Multi-body coupling calculation method and device for deep sea floating platform mooring system

Abstract

The application relates to the technical field of deep-sea oil and gas development, and particularly discloses a deep-sea floating platform mooring system multi-body coupling calculation method and device, wherein the method comprises the following steps: establishing a floating platform six-degree-of-freedom rigid body dynamic response model; establishing a rigid-flexible mixed dynamics model of a mooring cable which is coupled with the rigid body motion of an anchor chain and the flexible deformation of the anchor chain; establishing an anchor pile-soil interaction model which considers the soil arching effect and the nonlinearity of soil; setting geometric constraints and force transmission rules based on end geometric compatibility conditions and force-work duality relationships; assembling the rigid body dynamic response model, the rigid-flexible mixed dynamics model and the interaction model based on the geometric constraints and the force transmission rules in a unified generalized coordinate frame to form overall control equations; and performing time-domain synchronous coupling solution on the overall control equations to obtain real-time dynamic responses of the whole system. The above scheme improves the precision, reliability and engineering adaptability of deep-sea floating platform mooring system dynamics simulation.

Description

Technical Field

[0001] This invention relates to the field of deep-sea oil and gas development technology, and in particular to a multi-body coupling calculation method and apparatus for deep-sea floating platform mooring systems. Background Technology

[0002] The marine environment for deep-sea oil and gas development exhibits significant seasonal characteristics of wind, waves, and currents, and is frequently affected by typhoons. These environmental loads act directly on the floating platform and mooring cables, and then transfer the loads to the mooring anchors, which are key factors determining the service stability and safety redundancy design of the anchors.

[0003] Current mainstream simulation methods typically model and calculate floating platforms, mooring cables, and anchor piles as independent subsystems. For example, platform-fluid interactions are often analyzed using rigid body dynamics and hydrodynamic software, mooring cable dynamics is usually solved using specialized slender component dynamics software, and anchor pile-soil interactions rely on geotechnical analysis programs or empirical models. Due to differences in modeling assumptions, time steps, and physical field descriptions among different software, it is difficult to achieve unified solutions for the three, often requiring manual interfaces or equivalent parameters for result transfer in engineering. These traditional methods typically only enable unidirectional or weakly coupled analyses, such as calculating mooring cable responses from known platform motion or anchor pile bearing capacity from known mooring cable tension. They cannot directly predict the actual dynamic behavior of the third subsystem from the responses of any two subsystems. This problem is particularly prominent when dealing with slender chains, fluid interactions, rigid body motion, and soil nonlinearity, and has become a significant pain point in the refined analysis of deep-sea mooring systems.

[0004] There is currently no effective solution to the above problems. Summary of the Invention

[0005] This specification provides a multi-body coupling calculation method and apparatus for a deep-sea floating platform mooring system, which solves the technical problems of existing technologies that model the floating platform, mooring cable, and anchor pile-soil as independent subsystems, resulting in low calculation accuracy, large deviation between the results and actual engineering conditions, and difficulty in adapting to complex deep-sea conditions.

[0006] This specification provides a multi-body coupling calculation method for a deep-sea floating platform mooring system. The system includes a floating platform, a mooring cable, and anchor piles corresponding to the mooring cable. The mooring cable includes an anchor chain and a polyester cable. The top end of the mooring cable is connected to the floating platform, and the bottom end of the mooring cable is connected to the anchor hole of the corresponding anchor pile. The anchor pile is vertically inserted into the seabed soil. The method includes: A six-degree-of-freedom rigid body dynamic response model for a floating platform is established; a dynamic model of the mooring cable rigid-flexible hybrid motion coupled with the anchor chain rigid body motion and anchor chain flexible deformation is established; and an anchor pile-soil interaction model considering soil arching effect and soil nonlinearity is established. Based on the end geometric compatibility conditions and force-work duality, geometric constraints and force transmission rules matching the actual stress characteristics of deep-sea engineering are set for the connection interface between the floating platform and the top of the mooring cable, the connection interface between the anchor chain inside the mooring cable and the polyester cable section, and the connection interface between the end of the mooring cable and the anchor hole of the anchor pile. Under the unified generalized coordinate framework covering all system degrees of freedom, based on the geometric constraints and force transmission rules, the six-degree-of-freedom rigid body dynamic response model of the floating platform, the rigid-flexible hybrid dynamic model of the mooring cable, and the anchor pile-soil interaction model are assembled to form the multi-body coupled overall control equation of the whole system. The overall control equations of the multi-body coupling of the entire system are solved synchronously in the time domain. During the solution process, the soil reaction force at the anchor pile end and the dynamic parameters of the rigid-flexible coupling of the mooring cable are updated in real time. This achieves bidirectional real-time coupling of force and displacement between the floating platform, the mooring cable, and the anchor pile-soil, and obtains the real-time dynamic response of the entire system.

[0007] In one embodiment, an anchor pile-soil interaction model considering soil arching effect and soil nonlinearity is established, including: Based on the pile-soil interaction theory and soil arching effect, the longitudinal ultimate bearing capacity of the anchor pile is calculated under two working conditions: no soil plug and elastic soil plug. The longitudinal ultimate bearing capacity includes the ultimate bearing capacity of the outer side of the mooring anchor pile, the ultimate bearing capacity of the end of the mooring anchor pile, and the soil plug resistance inside the pile. The anchor pile is simplified as an elastic straight beam with uniform cross-section that satisfies the Euler-Bernoulli beam assumption. Combined with the soil reaction force that obeys the Winkler foundation assumption, the differential equation governing the transverse deflection of the anchor pile is established, and the transverse bearing capacity of the anchor pile is calculated. Based on the longitudinal ultimate bearing capacity and the transverse bearing capacity, a nonlinear constitutive relationship of the soil is constructed that is dynamically updated with the real-time displacement of the anchor pile and the cyclic loading process, and the dynamic control equations of the anchor pile-soil interaction model are obtained.

[0008] In one embodiment, a dynamic model of the mooring cable's rigid-flexible hybrid motion, which couples the rigid body motion and flexible deformation of the anchor chain, is established, including: The spatial motion of the anchor chain of the mooring cable is decomposed into rigid body motion characterizing overall translation and rotation, and flexible deformation characterizing axial tension and bending deformation. Using real-time axial tension as the coupling medium, a two-way coupling relationship between the rigid body motion and flexible deformation of the anchor chain is established, and the nonlinear dynamic control equation of the anchor chain is constructed. The polyester cable of the mooring cable is regarded as a continuous flexible cable that only bears axial tension. The absolute nodal coordinate method is used for discretization. Considering geometric nonlinearity and hydrodynamic effects, the nonlinear dynamic control equation of the polyester cable is established. Based on the inter-segment connection constraints between the anchor chain and the polyester cable, the nonlinear dynamic control equations of the anchor chain and the polyester cable are integrated to obtain a rigid-flexible hybrid dynamic model of the mooring cable.

[0009] In one embodiment, establishing the six-degree-of-freedom rigid body dynamic response model of the floating platform includes: The floating platform is regarded as an ideal rigid body, and the motion state of the floating platform is described by a global inertial coordinate system. The three-dimensional translational displacement of the platform's center of mass and the three attitude angles of roll, pitch, and yaw are used as the six-degree-of-freedom generalized coordinates. The total potential energy of the platform is calculated, which includes the platform's gravitational potential energy and the mooring system's restoring potential energy. The mooring system's restoring potential energy is calculated based on the length of the anchor chain and polyester cable and the initial tension, and is used to reflect the restoring capability of the mooring cable when the floating platform deviates. Based on the total potential energy of the platform, the platform's mass-inertia matrix and the system's restoring generalized force are calculated. Calculate the total tension of the mooring cables and the environmental loads acting on the platform, wherein the environmental loads include at least one of the following: wind load, ocean current load, and wave excitation load; By combining the floating platform mass, hydrodynamic added mass, radiation damping, viscous drag, the system restoring generalized force, the total tension of the mooring cable, and the environmental load, a six-degree-of-freedom rigid body dynamics control equation for the floating platform is established.

[0010] In one embodiment, based on end geometric compatibility conditions and force-work duality, geometric constraints and force transmission rules matching the actual stress characteristics of deep-sea engineering are set for the connection interface between the floating platform and the top of the mooring cable, the connection interface between the inner anchor chain of the mooring cable and the polyester cable segment, and the connection interface between the end of the mooring cable and the anchor hole of the anchor pile, respectively, including: The connection interface between the floating platform and the top of the mooring cable is equivalent to a hinge constraint. The corresponding geometric constraint is that the three-dimensional translational displacements of the connection point between the top of the mooring cable and the guide wire of the floating platform are completely synchronized and the angles are free. The corresponding force transmission rule is that the platform motion is completely transmitted to the mooring cable and there is no bending moment transmission. The connection interface between the anchor chain and the polyester cable in the mooring cable is equivalent to a tension-type hinge constraint. The corresponding geometric constraint is that the three-dimensional translational displacement of the connection point between the anchor chain and the polyester cable is completely synchronized and the angle is free. The corresponding force transmission rule is that the axial tensile force is transmitted without loss and there is no bending moment transmission. For the connection interface between the mooring cable end and the anchor pile eye, adaptive switching constraints are applied under tensioned and untensioned conditions. Under tensioned conditions, it is equivalent to a hinge constraint, with the corresponding geometric constraint that the three-dimensional translational displacement of the connection point is completely synchronized and angularly free, and the corresponding force transmission rule that the tension of the mooring cable is completely transmitted to the anchor pile. Under untensioned conditions, it is equivalent to a sliding hinge constraint, with the corresponding geometric constraint that allows limited sliding along the chain axis and angularly free, and the corresponding force transmission rule that only the force perpendicular to the chain axis is transmitted and no bending moment is transmitted.

[0011] In one embodiment, the overall control equations for the multi-body coupling of the entire system include:

[0012] in, X The generalized coordinate vector of the entire system. It is a generalized acceleration vector. It is a generalized velocity vector; The equivalent mass matrix of the entire system includes the rigid body mass and moment of inertia of the floating platform, the distributed mass and fluid-added mass of the mooring cables, and the equivalent mass of the anchor piles. The equivalent damping matrix of the entire system includes hydrodynamic damping, structural damping, and polyester cable material damping. The equivalent restoring force vector of the entire system includes the platform's hydrostatic restoring force, the internal forces and linear weight corresponding to the axial stiffness and bending stiffness of the mooring cable, and the elastic restoring force of the interaction between the anchor pile and the soil. Let η be the environmental load vector acting on the floating platform. p Here, t represents the elevation of the wave surface, and t represents time. B s This is the mooring cable-anchor pile end force mapping matrix, used to map the soil reaction force at the anchor pile end to a unified generalized coordinate frame; This is the equivalent soil reaction vector at the anchor pile end.

[0013] In one embodiment, the method further includes: Based on the overall control equations of the multi-body coupling of the entire system, the dynamic behavior of the third subsystem can be directly solved by using the known dynamic responses of any two subsystems in the system. Specifically, this includes: calculating the tension distribution and dynamic deformation of the mooring cable by back-calculating the motion response of the floating platform and the mechanical properties of the anchor pile and soil, and / or predicting the evolution process of the anchor pile displacement and soil reaction force by using the measured tension of the mooring cable and the motion data of the floating platform.

[0014] In one embodiment, the real-time dynamic response includes at least one of the following: the six-degree-of-freedom full-time-domain motion response of the floating platform, the tension distribution and dynamic deformation and fatigue damage of the entire mooring cable, the longitudinal and lateral displacement of the anchor pile and the reaction force and bearing capacity utilization rate of the surrounding soil.

[0015] This specification also provides a multi-body coupling calculation device for a deep-sea floating platform mooring system. The system includes a floating platform, a mooring cable, and anchor piles corresponding to the mooring cable. The mooring cable includes an anchor chain and a polyester cable. The top end of the mooring cable is connected to the floating platform, and the bottom end of the mooring cable is connected to the anchor hole of the corresponding anchor pile. The anchor pile is vertically inserted into the seabed soil. The device includes: The model building module is used to: build a six-degree-of-freedom rigid body dynamic response model for a floating platform; build a dynamic model of a mooring cable rigid-flexible hybrid motion model that couples the rigid body motion and flexible deformation of the anchor chain; and build an anchor pile-soil interaction model that considers the soil arching effect and soil nonlinearity. The connection interface setting module is used to set geometric constraints and force transmission rules that match the actual stress characteristics of deep-sea engineering, based on the end geometric compatibility conditions and force-work duality relationship, for the connection interface between the floating platform and the top of the mooring cable, the connection interface between the anchor chain inside the mooring cable and the polyester cable section, and the connection interface between the end of the mooring cable and the anchor pile and anchor eye. The model assembly module is used to assemble the six-degree-of-freedom rigid body dynamic response model of the floating platform, the rigid-flexible hybrid dynamic model of the mooring cable, and the anchor pile-soil interaction model under a unified generalized coordinate framework covering the entire system's degrees of freedom, based on the geometric constraints and force transmission rules, to form the overall control equations of the multi-body coupling of the entire system. The solution module is used to perform time-domain synchronous coupling solution of the overall control equation of the multi-body coupling of the entire system. During the solution process, the soil reaction force at the anchor pile end and the dynamic parameters of the rigid-flexible coupling of the mooring cable are updated in real time, realizing the bidirectional real-time coupling of force and displacement between the floating platform, mooring cable, anchor pile and soil, and obtaining the real-time dynamic response of the entire system.

[0016] This specification also provides a computer device, including a processor and a memory for storing processor-executable instructions, wherein the processor executes the instructions to implement the steps of the multi-body coupling calculation method for deep-sea floating platform mooring systems described in any of the above embodiments.

[0017] This specification also provides a computer-readable storage medium storing computer instructions that, when executed by a processor, implement the steps of the multi-body coupling calculation method for deep-sea floating platform mooring systems described in any of the above embodiments.

[0018] This specification also provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of the multi-body coupling calculation method for deep-sea floating platform mooring systems described in any of the above embodiments.

[0019] This specification provides a multi-body coupling calculation method for deep-sea floating platform mooring systems. It integrates the floating platform, mooring cable, and anchor pile-soil system into a unified generalized coordinate framework for overall equation assembly, eliminating the problems of inconsistent coordinate systems, energy non-conservation, and physical inconsistencies inherent in traditional discrete modeling. This method accurately reflects the overall dynamic characteristics of the multi-body system. By employing a rigid-flexible hybrid dynamic model that couples the rigid motion and flexible deformation of the anchor chain, it considers both the overall translational / rotational motion and local tensile / bending deformation of the anchor chain. Compared to traditional purely rigid or purely flexible simplified models, this method can more accurately calculate the real-time tension, dynamic deformation, and internal force distribution of the mooring cable, significantly improving the accuracy of mooring cable response analysis. Furthermore, by establishing an anchor pile-soil interaction model that considers the soil arching effect and soil nonlinearity, it can accurately simulate the soil plugging effect, nonlinear soil constitutive model, and changes in soil mechanical properties under cyclic loading. This overcomes the distortion in anchor pile bearing capacity and displacement calculations caused by traditional linear / static simplification assumptions, and better reflects the actual working conditions of deep-sea seabed soil. Based on end-point geometric compatibility conditions and force-work duality, three types of connection interface geometric constraints and force transmission rules matching engineering realities are set to accurately reproduce the actual connection force transmission characteristics of floating platform-mooring cable, anchor chain-polyester cable, and mooring cable-anchor pile, avoiding calculation deviations caused by idealized simplified boundaries. The overall control equations are solved synchronously in the time domain, with real-time updates to soil reaction forces and rigid-flexible coupling dynamic parameters of the mooring cable during the solution process. Iterative convergence using a unified time step results in a more stable solution process, accurately capturing the system's transient response under extreme sea conditions and cyclic loading. This enables bidirectional real-time coupling of force and displacement between the floating platform, mooring cable, and anchor pile-soil, forming a closed-loop feedback mechanism of displacement-driven force and force-constrained displacement. This fully reproduces the true multi-body linkage dynamics of deep-sea mooring systems, making the calculation results closer to engineering realities and providing more reliable theoretical support for the design, verification, and safety assessment of deep-sea floating platform mooring systems. The above-described scheme, by simultaneously introducing the rigid body motion of the floating platform, the slender dynamics of the mooring cable, fluid interactions, and the nonlinear interaction between the anchor pile and the soil within a unified computational framework, achieves simultaneous solution of multiple physics fields and multiple structures. It can directly complete the fully coupled analysis of the platform-mooring cable-anchor pile system without relying on multi-software co-simulation. Given the motion or force responses of any two subsystems within the system, this scheme can directly predict the dynamic response or bearing state of the third subsystem through the coupling relationship. For example, given the motion of the floating platform and the mechanical properties of the anchor pile, the tension distribution and dynamic morphology of the mooring cable can be directly calculated; also, given the forces on the mooring cable and the platform motion, the evolution of the anchor pile displacement and soil reaction force can be predicted.This solution achieves unified coupled modeling and synchronous solution of the floating platform, mooring cable, and anchor pile, avoiding the complex process of multi-software joint simulation. It supports direct prediction of the dynamic behavior of the third subsystem through the response of any two subsystems in the system, breaking through the unidirectional calculation limitation of existing simulation methods. It effectively solves the engineering pain point of difficulty in coupling slender chains, fluid action, rigid body motion, and soil nonlinearity. In other words, the above solution constructs a unified generalized coordinate framework covering the entire system's degrees of freedom, assembling and coupling the three major subsystems of floating platform, mooring cable, and anchor pile-soil under a unified mathematical system. Through synchronous time-domain solution, it achieves bidirectional real-time closed-loop linkage of forces and displacements among the three, completely solving the industry pain points of fragmented traditional discrete modeling and distorted unidirectional weak coupling calculations. It significantly improves the accuracy, reliability, and engineering adaptability of dynamic simulation of deep-sea floating platform mooring systems. Attached Figure Description

[0020] The accompanying drawings, which are included to provide a further understanding of this specification and form part of it, do not constitute a limitation thereof. In the drawings: Figure 1 A flowchart of a multi-body coupling calculation method for a deep-sea floating platform mooring system in one embodiment of this specification is shown; Figure 2 This specification shows a schematic diagram of the longitudinal bearing capacity of a deep-water tensioned mooring anchor pile and the soil plug in one embodiment; Figure 3 A schematic diagram of the forces acting on a mooring anchor pile in one embodiment of this specification is shown; Figure 4 A schematic diagram of a multibody coupling computing device for a deep-sea floating platform mooring system is shown in one embodiment of this specification; Figure 5 A schematic diagram of a computer device according to one embodiment of this specification is shown. Detailed Implementation

[0021] The principles and spirit of this specification will now be described with reference to several exemplary embodiments. It should be understood that these embodiments are given merely to enable those skilled in the art to better understand and implement this specification, and are not intended to limit the scope of this specification in any way. Rather, these embodiments are provided to make this disclosure more thorough and complete, and to fully convey the scope of this disclosure to those skilled in the art.

