Reduced order modeling and integrated fast prediction method for floating wind turbine power performance and structural response

Abstract

The application discloses a kind of floating wind turbine power motion and structural response reduced-order modeling and integrated fast prediction method, comprising: finite element modal analysis is carried out to floating wind turbine structure, extracts rigid body mode and main elastic mode, constructs low-dimensional modal space and orthogonalizes mass, stiffness matrix, reduces system degree of freedom;According to the initial position of structure, calculate hydrostatic force recovery, mooring, gravity stiffness and external excitation force, static water balance control equation is established by modal space transformation, and generalized displacement is solved by iteration;Based on radiation diffraction theory, water pressure is recalculated at structure grid gauss point, aerodynamic load is calculated by combining blade element momentum theory, and generalized external load is obtained after superposition and modal transformation;Motion equation is established in modal space, and generalized displacement is solved by numerical integration and reconstructs global displacement field, and stress time history is directly calculated, to realize integrated fast prediction.The method can keep the accuracy of key dynamic characteristics and response of structure, significantly improve the calculation efficiency, and provide reliable support for near real-time evaluation of floating wind turbine operation and maintenance.

Description

Technical Field

[0001] This invention relates to the technology of motion and structural response analysis of floating wind turbines, and in particular to a reduced-order modeling and integrated rapid prediction method for the dynamic motion and structural response of floating wind turbines. Background Technology

[0002] Compared to stationary offshore wind turbines, floating wind turbines face more complex marine environments during their service life. Their foundation structure and overall turbine operation exhibit dramatic dynamic response characteristics under the influence of waves, wind, currents, and other factors. This places higher demands on the safety and real-time monitoring capabilities of operation and maintenance. Accurately and efficiently predicting the motion response and stress state of the foundation structure is a key challenge in the operation and maintenance of floating wind turbines, enabling the development of maintenance strategies, ensuring structural safety, and reducing the risk of unplanned downtime.

[0003] In existing technologies for analyzing the motion and structural response of floating wind turbines, quasi-static analysis methods are commonly used due to the complexity of hydrodynamic pressure transmission. This means that time-domain motion response analysis and structural finite element analysis are performed separately, requiring multiple data transfers and model conversions between different software programs. This prevents integrated analysis, results in lengthy and inefficient calculations, and fails to meet the requirements for real-time or near-real-time response forecasting during operation and maintenance. Especially in routine operation and maintenance under mild sea conditions, the impact of hydrodynamic pressure is relatively small, but traditional finite element analysis of floating structures still consumes significant computational resources, making it difficult to balance computational efficiency and cost-effectiveness. To improve analysis efficiency, some studies have attempted to rapidly predict the motion and structural response of floating structures using reduced-order modeling, empirical formulas, or semi-empirical numerical models. However, these methods mostly replace traditional analysis steps with rapid prediction models, and computational efficiency still needs improvement, failing to achieve simultaneous solutions for motion and structural responses.

[0004] Although existing technologies have made some progress in rapid prediction and reduced-order modeling of motion and structural responses, the following shortcomings still limit their engineering applicability in floating wind turbine operation and maintenance scenarios:

[0005] First, traditional offshore structure analysis often relies on quasi-static methods and employs a separate analysis process. Even when considering the elasticity of the floating structure in time-domain motion response analysis, the structural analysis still relies on load transfer to apply nodal forces at various times to the finite element model for solution. This process requires multiple data conversions and model reconstructions, making the calculations cumbersome and unable to meet the real-time requirements for rapid assessment during operation and maintenance. Furthermore, it neglects dynamic effects in structural response calculations, making it difficult to fully reflect the dynamic characteristics of the structure under real service conditions. In addition, this type of method has low hydrodynamic pressure transfer efficiency, especially in the calculation of radiation pressure, which involves convolution calculations and has a large computational load. It is almost impossible to perform convolution calculations on every element, forcing the use of simplified methods, which reduces the calculation accuracy to some extent. This inaccuracy is particularly pronounced in local response prediction and complex sea state simulation. Simultaneously, traditional floating structure analysis software faces technical obstacles in converting structural meshes to hydrodynamic meshes. Some software only supports beam and plate elements for load transfer, but relying solely on these two types of elements in structural analysis often fails to meet accuracy requirements, limiting the fine-grained modeling of complex structures.

[0006] Secondly, while existing order-reduction models improve computational efficiency to some extent, they are mostly based on single-degree-of-freedom or simplified load assumptions, neglecting the coupling effect between local structural response and dynamic motion, leading to decreased prediction accuracy. Especially under complex sea conditions, the superposition effects of waves, wind, and currents cause significant six-degree-of-freedom motion and local stress concentration in floating wind turbine platforms. Single motion analysis or structural analysis is insufficient to accurately reflect their global and local response characteristics. Furthermore, some existing order-reduction models actually only replace a certain step in the traditional quasi-static separate calculation process. For example, they only use order reduction methods in the hydrodynamic load calculation stage or the structural finite element analysis stage, while the overall solution still relies on the separate solution framework. This approach continues the complexity and inefficiency of the traditional model in terms of computational process, making it difficult to meet the dual requirements of high efficiency and accuracy in real-time or near-real-time prediction scenarios.

[0007] To address these challenges, there is an urgent need to establish an integrated analysis method for dynamic motion and structural response that balances computational efficiency and forecast accuracy, enabling real-time or near-real-time forecasting of the motion and structural response of floating wind turbines.

[0008] It should be noted that the information disclosed in the background section above is only for understanding the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0009] The main objective of this invention is to overcome the deficiencies in the aforementioned background technology and provide a reduced-order modeling and integrated rapid prediction method for the dynamic motion and structural response of floating wind turbines, so as to achieve efficient, high-precision, integrated, and synchronous solution of the dynamic motion and structural response of floating wind turbines, thereby meeting the needs of near real-time evaluation for operation and maintenance.

[0010] To achieve the above objectives, the present invention adopts the following technical solution:

[0011] A reduced-order modeling and integrated rapid prediction method for the dynamic motion and structural response of floating wind turbines includes the following steps:

[0012] S1. Structural preprocessing stage: Finite element modal analysis is performed on the floating wind turbine structure to extract the rigid body modes and main elastic modes of the structure, construct a low-dimensional modal space, and orthogonalize the mass matrix and stiffness matrix to reduce the system degrees of freedom.

[0013] S2, Static Equilibrium Stage: Calculate the hydrostatic recovery stiffness, mooring stiffness, gravity stiffness, and external excitation force based on the initial position of the structure, and convert them into a generalized stiffness matrix and generalized load through modal space transformation. Establish the hydrostatic equilibrium control equations and solve the generalized displacement through iterative algorithm.

