs the floating body motion time history, wave load time history, and key spectrum analysis results, obtains the floating body's position, motion velocity, and motion attitude, and obtains the nonlinear hydrodynamic calculation results of the shallow water floating body, which can be used for motion response prediction and safety assessment of floating structures in shallow water environments. S1 includes: obtaining the spatiotemporal sequence η(x, y, t) of wave surface elevation from the original radar image sequence acquired by wave radar in a sea area with a radius of 1-3 kilometers centered on the floating body, and obtaining the direction spectrum S(ω,θ) of the incident wave through spectral analysis; where η represents the wave surface elevation, η > 0 represents the wave crest, η < 0 represents the wave trough, x and y represent the spatial coordinates in the horizontal plane, usually x represents the main wave direction, y represents the direction perpendicular to x, and t represents time; S(ω, θ) is a function representing the distribution density of wave energy relative to frequency ω and propagation direction θ; An acoustic Doppler current profiler is fixed to the bottom of the float or placed on the seabed near the float using a mooring device to obtain the vertical velocity distribution U(z, t); a pressure sensor array is deployed on the wet surface of the float in a non-uniform grid pattern to obtain the pressure distribution p(x,y,z,t) on the wet surface of the float; and the time history of the float's six degrees of freedom motion is obtained through motion sensors, including the displacement, angular velocity, and linear velocity corresponding to sway, roll, heave, pitch, pitch and yaw. The preprocessing of the multi-source data includes: synchronizing all the acquired multi-source data in time and unifying them into a body coordinate system with the center of mass of the floating body as the origin; using low-pass filtering to remove high-frequency noise from the original multi-source data to form a standardized dataset indexed by time.

[0029] The state vector is represented as , where η max Indicates the maximum wavefront elevation. d represents the surface flow velocity. seabed Indicates local water depth. Let X represent the pressure gradient vector, and let X represent the displacement vector of the floating body. This represents the velocity vector of the floating body. The velocity potential Green's function is:

[0030] Where G(x,y,z,ξ,ψ,ε) represents the velocity potential generated at the field point (x,y,z) after placing a unit point source at the source point (ξ,ψ,ε); r is the actual distance from the source point to the field point. ; Distance to the underwater mirror image point The integral term characterizes the shallow water wave propagation effect; Let k be the zeroth-order Bessel function, d be the water depth, and R be the horizontal distance between the source and field points. z represents the vertical coordinate of the field point; Calculate the horizontal distance R between the source point and the field point. If R > 5λ, where λ is the wavelength corresponding to the peak frequency, mark it as the far field; otherwise, mark it as the near field. When marked as far field, the phase function is solved to obtain the steady-state point. At the steady-state point, the magnitude function and phase function are expanded by Taylor series and retained to the second-order terms to calculate the accelerated integral. When labeled as near field, singularity stripping technique is used to identify singular terms, calculate the analytic singular part, perform numerical integration on the regularized part, and add the singular and regularized parts together; Specifically, the phase function is g(k) = kR - ωnΔt, where k is the wavenumber, ω represents the angular frequency, R represents the horizontal distance between the source and field points, n represents the number of solution steps, and Δt represents the time step. The amplitude function is f(k s )=2k s ·cosh[k s (z+d)]cosh[k s (ε+d)] / [ω²cosh(k s )-gk s sinh(k s )],k s Let z represent the steady-state wavenumber, z represent the vertical coordinate of the field point, ε represent the vertical coordinate of the source point, d represent the water depth, and g represent the gravitational acceleration. Perform a Taylor series expansion and retain the second-order terms. Then, perform an analytical Gaussian integral to obtain the acceleration integral. When labeled as near field, the velocity potential Green's function constructs an asymptotic singular term f as the wave number k→∞. singular (k), its integral result I singular Given the analytical quantity, subtract the original velocity potential Green's function from the above singular terms to obtain the regular part f. reg (k)=f(k)−f singular (k), the difference function decays rapidly according to an exponential law as k→∞, the integration interval is significantly truncated, and the 1 / r singularity is eliminated; for the regular part f reg (k) An adaptive Gaussian-Cronrod integral is used, with a relative error tolerance set to 1×10⁻⁶. -6 The points cap is automatically truncated to f. reg (k) Amplitude less than 10 -10 At this point, the near-field integral value I is determined as the analytic singular part I. singular With numerical rules Part I reg The sum of, i.e., I=I reg +I singular .