[0022] Those skilled in the art will recognize that the embodiments described in this specification can be implemented as a system, apparatus, method, or computer program product. Therefore, the disclosure of this specification can be specifically implemented in the following forms: entirely hardware, entirely software (including firmware, resident software, microcode, etc.), or a combination of hardware and software.

[0023] It should be noted that the information and data related to users involved in the embodiments of this specification are all information and data authorized by the user or fully authorized by the relevant parties. Furthermore, the collection, storage, use, processing, transmission, provision, disclosure, and application of the relevant data all comply with relevant laws, regulations, and standards, and necessary confidentiality measures have been taken. They do not violate public order and good morals, and corresponding operation entry points are provided for users or relevant parties to choose to authorize or refuse.

[0024] It should also be noted that in the embodiments of this specification, certain software, components, models and other existing solutions in the industry may be mentioned. These should be regarded as exemplary and are only intended to illustrate the feasibility of implementing the technical solution of this application. However, it does not mean that the applicant has used or necessarily used the solution.

[0025] This specification provides an embodiment of a multibody coupling calculation method for a deep-sea floating platform mooring system. Figure 1 A flowchart of a multi-body coupling calculation method for a deep-sea floating platform mooring system according to an embodiment of this specification is shown. While this specification provides method operation steps or apparatus structures as shown in the following embodiments or figures, more or fewer operation steps or module units may be included in the method or apparatus based on conventional or non-inventive effort. In steps or structures where there is no logically necessary causal relationship, the execution order of these steps or the module structure of the apparatus is not limited to the execution order or module structure described in the embodiments and figures of this specification. When the method or module structure is applied in actual devices or end products, it can be executed sequentially or in parallel (e.g., in a parallel processor or multi-threaded processing environment, or even a distributed processing environment) according to the method or module structure shown in the embodiments or figures.

[0026] Specifically, such as Figure 1 As shown in the figure, the multibody coupling calculation method for a deep-sea floating platform mooring system provided in one embodiment of this specification may include the following steps.

[0027] Step S101: Establish a six-degree-of-freedom rigid body dynamic response model for the floating platform; establish a dynamic model of the mooring cable rigid-flexible hybrid motion coupling the rigid body motion and flexible deformation of the anchor chain; establish an anchor pile-soil interaction model considering the soil arching effect and soil nonlinearity.

[0028] In this embodiment, the deep-sea floating platform mooring system is a complete power system that provides positioning, stabilization, and attitude maintenance functions for the floating platform in a deep-sea environment. The deep-sea floating platform mooring system may include a floating platform, mooring cables, and anchor piles corresponding to the mooring cables. The mooring cables may include anchor chains and polyester cables. The top end of the mooring cable is connected to the floating platform. The end of the mooring cable is connected to the anchor hole of the corresponding anchor pile. The anchor pile is vertically driven into the seabed soil. In this embodiment, the floating platform refers to a semi-submersible platform that can float and operate in a deep-sea environment, and can be considered as a rigid body with six degrees of freedom of motion. The mooring cable is the force-transmitting component connecting the floating platform and the anchor pile, and is the core force-transmitting bridge between the floating platform and the anchor pile. In one embodiment, the mooring cable can be a three-section composite mooring cable consisting of an anchor chain, a polyester cable, and an anchor chain. The anchor chain is the end section component of the mooring cable and can be divided into an upper anchor chain connected to the floating platform and a lower anchor chain connected to the anchor pile. Polyester cables are the middle section components of mooring cables, made of high-strength polyester fibers, and are flexible components of deep-sea catenary mooring systems. Anchor piles are tubular / solid steel structures that vertically penetrate the seabed soil for anchoring. An anchor eye is located at the top of the anchor pile and connects to the end of the mooring cable. Anchoring force is provided by the skin friction and end resistance of the surrounding soil. The seabed soil, a rock and soil medium covering the seabed, is typically a layered combination of clay, silty clay, silt, and sand. It forms the load-bearing matrix of the anchor piles, and its mechanical properties directly determine the anchoring capacity of the anchor piles.

[0029] The multi-body coupling calculation method in this embodiment can be applied to computer equipment. A six-degree-of-freedom rigid body dynamic response model for the floating platform, a dynamic model of the mooring cable rigid-flexible hybrid motion coupled with the anchor chain's rigid body motion and flexible deformation, and an anchor pile-soil interaction model considering soil arching effect and soil nonlinearity are established respectively, providing basic model support for the coupling calculation of the entire system.

[0030] The six-DOF rigid-body dynamic response model for floating platforms is used to describe the overall spatial motion of floating platforms in marine environments. Based on the three translational degrees of freedom (sway, roll, heave) and three rotational degrees of freedom (roll, pitch, yaw) of the platform's center of mass, this model integrates factors such as the platform's mass, damping, stiffness, and external loads to solve for the platform's motion response under environmental loads. The mooring cable rigid-flexible hybrid dynamic model considers both the overall motion and local deformation of the mooring cable and anchor chain. This model is a dynamic model established for the multi-scale mechanical characteristics of the mooring cable and anchor chain, taking into account both the overall rigid motion and local flexible deformation of the anchor chain, achieving their coupling, and integrating the flexible dynamic characteristics of the polyester cable to fully describe the spatial motion and mechanical response of the mooring cable.

[0031] The anchor pile-soil interaction model is a dynamic equation used to describe the mechanical interaction between the anchor pile and the surrounding seabed soil. It characterizes the mapping relationship between anchor pile displacement and soil reaction force, and is the core model connecting anchor pile motion and soil mechanical properties. The soil arching effect refers to the mechanical phenomenon where, under vertical load, the frictional resistance between the soil inside the anchor pile and the inner wall of the pile forms a soil arch structure, producing a soil plugging effect. This alters the distribution of the anchor pile's side friction and end resistance, affecting the anchor pile's longitudinal ultimate bearing capacity. Soil nonlinearity is a core mechanical characteristic of seabed soil, meaning that the stress-strain and force-displacement relationships of the soil are not linearly fixed, but dynamically change with the magnitude of anchor pile displacement, cyclic loading history, and stress state.

[0032] Step S102: Based on the end geometric compatibility conditions and force-work duality, geometric constraints and force transmission rules matching the actual stress characteristics of deep-sea engineering are set for the connection interface between the floating platform and the top of the mooring cable, the connection interface between the anchor chain inside the mooring cable and the polyester cable section, and the connection interface between the end of the mooring cable and the anchor hole of the anchor pile.

[0033] End geometric compatibility conditions refer to the requirement that the displacements of the components on both sides of the connection interface must be coordinated and consistent at the connection point, without any geometric misalignment such as separation or embedding, ensuring the geometric continuity of the system's motion. This is used to ensure that the displacement transfer between the floating platform, mooring cable, and anchor pile conforms to physical laws. End geometric compatibility conditions are the criteria for setting geometric constraints for the three types of connection interfaces, ensuring that the displacement transfer between the floating platform, mooring cable, and anchor pile conforms to physical laws. Force-work duality means that the interaction forces between the components on both sides of the connection interface satisfy the action-reaction law of equal magnitude and opposite direction, and the total work done by the forces on both sides of the interface is zero, ensuring the conservation of energy in the force transfer of the system. Force-work duality is the core criterion for setting force transfer rules for the three types of connection interfaces, ensuring that the force transfer between the floating platform, mooring cable, and anchor pile conforms to physical laws. The connection interface refers to the connection point between two adjacent components in the entire system and is the core node for displacement and force transfer. In this embodiment, three types of core connection interfaces are specifically referred to: the connection interface between the floating platform and the top of the mooring cable, the inter-segment connection interface between the anchor chain inside the mooring cable and the polyester cable, and the connection interface between the end of the mooring cable and the anchor hole of the anchor pile.

[0034] For various connection interfaces, geometric constraints and force transmission rules are set to match the actual stress characteristics of deep-sea engineering, based on end geometric compatibility conditions and force-work duality. Geometric constraints refer to displacement restriction rules set for connection interfaces, used to limit the relative displacement relationship between two components at the connection point, ensuring consistent interface displacement. These constraints are the core boundary conditions for realizing displacement transmission between subsystems, ensuring the geometric continuity of the entire system's motion. Force transmission rules are force transmission restriction rules set for connection interfaces, used to limit the force transmission method between two components at the connection point. These rules are the core boundary conditions for realizing bidirectional force feedback between subsystems, ensuring the physical self-consistency of force transmission throughout the system.

[0035] Step S103: Under the unified generalized coordinate framework covering the entire system's degrees of freedom, based on the geometric constraints and force transmission rules, the six-degree-of-freedom rigid body dynamic response model of the floating platform, the rigid-flexible hybrid dynamic model of the mooring cable, and the anchor pile-soil interaction model are assembled to form the overall multi-body coupled control equations of the entire system.

[0036] First, a generalized coordinate system is constructed that can completely and independently describe all degrees of freedom of motion of the entire system of floating platform, mooring cable, and anchor pile-soil. The originally independent local coordinates and degrees of freedom of the three models—the six-DOF rigid-body dynamic response model of the floating platform, the rigid-flexible hybrid dynamic model of the mooring cable, and the interaction model of the anchor pile-soil—are all mapped and integrated into this unified generalized coordinate framework. This eliminates problems such as incompatibility of coordinate systems between subsystems, cumulative errors caused by coordinate transformation, and fragmented data transmission that exist in traditional methods, achieving a unified mathematical description of the motion state of the entire system. Based on the established geometric constraints and force transmission rules, the core elements of the three system dynamic models, including equivalent mass matrix, equivalent damping matrix, equivalent stiffness matrix, external load vector, and internal force / reaction vector, are all mapped into the aforementioned unified generalized coordinate framework. Simultaneously, through constraint equations, the displacement compatibility conditions and force transmission rules of the connection interfaces are embedded into the overall model, ensuring that the linkage between subsystems fully conforms to the preset boundary rules. After mapping and assembling all system models, the dynamic equations of the three major subsystems are integrated into a single, complete second-order nonlinear dynamic differential equation, namely the overall multibody coupled control equation of the entire system. This equation uses unified generalized coordinates as the basic variable and fully integrates the inertial characteristics, damping characteristics, stiffness characteristics, external loads, and coupling constraints between subsystems of the entire system. It is a unified mathematical description of the dynamic behavior of the entire system of floating platform-mooring cable-anchor pile-soil.

[0037] Step S104: Perform time-domain synchronous coupling solution on the overall control equation of the multi-body coupling of the whole system. During the solution process, update the soil reaction force at the anchor pile end and the dynamic parameters of the rigid-flexible coupling of the mooring cable in real time to realize the bidirectional real-time coupling of force and displacement between the floating platform, mooring cable, anchor pile and soil, and obtain the real-time dynamic response of the whole system.

[0038] By performing time-domain synchronous iterative solution to the overall multi-body coupled control equations of the entire system, bidirectional real-time coupling of forces and displacements between the floating platform, mooring cables, and anchor piles-soil is achieved. The final output is the dynamic calculation results of the entire system, providing reliable data support for the design, verification, and safety assessment of deep-sea floating platform mooring systems. For the overall multi-body coupled control equations, a time-domain solution scheme is adopted, setting a unified solution time step, full-time domain solution duration, and iterative convergence threshold to ensure that the motion and mechanical response of all subsystems are calculated synchronously at the same time step, avoiding the problems of inconsistent time steps and data transmission lag in traditional step-by-step solutions. Within each solution time step, the overall control equations are solved synchronously iteratively. In one embodiment, the initial displacement state of the current time step is used as a basis to initially calculate the motion and force state of the entire system. Based on the real-time displacement of the current iteration step, the soil reaction force at the anchor pile end is updated in real time: according to the real-time displacement of the anchor pile and the nonlinear constitutive relationship of the soil, the reaction force of the surrounding soil on the anchor pile is recalculated, replacing the fixed soil stiffness / resistance assumption in the traditional method. Based on the real-time deformation of the current iteration step, the dynamic parameters of the mooring cable's rigid-flexible coupling are updated in real time. According to the real-time rigid motion and flexible deformation of the mooring cable anchor chain, the real-time axial tension, equivalent stiffness, and other core dynamic parameters of the mooring cable are recalculated, realizing real-time bidirectional coupling of the anchor chain's rigid motion and flexible deformation. The updated soil reaction force and mooring cable dynamic parameters are synchronously substituted into the overall control equation to recalculate the displacement, velocity, and acceleration state of the entire system, completing one iteration. This achieves closed-loop linkage of forward displacement transmission and reverse force feedback within the same time step. The forward displacement transmission path is as follows: displacement change of the floating platform → synchronously transmitted to the mooring cable through the connection interface, causing deformation and tension changes in the mooring cable → the tension of the mooring cable is synchronously transmitted to the anchor pile, causing displacement change of the anchor pile → the anchor pile displacement triggers the corresponding soil reaction force generated by the soil around the pile. The reverse force feedback path is as follows: soil reaction force acts in the opposite direction on the anchor pile to limit its displacement → the displacement constraint of the anchor pile is transmitted in the opposite direction through the tension of the mooring cable, correcting the tension and deformation of the mooring cable → the corrected tension of the mooring cable acts in the opposite direction on the floating platform, correcting the displacement and motion state of the floating platform. Forward transmission and reverse feedback iterate synchronously within the same time step until the force and displacement of the entire system reach equilibrium and meet the preset convergence threshold, thus completing the solution for the current time step. This truly achieves bidirectional, real-time, closed-loop coupling of force and displacement between the floating platform, mooring cable, and anchor pile-soil, without any time lag or data fragmentation. After completing the iterative convergence of the current time step, the real-time dynamic response of the entire system can be obtained. After solving all time steps in the full time domain, the system dynamics calculation results can be output continuously in the full time domain, providing complete data support for the engineering application of mooring systems.

[0039] In the above embodiments, by simultaneously introducing the rigid body motion of the floating platform, the slender dynamics of the mooring cable, fluid interaction, and the nonlinear interaction between the anchor pile and the soil within a unified computational framework, the synchronous solution of multiple physics fields and multiple structures is achieved. This allows for the direct completion of the fully coupled analysis of the platform-mooring cable-anchor pile system without relying on multi-software co-simulation. Given the motion or force response of any two subsystems in the system, this scheme can directly predict the dynamic response or bearing state of the third subsystem through the coupling relationship. For example, given the motion of the floating platform and the mechanical properties of the anchor pile, the tension distribution and dynamic morphology of the mooring cable can be directly calculated; similarly, given the force on the mooring cable and the platform motion, the evolution of the anchor pile displacement and soil reaction force can be predicted. This scheme achieves unified coupled modeling and synchronous solution of the floating platform, mooring cable, and anchor pile, avoiding the complex process of multi-software co-simulation. It supports the direct prediction of the dynamic behavior of the third subsystem through the response of any two subsystems in the system, breaking through the unidirectional computational limitations of existing simulation methods. It effectively solves the engineering pain point of the difficulty in coupling slender chains, fluid interaction, rigid body motion, and soil nonlinearity. By constructing a unified generalized coordinate framework covering the entire system's degrees of freedom, the three major subsystems—floating platform, mooring cable, and anchor pile-soil—are assembled and coupled under a unified mathematical system. Through synchronous time-domain solution, the two-way real-time closed-loop linkage of forces and displacements among the three is realized, completely solving the industry pain points of traditional discrete modeling and unidirectional weak coupling calculation distortion. This significantly improves the accuracy, reliability, and engineering adaptability of dynamic simulation of deep-sea floating platform mooring systems.

[0040] Considering the simplification and distortion in the calculation of anchor pile bearing capacity in existing technologies, the static solidification of soil constitutive structure, the inability to adapt to the cyclic dynamic loads of deep-sea mooring, and the disconnect from the dynamics of the entire system, in order to solve the above problems, in some embodiments of this specification, an anchor pile-soil interaction model considering soil arching effect and soil nonlinearity is established. This model may include: calculating the longitudinal ultimate bearing capacity of the anchor pile under two working conditions, namely, without soil plug formation and with elastic soil plug formation, based on the pile-soil interaction theory and soil arching effect. The longitudinal ultimate bearing capacity may include the ultimate bearing capacity of the outer side of the mooring anchor pile, the ultimate bearing capacity of the end of the mooring anchor pile, and the soil plug resistance inside the pile; simplifying the anchor pile into a uniform cross-section elastic straight beam that satisfies the Euler-Bernoulli beam assumption, and combining the soil reaction force that obeys the Winkler foundation assumption, establishing the differential equation for the transverse deflection control of the anchor pile, and calculating the transverse bearing capacity of the anchor pile; and constructing a nonlinear constitutive relationship of the soil that is dynamically updated with the real-time displacement and cyclic loading history of the anchor pile, thereby obtaining the dynamic control equation of the anchor pile-soil interaction model.