[0014] S3. Load Calculation Stage: Based on the radiation and diffraction theory, the incident, diffraction and radiation water pressure are recalculated at the Gaussian point of the structural mesh and transferred to the nodal loads through Gaussian integral and shape function. At the same time, the aerodynamic load is calculated based on the leaf element momentum theory. The aerodynamic and hydrodynamic loads are superimposed as the total external excitation and the generalized external load is obtained through modal space transformation.

[0015] S4. Structural Time Domain Analysis Stage: In modal space, the motion equations expressed in generalized coordinates are constructed, and the generalized displacement time history is solved by numerical integration. Then, the global displacement field is reconstructed, and the structural stress time history is directly calculated by combining the strain-displacement relationship and constitutive relationship, so as to realize the integrated and rapid prediction of dynamic motion and structural response.

[0016] Furthermore, the structural preprocessing stage in step S1 includes:

[0017] The structure is discretized using the finite element method. The displacement field of the element is interpolated based on the shape function. The element stiffness matrix and mass matrix are formed in the local coordinate system of the element according to the principle of virtual work or the principle of minimum potential energy.

[0018] The element stiffness matrix and mass matrix are transformed to the global coordinate system using orthogonal transformation matrices, and then assembled into a global stiffness matrix and a global mass matrix according to the nodal degrees of freedom.

[0019] To eliminate the singularity caused by rigid body modes, weak constraints with stiffness much smaller than the stiffness of the structure itself are applied to the structure, and the Lagrange multiplier method is used to introduce the constraint conditions into the system equations to construct an extended eigenvalue problem.

[0020] Solving the extended eigenvalue problem yields the modal natural frequencies and modal vectors, from which the first six rigid body modes and several main elastic modes are identified, together forming a low-dimensional modal space.

[0021] The global mass matrix and global stiffness matrix are orthogonalized in the modal space to obtain the generalized mass matrix and generalized stiffness matrix, thereby reducing the system's degrees of freedom while preserving the key dynamic characteristics of the structure.

[0022] Furthermore, the hydrostatic equilibrium stage described in step S2 includes:

[0023] Based on the initial position of the structure in still water, calculate the hydrostatic recovery stiffness matrix, mooring stiffness matrix, gravity stiffness matrix, and the external excitation force at the initial moment.

[0024] The stiffness matrix is ​​transformed into a generalized stiffness matrix through the modal space, and the external excitation force is transformed into a generalized external force. Based on this, a hydrostatic equilibrium control equation with generalized displacement as the variable is established.

[0025] The hydrostatic equilibrium control equations are solved using an iterative algorithm to obtain the generalized displacement of the system in hydrostatic equilibrium.

[0026] By performing modal space inversion transformation, the generalized displacement is reduced to nodal displacement, and the response of the structure under static water load is further solved.

[0027] Furthermore, the load calculation stage in step S3 includes:

[0028] At the Gaussian point of the structured grid, based on the calculation results of the radiation diffraction theory, the velocity potential is reconstructed by the Green's function and the source strength distribution, and the incident, diffraction and radiation water pressures are recalculated independently.

[0029] The Gaussian integration method is used to numerically integrate the water pressure in each part, and the integrated water pressure load is transferred to the structural nodes through the plate element shape function to ensure the balanced distribution of the load on the structural mesh.

[0030] Based on the blade element momentum theory, the wind turbine blade is divided into several blade element units. The blade element aerodynamic force is calculated according to the momentum conservation relationship, and the total aerodynamic thrust acting on the tower top is obtained by integrating along the blade.

[0031] The aerodynamic load and the hydrodynamic load are superimposed to obtain the total external excitation load, and the generalized external excitation load is obtained through modal transformation.

[0032] Furthermore, the recalculation and integration process of the water pressure includes:

[0033] Based on the continuity of the watershed velocity potential function, the velocity potential and water pressure at the Gaussian point of the structured grid are calculated using the hydrodynamic grid point source strength and Green's function.

[0034] Independent Gaussian numerical integrations were performed on the incident water pressure, diffracted water pressure, and radiated water pressure to avoid mutual interference between loads from different physical sources during transmission.

[0035] By transforming the shape function relationship of the plate element with the Jacobian matrix, the water pressure obtained by Gaussian point integration is converted into an equivalent nodal load.

[0036] Furthermore, in step S4, the process of constructing and numerically integrating the equations of motion in modal space includes:

[0037] In modal space, the Cummins equations are established, which include generalized mass, infinite-frequency added mass, radiation damping effect and generalized external force, where radiation damping is introduced in the form of impulse response function;

[0038] The motion equations are solved directly using numerical integration to obtain the time history responses of generalized displacement, generalized velocity, and generalized acceleration.

[0039] By utilizing the strain-displacement matrix and constitutive relation, the stress time history of the structure can be directly calculated based on the reconstructed global displacement field, without the need for dynamic load transfer in the time domain or calling a global finite element solver.

[0040] Furthermore, the structural time-domain analysis stage described in step S4 includes:

[0041] In the low-dimensional modal space, the time-domain motion equations of the system are constructed, which include a mass term composed of a generalized mass matrix and an infinite frequency additional mass matrix, a radiation damping memory term introduced by convolution of the impulse response function, and an excitation term composed of a generalized external excitation force, a generalized hydrostatic restoring force, and a generalized gravity.

[0042] The time-domain motion equations are solved directly using numerical integration methods to obtain the displacement, velocity, and acceleration response time histories of the generalized coordinates.

[0043] The generalized displacement response time history is reconstructed into the physical displacement time history of the global nodes of the structure using the modal matrix;

[0044] Based on the strain-displacement relationship matrix and material constitutive relation established in the preprocessing stage, the global stress time history is directly calculated according to the global physical displacement time history, thus eliminating the need to repeatedly perform hydrodynamic pressure transmission and global finite element calculations in the time-step solution.

[0045] Furthermore, the time-domain motion equation is in the form of the Cummins equation, whose excitation term integrates the effects of aerodynamic, hydrodynamic and gravity sources. Its radiation damping effect is represented by the impulse response function obtained by Fourier transform of the frequency-domain radiation damping coefficient, and is calculated in the time domain by convolution integral with the generalized velocity.

[0046] Furthermore, the calculation process of the stress time history is completed entirely within the reduced-order system after modal space transformation. By mapping the global displacement field back to the continuum strain field, and then directly solving the stress field according to the material constitutive relation, the synchronous and integrated solution of dynamic response and structural stress response is achieved.