[0031] The total wave force is decomposed as follows:

[0032] Among them, F FK Represents the Froude-Krylov force, F D F represents diffraction force. R F represents radiation force. wave Represents the total wave force; F FK The expression is , The incident potential is generated by nonlinear wave theory; F D The expression is , For the diffraction potential solved based on the Green's function, F R The expression is In the formula The diffraction and radiation potentials are solved based on the Green's function; ρ represents the fluid density; S B Represents the mesh of the wetted surface of an object; n i This represents the i-th component of the unit normal vector on the surface of the floating body. Dynamically trimming the wet surface mesh of the floating body S B Furthermore, by stabilizing the numerical process through relaxation iteration, an instantaneous wet surface update S is introduced into the boundary conditions of the object surface. B The iteration format is: ,in, This represents the wetted surface mesh of the object at the q-th iteration step, where q represents the iteration number and p... q denoted as the displacement of the floating body calculated in the qth iteration, and β represents the relaxation factor, which is a coefficient between 0 and 1 used to control and stabilize the iteration process; Solve the equations of motion for the floating body to establish the equations of motion for the floating body:

[0033] Among them, A ∞ B ∞ Mass and damping are added to the infinite frequency; K(t) is the time delay function kernel, obtained through the Fourier transform of the Green's function; X represents the displacement vector of the floating body. This represents the velocity vector of the floating body. Let G represent the acceleration vector of the floating body, G represent the structural mass matrix of the floating body, and C represent the restoring force coefficient matrix. Let F represent the convolution integral term, t represent the current time, τ represent the time integration variable, K() be the time delay function, and F be the time integral term. wave (t) represents the total wave force at the current time, F moor (t) represents the translational force acting on the floating body at the current time; To accelerate the computation of convolution terms, the integral term is transformed using the exponential basis recursive convolution method:

[0034] Among them, a m Let q represent the m-th weight coefficient. m (t) represents the m-th state variable, and M represents the number of variables used for the convolution integral; Memory variables Updated to

[0035] Among them, b m This represents the attenuation coefficient corresponding to the m-th state. Indicates the time step; The convergence criterion is:

[0036] Where α1, α2, α3 are weight coefficients, and satisfy α1+α2+α3=1; To account for the convergence tolerance, let X represent the displacement vector of the floating body, ΔX represent the increment of the displacement vector, and F wave Represents the total wave force, ΔF wave η represents the increment of the total wave force. max Indicates the maximum wavefront elevation, Δη max χ represents the increment of the maximum wavefront elevation; χ represents the overall convergence index. S5 includes: After the convergence criterion is satisfied, the floating body motion time history and wave load time history are extracted, and key spectrum analysis results are generated simultaneously. The floating body motion time history is sampled at intervals to form a data block containing displacement and velocity, and a dual timestamp index structure is adopted. The wave load time history is decomposed into four force vectors: first-order excitation, second-order difference frequency excitation, second-order sum frequency excitation, and slamming pulse excitation, and written into independent storage space respectively. The power spectral density of the floating body's motion and the stress at key structural points is calculated based on the floating body's motion time history to obtain the motion response power spectral density and tension power spectral density. Based on the above time history and spectral results, the real-time position, motion velocity, and motion attitude of the floating body are output for quantitative extraction of shallow water nonlinear hydrodynamic characteristics, and for prediction and safety assessment of the motion response of floating structures.

[0037] As a specific implementation, the displacement, angular velocity, and linear velocity corresponding to the sway, roll, heave, pitch, and yaw of the floating body are extracted, and data blocks are formed by interval sampling. A dual-timestamp index structure with a main timestamp and an auxiliary timestamp is set. The wave load time history decomposes the total wave force acting on the wet surface of the floating body into four force vectors: first-order excitation, second-order difference-frequency excitation, second-order sum-frequency excitation, and slamming pulse excitation. The first-order excitation is the linear wave-induced force, the second-order difference-frequency excitation is the low-frequency drift force, the second-order sum-frequency excitation is the high-frequency spring force, and the slamming pulse excitation is the transient force of the bottom slamming and outward drifting impact of the floating body. The power spectral density is calculated using a window function. Based on the nonlinear hydrodynamic characteristics of shallow water, a neural network model is used to predict the extreme values ​​of floating body motion in advance. Response thresholds are set, and the response level is judged based on the predicted values ​​and real-time fatigue damage. Different colored warning lights are set to remind users: green light indicates continuation, yellow light indicates warning, and red light indicates work stoppage. This completes the motion response prediction and safety assessment of floating structures.