[0041] In this embodiment, the anchor piles used for mooring deep-sea floating platforms generally adopt the form of large-diameter open steel pipe piles. The core influencing factor on their longitudinal tensile bearing capacity is the soil plug closure effect caused by the soil arching effect. After the anchor pile vertically penetrates the seabed soil, the frictional resistance between the soil inside the pile and the inner wall of the pile will form a soil arch structure. With the changes in pile penetration depth and load state, the soil plug will exhibit dynamic changes from non-formation to elastic closure to complete closure, directly determining the magnitude of the anchor pile's longitudinal ultimate bearing capacity. Traditional methods either completely ignore the soil plug effect or only calculate based on the complete closure condition, resulting in a large deviation from engineering reality. Therefore, in this embodiment, based on the classical pile-soil interaction theory and combined with the mechanical mechanism of the soil arching effect, the longitudinal ultimate bearing capacity of the anchor pile is accurately calculated under two core working conditions, and the bearing capacity composition completely covers the three core components. The longitudinal ultimate bearing capacity can include the ultimate bearing capacity of the outer side of the mooring anchor pile, the ultimate bearing capacity of the mooring anchor pile end, and the soil plug resistance inside the pile. Among them, the soil plug resistance inside the pile is specifically calculated under two working conditions. Before the soil plug is formed, the soil plug resistance inside the pile mainly comes from the frictional resistance between the inner wall of the pile and the seabed soil. After the elastic soil plug is formed, the anchor pile is equivalent to a closed pile, and the soil plug resistance inside the pile becomes dominated by the end resistance.

[0042] The top of a deep-sea mooring anchor is connected to the mooring cable via an anchor hole. The tension of the mooring cable not only applies axial tensile force to the anchor but also generates significant horizontal components and bending moments, causing lateral deflection deformation of the anchor. This directly affects the overall stability of the anchor and the displacement boundary at the end of the mooring cable. Traditional methods often neglect lateral bearing characteristics, leading to serious distortion in anchor deformation calculations. Therefore, in this embodiment, a differential equation controlling the lateral deflection of the anchor is established based on a beam-spring model to calculate the lateral bearing capacity of the anchor. The anchor is simplified as a uniform cross-section elastic straight beam satisfying the Euler-Bernoulli beam assumption. This assumption perfectly suits the structural characteristics of deep-sea mooring anchors, which have a large length-to-diameter ratio, are dominated by bending deformation, and have negligible shear deformation. This simplification is reasonable and computationally efficient, accurately describing the lateral deflection and bending moment distribution characteristics of the anchor. The soil around the pile is equivalent to a discrete linear spring obeying the Winkler foundation assumption, i.e., the lateral reaction force at any depth of the soil is proportional to the lateral displacement of the anchor at that location, accurately characterizing the constraint effect of the soil on the lateral deformation of the anchor. x=0 The location at the top of the pile can be considered a free end or partially constrained; x =L The location at the pile end is considered fully embedded, meaning both displacement and rotation are zero. ，L Let be the pile length. To simplify modeling, the additional mass and damping caused by seawater buoyancy and flow field, axial compression deformation of the pile, and interface slip between the soil and the pile can be ignored. Combining the beam bending equation of the anchor pile and the soil reaction force of the Winkler foundation, a differential equation governing the lateral deflection of the anchor pile is established. By solving this equation, the lateral displacement, bending moment, and shear force distribution of the anchor pile under horizontal load can be obtained, and then the lateral bearing capacity of the anchor pile can be calculated.

[0043] Subsequently, based on the longitudinal ultimate bearing capacity and transverse bearing capacity, a nonlinear constitutive relationship of the soil that is dynamically updated with the real-time displacement and cyclic loading process of the anchor pile can be constructed, thus obtaining the dynamic governing equations of the anchor pile-soil interaction model. In existing technologies, anchor pile-soil models generally employ static, linear, simplified constitutive models, where soil stiffness and ultimate reaction are preset fixed values ​​that do not change with the real-time displacement and cyclic loading process of the anchor pile. This fails to reproduce the true nonlinear characteristics of deep-sea soft soil under cyclic mooring loads, such as stiffness attenuation, plastic accumulation, and cyclic weakening, and cannot be adapted to the time-domain dynamics solution of the entire system, only enabling unidirectional forward calculations. To overcome these shortcomings, a nonlinear constitutive relationship of the soil that is dynamically updated with the real-time displacement and cyclic loading process of the anchor pile is constructed based on the longitudinal and transverse ultimate bearing caps obtained in the previous two steps. Specifically, using the longitudinal and transverse ultimate bearing caps of the anchor pile as upper limits, a nonlinear stress-strain skeleton curve of the soil is constructed to characterize the nonlinear characteristics of the soil throughout the entire process from elastic deformation to plastic yielding. By introducing the influencing factors of cyclic loading history, the stiffness decay, plastic deformation accumulation, and cyclic weakening characteristics of the soil under mooring cyclic loading are tracked in real time, allowing the soil constitutive parameters to be dynamically updated with the number of loading cycles and load amplitude. In the final nonlinear constitutive model of the soil, the soil reaction force around the pile is a dynamic function of the real-time displacement, velocity, and cyclic loading history of the anchor pile, rather than a fixed value. Substituting this dynamic nonlinear constitutive model into the axial and lateral mechanical equilibrium equations of the anchor pile, the dynamic control equations of the anchor pile-soil interaction model are obtained. These equations can be directly mapped to the unified generalized coordinate framework of the entire system and assembled with the floating platform and mooring cable models. Through this approach, the limitations of traditional static soil models are completely broken, enabling the anchor pile-soil model to have dynamic updating capabilities. The soil reaction force can be updated synchronously with the real-time displacement of the entire system, allowing the soil reaction force at the anchor pile end to be updated in real time during the solution process. This achieves bidirectional real-time coupling of force and displacement between the floating platform, mooring cable, and anchor pile-soil, realizing a deep integration of the geotechnical mechanics model and the marine multibody dynamics model.

[0044] In the above embodiments, an anchor pile-soil interaction model is constructed. In the final output dynamic control equation, the soil reaction force is a function of the real-time displacement of the entire system and can be updated synchronously in each solution time step. This provides the core support of the anchoring side for the two-way real-time coupling of the force and displacement of the entire system and realizes the closed-loop mechanism of soil reaction force in reverse correction of the displacement of the entire system.

[0045] In some embodiments of this specification, establishing a mooring cable rigid-flexible hybrid dynamics model that couples the rigid motion and flexible deformation of the anchor chain may include: decomposing the spatial motion of the anchor chain of the mooring cable into rigid motion characterizing overall translation and rotation, and flexible deformation characterizing axial tension and bending deformation; using real-time axial tension as the coupling medium, establishing a two-way coupling relationship between the rigid motion and flexible deformation of the anchor chain, and constructing the nonlinear dynamic control equations of the anchor chain; treating the polyester cable of the mooring cable as a continuous flexible cable subjected only to axial tension, discretizing it using the absolute nodal coordinate method, and considering geometric nonlinearity and hydrodynamic effects, establishing the nonlinear dynamic control equations of the polyester cable; and integrating the nonlinear dynamic control equations of the anchor chain and the polyester cable based on the inter-segment connection constraints of the anchor chain and the polyester cable to obtain the mooring cable rigid-flexible hybrid dynamics model.

[0046] In this embodiment, the anchor chain of the deep-sea mooring system exhibits two completely different scales of mechanical behavior under the combined loads of wind, waves, and currents. One is rigid body motion, where the anchor chain, as a whole, undergoes overall translation and rotation due to the low-frequency motion of the floating platform and the action of ocean currents, determining the overall geometry and tension basis of the mooring cable. The other is flexible deformation, where the anchor chain undergoes axial tension and local bending deformation under real-time tension and high-frequency wave excitation, determining the dynamic tension fluctuations, internal force distribution, and fatigue damage of the mooring cable. Traditional methods either simplify the anchor chain as a pure rigid body (ignoring high-frequency tension fluctuations, resulting in completely distorted fatigue analysis) or as a pure flexible cable (extremely low computational efficiency and difficulty in characterizing large-scale overall motion), neither of which can meet the high-precision simulation requirements of deep-sea mooring systems. To solve the above problems, this step adopts a complete process of motion decomposition-two-way coupling-equation construction, targeting the multi-scale characteristics of the anchor chain.

[0047] Specifically, the spatial motion of the anchor chain is explicitly decomposed into rigid body motion, representing overall translation and rotation, and flexible deformation, representing axial tension and bending deformation. This mathematically separates two different scales of mechanical behavior, laying the foundation for subsequent coupling. Using real-time axial tension as the core mechanical coupling medium, a two-way coupling relationship between the anchor chain's rigid body motion and flexible deformation is established. This two-way coupling can include forward coupling (rigid body motion → flexible deformation) and reverse coupling (flexible deformation → rigid body motion). Forward coupling refers to the fact that the overall rigid body motion of the anchor chain changes its geometric length, swing angle, and shape, thereby inducing axial tension and bending deformation, generating real-time axial tension and internal forces. Reverse coupling refers to the fact that the real-time axial tension and internal forces generated by the anchor chain's flexible deformation act in the opposite direction on the overall motion of the anchor chain, correcting its rigid body motion trajectory and attitude, forming a complete two-way closed-loop linkage. Based on the aforementioned rigid-flexible decomposition and two-way coupling relationship, factors such as the distributed mass, added mass, structural damping, geometric nonlinearity, and material nonlinearity of the anchor chain are integrated to construct a nonlinear dynamic control equation for the anchor chain. This equation can simultaneously describe the rigid motion and flexible deformation of the anchor chain, and the two are linked in real time through real-time axial tension. This approach overcomes the limitations of traditional single simplified models. By combining rigid-flexible decomposition and two-way coupling, it simultaneously considers the large-scale overall motion and small-scale local deformation of the anchor chain. This ensures an accurate description of the overall geometry of the mooring cable while precisely capturing dynamic tension fluctuations and internal force distribution, significantly improving the accuracy and reliability of the mooring cable response analysis and providing support for subsequent full-system coupling.

[0048] A model can be created for the continuous flexible cable of a polyester cable, constructing its nonlinear dynamic governing equations. The polyester cable in the middle section of the mooring cable, made of high-strength polyester fiber, is the main force-transmitting component of a deep-sea, long-span catenary mooring system. Its mechanical behavior is primarily characterized by a large deformation flexible response under axial tension. This step, tailored to the specific characteristics of the polyester cable, employs a complete process of model simplification, discretization, element integration, and equation construction. The polyester cable is treated as a continuous flexible cable subjected only to axial tension, ignoring its bending stiffness and shear deformation. This approach perfectly matches the actual stress characteristics of the polyester cable, offering a simplified and computationally efficient solution. The Absolute Nodal Coordinates (ANCF) method is used to discretize the polyester cable. This method is particularly suitable for describing the large deformation geometric nonlinear behavior of flexible cables, eliminating the need for small deformation assumptions and accurately characterizing the axial tension and spatial deformation of the polyester cable in a long-span catenary configuration. The model fully considers geometric nonlinearity (stiffness changes caused by large deformation) and hydrodynamic effects (the drag force and inertial force of ocean currents on the polyester cable), ensuring that the model perfectly reflects the real stress scenarios in the deep-sea environment. Based on the discretization results of the absolute node coordinate method, and integrating geometric nonlinearity and hydrodynamic effects, a nonlinear dynamic control equation for the polyester cable is constructed. This equation can accurately describe the axial tension, spatial morphology, and tension transmission characteristics of the polyester cable. The absolute node coordinate method ensures the calculation accuracy under large deformations, while the integration of hydrodynamic effects conforms to the deep-sea environment. Together with the anchor chain submodule, it forms a rigid-flexible complementary full-link model of the mooring cable, providing a foundation for the integration of rigid-flexible hybrid models of mooring cables.

[0049] Subsequently, based on the inter-segment connection constraint integration model, a rigid-flexible hybrid dynamic model of the mooring cable is obtained. Integrating the anchor chain sub-module and the polyester cable module into a complete rigid-flexible hybrid dynamic model of the mooring cable can open up the displacement transmission and force feedback channels between the anchor chain and the polyester cable, forming a complete mooring cable model that can be directly mapped to the unified generalized coordinate frame of the entire system.

[0050] In the above embodiments, by constructing a rigid-flexible hybrid dynamic model of the mooring cable and using real-time axial tension as the coupling medium, the bidirectional linkage between the rigid motion and flexible deformation of the anchor chain is realized. The rigid-flexible coupling dynamic parameters (real-time axial tension, equivalent stiffness, etc.) in the model can be updated synchronously with the real-time displacement of the entire system, so that the rigid-flexible coupling dynamic parameters of the mooring cable can be updated in real time during the solution process, thereby realizing the bidirectional real-time coupling of force and displacement of the entire system.

[0051] In some embodiments of this specification, establishing the six-degree-of-freedom rigid body dynamic response model of the floating platform may include: treating the floating platform as an ideal rigid body, using a global inertial coordinate system to describe the motion state of the floating platform, and using the three-dimensional translational displacement of the platform's center of mass and the three attitude angles of roll, pitch, and yaw as the six-degree-of-freedom generalized coordinates; calculating the total potential energy of the platform, which may include the platform's gravitational potential energy and the mooring system's restoring potential energy, the mooring system's restoring potential energy being calculated based on the length of the anchor chain and polyester cable and the initial tension, to reflect the restoring capability of the mooring cable when the floating platform deviates; calculating the platform's mass-inertia matrix and the system's restoring generalized force based on the total potential energy of the platform; calculating the total tension of the mooring cable and the environmental loads acting on the platform, the environmental loads may include at least one of the following: wind load, ocean current load, and wave excitation load; and establishing the six-degree-of-freedom rigid body dynamic control equations of the floating platform by combining the floating platform's mass, hydrodynamic added mass, radiation damping, viscous drag, the system's restoring generalized force, the total tension of the mooring cable, and the environmental loads.

[0052] In this embodiment, the deep-sea floating platform (semi-submersible production platform, semi-submersible drilling platform, etc.) is regarded as an ideal rigid body. This assumption is in full compliance with the general specifications in the field of marine engineering: the deep-sea floating platform is a fully welded steel structure with extremely high overall rigidity. The influence of its own structural elastic deformation on the overall rigid body motion of the platform is negligible. This simplifies the process and greatly improves the efficiency and stability of the dynamic solution.

[0053] A global inertial coordinate system (geocentric coordinate system) is used to describe the motion state of the floating platform. The origin of this coordinate system is fixed at the mean sea level, and the coordinate axes remain relatively stationary with respect to the seabed, completely consistent with the reference coordinate system of the anchor pile-soil model. Unlike the body-dependent coordinate system commonly used in traditional methods, the global inertial coordinate system can directly map the platform's motion state to a unified generalized coordinate framework for the entire system, eliminating the need for complex multi-coordinate system transformations and fundamentally avoiding the computational errors and model fragmentation problems caused by coordinate transformations.

[0054] Using six independent parameters—the three-dimensional translational displacement and three-dimensional rotational attitude angles of the platform's center of mass—as generalized coordinates to describe the platform's spatial motion state, this approach comprehensively covers all rigid body motion patterns of floating platforms in marine environments. Translational degrees of freedom: sway (horizontal forward / backward motion along the X-axis), roll (horizontal left / right motion along the Y-axis), and heave (vertical up / down motion along the Z-axis). Rotational degrees of freedom: roll (rotation about the X-axis), pitch (rotation about the Y-axis), and yaw (rotation about the Z-axis). A platform motion description benchmark fully adapted to the entire system's coupled framework was established, resolving the core issue of incompatibility between the platform model and the coordinate systems of mooring and anchor pile models in traditional methods. This provides a unified mathematical benchmark for subsequent assembly of the entire system model and synchronous coupled solution.

[0055] Next, the total potential energy of the platform is calculated. The total potential energy consists of two parts: the platform's gravitational potential energy and the mooring system's restoring potential energy, fully covering the potential energy changes caused by the platform's own gravity and the constraints of the mooring system. The platform's gravitational potential energy is determined by the heave displacement and roll / pitch angles of the platform's center of mass, characterizing the potential energy changes caused by the platform's gravity and still-water buoyancy, and is the core source of the platform's still-water restoring force. The mooring system's restoring potential energy is the core interface for the linkage between the platform model and the mooring system, and can be calculated based on the initial length and initial tension of the mooring cables, anchor chains, and polyester cables. When the floating platform deviates, the elastic potential energy change caused by the stretching / slackening of the mooring cables directly reflects the mooring cables' restoring constraint capability on the platform. Unlike traditional methods that treat mooring forces as external loads superimposed after the fact, this embodiment directly incorporates the mooring system's restoring potential energy into the platform's total potential energy, achieving a deep binding between the platform model and the mooring system at the energy level.