[0047] A computer program product includes a computer program that, when executed by a processor, implements a reduced-order modeling and integrated rapid prediction method for the dynamic motion and structural response of a floating wind turbine.

[0048] The present invention has the following beneficial effects:

[0049] This invention presents a reduced-order modeling and integrated rapid prediction method for the dynamic motion and structural response of floating wind turbines. By performing finite element modal analysis on the floating wind turbine structure, rigid body modes and main elastic modes are extracted to construct a low-dimensional modal space. Orthogonalization of the mass and stiffness matrices significantly reduces the system's degrees of freedom and equation scale while maintaining key structural dynamic characteristics and accurate response. This effectively avoids redundant calls to full-domain finite element methods in time-domain calculations, improving computational efficiency by tens of times compared to full-model time-domain simulation. This provides a foundation for near-real-time dynamic response analysis and performance degradation tracking during operation and maintenance, thereby reducing operation and maintenance monitoring costs and improving the timeliness and reliability of structural safety early warnings. In the load calculation stage, based on radiation and diffraction theory, the incident, diffracted, and radiated water pressures are recalculated at Gaussian points in the structural mesh and transferred to nodal loads through Gaussian integrals and shape functions, ensuring that hydrodynamic loads are effectively distributed across the structural mesh. The load distribution is completely balanced, effectively avoiding the problems of uneven load distribution, mechanical imbalance and local stress concentration caused by interpolation mapping between traditional hydrodynamic grids and structural grids. This provides a reliable load input guarantee for the long-term operation of floating wind turbines under complex sea conditions. In the structural time-domain analysis stage, by constructing the motion equations represented by generalized coordinates in modal space, solving the generalized displacement time history through numerical integration and reconstructing the global displacement field, and then directly calculating the structural stress time history by combining the strain-displacement relationship and constitutive relationship, an integrated and rapid prediction of external environmental loads, dynamic motion and structural response is realized. This avoids the drawbacks of the gradual mapping of hydrodynamic pressure and structural loads and the repeated calculation of the global finite element method in traditional quasi-static methods. It significantly improves the computational efficiency and response accuracy of time-domain structural finite element analysis, and can widely support the structural design, operational performance evaluation and operation and maintenance strategy optimization of floating wind turbines. It provides an efficient, reliable and near real-time numerical analysis tool for engineering practice.

[0050] This invention provides a reduced-order modeling and integrated rapid prediction method for the dynamic motion and structural response of floating wind turbines. This method effectively solves the problems of cumbersome calculation steps and low computational efficiency caused by the separation of time-domain motion analysis and structural finite element analysis in traditional quasi-static structural analysis, as well as the problems of insufficient real-time response prediction and lack of efficient coupled analysis methods during operation and maintenance caused by the separate solutions of traditional floating body motion analysis and structural finite element analysis. This invention utilizes coupled boundary element theory, time-domain computation methods, and structural finite element methods to construct a reduced-order dynamic model based on modal space transformation, enabling simultaneous and rapid solutions for the dynamic motion response and local structural response of floating wind turbines. Simultaneously, by combining the hydrostatic pressure superposition method to account for the influence of local loads on the structural response, it can significantly improve the accuracy and timeliness of structural state prediction under complex sea conditions, effectively replacing traditional methods that rely on high-cost full-model simulation.

[0051] As an integrated analysis method for dynamic motion and structural response that balances computational efficiency and forecasting accuracy, this invention can efficiently capture the complex coupling mechanism between multi-source environmental loads (such as waves, wind, and currents) and structural dynamic characteristics, and accurately reflect the dynamic evolution characteristics of the foundation structure and the entire turbine throughout its life cycle. Simultaneously, while ensuring the reliability of the prediction results, it can significantly shorten the computation time, fully meeting the needs of rapid response forecasting in practical engineering. Furthermore, by constructing a reduced-order modeling and integrated rapid forecasting method for dynamic motion and structural response in floating wind turbine operation and maintenance scenarios, a computational method that couples time-domain motion response analysis with structural finite element analysis is established. Reduced-order modeling further improves computational efficiency, enabling integrated forecasting of floating wind turbine motion and structural response. This effectively improves the efficiency of safety assessment and structural condition monitoring during the operation and maintenance phase, providing strong support for formulating maintenance strategies, ensuring structural safety, and reducing the risk of unplanned downtime.

[0052] By integrating with real-time monitoring data, the method of this invention can not only provide a scientific and timely basis for operation and maintenance decisions, but also enable early warning of potential structural risks, thereby optimizing maintenance strategies, improving operational safety and economy, and effectively reducing the risk of unplanned downtime and operation and maintenance costs. Ultimately, it provides an efficient technical path for near real-time structural safety assessment and health status monitoring in the operation and maintenance process of floating wind turbines.

[0053] Other beneficial effects of the embodiments of the present invention will be further described below. Attached Figure Description

[0054] Figure 1 This is a flowchart illustrating the overall process of the reduced-order modeling and integrated rapid prediction method for the dynamic motion and structural response of floating wind turbines according to the present invention.

[0055] Figure 2 This is a schematic diagram of rigid body and elastic modes in an embodiment of the present invention.

[0056] Figure 3 This is a schematic diagram of water pressure transmission on the structural surface in an embodiment of the present invention.

[0057] Figure 4 This is a flowchart of the global displacement field inversion in an embodiment of the present invention. Detailed Implementation

[0058] The embodiments of the present invention will be described in detail below. It should be emphasized that the following description is merely exemplary and not intended to limit the scope and application of the present invention.

[0059] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of the present invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0060] This invention aims to address the problems of cumbersome and inefficient calculation steps in traditional floating wind turbine dynamic motion and structural response analysis, which also fail to meet the near-real-time forecasting requirements of the operation and maintenance phase. It proposes a reduced-order modeling and integrated rapid forecasting method for floating wind turbine dynamic motion and structural response. This method achieves integrated rapid forecasting of dynamic motion and structural response by constructing a low-dimensional modal space to reduce the system's degrees of freedom in the structural preprocessing stage, iteratively solving for generalized displacements in the hydrostatic equilibrium stage, accurately superimposing hydrodynamic and aerodynamic loads in the load calculation stage, and simultaneously solving for displacement and stress in the structural time-domain analysis stage. This method significantly improves computational efficiency while maintaining the key dynamic characteristics and response accuracy of the structure, and also avoids the unevenness problem of traditional load mapping, providing reliable support for near-real-time evaluation of floating wind turbine operation and maintenance.