[0038] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0039] Furthermore, those skilled in the art will understand that although some embodiments herein include certain features included in other embodiments but not others, combinations of features from different embodiments are intended to be within the scope of the invention and form different embodiments. Any of the claimed embodiments can be used in any combination.

Claims

1. A nonlinear hydrodynamic calculation method for shallow-water floating bodies based on Green's function for finite water depth, characterized in that, Includes the following steps: S1. Real-time acquisition of multi-source data is carried out using a sensor network deployed around the floating body. The wave surface elevation spatiotemporal sequence is obtained by wave radar, and the direction spectrum of the incident wave is obtained by spectral analysis. The vertical distribution of current velocity at the location of the floating body is obtained by acoustic Doppler current profiler. The pressure distribution of the wetted surface of the floating body is obtained by pressure sensor array. The time history of the six degrees of freedom motion of the floating body is obtained by motion sensor. The multi-source data is preprocessed to form a standardized dataset. S2. Construct the floating body state vector based on the standardized dataset, use the velocity potential Green's function that satisfies the bottom boundary conditions of finite water depth as the basic solution, and use the steady phase method to analytically approximate the far-field wave effect to calculate the acceleration integral; use the singularity stripping technique to ensure the accuracy of the near-field integral and reduce the complexity of the Green's function convolution. S3, decompose the total wave force, and at each time step, dynamically trim and update the wetted surface mesh of the floating body according to the instantaneous motion attitude of the floating body to establish the motion equation of the floating body; S4 defines the convergence criterion as a weighted combination of three indicators and performs multi-objective convergence criterion. If the convergence condition is not met, the relaxation factor is adjusted and the time step is reduced, and the calculation is re-iterated until convergence. S5, after the calculation converges, outputs the floating body motion time history, wave load time history, and key spectrum analysis results, obtains the floating body's position, motion velocity, and motion attitude, and obtains the nonlinear hydrodynamic calculation results of the shallow water floating body, which can be used for motion response prediction and safety assessment of floating structures in shallow water environments. The convergence criterion in S4 is: Where α1, α2, α3 are weight coefficients, and satisfy α1+α2+α3=1; To account for the convergence tolerance, let X represent the displacement vector of the floating body, ΔX represent the increment of the displacement vector, and F wave Represents the total wave force, ΔF wave η represents the increment of the total wave force. max Indicates the maximum wavefront elevation, Δη max χ represents the increment of the maximum wavefront elevation; χ represents the comprehensive convergence index.

2. The nonlinear hydrodynamic calculation method for shallow-water floating bodies based on Green's function with finite water depth as described in claim 1, characterized in that, The velocity potential Green's function in S2 is: Where G(x,y,z,ξ,ψ,ε) represents the velocity potential generated at the field point (x,y,z) after placing a unit point source at the source point (ξ,ψ,ε); r is the actual distance from the source point to the field point. ; Distance to the underwater mirror image point The integral term characterizes the shallow water wave propagation effect; Let k be the zeroth-order Bessel function, and k be the wave number. Let R be the water depth, and R be the horizontal distance between the source point and the field point. R = z represents the vertical coordinate of the field point, and d represents the wavenumber element.

3. The nonlinear hydrodynamic calculation method for shallow-water floating bodies based on Green's function with finite water depth as described in claim 2, is characterized in that, S2 further includes: Calculate the horizontal distance R between the source point and the field point. If R > 5λ, where λ is the wavelength corresponding to the peak frequency, mark it as the far field; otherwise, mark it as the near field. When marked as far field, the phase function is solved to obtain the steady-state point. At the steady-state point, the magnitude function and phase function are expanded by Taylor series and retained to the second-order terms to calculate the accelerated integral. When labeled as near field, singularity stripping technique is used to identify singular terms, calculate the analytic singular part, perform numerical integration on the regularized part, and add the singular and regularized parts together.