[0056] The platform's mass-inertia matrix can be derived from its rigid body kinetic energy. This matrix integrates the platform's rigid body mass and moment of inertia about its center of mass, fully characterizing the platform's inertial characteristics and serving as the core inertial term in the rigid body dynamics equations. The system's restoring generalized force can be derived from the partial derivative of the platform's total potential energy with respect to its six-degree-of-freedom generalized coordinates. This force comprises both still-water restoring and mooring system restoring forces, directly characterizing the reverse restoring constraint effect of still-water buoyancy and the mooring system on the platform when displacement occurs. It is the core carrier of the bidirectional linkage between platform displacement and mooring cable tension.

[0057] The total tension of the mooring cables and the environmental loads acting on the platform are calculated. The total tension of the mooring cables is the resultant force of the tension of all mooring cables at the connection point of the platform's guide wire. Through coordinate transformation, it is mapped to a generalized force in the platform's six-degree-of-freedom generalized coordinate system, serving as the core carrier for force feedback from the mooring cable model to the platform model. This tension directly originates from the calculation results of the mooring cable rigid-flexible hybrid dynamic model. Platform displacement changes the mooring cable tension, which in turn constrains the platform displacement, thus achieving bidirectional coupling of the system. Environmental loads are the core excitation source for the motion of deep-sea floating platforms. This embodiment fully covers the three core environmental loads in deep-sea engineering and can be flexibly combined according to actual working conditions. Wind loads are calculated based on the windward area, wind pressure coefficient, and measured wind speed spectrum of the platform's superstructure, characterizing the excitation effect of steady-state wind and pulsating wind on the platform. Ocean current loads are calculated based on the Morrison equation and the drag coefficient of the platform's underwater components, used to characterize the steady-state drag effect of ocean currents on the platform. The wave-induced load is calculated based on the potential flow theory and includes the first-order wave excitation force (high-frequency wave load) and the second-order slow drift force (low-frequency slow drift load). At the same time, the hydrodynamic added mass and radiation damping caused by the wave are calculated to fully characterize the dynamic excitation effect of the wave on the platform.

[0058] Finally, by combining the floating platform mass, hydrodynamic added mass, radiation damping, viscous drag, the system's restoring generalized force, the total tension of the mooring cables, and the environmental loads, the six-degree-of-freedom rigid body dynamics governing equations for the floating platform can be established. The six-degree-of-freedom rigid body dynamics governing equations for the floating platform are as follows:

[0059] in, The platform mass-inertia matrix, in kg; It is the platform's generalized acceleration vector, in m / s²; It is the platform's generalized velocity vector, in m / s; C p Represents the generalized nonconservative forces such as hydrodynamic added mass, Coriolis force, and damping, in Ns / m; The restoring generalized force provided to the mooring system, N; F mooring It is the tension of the mooring cable, in N. It is wind load, N. It is the total force of wave excitation, N. It is the ocean current load, N.

[0060] In the above embodiments, a floating platform model was constructed, whose six-degree-of-freedom generalized coordinates were directly incorporated into the unified generalized coordinate framework of the entire system, the mooring restoring force term was directly linked with the mooring cable model, and the final dynamic control equations could be directly assembled into the overall control equations of the entire system.

[0061] In some embodiments of this specification, based on end geometric compatibility conditions and force-work duality, geometric constraints and force transmission rules matching the actual stress characteristics of deep-sea engineering are set for the connection interface between the floating platform and the top of the mooring cable, the connection interface between the anchor chain inside the mooring cable and the polyester cable segment, and the connection interface between the end of the mooring cable and the anchor pile / anchor eye. These constraints may include: treating the connection interface between the floating platform and the top of the mooring cable as an equivalent hinge constraint, with the corresponding geometric constraint being that the three-dimensional translational displacements of the connection point between the top of the mooring cable and the guide wire of the floating platform are completely synchronized and angularly free; and the corresponding force transmission rule being that the platform motion is completely transmitted to the mooring cable with no bending moment transmission; and treating the connection interface between the anchor chain inside the mooring cable and the polyester cable segment as an equivalent tension constraint. The force-type articulated constraint corresponds to the geometric constraint that the three-dimensional translational displacements of the connection point between the anchor chain and the polyester cable are completely synchronized and angularly free. The corresponding force transmission rule is that the axial tensile force is transmitted without loss and there is no bending moment transmission. For the connection interface between the end of the mooring cable and the anchor pile, the constraint is adaptively switched between tensioned and untensioned conditions. Under tensioned conditions, it is equivalent to an articulated constraint, with the corresponding geometric constraint that the three-dimensional translational displacements of the connection point are completely synchronized and angularly free. The corresponding force transmission rule is that the tension of the mooring cable is completely transmitted to the anchor pile. Under untensioned conditions, it is equivalent to a sliding hinge constraint, with the corresponding geometric constraint that allows limited sliding along the chain axis and angularly free. The corresponding force transmission rule is that only the force perpendicular to the chain axis is transmitted and there is no bending moment transmission.

[0062] In this embodiment, all constraints and force transmission rules strictly adhere to the two fundamental principles of classical mechanics, and are specifically defined in an engineering manner for the deep-sea mooring system scenario, ensuring the geometric continuity of the connection interface and the physical self-consistency of force transmission. The two fundamental principles are: end geometric compatibility conditions and force-work duality. End geometric compatibility conditions mean that the displacements of the components on both sides of the connection interface at the connection point must be coordinated and consistent, without any geometric misalignment such as separation or embedding, ensuring the geometric continuity of the entire system's motion. This is the core principle for the positive synchronous transmission of displacement between subsystems. Force-work duality means that the interaction forces between the components on both sides of the connection interface strictly follow Newton's third law, which states that the forces are equal in magnitude and opposite in direction, and the work done by the force corresponding to the released degrees of freedom at the interface is zero, ensuring energy conservation during the force transmission process of the entire system. This is the core principle for the reverse closed-loop feedback of forces between subsystems.

[0063] The connection interface between the floating platform and the top of the mooring cable corresponds to the connection node between the floating platform's guide wire and the anchor chain on the mooring cable in deep-sea engineering. In engineering, this node is connected via a shackle. The guide wire can rotate freely with the mooring cable's swing angle, transmitting only translational displacement and axial tension, but not bending moment. It is the upstream core node for transmitting platform motion to the mooring cable. This interface is equivalent to a hinge constraint, with the core principle being complete synchronization of the three-dimensional translational displacements and complete angular freedom between the top of the mooring cable and the connection point of the floating platform's guide wire. Complete synchronization of the three-dimensional translational displacements strictly adheres to geometric compatibility conditions, ensuring a 1:1 transmission of the platform guide wire's translational displacement to the top of the mooring cable, preventing any separation or misalignment, and accurately replicating the driving effect of the platform's motion on the mooring cable. Complete angular freedom means releasing all rotational degrees of freedom at the connection point, perfectly matching the actual rotational characteristics of the shackle-guide wire, without additional rotational constraints. The core of the force transmission rule setting is that the platform's motion is completely transmitted to the mooring cable, with no bending moment transmission. The complete transmission of platform motion ensures the continuity of forward displacement transmission, while the tension of the mooring cable can be transmitted back to the platform through this interface, forming a two-way linkage. The moment-free transmission strictly adheres to the force-work duality relationship. Because the rotational degrees of freedom are completely released, the work done by the bending moment at the interface is zero, only the axial tension is transmitted, perfectly matching the actual stress characteristics of the engineering project and avoiding the distortion in bending moment calculations caused by traditional rigid connections. Through this method, both the forward synchronous transmission of platform motion to the mooring cable and the reverse feedback of mooring cable tension to the platform are ensured, providing the upstream core interface for the two-way coupling of the entire system.

[0064] The interface between the anchor chain and the polyester cable in the mooring cable is equivalent to a tension-type hinge constraint. This interface corresponds to the docking nodes between the upper anchor chain and the polyester cable, and between the polyester cable and the lower anchor chain in deep-sea engineering. In engineering, this node is connected via a special shackle and can only transmit axial tension, unable to withstand bending moment or shear force. It is the core intermediate node for force and displacement transmission within the composite mooring cable. When setting geometric constraints, this interface is equivalent to a tension-type hinge constraint, with the core principle being complete synchronization of the three-dimensional translational displacements and complete angular freedom at the connection point between the anchor chain and the polyester cable. Complete synchronization of the three-dimensional translational displacements means strictly adhering to geometric compatibility conditions, ensuring no relative translation, separation, or misalignment at the connection point between the anchor chain and the polyester cable, thus ensuring the continuity of the overall geometry of the mooring cable. Complete angular freedom means releasing all rotational degrees of freedom at the connection point, matching the actual structural characteristics of the shackle connection, with no rotational constraints. The core of the force transmission rules is the lossless transmission of axial tension and the absence of bending moment transmission. Lossless axial tensile force transmission means that, strictly adhering to the force-work duality, the axial tensile force of the anchor chain is transmitted 1:1 to the polyester cable, and conversely, the tensile force of the polyester cable is transmitted 1:1 back to the anchor chain, ensuring the continuity of force transmission within the mooring cable without energy loss. No moment transmission means that, due to the complete release of rotational freedom, the work done by moment at the interface is zero, and no moment or shear force is transmitted. This perfectly matches the actual force characteristics of the joints between sections of the composite mooring cable, avoiding the distortion of mooring cable internal force calculations caused by moment transmission in traditional models. Through these methods, the inter-segment force transmission and displacement coordination characteristics within the three-segment composite mooring cable are accurately reproduced. This is the core boundary condition for integrating the rigid-flexible hybrid model of the anchor chain and the flexible model of the polyester cable, ensuring the self-consistency and calculation accuracy of the rigid-flexible hybrid dynamic model of the mooring cable, and providing reliable boundary support for the real-time updating of the dynamic parameters of the rigid-flexible coupling within the mooring cable.

[0065] The connection interface between the mooring cable end and the anchor pile / anchor eye undergoes adaptive switching constraints under tensioned / untensioned conditions. This connection interface corresponds to the connection node between the mooring cable's lower anchor chain and the top anchor eye of the anchor pile in deep-sea engineering. It is the anchoring terminal node of the mooring system and the downstream core node for force transmission in the entire system. In engineering, this node is connected by a shackle inserted into the anchor eye. Under normal service conditions, the mooring cable remains tensioned, and the shackle and anchor eye are tightly fitted. In extreme sea states or when the platform experiences significant movement, the mooring cable may slack (untensioned) conditions, allowing the shackle to slide freely along the chain axis within the anchor eye. Traditional fixed hinged models cannot simulate this slack condition, leading to severe distortion in mooring cable tension calculations. For both tensioned and untensioned core conditions, an adaptive switching constraint mode is implemented, with both conditions strictly adhering to geometric compatibility conditions and force-work duality. For the tensioned condition (mooring cable straightened, shackle and anchor eye tightly fitted), it is equivalent to a hinged constraint. The geometric constraints are as follows: the three-dimensional translational displacements at the connection point are completely synchronized, and the angles are completely free, ensuring no relative translational movement or misalignment between the mooring cable end and the anchor pile / anchor eye, thus meeting the geometric compatibility condition. The force transmission rule is that the mooring cable tension is completely transmitted to the anchor pile, with no bending moment transmission, ensuring a 1:1 transmission of the mooring cable tension to the anchor pile. Simultaneously, the soil reaction force of the anchor pile can confine the mooring cable in the opposite direction, conforming to the force-work duality relationship and adapting to the core operating conditions of the mooring system's normal operation. For non-tensioned operating conditions (mooring cable slack, shackle separation from the anchor eye), the equivalent constraint is a sliding hinge constraint. The geometric constraints allow limited sliding along the chain axis and complete angular freedom, only restricting synchronized translational displacement along the vertical chain axis. This perfectly matches the actual motion state of the shackle freely sliding along the chain axis within the anchor eye when the mooring cable is slack, without excessive constraints, thus meeting the geometric compatibility condition. The force transmission rule only transmits the axial force of the vertical chain, with no bending moment transmission. Because the mooring cable is slack, there is no axial tension, therefore no axial force is transmitted. This perfectly matches the actual force characteristics of the slack condition and conforms to the force-work duality relationship, solving the core defect of traditional fixed hinges that still incorrectly calculate axial tension under slack conditions. Through this method, the inherent industry limitation of traditional fixed hinge constraints being unable to simulate the slack condition of mooring cables is overcome. It accurately reproduces the real mechanical behavior of the mooring cable tension-slack cycle under extreme sea conditions, ensuring that the constraints of the connection interface perfectly match the actual engineering situation regardless of whether the mooring cable is tensioned or slack during the full-time domain solution process. This significantly improves the accuracy of mooring cable tension and anchor pile displacement calculations under extreme conditions. Simultaneously, it opens up the reverse transmission channel of the anchor pile soil reaction force to the mooring cable, providing core support for the anchoring terminal for the bidirectional real-time coupling of force and displacement in the entire system.

[0066] In the above embodiments, through precise constraint settings of three types of interfaces, a complete closed loop of the entire chain is established, from floating platform displacement → mooring cable deformation and tension → anchor pile displacement → soil reaction around the pile → reverse constraint of mooring cable tension → reverse correction of platform displacement. This ensures the continuity and accuracy of forward displacement transmission and reverse force feedback at the boundary level, and realizes model assembly under a unified generalized coordinate framework, synchronous temporal coupling solution, and bidirectional real-time coupling of force and displacement.

[0067] In some embodiments of this specification, the overall control equations for the multibody coupling of the entire system may include:

[0068] in, X The generalized coordinate vector of the entire system. It is a generalized acceleration vector. It is a generalized velocity vector; The equivalent mass matrix of the entire system includes the rigid body mass and moment of inertia of the floating platform, the distributed mass and fluid-added mass of the mooring cables, and the equivalent mass of the anchor piles. The equivalent damping matrix of the entire system includes hydrodynamic damping, structural damping, and polyester cable material damping. The equivalent restoring force vector of the entire system includes the platform's hydrostatic restoring force, the internal forces and linear weight corresponding to the axial stiffness and bending stiffness of the mooring cable, and the elastic restoring force of the interaction between the anchor pile and the soil. Let η be the environmental load vector acting on the floating platform. p Here, t represents the elevation of the wave surface, and t represents time. B s This is the mooring cable-anchor pile end force mapping matrix, used to map the soil reaction force at the anchor pile end to a unified generalized coordinate frame; This is the equivalent soil reaction vector at the anchor pile end.

[0069] The overall control equations for the multi-body coupling system in this embodiment are an extension of the classical Newton-Euler rigid body dynamics equations in a deep-sea floating platform-mooring cable-anchor multi-body coupling system. Essentially, these equations are the force balance equations for the entire multi-body coupling system, following the dynamic balance criterion: inertial force + damping force + restoring force = external load + coupling feedback force. The left side of the equation... For inertial force, It is a damping / coupling term. This is the restoring force term. The right-hand side of the equation... For environmental loads, This is the soil reaction force.

[0070] X is the generalized coordinate vector of the entire system. It is a unified set of coordinates covering all degrees of freedom of the floating platform, mooring cable, and anchor pile-soil system. Its core components include: the six-degree-of-freedom generalized coordinates of the floating platform (three-way translational displacement + three-way rotational attitude angle), the rigid body motion generalized coordinates and flexible deformation generalized coordinates of the mooring cable and anchor chain, the flexible large deformation generalized coordinates of the mooring cable polyester cable, and the longitudinal and lateral displacement generalized coordinates of the anchor pile.

[0071] The equivalent mass matrix M(X) of the entire system characterizes the inertial properties of the entire system, describing its ability to resist changes in acceleration, and corresponds to the inertial force term in dynamic equilibrium. This matrix is ​​a unified integration of the inertial characteristics of the three subsystems, completely corresponding to the previous sub-model implementation examples. This matrix includes the rigid body mass and rotational inertia of the floating platform, the distributed mass and fluid-added mass of the mooring cables, and the equivalent mass of the anchor piles. The rigid body mass and rotational inertia of the floating platform are derived from the six-degree-of-freedom rigid body dynamic response model of the floating platform, describing the translational and rotational inertia of the platform. The distributed mass and fluid-added mass of the mooring cables are derived from the rigid-flexible hybrid dynamics model of the mooring cables, including the self-distributed mass of the anchor chain and polyester cable, as well as the fluid-added mass of the mooring cables from the seawater. The equivalent mass of the anchor piles is derived from the anchor pile-soil interaction model, describing the longitudinal and lateral motion inertia of the anchor piles. M(X) is a function of X, meaning the mass matrix is ​​dynamically updated with the real-time displacement of the entire system. This is because the geometry of the mooring cable changes with displacement, and the inertial contribution of its distributed mass and the magnitude of the fluid-added mass also change accordingly, enabling real-time updates of the dynamic parameters of the rigid-flexible coupling of the mooring cable.

[0072] Equivalent damping matrix of the whole system This describes the energy dissipation characteristics of the entire system, depicting the energy loss caused by damping during the system's motion, corresponding to the damping force term in dynamic equilibrium. The equivalent damping matrix of the entire system includes hydrodynamic damping, structural damping, and polyester cable material damping. Hydrodynamic damping mainly originates from the wave radiation damping of the floating platform and the fluid viscous damping of the mooring cable. Structural damping originates from the structural damping of the mooring cable anchor chain. Polyester cable material damping originates from the polymer material damping of the mooring cable and is an important component of energy dissipation in deep-sea mooring systems. It is X and The function, namely the damping matrix, is dynamically updated with the real-time displacement and velocity of the entire system, which fits the nonlinear characteristics of damping in deep-sea mooring systems.