[0061] See Figure 1 This invention provides a reduced-order modeling and integrated rapid prediction method for the dynamic motion and structural response of floating wind turbines, comprising the following steps:

[0062] Step S1, Structural Preprocessing Stage: Finite element modal analysis is performed on the floating wind turbine structure to extract the rigid body modes and main elastic modes of the structure, construct a low-dimensional modal space, and orthogonalize the mass matrix and stiffness matrix to reduce the system degrees of freedom.

[0063] In some embodiments, the structural preprocessing stage in step S1 includes: discretizing the structure using finite element methods, interpolating the element displacement field based on shape functions, and forming the element stiffness matrix and mass matrix in the local coordinate system of the element according to the principle of virtual work or the principle of minimum potential energy; transforming the element stiffness matrix and mass matrix to the global coordinate system through orthogonal transformation matrices, and assembling them into a global stiffness matrix and a global mass matrix according to the nodal degrees of freedom; to eliminate the singularity caused by rigid body modes, applying weak constraints with stiffness much smaller than the stiffness of the structure itself to the structure, and using the Lagrange multiplier method to introduce the constraint conditions into the system equations to construct an extended eigenvalue problem; solving the extended eigenvalue problem to obtain the modal natural frequencies and modal vectors, identifying the first six rigid body modes and several main elastic modes, which together constitute a low-dimensional modal space; orthogonalizing the global mass matrix and global stiffness matrix in the modal space to obtain a generalized mass matrix and a generalized stiffness matrix, thereby reducing the system degrees of freedom while retaining the key dynamic characteristics of the structure.

[0064] Step S2, hydrostatic equilibrium stage: Calculate the hydrostatic recovery stiffness, mooring stiffness, gravity stiffness and external excitation force based on the initial position of the structure, and convert them into a generalized stiffness matrix and generalized load through modal space transformation, establish the hydrostatic equilibrium control equations, and solve the generalized displacement through iterative algorithm.

[0065] In some embodiments, the hydrostatic equilibrium stage in step S2 includes: calculating the hydrostatic recovery stiffness matrix, mooring stiffness matrix, gravity stiffness matrix, and the external excitation force at the initial moment based on the initial position of the structure in still water; transforming the stiffness matrix into a generalized stiffness matrix and the external excitation force into a generalized external force through the modal space, thereby establishing a hydrostatic equilibrium control equation with generalized displacement as the variable; solving the hydrostatic equilibrium control equation using an iterative algorithm to obtain the generalized displacement of the system in the hydrostatic equilibrium state; restoring the generalized displacement to nodal displacement through modal space inversion transformation, and further solving to obtain the response of the structure under still water load.

[0066] Step S3, Load Calculation Stage: Based on the radiation and diffraction theory, the incident, diffraction, and radiation water pressures are recalculated at the Gaussian points of the structural mesh and transferred to the nodal loads through Gaussian integrals and shape functions. At the same time, the aerodynamic loads are calculated based on the leaf element momentum theory. The aerodynamic and hydrodynamic loads are superimposed as the total external excitation and the generalized external loads are obtained through modal space transformation.

[0067] In some embodiments, the load calculation stage in step S3 includes: at the Gaussian point of the structural mesh, based on the calculation results of radiation diffraction theory, reconstructing the velocity potential through Green's function and source strength distribution, and independently recalculating the incident, diffracted, and radiated water pressure; using the Gaussian integration method to numerically integrate the water pressure of each part, and transferring the integrated water pressure load to the structural nodes through the plate element shape function to ensure the balanced distribution of the load on the structural mesh; based on the blade element momentum theory, dividing the wind turbine blade into several blade element elements, calculating the blade element aerodynamic force according to the momentum conservation relationship, and integrating along the blade to obtain the total aerodynamic thrust acting on the tower top; superimposing the aerodynamic load and the hydrodynamic load to obtain the total external excitation load, and obtaining the generalized external excitation load through modal transformation.

[0068] In some embodiments, the recalculation and integration process of the water pressure includes: calculating the velocity potential and water pressure at the Gaussian points of the structural grid based on the continuity of the watershed velocity potential function and using the hydrodynamic grid point source strength and Green's function; performing independent Gaussian numerical integration on the incident water pressure, diffracted water pressure and radiated water pressure to avoid mutual interference between loads from different physical sources during transmission; and converting the water pressure obtained by Gaussian point integration into equivalent nodal loads through the shape function relationship of the plate element and the Jacobian matrix transformation.

[0069] Step S4, Structural Time Domain Analysis Stage: Construct motion equations in modal space expressed in generalized coordinates, solve the generalized displacement time history through numerical integration, reconstruct the global displacement field, and directly calculate the structural stress time history by combining the strain-displacement relationship and constitutive relationship, so as to realize the integrated and rapid prediction of dynamic motion and structural response.

[0070] In some embodiments, step S4, the process of constructing and numerically integrating the equations of motion in modal space, includes: establishing Cummins equations in modal space that include generalized mass, infinite-frequency additional mass, radiation damping effect, and generalized external force, wherein radiation damping is introduced in the form of an impulse response function; directly solving the equations of motion using numerical integration to obtain the time history responses of generalized displacement, generalized velocity, and generalized acceleration; and directly calculating the structural stress time history based on the reconstructed global displacement field using the strain-displacement matrix and constitutive relation, without needing to perform dynamic load transfer in the time domain or call a global finite element solver.

[0071] In some embodiments, the structural time-domain analysis stage in step S4 includes: constructing the system's time-domain motion equations in the low-dimensional modal space, which includes a mass term composed of a generalized mass matrix and an infinite frequency additional mass matrix, a radiation damping memory term introduced by convolution of the impulse response function, and an excitation term composed of a generalized external excitation force, a generalized hydrostatic restoring force, and a generalized gravity; directly solving the time-domain motion equations using numerical integration methods to obtain the displacement, velocity, and acceleration response time histories of the generalized coordinates; reconstructing the generalized displacement response time histories into physical displacement time histories of the global nodes of the structure using the modal matrix; and directly calculating the global stress time histories based on the strain-displacement relationship matrix and material constitutive relations established in the preprocessing stage, thereby eliminating the need for repeated hydrodynamic pressure transmission and global finite element calculations in the time-step solution.

[0072] In some embodiments, the time-domain motion equation is in the form of the Cummins equation, whose excitation term integrates the effects of aerodynamic, hydrodynamic and gravity sources, and whose radiation damping effect is represented by the impulse response function obtained by Fourier transform of the frequency-domain radiation damping coefficient, and is calculated in the time domain by convolution integral with the generalized velocity.