4. The nonlinear hydrodynamic calculation method for shallow-water floating bodies based on Green's function with finite water depth as described in claim 1, characterized in that, S3 includes: The total wave force is decomposed as follows: Among them, F FK Represents the Froude-Krylov force, F D F represents diffraction force. R F represents radiation force. wave Represents the total wave force; F FK The expression is , The incident potential is generated by nonlinear wave theory; F D The expression is , For the diffraction potential solved based on the Green's function, F R The expression is In the formula The diffraction and radiation potentials are solved based on the Green's function; ρ represents the fluid density; S B Represents the mesh of the wetted surface of an object; n i Let represent the i-th component of the unit normal vector on the surface of the floating body; t represents time t; and d represents the area element.

5. The nonlinear hydrodynamic calculation method for shallow-water floating bodies based on Green's function with finite water depth as described in claim 4, characterized in that, S3 further includes: Dynamically trimming the wet surface mesh of the floating body S B Furthermore, by stabilizing the numerical process through relaxation iteration, an instantaneous wet surface update S is introduced into the boundary conditions of the object surface. B The iteration format is: ,in, This represents the wetted surface mesh of the object at the q-th iteration step, where q represents the iteration number and p... q denoted as the displacement of the floating body calculated in the q-th iteration, and β as the relaxation factor, a coefficient between 0 and 1 used to control and stabilize the iteration process.

6. The nonlinear hydrodynamic calculation method for shallow-water floating bodies based on Green's function with finite water depth as described in claim 5, characterized in that, S3 further includes: Solve the equations of motion for the floating body to establish the equations of motion for the floating body: Among them, A ∞ B ∞ Mass and damping are added to the infinite frequency; K(t) is the time delay function kernel, obtained through the Fourier transform of the Green's function; X represents the displacement vector of the floating body. This represents the velocity vector of the floating body. Let G represent the acceleration vector of the floating body, G represent the structural mass matrix of the floating body, and C represent the restoring force coefficient matrix. Let F represent the convolution integral term, t represent the current time, τ represent the time integration variable, K() be the time delay function, and F be the time integral term. wave (t) represents the total wave force at the current time, F moor (t) represents the translational force acting on the floating body at the current time, and d represents the time element; To accelerate the computation of convolution terms, the integral term is transformed using the exponential basis recursive convolution method: Among them, a m Let q represent the m-th weight coefficient. m (t) represents the m-th state variable, and M represents the number of variables used for convolution integration.

7. The nonlinear hydrodynamic calculation method for shallow-water floating bodies based on Green's function with finite water depth as described in claim 6, characterized in that, State variables Updated to Among them, b m This represents the attenuation coefficient corresponding to the m-th state. Indicates the time step.

8. The nonlinear hydrodynamic calculation method for shallow-water floating bodies based on Green's function with finite water depth according to claim 1, characterized in that, S5 includes: After the convergence criterion is satisfied, the floating body motion time history and wave load time history are extracted, and the spectral analysis results are generated simultaneously. The floating body motion time history is sampled at intervals to form a data block containing displacement and velocity, and a dual timestamp index structure is adopted. The wave load time history is decomposed into four force vectors: first-order excitation, second-order difference frequency excitation, second-order sum frequency excitation, and slamming pulse excitation, and written into independent storage space respectively. The power spectral density of the floating body motion and the stress at key structural points is calculated based on the floating body motion time history to obtain the motion response power spectral density and tension power spectral density. Based on the above floating body motion time history, wave load time history and spectral analysis results, the real-time position, motion velocity and motion attitude of the floating body are output for quantitative extraction of shallow water nonlinear hydrodynamic characteristics, and for prediction and safety assessment of the motion response of floating structures.

9. The nonlinear hydrodynamic calculation method for shallow-water floating bodies based on Green's function with finite water depth according to claim 8, characterized in that, The process of predicting and assessing the motion response of floating structures includes: using a neural network model driven by the nonlinear hydrodynamic characteristics of shallow water to predict the extreme values ​​of the floating body's motion in advance; setting response thresholds; determining the response level based on the predicted values ​​and real-time fatigue damage; setting different colored warning lights to remind workers: green light to continue, yellow light to remind workers, and red light to stop work; and thus completing the prediction and assessment of the motion response of floating structures.

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