[0073] The equivalent restoring force vector R(X) of the entire system characterizes the elastic recovery properties of the entire system, describing the reverse restoring force generated when the entire system undergoes displacement, corresponding to the restoring force term in dynamic equilibrium. The equivalent restoring force vector R(X) of the entire system includes the platform's hydrostatic restoring force, the internal forces and linear weight corresponding to the axial and bending stiffness of the mooring cable, and the elastic restoring force from the interaction between the anchor pile and the soil. The platform's hydrostatic restoring force originates from the six-degree-of-freedom rigid-body dynamic response model of the floating platform, generated by the imbalance between the platform's gravity and buoyancy. The internal forces and linear weight corresponding to the axial and bending stiffness of the mooring cable originate from the rigid-flexible hybrid dynamic model of the mooring cable, including the elastic internal forces generated by the tensile / bending deformation of the mooring cable, and the restoring force generated by the linear weight of the mooring cable itself; these are core components of the dynamic parameters of the rigid-flexible coupling of the mooring cable. The elastic restoring force from the interaction between the anchor pile and the soil originates from the anchor pile-soil interaction model, generated by the elastic deformation of the soil around the pile. R(X) is a function of X, meaning the restoring force vector is dynamically updated with the real-time displacement of the entire system. This is because the axial / bending stiffness of the mooring cable changes with tension, and the elastic restoring force of the soil changes nonlinearly with displacement, thus enabling bidirectional real-time coupling of force and displacement.

[0074] Environmental load vector This vector describes the external excitation effect of the marine environment on the floating platform and is the driving source of the entire system's motion. It primarily acts on the generalized coordinates of the floating platform and includes wind loads, ocean current loads, and wave excitation loads, perfectly corresponding to the environmental load calculations in the floating platform model embodiment. ηp represents the wave surface elevation, and t represents time, indicating that the environmental load is a dynamically changing random load over time.

[0075] Coupled feedback force term The reverse coupling feedback force, described by the anchor pile-soil interface and transmitted to the mooring cable and subsequently to the entire system, is the core component for achieving bidirectional real-time coupling of force and displacement. The negative sign indicates that this force is a restorative / constraint feedback force opposite to the displacement direction. The equivalent soil reaction vector at the anchor pile end is also described. Derived from the anchor pile-soil interaction model, it is a dynamic function of the anchor pile's real-time displacement, velocity, and cyclic loading history, rather than a fixed value. This means that the soil reaction force is updated synchronously with the real-time displacement of the entire system, enabling real-time updates of the soil reaction force at the anchor pile end during the solution process. This achieves a closed-loop mechanism where displacement drives soil reaction force, and soil reaction force conversely constrains displacement. The mooring cable-anchor pile end force mapping matrix Bs is a mathematical representation of the force transmission rules at the connection interface, fully corresponding to the constraint settings in the three types of connection interface embodiments. Its function is to map the soil reaction force in the local coordinate system at the anchor pile end to the unified generalized coordinate framework of the entire system, achieving seamless assembly of the anchor pile-soil model and the entire system model, ensuring the physical self-consistency of force transmission.

[0076] The multi-body coupled overall control equations constructed in the above embodiments overcome the limitations of independent subsystem equations and delayed manual data transmission in traditional discrete modeling. For the first time, it integrates the three major subsystems—floating platform, mooring cable, and anchor pile-soil—along with interface constraints, into a single set of second-order nonlinear dynamic differential equations, achieving strong coupling of the entire system from the underlying mathematical architecture. Each term in the equation has a clear physical meaning, corresponding to previous sub-models or interface implementations, with no physical contradictions. Simultaneously, it is fully adaptable to real-world engineering scenarios of deep-sea mooring systems, allowing for direct time-domain synchronous solutions using numerical methods, possessing significant engineering practical value. This equation is the sole mathematical foundation for the time-domain synchronous coupled solution of the entire system; all solution processes revolve around this equation, ensuring that the motion and mechanical responses of all subsystems are calculated synchronously within the same time step, breaking the limitations of traditional step-by-step asynchronous solutions.

[0077] In some embodiments of this specification, the method may further include: based on the overall control equations of the multi-body coupling of the entire system, directly solving the dynamic behavior of the third subsystem using the known dynamic responses of any two subsystems in the system; specifically, it may include: calculating the mooring cable tension distribution and dynamic deformation by back-calculating the floating platform motion response and the mechanical properties of the anchor pile and soil, and / or predicting the evolution process of anchor pile displacement and soil reaction force by using the measured tension of the mooring cable and the motion data of the floating platform.

[0078] In this embodiment, the overall control equations for the multi-body coupling of the entire system integrate all degrees of freedom, mechanical parameters, and coupling relationships of the three subsystems—the floating platform, mooring cable, and anchor pile-soil—into a single set of second-order nonlinear dynamic equations. The dynamic responses of the three subsystems are mutually coupled, causally related, and completely closed-loop. Mathematically, the unknown quantity in this equation set is the generalized coordinate vector X of the entire system (containing all motion and mechanical parameters of the three subsystems). When the dynamic response / mechanical characteristics of any two subsystems are known, they can be substituted into the equations as known boundary conditions to close the equation set and directly solve for the entire dynamic behavior of the third subsystem without step-by-step iterations or accumulated errors. The cross-subsystem solution in this embodiment follows the following general implementation steps, which can be adapted to the needs of different engineering scenarios. The dynamic response / mechanical characteristics of two measurable and surveyable subsystems in the engineering are used as known boundary conditions and substituted into the overall control equations for the multi-body coupling of the entire system. The generalized coordinates and mechanical parameters corresponding to the known quantities are fixed, reducing the dimension of the unknown quantity in the equation set, transforming the originally underdetermined equation set into a closed and solvable equation set. For the closed-loop overall control equations, a synchronous coupling solution method is used to complete iterative calculations. The solution yields the full-time dynamic behavior of the third subsystem, including parameters across all dimensions such as displacement, velocity, tension, reaction force, and deformation.

[0079] In one embodiment, the tension distribution and dynamic deformation of the mooring cable are calculated by inversely using the motion response of the floating platform and the mechanical properties of the anchor pile-soil system. The main section of the deep-sea mooring cable is located in an underwater environment hundreds to thousands of meters deep. Real-time monitoring of the tension distribution and dynamic deformation of the entire section is extremely difficult and costly. Existing technologies can only install a small number of sensors at the top of the mooring cable, making it impossible to obtain tension and deformation data for the entire section. However, the tension distribution of the entire mooring cable is the core basis for fatigue life assessment and fracture risk warning. In this embodiment, the motion response of the floating platform is measured in real time using GPS and attitude sensors on the platform, obtaining the six-degree-of-freedom full-time-domain motion response, which is then substituted into the overall control equation as known quantities. The mechanical properties of the anchor pile-soil system are determined through preliminary geological surveys and static load tests of the pile foundation, determining the mechanical parameters, constitutive relationship, and ultimate bearing capacity of the soil surrounding the anchor pile, which are also substituted into the overall control equation as known quantities. By using the platform's motion response and the mechanical properties of the anchor pile and soil as fixed boundary conditions, and substituting them into the overall multi-body coupled control equations of the entire system, a closed set of equations is solved synchronously in the time domain. This allows for direct back-calculation of the tension distribution and dynamic deformation data of the entire mooring cable section. Using this method, there is no need to install numerous monitoring sensors on the underwater mooring cable. Measurable motion data from the platform and previously surveyed soil parameters can be used to accurately obtain the mechanical and deformation data of the entire mooring cable section. This significantly reduces the monitoring cost of deep-sea mooring systems and provides comprehensive data support for fatigue assessment and fracture risk early warning of the mooring cable.

[0080] In another embodiment, the evolution of anchor pile displacement and soil reaction force is predicted using measured tension of the mooring cable and motion data of the floating platform. The anchor pile is the final anchoring terminal of the mooring system, vertically penetrating the seabed soil. As a concealed engineering project, the longitudinal and lateral displacement of the anchor pile, the soil reaction force around the pile, and the process of bearing capacity degradation cannot be monitored in real time using conventional methods. Traditional methods can only rely on periodic underwater inspections and post-construction excavation and assessment, failing to achieve real-time status assessment and safety early warning during service. Furthermore, anchor pile slippage and bearing capacity degradation are core causes of overall instability in deep-sea mooring systems. In this embodiment, the measured tension of the mooring cable is obtained in real time through tension sensors and fiber optic monitoring systems installed at the top / section of the mooring cable, and this data is substituted into the overall control equation as a known quantity. The motion data of the floating platform is obtained in real time through GPS and attitude sensors on the platform, yielding the platform's six-degree-of-freedom full-time-domain motion response, which is also substituted into the overall control equation as a known quantity. By using the measured tension of the mooring cable and the platform's motion response as fixed boundary conditions, and substituting them into the overall multi-body coupled control equations of the entire system, a closed set of equations is solved synchronously in the time domain. This directly predicts the longitudinal and lateral displacement time histories of the anchor piles, the distribution of soil reaction forces around the piles, and the evolution of soil stiffness and bearing capacity. Through this method, there is no need for invasive monitoring of the anchor piles within the seabed. Only easily measurable real-time data from the mooring cable and platform can accurately determine the service status of the anchor piles and the degradation of soil bearing capacity. This enables real-time health monitoring and early warning of instability risks for deep-sea mooring and anchoring systems, significantly improving the service safety of deep-sea floating platforms.

[0081] The methods described in the above embodiments can cover the entire lifecycle engineering application of deep-sea floating platform mooring systems. During the design phase, the structural design of the mooring cable can be optimized by pre-setting platform motion and anchor pile parameters; during the construction phase, the actual bearing capacity of the anchor pile can be verified by measuring the platform motion and mooring cable tension; during the service phase, real-time health monitoring and safety early warning of the mooring cable and anchor pile can be achieved; and during the accident analysis phase, the failure process of the anchor pile can be inverted using measured data from the platform and mooring cable, providing data support for accident analysis.

[0082] In some embodiments of this specification, the real-time dynamic response may include at least one of the following: the six-degree-of-freedom full-time-domain motion response of a floating platform, the tension distribution and dynamic deformation and fatigue damage of the entire mooring cable, and the longitudinal and lateral displacement of anchor piles and the reaction force and bearing capacity utilization rate of the surrounding soil.

[0083] The real-time dynamic response described in this embodiment refers to the core dynamic and mechanical performance indicators that are synchronously output within the same time step after the method performs a time-domain synchronous coupling solution on the overall control equations of the multi-body coupling of the entire system. These indicators cover the entire link of the floating platform, mooring cable, anchor pile, and soil, and fully correspond to the real-time service status of the three core subsystems. This serves as the core basis for the design, verification, health monitoring, and safety assessment of the deep-sea floating platform mooring system. The six-degree-of-freedom full-time-domain motion response of the floating platform refers to the displacement, velocity, and acceleration time history data of the three translational degrees of freedom (sway, roll, heave) and three rotational degrees of freedom (roll, pitch, yaw) of the floating platform's center of mass, synchronously output at each time step during the full-time-domain solution process. This data fully characterizes the full-time-domain spatial motion law of the floating platform under the combined loads of wind, waves, and current, and the mooring constraints. Based on the six-degree-of-freedom rigid body dynamic response model of the floating platform in this embodiment, it is obtained through the synchronous coupling solution of the overall control equations of the entire system. The platform's motion displacement is transmitted to the mooring cable in real time, causing changes in the mooring cable tension and deformation; the mooring cable tension and the soil reaction force at the anchor pile end then act in the opposite direction on the platform in real time, correcting the platform's motion state. This is the core linkage of the two-way coupling of force and displacement in the entire system.

[0084] The tension distribution, dynamic deformation, and fatigue damage of the mooring cable along its entire length are used to describe the mechanical state, geometry, and long-term service life of the mooring cable. They are the core basis for assessing the strength, stiffness, and fatigue safety of the mooring system, covering the core design and monitoring needs throughout the mooring cable's entire lifecycle. The tension distribution along the entire length of the mooring cable is the time-history data of the axial tension distribution along its entire length, from the top platform guide connection point to the end anchor bolt connection point, at every time step in the entire time domain. This includes core parameters such as maximum tension, minimum tension, and dynamic tension fluctuation amplitude. It can be obtained synchronously by solving the overall system control equations based on the mooring cable's rigid-flexible hybrid dynamics model. The platform's motion displacement changes the tension distribution of the mooring cable in real time, and the tension changes, in turn, constrain the platform's motion in real time. Simultaneously, the soil reaction force at the anchor bolt end updates the tension boundary at the end of the mooring cable in real time, serving as the core force transmission carrier for the bidirectional coupling of the entire system. The dynamic deformation of the mooring cable is the time-history data of its spatial geometry, axial tensile deformation, and bending deformation at every time step in the entire time domain, comprehensively depicting the real-time configuration and local deformation characteristics of the mooring cable. According to the rigid-flexible hybrid dynamic model of the mooring cable, the rigid motion of the anchor chain determines the overall configuration of the mooring cable, while the flexible deformation determines the local deformation. These two are coupled bidirectionally through real-time axial tension. Simultaneously, the displacement boundaries of the platform and anchor piles are updated in real time and solved synchronously through the overall control equations. Mooring cable fatigue damage refers to the fatigue damage degree and remaining fatigue life calculated at various locations along the entire length of the mooring cable based on the full-time dynamic tension time-history data, thus comprehensively characterizing the long-term service safety of the mooring cable. This can be calculated based on the full-segment tension time-history data combined with the mooring cable material's SN curve. The synchronous coupling solution in this embodiment can accurately capture tension fluctuations under long-term cyclic loading, providing reliable basic data for fatigue damage calculation.

[0085] The longitudinal and lateral displacements of anchor piles, along with the soil reaction force and bearing capacity utilization rate, characterize the service status of the anchor piles, the mechanical response of the surrounding soil, and the bearing safety margin of the anchoring system. This serves as the core basis for the safety assessment of concealed works in deep-sea mooring anchoring systems, addressing the long-standing industry challenge of accurately monitoring and assessing the condition of anchor piles buried in the seabed. The longitudinal and lateral displacements of the anchor piles are time-history data for each time step across the entire time domain, representing the longitudinal displacement along the pile axis and the lateral deflection perpendicular to the pile axis. This comprehensively characterizes the real-time deformation and overall slippage risk of the anchor piles under the tension of the mooring cable. This data can be obtained by simultaneously solving the overall system control equations using an anchor pile-soil interaction model that considers soil arching and soil nonlinearity. The tension of the mooring cable is transmitted to the anchor piles in real time, inducing displacement. The soil reaction force induced by the anchor pile displacement then constrains the anchor piles and mooring cable in real time, forming a core component of the bidirectionally coupled anchoring terminal of the entire system. The longitudinal and lateral displacements of anchor piles are core control indicators in anchor pile design. They are used to verify whether the uplift displacement and lateral deformation of anchor piles meet the specifications, assess the overall slippage and pull-out instability risks of anchor piles, and verify the rationality of the anchor pile's embedment depth and diameter design. The soil reaction force around the pile is the time history data of the longitudinal skin friction, lateral soil resistance, and pile end resistance of the soil around the pile at each time step in the entire time domain, comprehensively depicting the real-time mechanical state of the pile-soil interaction. Based on the anchor pile-soil interaction model, the nonlinear constitutive structure of the soil can be dynamically updated according to the real-time displacement and cyclic loading history of the anchor pile, and the soil reaction force can be calculated in real time. Simultaneously, the soil reaction force is transmitted back to the mooring cable and platform through the overall control equations, serving as the core feedback term for the two-way real-time coupling of the entire system. The anchor pile bearing capacity utilization rate refers to the ratio of the real-time load borne by the anchor pile to the longitudinal / lateral ultimate bearing capacity (also called the load ratio). It is a core dimensionless indicator characterizing the safety margin of the anchor pile's bearing capacity, including the longitudinal bearing capacity utilization rate and the lateral bearing capacity utilization rate. Based on the accurate calculation of the longitudinal / lateral ultimate bearing capacity of the anchor pile using this method, combined with the actual load borne by the anchor pile obtained in real time, the bearing capacity utilization time history data for each time step can be calculated, and key indicators such as the maximum utilization rate and average utilization rate in the entire time domain can be output.

[0086] In the above embodiments, all output items are solved synchronously within the same time step, covering the entire life cycle application scenarios of deep-sea floating platform mooring systems, from design, verification, construction validation to service life health monitoring and accident inversion, and possessing extremely strong engineering practical value.

[0087] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on describing the differences from other embodiments. For details, please refer to the foregoing descriptions of the relevant processing embodiments; they will not be repeated here.

[0088] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0089] The above method will be described below with reference to a specific embodiment. However, it is worth noting that this specific embodiment is only for better illustration of this specification and does not constitute an improper limitation of this specification.

[0090] This specification provides a multi-body coupling calculation method for a deep-sea floating platform mooring system. The method in this specific embodiment includes the following:

[0091] During the service life of deep-water mooring anchor piles, a reasonable assessment of their bearing capacity is crucial to ensuring the long-term stability of floating production systems. The bearing capacity of anchor piles is mainly reflected in two aspects: longitudinal ultimate bearing capacity, which reflects their ability to resist axial tensile and compressive loads; and lateral bearing capacity, which characterizes the static lateral resistance under pile-soil interaction, with the embedded end reflecting the distribution of the anchor pile in a zero-displacement state. Therefore, establishing a theoretical basis for the service stability of anchor piles can provide important reference for deep-water engineering design.

[0092] like Figure 2 As shown, deep-sea mooring anchors must withstand the tension force from the anchor chain, their own weight, the frictional resistance provided by the seabed soil, and the interaction force between the pile and the soil interface during their service, in order to maintain their stability under complex tensile loads.