[0073] In some embodiments, the calculation process of the stress time history is completed entirely within the reduced-order system after modal space transformation. By mapping the global displacement field back to the continuum strain field and then directly solving the stress field according to the material constitutive relation, the synchronous and integrated solution of dynamic response and structural stress response is achieved, avoiding the load mapping and separate solution process in the traditional quasi-static method.

[0074] This invention provides a reduced-order modeling and integrated rapid prediction method for the dynamic motion and structural response of floating wind turbines. By constructing a low-dimensional modal space through structural modal analysis and orthogonalizing the system matrix, the computational degrees of freedom are significantly reduced. This avoids the repetitive calculations inherent in traditional full-domain finite element time-domain calculations, improving computational efficiency by tens of times compared to full-model simulation. This provides a highly efficient foundation for near-real-time dynamic response analysis and operation and maintenance monitoring. In load calculation, water pressure is recalculated based on Gaussian points in the structural mesh, and nodal loads are transferred through Gaussian integrals and shape functions, ensuring balanced load distribution and effectively avoiding stress concentration problems in traditional mesh interpolation mapping. This provides reliable load input for structural safety under complex sea conditions. In the time-domain analysis stage, by constructing generalized motion equations in the modal space and numerically solving displacement and stress time histories, integrated rapid prediction from environmental loads to dynamic response is achieved. This avoids the problems of gradual load transfer and repetitive finite element calculations in traditional quasi-static methods, significantly improving computational efficiency and accuracy. This method can widely support the design, performance evaluation, and operation and maintenance decisions of floating wind turbines, and by integrating with real-time monitoring data, it provides near-real-time technical means for structural safety early warning and operation optimization.

[0075] The following further describes specific embodiments of the present invention and examples of its algorithm implementation.

[0076] A method for reduced-order modeling and integrated rapid prediction of dynamic motion and structural response of floating wind turbines mainly includes a structural preprocessing stage, a hydrostatic equilibrium stage, a load calculation stage, and a structural time-domain analysis stage. The structural preprocessing stage includes: performing modal analysis on the structural model within the finite element theory framework, extracting its inherent modal characteristics, and constructing a reduced-order model. Specifically, this includes steps such as structural element discretization, element stiffness and mass matrix formation, coordinate system transformation, overall matrix assembly, modal solution and selection; by introducing weak constraints and employing the Lagrange multiplier method, matrix singularities caused by rigid body modes are avoided; after solving the generalized eigenvalue problem, the first six rigid body modes and several main elastic modes are combined to form a modal space, and the original mass and stiffness matrices are orthogonalized within this space, thereby significantly reducing the system's degrees of freedom while maintaining the structural dynamic characteristics. The hydrostatic equilibrium stage includes: calculating the hydrostatic recovery stiffness, gravity stiffness, mooring stiffness, and external forces based on the initial position of the structure, and converting them into a generalized stiffness matrix and generalized loads in modal space to establish the hydrostatic equilibrium governing equations; solving for the generalized displacement using iterative algorithms (including but not limited to Newton's iteration method), and completing the finite element analysis of the structure under hydrostatic conditions. The load calculation stage includes: addressing the difference in mesh accuracy between hydrodynamic analysis and structural finite element analysis, recalculating the incident, diffracted, and radiated hydrodynamic pressures at Gaussian points in the structural mesh based on the continuity of the hydrodynamic potential function, and transferring them to the structural mesh through Gaussian point integration to achieve complete load balance, avoiding load unevenness and stress concentration caused by direct interpolation. The water pressure is transferred to the nodal loads through the plate element shape function. Aerodynamic load calculation is based on blade element momentum theory, obtaining the aerodynamic thrust at the top of the wind turbine tower through integration along the blades. The aerodynamic and hydrodynamic loads are superimposed as a total external excitation, and a generalized external load is obtained through modal space transformation for subsequent dynamic response analysis. The time-domain dynamic response analysis stage includes: Within the modal space transformation framework, the structural dynamic response is characterized using low-dimensional generalized coordinates. The equations of motion are in the form of the Cummins equations. Radiation damping is introduced through the impulse response function, achieving unified modeling of added mass, radiation effects, and external loads. The time histories of generalized displacements for each mode are obtained through numerical integration. The generalized displacements are reconstructed into a global displacement field using the modal matrix. Combining the strain-displacement matrix and constitutive relations, the time-domain stress time histories are directly calculated without the need for hydrodynamic pressure transfer in the time domain or repeated global finite element solutions, thus significantly reducing computational load and improving analysis efficiency. See the overall flowchart for details. Figure 1 .

[0077] The method of the present invention will now be described in detail with reference to the accompanying drawings:

[0078] 1. Structural pretreatment stage

[0079] To perform efficient structural analysis, this invention first conducts modal analysis on the structural model within the framework of the finite element method (FEM) to extract and utilize its inherent modal characteristics. The overall method includes steps such as element discretization, formation of element stiffness and mass matrices, coordinate system transformation, global matrix assembly, and modal extraction. In the FEM method, the structure is discretized into several elements, each consisting of several nodes. The displacement field within the element is represented by shape functions. Interpolation is performed, and the selection of the shape function depends on the element type and the required interpolation accuracy. Based on the principle of virtual work or the principle of minimum potential energy, the element stiffness matrix is ​​obtained in the local coordinate system. To achieve overall assembly, it needs to be transformed to the global coordinate system using an orthogonal transformation matrix. The global stiffness matrix in the global coordinate system is then obtained. for:

[0080]

[0081] In the formula, The strain-displacement matrix is ​​derived from the shape function. Differentiation yields, The constitutive relation matrix is... This refers to the volume (or area) of a unit cell. The orthogonal transformation matrix also applies to the mass matrix. The mass matrix can be a lumped mass matrix or a uniform mass matrix, and can be transformed into a global mass matrix using a coordinate transformation matrix. All units and The global stiffness matrix is ​​obtained by assembling according to the correspondence of nodal degrees of freedom. and mass matrix To avoid singularities caused by rigid body modes while preserving the natural characteristics of the structure, this invention applies very weak constraints to the structure (stiffness values ​​much smaller than the structure's own stiffness) to ensure that the stiffness matrix is ​​invertible during solution. The constraints are introduced into the system equations using the Lagrange multiplier method, resulting in:

[0082]

[0083] In the formula, Let be the nodal displacement vector. The constraint coefficient matrix, These are Lagrange multiplier vectors, corresponding to constraint reactions. These are the modal natural frequencies. The eigenvalue problem is then solved to obtain the modal natural frequencies and modal vectors. Due to the very weak constraints, the modal results are classified: the first six are rigid body modes, and the rest are elastic modes. Figure 2 This diagram illustrates rigid body and elastic modes. Rigid body modes represent overall motion, while elastic modes represent local deformation. The first N principal elastic modes, together with the rigid body modes, constitute a 6+N dimensional modal space. In modal space, the original mass and stiffness matrices can be orthogonally transformed into a generalized mass matrix. and generalized stiffness matrix :

[0084]

[0085] Through the above steps, the present invention significantly reduces the system's degrees of freedom while maintaining the structural physical characteristics, thereby improving the efficiency of motion and structural analysis.