[0093] Based on the stress characteristics and mechanical equilibrium relationship of anchor piles, the corresponding theoretical analysis model can be established as follows: (1) Based on the pile-soil interaction theory, the ultimate bearing capacity, end resistance, and soil plug resistance models of the outer side of the mooring anchor pile can be obtained.

[0094] Model of ultimate bearing capacity of outer side of mooring anchor pile: (2) Ultimate bearing capacity model of mooring anchor pile ends: (3) in, T The tension in the mooring chain on the mooring anchor pile, in N; T z Let T be the longitudinal force, in N, exerted by the mooring anchor chain on the mooring anchor pile.T x Let T be the lateral force, in N, exerted by the mooring anchor chain on the mooring anchor pile. N P The supporting force at the end is N; N L The lateral support force is N; N L1 The lateral support force of the soil above the mooring anchor hole, in N; N L2 The lateral support force of the soil below the mooring anchor is N; G The buoyant weight of the anchor pile in the sea is N; f Let N be the lateral frictional force exerted on the mooring anchor pile in the soil; F u It is the ultimate bearing capacity of the outer side of the mooring anchor pile, in N; L It is the total length of the mooring anchor piles, in meters (m). L M d is the total length of the mooring anchor into the mudline, in meters; d is the outer diameter of the mooring anchor, in meters. F p It is the ultimate bearing capacity at the end of the mooring anchor pile, in N; It is the resistance of the mooring anchor pile per unit area, in N / m 2 ; A P It is the cross-sectional area of ​​the mooring anchor pile, in meters. 2 θ is the angle between the mooring chain and the mudline, in degrees.

[0095] Based on the soil arching effect in pile-soil interaction, the soil inside the anchor pile will compress and form a soil plug under ballast. Before the soil plug is formed, the bearing capacity of the anchor pile mainly comes from the frictional resistance between the inner wall of the pile and the seabed soil; after the elastic soil plug is formed, the anchor pile is equivalent to a closed pile, and its bearing capacity becomes dominated by end resistance.

[0096] When the soil penetrates to a depth of the mooring anchor pile, When it is at this point, its total ultimate bearing capacity is: (4) Assuming that a soil plug forms inside the mooring anchor pile after it is installed, the ultimate bearing capacity model is as follows: (5) Therefore, the ultimate longitudinal bearing capacity of the mooring anchor pile in the absence of soil plug formation is: (6) The ultimate longitudinal bearing capacity of the mooring anchor piles under the condition of soil plug formation is: (7) The real-time bearing capacity of the mooring anchor piles gradually recovers and increases after installation, but changes during service. The real-time bearing capacity is as follows: (8) in, z It is the height of the soil within the mooring anchor pile, in meters (m). N s It is the ultimate bearing capacity of the soil inside the mooring anchor pile, in N; q s It is the resistance within a unit area of ​​the mooring anchor pile, in N / m. 2 ; A s It is the internal cross-sectional area of ​​the mooring anchor pile, in meters. 2 ; f d is the lateral frictional force exerted on the mooring anchor pile in the soil, in N; d is the outer diameter of the mooring anchor pile, in m. F v It is the ultimate bearing capacity of the mooring anchor pile, in N; F vt It is the real-time bearing capacity of the mooring anchor pile, in N; k Parameters for evaluating the variation of dimensionless bearing capacity; It is the resistance of the mooring anchor pile per unit area, in N / m 2 ; A P It is the cross-sectional area of ​​the mooring anchor pile, in meters. 2 ; The frictional force per unit area between the mooring anchor pile and the seabed soil is a crucial factor determining its bearing capacity. In clay, this frictional force is related to the undrained shear strength of the soil, and the expression is: (9) In the formula: f Let N be the lateral frictional force exerted on the mooring anchor pile in the soil; α Coefficient of adhesion ; This represents the undrained shear strength, expressed in Pa.

[0097] The formula for calculating its value is: (10) in, The total earth pressure above this location, Pa; s u This represents the undrained shear strength, expressed in Pa.

[0098] The formula for calculating the end resistance per unit area of ​​cohesive soil is: (11) In the formula: This is the load-bearing capacity assessment value.

[0099] Side friction resistance per unit area of ​​sandy soil: (12) In the formula, f The lateral friction force (N) experienced by the mooring anchor pile in the soil is: K This is the lateral pressure coefficient; For effective overburden pressure, Pa; δ Let be the pile-soil friction angle, taken as... , The internal friction angle of the soil.

[0100] The formula for calculating the end resistance per unit area of ​​sand is: (13) In the formula: N p This is the bearing capacity coefficient.

[0101] The soil plug resistance within the pile, specifically the unit area skin friction generated by the soil plug, is directly proportional to the weight of the overlying soil, i.e.: (14) In the formula: for z Frictional resistance per unit area in the radial direction at depth, in Pa; μ The friction coefficient between the soil plug and the mooring anchor pile; K This refers to the lateral pressure coefficient; For the first i Weight of soil layer, N / m³; h i To calculate the depth above the first i The thickness of the soil layer, in meters (m).

[0102] In deep-water mooring systems, anchor piles primarily bear the vertical forces transmitted through the anchor chains from the wind, wave, and current loads on the floating platform, as well as the reactions provided by the seabed soil. For simplicity, this paper considers only the force characteristics of anchor piles under static lateral loads in a two-dimensional plane. For example... Figure 3 The diagram shown illustrates the forces acting on the mooring anchor pile. Establishment is as follows... Figure 3 The simplified model shown: Assuming the anchor pile is a uniform and isotropic elastic straight beam with a constant cross-section, installed in the seabed soil, satisfying the following conditions... Euler- Bernoulli Beam assumption; Load T is applied to the middle of the anchor pile a At this location, the lateral load is... T x , 0 < a < L, L The length of the pile; The reaction force provided by the seabed soil to the anchor pile p(x) ,obey WinklerThe foundation assumption, i.e., the soil reaction force at any location. p (x) It is proportional to the displacement at that point: p(x) = ky(x) ; Anchor piles x=0 The location at the top of the pile can be considered a free end or partially constrained; x=L The point at the pile end is considered to be fully embedded, meaning that both displacement and rotation are zero.

[0103] To simplify modeling, this embodiment ignores the additional mass and damping caused by seawater buoyancy and flow field, the axial compression deformation of the pile, and the interface slip between the soil and the pile.

[0104] Total lateral bearing capacity of anchor piles F L satisfy: (15) Anchor piles can be placed at any location. x tiny units dx According to the shear force equilibrium and bending moment equilibrium equations, the relationship between shear force and bending moment satisfies: (16) Based on the vertical force balance relationship of the anchor pile, the shear force and lateral load relationship satisfy: (17) according to Euler-Bernoulli According to beam theory, the relationship between bending moment and lateral displacement is: (18) Combining equations (16) and (17), we obtain the differential equation governing the lateral deflection of the anchor pile on the seabed as follows: (19) in, k The soil foundation reaction coefficient is given in kN / m. 3 ; y(x) Let m be the lateral displacement. E The elastic modulus of the pile; I The moment of inertia of the cross section; M(x) The value represents the bending moment of a small segment of the mooring anchor pile, in N·m. N(x) Let N be the axial force on the mooring anchor pile. E sc I sc This represents the bending stiffness of the mooring anchor pile, in N·m². x The distance between the anchor pile and the anchoring point is in meters (m). y This indicates a position of the anchor pile along its length. x Deflection at point, in meters (m); F τThis represents the shear force of a small segment of the anchor pile, expressed in N. p(x) This represents the soil reaction force per unit length, expressed in N / m.

[0105] Deep-sea tensioned moored floating platforms must withstand the combined effects of multiple environmental loads, including wind, waves, and currents, during service, and maintain their positioning stability by connecting to seabed anchor piles via multiple mooring cables. The dynamic response of the floating platform-mooring cable-anchor pile system exhibits significant characteristics such as nonlinear coupling, rigid-flexible hybridity, and multiple time scales. To systematically characterize the global motion laws of this type of structure in complex marine environments, a unified coupled dynamic equation for the floating platform-mooring cable (anchor chain + polyester cable)-anchor pile is constructed based on multibody system dynamics theory.

[0106] The following reasonable assumptions and constraints are introduced in the derivation process: ① The floating platform is considered an ideal rigid body, and its motion is determined by a six-degree-of-freedom generalized coordinate system. q p3 Characterization; ② The anchor pile is fixed to the seabed at its root, and the pile stiffness and soil reaction are applied through equivalent boundary conditions; ③ The steady-state flow field assumption is adopted, and the high-frequency pulsation component caused by transient vortex shedding is ignored; ④ Based on the linear potential flow theory, wave excitation consists of Froude–Krylov force and diffraction force; ⑤ Expressed using empirical air resistance formulas; ⑥ Use the global inertial coordinate system O- XYZ To describe the system's motion state, the platform's attitude angles are expressed using Euler angles in a right-handed coordinate system. , θ , ψ ) express.

[0107] A multibody dynamics model of the floating platform at sea level is established, and the effects of the mooring system are introduced into the platform equations through equivalent parameterization. The generalized coordinates of the platform in the inertial coordinate system are defined as follows: (20) x , y , z : Translational displacement of the center of mass in the inertial coordinate system, in meters; , θ, : These represent the platform's roll, pitch, and yaw, respectively, in degrees.

[0108] The platform's potential energy mainly includes gravitational potential energy and mooring restoring potential energy, which can be expressed as: (twenty one) The first term is gravitational potential energy, the second term is the equivalent potential energy of the mooring system, and K m The value is calculated from the length of the anchor chain and polyester cable, and the initial tension, to reflect the recovery capability of the mooring cable when the platform experiences a small displacement.

[0109] The generalized force of wind load is expressed using an empirical drag formula: (twenty two) in, It is the density of air, kg / m³; drag coefficient; It is the windward projected area, in meters. 2 ; It is the relative wind speed of the platform, in m / s.

[0110] Using the Morison drag term, excluding the inertial term, the ocean current load is: (twenty three) in, It is the resistance of the ocean current acting on the structure, N; It is the density of seawater, kg / m³; It is the drag coefficient; s It is the projected area facing the wind, in m²; It is the relative flow velocity, in m / s.

[0111] Wave excitation force comprises Froude–Krylov force and diffraction force, and wave excitation is uniformly represented as: (twenty four) in ，F wave It is the total force of wave excitation, N; F FK It is the Froude-Krylov force, which refers to the wave pressure acting directly on the surface of the structure, in N; F diff It is the diffraction force caused by wave diffraction, N.

[0112] The total tension of the mooring cable is recorded as: (25) By considering the platform's mass, added mass, radiation damping, viscous drag, mooring restoring force, and environmental excitations, the generalized dynamic equations of the platform are obtained. (26) in, The platform mass-inertia matrix, in kg; It is the platform's generalized acceleration vector, in m / s²; It is the platform's generalized velocity vector, in m / s; C p This represents the generalized nonconservative forces such as hydrodynamic added mass, Coriolis force, and damping. The restoring generalized force provided to the mooring system; F mooring It is the tension of the mooring cable. It is wind load. It is the total force of wave excitation. It is ocean current load.

[0113] In practical engineering, deep-sea tensioned mooring cables often adopt a three-section structure arrangement of anchor chain-polyester cable-anchor chain. High-stiffness, wear-resistant anchor chain sections are placed at the platform end and the anchor pile end, while a lightweight, low-stiffness polyester cable section is laid in the middle section, thus balancing load-bearing capacity, compliance, and fatigue resistance. Based on this structural characteristic, this paper proposes an anchor chain modeling method based on rigid-flexible hybrid dynamics theory. This method uses "rigid body motion + flexible motion" as the core modeling framework. By constructing a unified kinematic expression, it synergistically couples the dynamic behavior of the anchor chain at different scales, simulating the dynamic response of the tensioned mooring system at multiple scales and frequencies. The polyester cable, under tension, has high axial elongation and good energy dissipation capacity, effectively mitigating the transmission of wave and platform motion tension to the anchor pile. In the mooring system, it mainly plays a role in buffering, energy absorption, and response regulation. Based on the working characteristics of the polyester cable, it is considered a flexible component, and its damping effect is taken into account in the dynamic analysis.

[0114] This method, within a unified kinematic description framework, simultaneously introduces the rigid and flexible degrees of freedom of the anchor chain element, incorporating overall displacement, rotation, and local axial deformation into a single dynamic system for modeling. In this framework, the rigid degrees of freedom of the anchor chain describe its overall translational and rotational behavior under platform motion and environmental loads, while the flexible degrees of freedom characterize the local continuous deformation of the anchor chain and polyester cable under tension and vibration. By using axial tension as the core mechanical coupling medium between rigid body motion and flexible deformation, changes in rigid body displacement can be directly converted into the strain and internal force response of the flexible component. The tension generated by flexible deformation, in turn, acts inversely on the overall motion of the anchor chain, the platform restoring force, and the stress state of the anchor pile, thus forming a complete two-way coupling mechanism. Based on this coupling relationship, the rigid body inertia effect, the internal force evolution caused by flexible deformation, and the material and fluid damping effects can be solved collaboratively on the same time scale, enabling this method to accurately characterize the true dynamic response features of a tensioned mooring system under the combined action of multi-scale and multi-frequency environmental loads.

[0115] The spatial motion of the anchor chain element at any given time can be decomposed into two parts: Rigid body motion: describes the translation and rotation of the anchor chain unit as a whole moves with the platform and is excited by waves; Flexible deformation: describes the relative displacement of the anchor chain under axial tension, bending and local vibration.

[0116] In dynamic modeling, the principles of rigid-flexible hybrid dynamics (such as the principle of virtual work or Hamilton's principle) are adopted to simultaneously introduce the rigid and flexible degrees of freedom into the generalized coordinate system.

[0117] Axial tension serves as the core bridge in rigid-flexible coupling. In tensioned mooring systems, axial tension is a key physical quantity in this coupling process. Rigid body motion (platform displacement, attitude changes) alters the geometry of the anchor chain / polyester cable, inducing axial tension in the flexible components. This tension is the result of the axial tension generated by the flexible components.

[0118] By introducing rigid and flexible degrees of freedom under a unified kinematic description and using axial tension as the mechanical coupling medium, a two-way coupling between the overall motion and local deformation of the anchor chain is achieved, thus enabling accurate characterization of the real dynamic response of the tensioned mooring system under multi-scale and multi-frequency loads.

[0119] During the service of deep-sea tensioned mooring systems, anchor chains must withstand multi-directional cyclic loads transmitted from floating platforms over extended periods. Their dynamic response is highly complex, exhibiting a coupling of rigid motion and flexible deformation. On a macroscopic scale, the anchor chain undergoes low-frequency translation and oscillation driven by the overall platform motion; this motion can be approximated as a rigid body response, primarily reflecting large-scale inertial effects and the platform's tension transmission mechanism. On a microscopic scale, the anchor chain undergoes bending, axial elongation, and localized undulations under high-frequency wave excitation or environmental disturbances, exhibiting significant flexible characteristics. These two types of responses differ significantly in spatial distribution and frequency range, but they are coupled during temporal evolution, jointly determining the overall mechanical performance and fatigue life of the anchor chain system.

[0120] Assume the anchor chain, under the reference configuration, is composed of arc length Description, initial position vector is If ), then any point at time is t The position can be represented as: (27) (28) Among them, R( t ) is the overall centroid translation vector of the anchor chain, m; A( t ) is the direction cosine matrix of the overall rotation of the anchor chain; r o ( s ) represents the spatial position of a point on the chain under the reference configuration, m; Φ ( s ) is a flexible shape function or mode matrix; It is a flexible generalized coordinate vector, m.

[0121] The total kinetic energy of the anchor chain can be decomposed into two parts: the first is the kinetic energy generated by rigid body motion, mainly reflecting the inertial response of the anchor chain as the platform undergoes large-scale translation and oscillation; the second is the kinetic energy of local flexible deformation, mainly reflecting the energy storage and release of the chain segments during tension wave propagation, high-frequency disturbances, and local curvature changes. It is worth noting that even at low tension levels, the chain links in the meshed state still exhibit a certain degree of bending stiffness, but this stiffness is significantly lower than that of steel pipe structures. Especially when the anchor chain is dragged in water and the platform experiences significant horizontal displacement, the relative motion between the chain links causes changes in local curvature, resulting in a non-negligible bending response in the chain segments.

[146] Therefore, the kinetic energy expression for the rigid domain of the anchor chain can be stated as: (29) It is the total kinetic energy of the rigid domain of the anchor chain. It is the equivalent mass of the anchor chain unit (including structural mass and additional mass). It is the linear velocity vector of the center of mass of the anchor chain unit. It is the angular velocity vector of the anchor chain element. It is the rotational inertia tensor of the anchor chain element relative to the center of mass.

[0122] The potential energy expression for the rigid domain of its anchor chain can be written as: (30) It is the rigid domain potential energy of the anchor chain. These are node coordinates. It is the stiffness coefficient of the anchor chain.

[0123] When the anchor chain segment undergoes bending deformation under the horizontal displacement of the platform or the load of ocean currents, the relative motion between the chain links and the local curvature changes cause the structure to store corresponding elastic strain energy. This process not only reflects the adaptability of the anchor chain to external disturbances within the flexible response domain, but also directly affects the tension wave propagation characteristics and fatigue damage accumulation of the system. In dynamic modeling, the energy corresponding to this bending response can be described by the kinetic energy expression of the flexible domain, and its mathematical form can be written as: (31) For the total kinetic energy of the anchor chain's flexible domain, These are the coordinates of the anchor chain nodes. It is the weight of the anchor chain.