[0086] 2. Static equilibrium stage

[0087] Based on the initial position of the structure, the hydrostatic restoring stiffness, mooring stiffness, and external excitation force are solved, and then transformed into a generalized stiffness matrix and generalized loads through modal space transformation to establish the equilibrium governing equations:

[0088]

[0089] In the formula, The hydrostatic recovery stiffness matrix is... Here is the mooring stiffness matrix. Here is the gravity stiffness matrix. Let be the initial displacement of the system in modal space. The initial external excitation force is given. Hydrostatic equilibrium is an iterative process because the generalized stiffness and generalized load change with the object's position. Various iterative algorithms, such as Newton's method, can be used to solve for the generalized displacement after hydrostatic equilibrium. After obtaining the hydrostatic equilibrium displacement, the water pressure and gravity load are inverted through modal space transformation and applied to the structural mesh for finite element analysis.

[0090] 3. Load Calculation Stage

[0091] To ensure computational efficiency, hydrodynamic analysis typically employs coarser hydrodynamic meshes to control the number of meshes and avoid the high computational load and long computation time associated with direct integration, thus ensuring the feasibility and efficiency of hydrodynamic calculations. In contrast, structural finite element analysis requires higher mesh accuracy, necessitating the use of finer structural meshes to ensure analytical precision. Therefore, structural meshes cannot be directly used for hydrodynamic analysis. Directly mapping water pressure from the hydrodynamic mesh to the structural mesh via interpolation often leads to uneven load distribution and load imbalance, resulting in stress concentration at structural supports, affecting structural safety and analytical accuracy. Given the continuity of the watershed velocity potential function, this invention employs a method for recalculating the hydrodynamic pressure at structural mesh points. Gaussian points are placed on the structural mesh, and the hydrodynamic pressure at these points is recalculated based on radiation and diffraction calculations. Gaussian point integration is used to calculate the hydrodynamic pressure of the structural mesh, and incident, diffracted, and radiated water pressures are transferred independently to obtain a completely balanced load condition, avoiding stress concentration problems in structural analysis. For any structural Gaussian point within the watershed, its velocity potential... It can be calculated based on hydrodynamic grid points and Green's function:

[0092]

[0093] In the formula Represents the Gaussian point. Representing hydrodynamic grid points, For point source intensity, It is a hydrodynamically wetted surface. Incident force. and diffraction force The additional mass and radiation damping are obtained by integrating the incident and diffracted water pressures using Gaussian points, respectively. The additional mass and radiation damping are obtained by integrating the real and imaginary parts of the radiation water pressure, respectively. Multiplying the radiation water pressure by the six-dimensional normal vector yields the additional mass and radiation damping. The restoring stiffness matrix consists of two parts: the first is the integral of the hydrostatic restoring water pressure, and the second is the additional gravity term considering the change in coordinate system.

[0094] Figure 3 This is a schematic diagram illustrating the transmission of water pressure on the structural surface. The water pressure on the structural surface is transmitted through the shape functions of the plate elements. The load is transferred to the nodes. Borrowing from the concept of isoparametric plate elements, the point coordinates of arbitrary-shaped plate elements can be represented by the nodal coordinates and shape functions. The total water pressure of each quadrilateral element... It can be calculated using Gaussian point integral, and the formula is as follows:

[0095]

[0096] In the formula, where, , For Gaussian point weights, , Standardized node coordinates within a plate element. The global coordinates of the Gaussian point are... It is a Jacobian matrix.

[0097] Aerodynamic load calculations are based on blade element momentum theory. The wind turbine blades are divided into several blade element units, and the local forces are calculated using the aerodynamic force and momentum conservation relationship at the blade elements.

[0098]

[0099] In the formula, For the angle of attack, The ratio of leaf area to total leaf area. The lift coefficient is given. The blade element aerodynamic force is integrated along the blade to obtain the total aerodynamic thrust acting on the top of the wind turbine tower. The aerodynamic and hydrodynamic loads are superimposed to form the external excitation load. The total load is transformed into modal space using the structural modal matrix to obtain the generalized external excitation load. .

[0100] 4. Structural Time Domain Analysis Stage

[0101] Within the framework of modal superposition, modal truncation retains only the modal features. degrees of freedom (of which) rigid body modes, (first-order elastic modes), which can be expressed using low-dimensional generalized coordinates. The main dynamic response of the structure is characterized. The time-domain equations of motion adopt the Cummins equations:

[0102]

[0103] in, , These are the structural mass matrix and the infinite frequency additional mass matrix, respectively. , , These are, respectively, generalized external excitation force, generalized hydrostatic pressure, and generalized gravity. , , These are generalized acceleration, velocity, and displacement response, respectively. The impulse response function can be affected by radiation damping. The equation can be solved using explicit or implicit numerical integration methods to obtain the generalized displacement time history for each mode. .

[0104] Figure 4 Flowchart of global displacement field inversion. Global displacement field of the structure. Through the mode matrix and generalized nodal displacement Displacement reconstruction from low-dimensional modal space to global structure space was achieved. In the preprocessing stage, shape functions were used... Derive the strain-displacement matrix Combining constitutive relations This allows for the direct calculation of stress time history from nodal displacement time history in the time domain. :

[0105]

[0106] Since the entire process no longer involves the transmission of hydrodynamic pressure in the time domain, and there is no need to stepwise call the structural finite element solver for global calculations, the computational load is significantly reduced and the efficiency of time-domain analysis is improved.

[0107] In summary, the key innovative contributions and design features of this invention include:

[0108] The proposed method for reduced-order modeling and integrated rapid prediction of dynamic motion and structural response of floating wind turbines employs a structural mesh hydraulic pressure reconstruction scheme based on Gaussian point integrals to achieve coupled analysis of the boundary element method and finite element theory. Based on modal space variation and modal truncation methods, a low-dimensional orthogonal system mass matrix, stiffness matrix, and force vector are constructed to solve the structural dynamic equations. Based on generalized modal displacements and modal information, equivalent nodal displacements are inverted, and the structural stress field is rapidly reconstructed based on strain-displacement relationships and constitutive relations, achieving reduced-order modeling and rapid prediction of dynamic motion and structural responses.

[0109] By extracting the rigid body modes and main elastic modes of the structure through finite element modal analysis, a low-dimensional generalized coordinate space is constructed according to the modal truncation method. The mass matrix, stiffness matrix and force vector are modally orthogonalized, thereby significantly reducing the system's degrees of freedom while maintaining key dynamic characteristics, and achieving efficient time-domain response calculation.

[0110] In the load transfer stage, the incident, diffraction and radiated water pressure are directly recalculated at the Gaussian integration points of the structural mesh based on the radiation and diffraction calculation theory, and transferred to the equivalent nodal load through shape functions to ensure strict balance of load distribution and avoid load unevenness and local stress concentration caused by traditional mesh interpolation.

[0111] Within the framework of modal space transformation, the global displacement field of the structure can be directly reconstructed in the time domain. By combining the strain-displacement matrix and constitutive relation, the strain and stress time histories can be directly calculated without the need for stepwise hydrodynamic pressure mapping and global finite element method calls. This enables direct, efficient, and accurate prediction of external loads to structural stresses.

[0112] This method is applicable to the full life cycle analysis of floating wind turbines. It can complete the synchronous prediction of local and global structural responses under near real-time conditions, significantly improving the timeliness and engineering applicability of operation and maintenance safety early warning, and reducing the high computational cost brought by quasi-static finite element analysis.

[0113] Compared with the prior art, the significant advantages of the present invention are reflected in the following aspects:

[0114] 1. This invention extracts the rigid body modes and main elastic modes of a structure through finite element modal analysis, constructs a 6+N-dimensional low-dimensional generalized coordinate space, and orthogonalizes the system mass matrix and stiffness matrix based on modal truncation. While maintaining the accuracy of key dynamic characteristics and the actual response of the structure, it significantly reduces the computational degrees of freedom and equation scale, avoids the repeated use of full-domain finite element analysis in time-domain calculations, and improves the computational efficiency by tens of times compared to full-model time-domain simulation. It can realize near real-time dynamic response analysis and performance degradation tracking of floating wind turbine operation and maintenance process, thereby reducing operation and maintenance monitoring costs and improving the timeliness and reliability of structural safety early warning.

[0115] 2. This invention innovatively introduces a method for recalculating hydrodynamic pressure based on Gaussian points in the structural mesh and employing high-precision integration in the load transfer process. It directly reconstructs the incident, diffracted, and radiated water pressures at the Gaussian point locations and performs independent integration transfer for each, ensuring a completely balanced distribution of hydrodynamic loads on the structural mesh. This method effectively avoids the uneven load distribution and mechanical imbalance problems that arise during the traditional interpolation mapping process between hydrodynamic and structural meshes, thereby preventing stress concentration at local locations and providing reliable load input assurance for the long-term operation of floating wind turbines in complex sea conditions.

[0116] 3. Under the framework of modal superposition, this invention directly reconstructs the global displacement field of the structure in the time domain using low-dimensional generalized coordinates, and simultaneously solves the strain and stress time histories by combining the strain-displacement relationship with the constitutive equations. This avoids the stepwise mapping of hydrodynamic pressure and structural loads and the repetitive calculation process of the global finite element method in the quasi-static method, realizing the integrated analysis from external environmental loads to dynamic motion and structural response. It significantly improves the computational efficiency and response accuracy of time-domain structural finite element analysis, and can be widely applied to the structural design, operation performance evaluation and operation and maintenance strategy optimization of floating wind turbines, providing engineering with an efficient, reliable and near real-time numerical analysis tool.

[0117] This invention also provides a storage medium for storing a computer program, which, when executed, performs at least the methods described above.

[0118] This invention also provides a control device, including a processor and a storage medium for storing a computer program; wherein the processor executes the computer program by performing at least the method described above.

[0119] This invention also provides a processor that executes a computer program, at least performing the methods described above.

[0120] The storage medium can be implemented by any type of non-volatile storage device, or a combination thereof. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), magnetic random access memory (FRAM), flash memory, magnetic surface memory, optical disc or CD-ROM; magnetic surface memory can be disk storage or magnetic tape storage. The storage media described in the embodiments of this invention are intended to include, but are not limited to, these and any other suitable types of memory.

[0121] In the several embodiments provided by this invention, it should be understood that the disclosed systems and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0122] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the units may be selected to achieve the purpose of this embodiment according to actual needs.

[0123] In addition, in the various embodiments of the present invention, each functional unit can be integrated into one processing unit, or each unit can be a separate unit, or two or more units can be integrated into one unit; the integrated unit can be implemented in hardware or in the form of hardware plus software functional units.

[0124] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0125] Alternatively, if the integrated units of this invention are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this invention, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROM, RAM, magnetic disks, or optical disks.

[0126] The methods disclosed in the several method embodiments provided by this invention can be arbitrarily combined without conflict to obtain new method embodiments.

[0127] The features disclosed in the several product embodiments provided by this invention can be arbitrarily combined without conflict to obtain new product embodiments.

[0128] The features disclosed in the several method or device embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new method or device embodiments.

[0129] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various equivalent substitutions or obvious modifications can be made without departing from the concept of the present invention, and all such modifications, achieving the same performance or application, should be considered within the scope of protection of the present invention.