[0124] (32) For flexible domain potential energy, For anchor chain density, This is the cross-section of the anchor chain.

[0125] The potential energy of the flexible domain contains only the axial elongation term: (33) It is the strain energy of the flexible domain. It is the flexibility coefficient of the anchor chain.

[0126] Seawater resistance is expressed in discrete form using the Morison equation: (34) It is hydrodynamic resistance. It is the drag coefficient. It is the equivalent diameter of the anchor chain. The speed of the anchor chain relative to the water.

[0127] Additional quality items: (35) To add mass force, This is the additional mass factor for the anchor chain. Fluid relative acceleration.

[0128] The nonlinear dynamic equations for the rigid-flexible hybrid anchor chain segment are obtained as follows: (36) in, This represents the displacement of the anchor chain; It is the speed of the anchor chain; It is the acceleration of the anchor chain; It is the total mass matrix of the anchor chain (including structural mass and additional mass). It is the total damping matrix of the anchor chain (including structural damping and fluid damping). It is the total stiffness matrix (including geometric stiffness and material stiffness); It is the force exerted on the platform; It is the force on the pile; It is the stress on the polyester cable.

[0129] The following assumptions are made when modeling the dynamic equations of a purely flexible polyester cable segment: ① Polyester cable is considered as a continuous flexible cable, which only bears axial tension and does not bear compression; ② Discretize using the absolute node coordinate method; ③ Hydrodynamic effects include structural damping, hydrodynamic damping, and added mass; ④ Both ends are connected to the anchor chain segment and the anchor pile fixing end, respectively.

[0130] Location of any point in the unit: (37) in, This represents any point position within a polyester cable unit. It is a matrix of shape functions; is the node coordinate vector; S is the local coordinate along the cable.

[0131] The kinetic energy and mass matrix is ​​as follows: ,in, The mass matrix of the polyester cable. It is the kinetic energy of the polyester cable.

[0132] (38)

[0133] in, For the area of ​​the polyester cable, It is the density of the polyester cable.

[0134] The potential energy and stiffness matrix are: (39) in, K f It takes geometric nonlinearity into account.

[0135] The structural damping is: (40) For structural damping, α , β It is the Rayleigh damping coefficient. , These are the mass and stiffness matrices, respectively.

[0136] The hydrodynamic damping is: (41) For hydrodynamic damping, yes ds The damping distribution matrix within the length of . L f Total length, It is the diameter of the polyester cable. It is the hydrodynamic coefficient of the polyester cable.

[0137] The added mass is: (42) It is an added quality of polyester cable. It is the density of the polyester cable. The added mass factor of polyester cable, It is the diameter of the polyester cable.

[0138] The dynamic equation for the polyester cable segment is: (43) It's about the quality of the polyester cable. It is an added quality of polyester cable. These are the coordinates of the polyester cable nodes. It is a polyester cable structure damping, It is a polyester cable hydrodynamic damping, It is the platform that is under pressure. The anchor pile is under stress. The anchor chain is under stress. It is the stiffness matrix.

[0139] The overall governing equations for the anchor chain segment and the polyester cable segment are as follows: (44) in, It is the sum of structural mass and added mass. It is the viscous resistance of seawater. It is an axial force. ) is bending force, Equivalent buoyancy, It is the tension of the platform. It is the soil reaction force of the anchor pile.

[0140] In a multibody system consisting of a floating platform, mooring cable, and anchor pile, the handling of connection relationships is crucial for accurately characterizing the overall dynamic properties. Especially in multibody dynamics modeling, the connection forms between the floating platform and mooring cable, anchor chain and anchor pile, and anchor chain and polyester cable directly determine the load transfer path and the system's deformation response characteristics.

[77] Therefore, theoretical models will be established for the above three types of key connection relationships, and a systematic analysis will be conducted in conjunction with their mechanical characteristics and boundary conditions.

[0141] For the connection types and characteristics of floating platform-mooring cables.

[0142] The connection between a floating platform and its mooring cable is typically located within the platform's hull, and in practice, is achieved through a hinged structure. Its main characteristic is that platform motion is fully transmitted to the mooring cable end without relative slippage; simultaneously, to prevent excessive bending moments from being transmitted to the mooring cable, the connection at the platform end is usually allowed to rotate freely. This connection can be equivalent to a hinge, and the constraints are expressed as follows: The displacement changes are equal: (45) Angle freedom: (46) in, u It is a displacement vector. θ For the angle, the degree of freedom is allowed in rotation.

[0143] For anchor chain-anchor pile connection types and characteristics.

[0144] The anchor chain is secured to the anchor pile's anchor hole via chain links, and its stress state differs. Under tension, the chain links are in close contact with the anchor hole, force transmission is clear, relative slippage does not occur, and only rotation is allowed. Under de-tension, the chain links can slide to some extent within the anchor hole while maintaining free rotation. Tensioned state: A hinged constraint restricts the chain end's displacement degree of freedom but allows rotational freedom, ensuring no loss of force transmission. De-tensioned state: A sliding hinge is used, allowing limited slippage of the chain end along the contact surface direction.

[0145] The tension condition is as follows: The displacement changes are equal: (47) Angle freedom: Free rotation (48) The non-tensioned condition is as follows: Calculation of displacement change: (49) Where Δs allows sliding along the chain axis, θ is the rotation angle, and the degree of freedom allows rotation.

[0146] For anchor chain-polyester cable connection types and characteristics.

[0147] The connection between the anchor chain and the polyester cable is typically located above the mudline, exhibiting characteristics of rigid-flexible coupling: the chain segment has high stiffness, significant self-weight, and strong inertia; the polyester cable, on the other hand, is lightweight, highly elongated, and exhibits non-linear tensile properties. The design goal of the connector is to ensure complete transmission of axial tensile force while avoiding bending moment transmission, and allowing free rotation between the two. It is considered a tension unit type hinge. The mechanical equilibrium is as follows: Tension and bending moment: (50) The degree of freedom condition is: The displacement changes are equal: (51) The three key connection types for floating platforms—mooring cables, anchor chains-anchor piles, and anchor chains-polyester cables—each differ in their engineering characteristics, and their combined effect determines the load transfer path and energy dissipation mechanism within the system. Reasonable connection modeling not only ensures the accurate reflection of local mechanical characteristics but also lays the foundation for reliable prediction of the overall dynamic response.

[0148] In the dynamics study of deep-sea tensioned mooring systems, the floating platform, mooring cable, and anchor pile-soil interaction constitute a highly coupled multibody system. Each subsystem exhibits significant differences across different spatial and temporal scales: the floating platform, as a rigid body, bears the primary global inertial response; the mooring cable evolves coupled between large-scale servo motion and small-scale flexible vibration; and the soil reaction force at the anchor pile end is not only affected by tension-compression nonlinearity but also exhibits significant cyclic weakening and rate dependence. To comprehensively reflect the dynamic characteristics of this system under multiple environmental excitations such as wind, waves, and currents, it is necessary to assemble the dynamic equations of each part within a unified generalized coordinate framework, thereby forming a comprehensive governing equation that can simultaneously describe the platform motion, mooring cable response, and anchor pile-soil interaction.

[0149] The basic idea behind this holistic modeling is to seamlessly integrate the equations of the platform, mooring cable, and anchor pile into a single set of nonlinear second-order equations while preserving the physical mechanisms of each subsystem. This is achieved through end-geometric compatibility conditions and force-work duality. Specifically, the connection between the platform and the mooring cable is achieved through constraints on the position of the cable guide hole, with the tension at the cable end transmitted between them as an action-reaction pair. The soil reaction force at the anchor pile end is applied to the mooring cable end degree of freedom through a local-global coordinate transformation. With this assembly method, only two types of true external loads are retained on the right side of the system: one is the environmental excitations of wind, waves, and currents acting directly on the platform, and the other is the reaction force from the soil at the anchor pile end; all internal interaction forces are self-equilibrating within the system through end force mapping operators.

[0150] After obtaining the explicit mathematical expressions of the above three types of equations, the dynamic equations of the platform, n mooring cables, and n anchor piles can be assembled within a unified generalized coordinate framework. The core of the assembly process is to correctly map the cable forces at the platform ends and the soil reactions at the anchor pile ends to the degrees of freedom of the entire system through end constraints and force-work duality, ensuring the self-consistency of the internal interaction forces in the overall energy balance of the system.

[150] Based on this assembly principle, the following system control equations can be obtained: (52) in, The generalized coordinate vector of the entire system. It is a generalized acceleration vector. It is a generalized velocity vector; The equivalent mass matrix of the entire system includes the rigid body mass and moment of inertia of the floating platform, the distributed mass and fluid-added mass of the mooring cables, and the equivalent mass of the anchor piles. The value of this matrix is ​​equal to the platform's equivalent mass. With each mooring cable Diagonal combination of blocks, and The fluid inertia is an added mass, and its parameters are derived from the hydrodynamic characteristics of the platform and the cable. The equivalent damping matrix of the entire system includes hydrodynamic damping, structural damping, and polyester cable material damping. The equivalent restoring force vector of the entire system includes the platform's hydrostatic restoring force, the internal forces and linear weight corresponding to the axial stiffness and bending stiffness of the mooring cable, and the elastic restoring force of the interaction between the anchor pile and the soil. Let η be the environmental load vector acting on the floating platform. p Here, t represents the elevation of the wave surface, and t represents time. B s This is the mooring cable-anchor pile end force mapping matrix, used to map the soil reaction force at the anchor pile end to a unified generalized coordinate frame; This is the equivalent soil reaction vector at the anchor pile end.

[0151] The system control equations obtained under the above assembly principles essentially describe the overall dynamic balance relationship of the multibody system of floating platform-mooring cable-anchor pile-soil under the action of external environmental loads. Its physical meaning can be understood from the following levels.

[0152] First, from an overall structural perspective, the system's governing equations are dynamic equilibrium equations that synchronously describe the rigid body motion of the platform, the rigid-flexible hybrid motion of the mooring cable, and the interaction between the anchor pile and the soil, all within a unified generalized coordinate space. The terms on the left-hand side of the equations collectively characterize the system's inertial effects, damping dissipation effects, and elastic recovery effects at any given time. The right-hand side, however, uniformly incorporates external forces such as environmental loads, platform external loads, and soil reactions at the anchor pile ends, thus reflecting the system's true dynamic response under transient or steady-state conditions.

[0153] Secondly, from the perspective of mass and inertia terms, the system mass matrix not only includes the rigid body mass and rotational inertia of the platform itself, but also integrates the distributed mass of the mooring cable, its additional mass, and the equivalent mass contribution of the anchor pile. This term characterizes the inertial coupling relationship between platform motion, cable vibration, and anchor pile response, ensuring that any acceleration change in any subsystem will affect other subsystems through inertial transmission. This is a key feature that is difficult to reflect using traditional step-by-step or weakly coupled methods.

[0154] Furthermore, from the physical meaning of the damping and stiffness terms, the system damping matrix comprehensively reflects hydrodynamic damping, structural damping, and the energy dissipation effect of the polyester cable, while the system stiffness matrix simultaneously includes the axial stiffness of the mooring cable, the geometric nonlinear stiffness, and the equivalent foundation stiffness introduced by the interaction between the anchor pile and the soil. This unified expression creates a closed-loop feedback between platform displacement, cable tension changes, and anchor pile end reactions, effectively ensuring the consistency of the force transmission path and energy evolution process.

[0155] Finally, from the perspective of mechanical consistency and energy conservation, the system's governing equations, through the introduction of end constraints and force-work duality, ensure that the cable force applied by the mooring cable at the platform end and the soil reaction force generated at the anchor pile end are strictly self-consistent in the system's energy balance. In other words, any internal interaction force appears in pairs as "internal forces" and does not make a false contribution to the total energy of the system, thus guaranteeing the numerical stability and physical reliability of the multibody coupling solution.

[0156] Based on the same inventive concept, this specification also provides a multi-body coupling calculation device for a deep-sea floating platform mooring system, as described in the following embodiments. The system includes a floating platform, a mooring cable, and anchor piles corresponding to the mooring cable. The mooring cable includes an anchor chain and a polyester cable. The top end of the mooring cable is connected to the floating platform, and the bottom end of the mooring cable is connected to the anchor eye of the corresponding anchor pile. The anchor pile is vertically inserted into the seabed soil. The principle of solving the problem using the multi-body coupling calculation device for a deep-sea floating platform mooring system is similar to that of the multi-body coupling calculation method for a deep-sea floating platform mooring system. Therefore, the implementation of the multi-body coupling calculation device for a deep-sea floating platform mooring system can refer to the implementation of the multi-body coupling calculation method for a deep-sea floating platform mooring system, and repeated details will not be elaborated further. As used below, the terms "unit" or "module" can refer to a combination of software and / or hardware that performs a predetermined function. Although the device described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated. Figure 4 This is a structural block diagram of a multi-body coupling computing device for a deep-sea floating platform mooring system, as described in an embodiment of this specification. Figure 4 As shown, it includes: model building module 401, connection interface setting module 402, model assembly module 403 and solution module 404. The structure is described below.

[0157] Model building module 401 is used to build a six-degree-of-freedom rigid body dynamic response model for a floating platform; to build a dynamic model of a mooring cable rigid-flexible hybrid motion model in which the rigid body motion and flexible deformation of the anchor chain are coupled; and to build an anchor pile-soil interaction model that considers soil arching effect and soil nonlinearity.

[0158] The connection interface setting module 402 is used to set geometric constraints and force transmission rules that match the actual stress characteristics of deep-sea engineering based on the end geometric compatibility conditions and force-work duality relationship for the connection interface between the floating platform and the top of the mooring cable, the connection interface between the anchor chain inside the mooring cable and the polyester cable section, and the connection interface between the end of the mooring cable and the anchor hole of the anchor pile.

[0159] The model assembly module 403 is used to assemble the six-degree-of-freedom rigid body dynamic response model of the floating platform, the rigid-flexible hybrid dynamic model of the mooring cable, and the anchor pile-soil interaction model under a unified generalized coordinate framework covering the entire system's degrees of freedom, based on the geometric constraints and force transmission rules, to form the overall control equations of the multi-body coupling of the entire system.

[0160] The solver module 404 is used to perform time-domain synchronous coupling solution of the overall control equation of the multi-body coupling of the whole system. During the solution process, the soil reaction force at the anchor pile end and the dynamic parameters of the rigid-flexible coupling of the mooring cable are updated in real time, realizing the bidirectional real-time coupling of force and displacement between the floating platform, the mooring cable, and the anchor pile-soil, so as to obtain the real-time dynamic response of the whole system.

[0161] In some embodiments of this specification, the model building module is specifically used for: calculating the longitudinal ultimate bearing capacity of the anchor pile under two working conditions—without a soil plug and with an elastic soil plug—based on the pile-soil interaction theory and the soil arching effect. The longitudinal ultimate bearing capacity includes the ultimate bearing capacity of the outer side of the mooring anchor pile, the ultimate bearing capacity of the end of the mooring anchor pile, and the soil plug resistance inside the pile; simplifying the anchor pile into a uniform cross-section elastic straight beam that satisfies the Euler-Bernoulli beam assumption, and combining the soil reaction force that obeys the Winkler foundation assumption, establishing the differential equation for the transverse deflection control of the anchor pile, and calculating the transverse bearing capacity of the anchor pile; and based on the longitudinal ultimate bearing capacity and the transverse bearing capacity, constructing a nonlinear constitutive relationship of the soil that is dynamically updated with the real-time displacement and cyclic loading history of the anchor pile, thereby obtaining the dynamic control equation of the anchor pile-soil interaction model.

[0162] In some embodiments of this specification, the model building module is specifically used to: decompose the spatial motion of the anchor chain of the mooring cable into rigid body motion characterizing overall translation and rotation, and flexible deformation characterizing axial tension and bending deformation; establish a two-way coupling relationship between the rigid body motion and flexible deformation of the anchor chain using real-time axial tension as the coupling medium, and construct the nonlinear dynamic control equation of the anchor chain; regard the polyester cable of the mooring cable as a continuous flexible cable that only bears axial tension, discretize it using the absolute nodal coordinate method, and consider geometric nonlinearity and hydrodynamic effects to establish the nonlinear dynamic control equation of the polyester cable; and integrate the nonlinear dynamic control equation of the anchor chain and the nonlinear dynamic control equation of the polyester cable based on the inter-segment connection constraints of the anchor chain and the polyester cable to obtain the rigid-flexible hybrid dynamic model of the mooring cable.

[0163] In some embodiments of this specification, the model building module is specifically used for: treating the floating platform as an ideal rigid body, describing the motion state of the floating platform using a global inertial coordinate system, and using the three-dimensional translational displacement of the platform's center of mass and the three attitude angles of roll, pitch, and yaw as six-degree-of-freedom generalized coordinates; calculating the total potential energy of the platform, which includes the platform's gravitational potential energy and the mooring system's restoring potential energy, which is calculated based on the length of the anchor chain and polyester cable and the initial tension, to reflect the restoring capability of the mooring cable when the floating platform deviates; calculating the platform's mass-inertia matrix and the system's restoring generalized force based on the total potential energy of the platform; calculating the total tension of the mooring cable and the environmental loads acting on the platform, which include at least one of the following: wind load, ocean current load, and wave excitation load; and establishing the six-degree-of-freedom rigid body dynamics control equations of the floating platform by combining the floating platform's mass, hydrodynamic added mass, radiation damping, viscous drag, the system's restoring generalized force, the total tension of the mooring cable, and the environmental loads.