Claims

1. A rapid prediction method integrating dynamic motion and structural response of a floating wind turbine, characterized in that, Includes the following steps: S1. Structural preprocessing stage: Finite element modal analysis is performed on the floating wind turbine structure to extract the rigid body modes and elastic modes of the structure, construct a low-dimensional modal space, and orthogonalize the mass matrix and stiffness matrix to reduce the system degrees of freedom. S2, Static Equilibrium Stage: Calculate the hydrostatic recovery stiffness, mooring stiffness, gravity stiffness, and external excitation force based on the initial position of the structure, and convert them into a generalized stiffness matrix and generalized load through modal space transformation. Establish the hydrostatic equilibrium control equations and solve the generalized displacement through iterative algorithm. S3. Load Calculation Stage: Based on the radiation and diffraction theory, the incident, diffraction and radiation water pressure are recalculated at the Gaussian point of the structural mesh and transferred to the nodal loads through Gaussian integral and shape function. At the same time, the aerodynamic load is calculated based on the leaf element momentum theory. The aerodynamic and hydrodynamic loads are superimposed as the total external excitation and the generalized external load is obtained through modal space transformation. The load calculation stage specifically includes: at the Gaussian point of the structural grid, based on the calculation results of the radiation and diffraction theory, independently recalculating the incident, diffraction, and radiation water pressures; numerically integrating each part of the water pressure and transferring the integrated water pressure load to the structural nodes to ensure the balanced distribution of the load on the structural grid; based on the blade element momentum theory, dividing the wind turbine blades into several blade element units, calculating the blade element aerodynamic force according to the momentum conservation relationship, and integrating along the blades to obtain the total aerodynamic thrust acting on the tower top; superimposing the aerodynamic load with the hydrodynamic load to obtain the total external excitation load, and obtaining the generalized external excitation load through modal transformation; S4. Structural Time-Domain Analysis Stage: In modal space, motion equations expressed in generalized coordinates are constructed. The generalized displacement time history is solved through numerical integration, thereby reconstructing the global displacement field. The structural stress time history is then directly calculated using strain-displacement and constitutive relations, achieving integrated and rapid prediction of dynamic motion and structural response. The process of constructing and solving the motion equations in modal space includes: establishing motion equations in modal space that include generalized mass, infinite-frequency added mass, radiation damping effects, and generalized external forces; directly solving the motion equations using numerical integration to obtain the time history responses of generalized displacement, generalized velocity, and generalized acceleration; and directly calculating the structural stress time history based on the reconstructed global displacement field using the strain-displacement matrix and constitutive relations, without needing to perform dynamic load transfer in the time domain or call the global finite element method. The solution process includes the following steps: In the low-dimensional modal space, constructing the system's temporal motion equations, which include a mass term composed of a generalized mass matrix and an infinite-frequency additional mass matrix, a radiation damping memory term introduced by convolution of the impulse response function, and an excitation term composed of a generalized external excitation force, a generalized hydrostatic restoring force, and a generalized gravity. The temporal motion equations are directly solved using numerical integration to obtain the displacement, velocity, and acceleration response time histories of the generalized coordinates. The generalized displacement response time histories are reconstructed into physical displacement time histories of the global nodes of the structure using the modal matrix. Based on the strain-displacement relationship matrix and the material constitutive relation, the global stress time histories are directly calculated from the global physical displacement time histories, thus eliminating the need for repeated hydrodynamic pressure transmission and global finite element calculations during time-stepping solutions.

2. The integrated rapid prediction method for dynamic motion and structural response of floating wind turbines according to claim 1, characterized in that, The structural preprocessing stage in step S1 includes: The structure is discretized using the finite element method. The displacement field of the element is interpolated based on the shape function. The element stiffness matrix and mass matrix are formed in the local coordinate system of the element according to the principle of virtual work or the principle of minimum potential energy. The element stiffness matrix and mass matrix are transformed to the global coordinate system using orthogonal transformation matrices, and then assembled into a global stiffness matrix and a global mass matrix according to the nodal degrees of freedom. To eliminate the singularity caused by rigid body modes, weak constraints with stiffness much smaller than the stiffness of the structure itself are applied to the structure, and the Lagrange multiplier method is used to introduce the constraint conditions into the system equations to construct an extended eigenvalue problem. Solving the extended eigenvalue problem yields the modal natural frequencies and modal vectors, from which the first six rigid body modes and several elastic modes are identified, together forming a low-dimensional modal space. The global mass matrix and global stiffness matrix are orthogonalized in the modal space to obtain the generalized mass matrix and generalized stiffness matrix, thereby reducing the system's degrees of freedom while preserving the key dynamic characteristics of the structure.

3. The integrated rapid prediction method for dynamic motion and structural response of floating wind turbines according to claim 1, characterized in that, The hydrostatic equilibrium stage described in step S2 includes: Based on the initial position of the structure in still water, calculate the hydrostatic recovery stiffness matrix, mooring stiffness matrix, gravity stiffness matrix, and the external excitation force at the initial moment. The stiffness matrix is ​​transformed into a generalized stiffness matrix through the modal space, and the external excitation force is transformed into a generalized external force. Based on this, a hydrostatic equilibrium control equation with generalized displacement as the variable is established. The hydrostatic equilibrium control equations are solved using an iterative algorithm to obtain the generalized displacement of the system in hydrostatic equilibrium. By performing modal space inversion transformation, the generalized displacement is reduced to nodal displacement, and the response of the structure under static water load is further solved.

4. The integrated rapid prediction method for dynamic motion and structural response of floating wind turbines according to claim 1, characterized in that, In step S3, the velocity potential is reconstructed using the Green's function and the source strength distribution, and the incident, diffracted, and radiated water pressures are recalculated independently. The Gaussian integral method is used to numerically integrate the water pressure in each part, and the integrated water pressure load is transferred to the structural nodes through the plate element shape function.

5. The integrated rapid prediction method for dynamic motion and structural response of floating wind turbines according to claim 4, characterized in that, The recalculation and integration process of the water pressure includes: Based on the continuity of the watershed velocity potential function, the velocity potential and water pressure at the Gaussian point of the structured grid are calculated using the hydrodynamic grid point source strength and Green's function. Independent Gaussian numerical integrations were performed on the incident water pressure, diffracted water pressure, and radiated water pressure to avoid mutual interference between loads from different physical sources during transmission. By transforming the shape function relationship of the plate element with the Jacobian matrix, the water pressure obtained by Gaussian point integration is converted into an equivalent nodal load.

6. The integrated rapid prediction method for dynamic motion and structural response of floating wind turbines according to claim 1, characterized in that, In step S4, the Cummins equations, which include generalized mass, infinite-frequency additional mass, radiation damping effect, and generalized external force, are established in modal space, where radiation damping is introduced in the form of an impulse response function.

7. The integrated rapid prediction method for dynamic motion and structural response of floating wind turbines according to claim 1, characterized in that, In step S4, the strain-displacement relationship matrix is ​​established during the preprocessing stage.

8. The integrated rapid prediction method for dynamic motion and structural response of floating wind turbines according to claim 7, characterized in that, The time-domain motion equation is in the form of the Cummins equation, and its excitation term integrates the effects of aerodynamic, hydrodynamic and gravity sources. Its radiation damping effect is represented by the impulse response function obtained by Fourier transform of the frequency-domain radiation damping coefficient, and is calculated in the time domain by convolution integral with the generalized velocity.

9. The integrated rapid prediction method for dynamic motion and structural response of floating wind turbines according to claim 7, characterized in that, The calculation process of the stress time history is completed entirely within the reduced-order system after modal space transformation. By mapping the global displacement field back to the continuum strain field, and then directly solving the stress field according to the material constitutive relation, the synchronous and integrated solution of dynamic response and structural stress response is achieved.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the integrated rapid prediction method for dynamic motion and structural response of floating wind turbines as described in any one of claims 1 to 9.

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