[0164] In some embodiments of this specification, the connection interface setting module is specifically used to: treat the connection interface between the floating platform and the top of the mooring cable as an equivalent hinge constraint, with the corresponding geometric constraint being that the three-dimensional translational displacements of the top of the mooring cable and the connection point of the floating platform's guide wire are completely synchronized and angularly free; and the corresponding force transmission rule being that the platform motion is completely transmitted to the mooring cable with no bending moment transmission; and treat the inter-segment connection interface between the anchor chain inside the mooring cable and the polyester cable as an equivalent tension-type hinge constraint, with the corresponding geometric constraint being that the three-dimensional translational displacements of the connection point of the anchor chain and the polyester cable are completely synchronized and angularly free; and the corresponding force transmission rule being that the platform motion is completely transmitted to the mooring cable with no bending moment transmission. The force transmission rule is that axial tensile force is transmitted without loss and bending moment is transmitted. For the connection interface between the end of the mooring cable and the anchor hole of the anchor pile, the constraint is adaptively switched between tensioned and untensioned conditions. Under tensioned conditions, it is equivalent to a hinge constraint, and the corresponding geometric constraint is that the three-dimensional translational displacement of the connection point is completely synchronized and the angle is free. The corresponding force transmission rule is that the tension of the mooring cable is completely transmitted to the anchor pile. Under untensioned conditions, it is equivalent to a sliding hinge constraint, and the corresponding geometric constraint is that limited sliding along the chain axis is allowed and the angle is free. The corresponding force transmission rule is that only the force perpendicular to the chain axis is transmitted and there is no bending moment transmission.

[0165] In some embodiments of this specification, the overall control equations for the multibody coupling of the entire system include:

[0166] in, X The generalized coordinate vector of the entire system. It is a generalized acceleration vector. It is a generalized velocity vector; The equivalent mass matrix of the entire system includes the rigid body mass and moment of inertia of the floating platform, the distributed mass and fluid-added mass of the mooring cables, and the equivalent mass of the anchor piles. The equivalent damping matrix of the entire system includes hydrodynamic damping, structural damping, and polyester cable material damping. The equivalent restoring force vector of the entire system includes the platform's hydrostatic restoring force, the internal forces and linear weight corresponding to the axial stiffness and bending stiffness of the mooring cable, and the elastic restoring force of the interaction between the anchor pile and the soil. Let η be the environmental load vector acting on the floating platform. p Here, t represents the elevation of the wave surface, and t represents time. B s This is the mooring cable-anchor pile end force mapping matrix, used to map the soil reaction force at the anchor pile end to a unified generalized coordinate frame; This is the equivalent soil reaction vector at the anchor pile end.

[0167] In some embodiments of this specification, the solution module is also used to: based on the overall control equations of the multi-body coupling of the whole system, directly solve the dynamic behavior of the third subsystem by using the known dynamic responses of any two subsystems in the system; specifically including: back-calculating the tension distribution and dynamic deformation of the mooring cable by using the motion response of the floating platform and the mechanical properties of the anchor pile and soil, and / or predicting the evolution process of the anchor pile displacement and soil reaction force by using the measured tension of the mooring cable and the motion data of the floating platform.

[0168] In some embodiments of this specification, the real-time dynamic response includes at least one of the following: the six-degree-of-freedom full-time-domain motion response of a floating platform, the tension distribution and dynamic deformation and fatigue damage of the entire mooring cable, and the longitudinal and lateral displacement of anchor piles and the reaction force and bearing capacity utilization rate of the surrounding soil.

[0169] This specification also provides a computer device, which can be found in the following description. Figure 5 The diagram shown illustrates the computer device structure for the multi-body coupling calculation method for a deep-sea floating platform mooring system provided in the embodiments of this specification. Specifically, the computer device may include an input device 51, a processor 52, and a memory 53. The memory 53 stores processor-executable instructions. When the processor 52 executes the instructions, it implements the steps of the multi-body coupling calculation method for a deep-sea floating platform mooring system described in any of the above embodiments.

[0170] In this embodiment, the input device can specifically be one of the main devices for information exchange between the user and the computer system. The input device may include a keyboard, mouse, camera, scanner, light pen, handwriting input tablet, voice input device, etc.; the input device is used to input raw data and programs for processing these data into the computer. The input device can also receive data transmitted from other modules, units, and devices. The processor can be implemented in any suitable manner. For example, the processor can take the form of a microprocessor or processor and a computer-readable medium storing computer-readable program code (e.g., software or firmware) executable by the (micro)processor, logic gates, switches, application-specific integrated circuits (ASICs), programmable logic controllers, and embedded microcontrollers, etc. The memory can specifically be a memory device used to store information in modern information technology. The memory can include multiple layers; in digital systems, anything that can store binary data can be considered memory; in integrated circuits, a circuit without physical form but with storage function is also called memory, such as RAM, FIFO, etc.; in a system, a storage device with physical form is also called memory, such as a memory stick, TF card, etc.

[0171] In this embodiment, the specific functions and effects implemented by the computer device can be explained in comparison with other embodiments, and will not be repeated here.

[0172] This specification also provides a computer storage medium based on a multi-body coupling calculation method for a deep-sea floating platform mooring system. The computer storage medium stores computer program instructions, which, when executed by a processor, implement the steps of the multi-body coupling calculation method for a deep-sea floating platform mooring system described in any of the above embodiments.

[0173] In this embodiment, the storage medium includes, but is not limited to, random access memory (RAM), read-only memory (ROM), cache, hard disk drive (HDD), or memory card. The memory can be used to store computer program instructions. The network communication unit can be an interface configured according to standards specified in the communication protocol for network connection communication.

[0174] In this embodiment, the specific functions and effects implemented by the program instructions stored in the computer storage medium can be explained by comparison with other embodiments, and will not be repeated here.

[0175] This specification also provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of the multi-body coupling calculation method for deep-sea floating platform mooring systems described in any of the above embodiments.

[0176] Obviously, those skilled in the art will understand that the modules or steps of the embodiments described above can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Optionally, they can be implemented using computer-executable program code, thereby storing them in a storage device for execution by a computing device. In some cases, the steps shown or described can be performed in a different order than those presented herein, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the embodiments of this specification are not limited to any particular combination of hardware and software.

[0177] It should be understood that the above description is for illustrative purposes and not for limitation. Many embodiments and applications beyond the provided examples will be apparent to those skilled in the art upon reading the above description. Therefore, the scope of this specification should not be determined by reference to the above description, but rather by reference to the foregoing claims and the full scope of their equivalents.

[0178] The above description is merely a preferred embodiment of this specification and is not intended to limit this specification. Various modifications and variations can be made to the embodiments described herein by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this specification should be included within the scope of protection of this specification.

Claims

1. A multi-body coupling calculation method for a deep-sea floating platform mooring system, characterized in that, The system includes a floating platform, mooring cables, and corresponding anchor piles. The mooring cables include anchor chains and polyester cables. The top end of the mooring cables is connected to the floating platform, and the bottom end is connected to the anchor hole of the corresponding anchor pile. The anchor piles are vertically driven into the seabed soil. The method includes: A six-degree-of-freedom rigid body dynamic response model for a floating platform is established; a dynamic model of the mooring cable rigid-flexible hybrid motion coupled with the anchor chain rigid body motion and anchor chain flexible deformation is established; and an anchor pile-soil interaction model considering soil arching effect and soil nonlinearity is established. Based on the end geometric compatibility conditions and force-work duality, geometric constraints and force transmission rules matching the actual stress characteristics of deep-sea engineering are set for the connection interface between the floating platform and the top of the mooring cable, the connection interface between the anchor chain inside the mooring cable and the polyester cable section, and the connection interface between the end of the mooring cable and the anchor hole of the anchor pile. Under the unified generalized coordinate framework covering all system degrees of freedom, based on the geometric constraints and force transmission rules, the six-degree-of-freedom rigid body dynamic response model of the floating platform, the rigid-flexible hybrid dynamic model of the mooring cable, and the anchor pile-soil interaction model are assembled to form the multi-body coupled overall control equation of the whole system. The overall control equations of the multi-body coupling of the entire system are solved synchronously in the time domain. During the solution process, the soil reaction force at the anchor pile end and the dynamic parameters of the rigid-flexible coupling of the mooring cable are updated in real time. This achieves bidirectional real-time coupling of force and displacement between the floating platform, the mooring cable, and the anchor pile-soil, and obtains the real-time dynamic response of the entire system.

2. The multi-body coupling calculation method for deep-sea floating platform mooring systems according to claim 1, characterized in that, Establish an anchor pile-soil interaction model that considers soil arching effect and soil nonlinearity, including: Based on the pile-soil interaction theory and soil arching effect, the longitudinal ultimate bearing capacity of the anchor pile is calculated under two working conditions: no soil plug and elastic soil plug. The longitudinal ultimate bearing capacity includes the ultimate bearing capacity of the outer side of the mooring anchor pile, the ultimate bearing capacity of the end of the mooring anchor pile, and the soil plug resistance inside the pile. The anchor pile is simplified as an elastic straight beam with uniform cross-section that satisfies the Euler-Bernoulli beam assumption. Combined with the soil reaction force that obeys the Winkler foundation assumption, the differential equation governing the transverse deflection of the anchor pile is established, and the transverse bearing capacity of the anchor pile is calculated. Based on the longitudinal ultimate bearing capacity and the transverse bearing capacity, a nonlinear constitutive relationship of the soil is constructed that is dynamically updated with the real-time displacement of the anchor pile and the cyclic loading process, and the dynamic control equations of the anchor pile-soil interaction model are obtained.

3. The multi-body coupling calculation method for deep-sea floating platform mooring systems according to claim 1, characterized in that, A dynamic model of the mooring cable's rigid-flexible hybrid motion, which couples the rigid body motion and flexible deformation of the anchor chain, is established, including: The spatial motion of the anchor chain of the mooring cable is decomposed into rigid body motion characterizing overall translation and rotation, and flexible deformation characterizing axial tension and bending deformation. Using real-time axial tension as the coupling medium, a two-way coupling relationship between the rigid body motion and flexible deformation of the anchor chain is established, and the nonlinear dynamic control equation of the anchor chain is constructed. The polyester cable of the mooring cable is regarded as a continuous flexible cable that only bears axial tension. The absolute nodal coordinate method is used for discretization. Considering geometric nonlinearity and hydrodynamic effects, the nonlinear dynamic control equation of the polyester cable is established. Based on the inter-segment connection constraints between the anchor chain and the polyester cable, the nonlinear dynamic control equations of the anchor chain and the polyester cable are integrated to obtain a rigid-flexible hybrid dynamic model of the mooring cable.

4. The multi-body coupling calculation method for deep-sea floating platform mooring systems according to claim 1, characterized in that, Establish the six-degree-of-freedom rigid body dynamic response model of the floating platform, including: The floating platform is regarded as an ideal rigid body, and the motion state of the floating platform is described by a global inertial coordinate system. The three-dimensional translational displacement of the platform's center of mass and the three attitude angles of roll, pitch, and yaw are used as the six-degree-of-freedom generalized coordinates. The total potential energy of the platform is calculated, which includes the platform's gravitational potential energy and the mooring system's restoring potential energy. The mooring system's restoring potential energy is calculated based on the length of the anchor chain and polyester cable and the initial tension, and is used to reflect the restoring capability of the mooring cable when the floating platform deviates. Based on the total potential energy of the platform, the platform's mass-inertia matrix and the system's restoring generalized force are calculated. Calculate the total tension of the mooring cables and the environmental loads acting on the platform, wherein the environmental loads include at least one of the following: wind load, ocean current load, and wave excitation load; By combining the floating platform mass, hydrodynamic added mass, radiation damping, viscous drag, the system restoring generalized force, the total tension of the mooring cable, and the environmental load, a six-degree-of-freedom rigid body dynamics control equation for the floating platform is established.

5. The multi-body coupling calculation method for deep-sea floating platform mooring systems according to claim 1, characterized in that, Based on end-geometric compatibility conditions and force-work duality, geometric constraints and force transmission rules matching the actual stress characteristics of deep-sea engineering are set for the connection interfaces between the floating platform and the top of the mooring cable, the connection interfaces between the inner anchor chain of the mooring cable and the polyester cable section, and the connection interfaces between the end of the mooring cable and the anchor pile eye, including: The connection interface between the floating platform and the top of the mooring cable is equivalent to a hinge constraint. The corresponding geometric constraint is that the three-dimensional translational displacements of the connection point between the top of the mooring cable and the guide wire of the floating platform are completely synchronized and the angles are free. The corresponding force transmission rule is that the platform motion is completely transmitted to the mooring cable and there is no bending moment transmission. The connection interface between the anchor chain and the polyester cable in the mooring cable is equivalent to a tension-type hinge constraint. The corresponding geometric constraint is that the three-dimensional translational displacement of the connection point between the anchor chain and the polyester cable is completely synchronized and the angle is free. The corresponding force transmission rule is that the axial tensile force is transmitted without loss and there is no bending moment transmission. For the connection interface between the mooring cable end and the anchor pile eye, adaptive switching constraints are applied under tensioned and untensioned conditions. Under tensioned conditions, it is equivalent to a hinge constraint, with the corresponding geometric constraint that the three-dimensional translational displacement of the connection point is completely synchronized and angularly free, and the corresponding force transmission rule that the tension of the mooring cable is completely transmitted to the anchor pile. Under untensioned conditions, it is equivalent to a sliding hinge constraint, with the corresponding geometric constraint that allows limited sliding along the chain axis and angularly free, and the corresponding force transmission rule that only the force perpendicular to the chain axis is transmitted and no bending moment is transmitted.

6. The multi-body coupling calculation method for deep-sea floating platform mooring systems according to claim 1, characterized in that, The overall control equations for the multi-body coupling of the entire system include: in, X The generalized coordinate vector of the entire system. It is a generalized acceleration vector. It is a generalized velocity vector; The equivalent mass matrix of the entire system includes the rigid body mass and moment of inertia of the floating platform, the distributed mass and fluid-added mass of the mooring cables, and the equivalent mass of the anchor piles. The equivalent damping matrix of the entire system includes hydrodynamic damping, structural damping, and polyester cable material damping. The equivalent restoring force vector of the entire system includes the platform's hydrostatic restoring force, the internal forces and linear weight corresponding to the axial stiffness and bending stiffness of the mooring cable, and the elastic restoring force of the interaction between the anchor pile and the soil. Let η be the environmental load vector acting on the floating platform. p Here, t represents the elevation of the wave surface, and t represents time. B s This is the mooring cable-anchor pile end force mapping matrix, used to map the soil reaction force at the anchor pile end to a unified generalized coordinate frame; This is the equivalent soil reaction vector at the anchor pile end.

7. The multi-body coupling calculation method for deep-sea floating platform mooring systems according to claim 1, characterized in that, Also includes: Based on the overall control equations of the multi-body coupling of the entire system, the dynamic behavior of the third subsystem can be directly solved by using the known dynamic responses of any two subsystems in the system. Specifically, this includes: calculating the tension distribution and dynamic deformation of the mooring cable by back-calculating the motion response of the floating platform and the mechanical properties of the anchor pile and soil, and / or predicting the evolution process of the anchor pile displacement and soil reaction force by using the measured tension of the mooring cable and the motion data of the floating platform.

8. The multi-body coupling calculation method for deep-sea floating platform mooring systems according to claim 1, characterized in that, The real-time dynamic response includes at least one of the following: the six-degree-of-freedom full-time-domain motion response of the floating platform, the tension distribution and dynamic deformation and fatigue damage of the entire mooring cable, the longitudinal and lateral displacement of the anchor pile and the reaction force and bearing capacity utilization rate of the surrounding soil.

9. A multi-body coupling computing device for a deep-sea floating platform mooring system, characterized in that, The system includes a floating platform, mooring cables, and corresponding anchor piles. The mooring cables include anchor chains and polyester cables. The top end of the mooring cables is connected to the floating platform, and the bottom end is connected to the anchor hole of the corresponding anchor pile. The anchor piles are vertically driven into the seabed soil. The device includes: The model building module is used to: build a six-degree-of-freedom rigid body dynamic response model for a floating platform; build a dynamic model of a mooring cable rigid-flexible hybrid motion model that couples the rigid body motion and flexible deformation of the anchor chain; and build an anchor pile-soil interaction model that considers the soil arching effect and soil nonlinearity. The connection interface setting module is used to set geometric constraints and force transmission rules that match the actual stress characteristics of deep-sea engineering, based on the end geometric compatibility conditions and force-work duality relationship, for the connection interface between the floating platform and the top of the mooring cable, the connection interface between the anchor chain inside the mooring cable and the polyester cable section, and the connection interface between the end of the mooring cable and the anchor pile and anchor eye. The model assembly module is used to assemble the six-degree-of-freedom rigid body dynamic response model of the floating platform, the rigid-flexible hybrid dynamic model of the mooring cable, and the anchor pile-soil interaction model under a unified generalized coordinate framework covering the entire system's degrees of freedom, based on the geometric constraints and force transmission rules, to form the overall control equations of the multi-body coupling of the entire system. The solution module is used to perform time-domain synchronous coupling solution of the overall control equation of the multi-body coupling of the entire system. During the solution process, the soil reaction force at the anchor pile end and the dynamic parameters of the rigid-flexible coupling of the mooring cable are updated in real time, realizing the bidirectional real-time coupling of force and displacement between the floating platform, mooring cable, anchor pile and soil, and obtaining the real-time dynamic response of the entire system.

10. A computer-readable storage medium storing computer instructions thereon, characterized in that, When the instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 8.

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