Modelica-based FPSO complex equipment multi-field coupling modeling method

Abstract

The invention relates to the field of ocean equipment digital design, and particularly discloses a Modelica-based FPSO complex equipment multi-field coupling modeling method, which comprises the following steps: carrying out top-down hierarchical decomposition on a riser support system, and designing a unified model library architecture and interface specifications; a modular model component library of a control system, a hydraulic system and a mechanical system is developed based on Modelica; designing a mechanical-hydraulic energy coupling interface, a control-hydraulic signal coupling interface and a control-mechanical feedback coupling interface, integrating multi-field equations into a unified differential algebraic system by using Modelica non-causal modeling characteristics, and processing multiple time scales and discrete events; and integrating model components of all fields to construct a system digital prototype, and carrying out full-coupling simulation verification of typical working conditions. According to the method, unified description and seamless coupling of the FPSO complex equipment multi-field model are realized, the design collaboration and the model reusability are improved, and the design verification cost is greatly reduced.

Description

Technical Field

[0001] This invention relates to the field of digital design technology for marine equipment, and in particular to a multi-domain coupled modeling method for complex FPSO equipment based on Modelica. Background Technology

[0002] FPSO (Floating Production Storage and Offloading) is an offshore floating unit that integrates oil and gas production, storage, and offloading functions. As a core piece of equipment for deep-sea oil and gas development, it is widely used in oil and gas field development in major sea areas worldwide. An FPSO typically consists of a hull, topside modules, mooring systems, and riser systems. The riser system connects the subsea wellhead to the FPSO deck facilities to facilitate oil and gas transportation. As a crucial piece of equipment in the field of marine engineering, the safety and reliability of FPSOs directly affect the continuity of offshore oil and gas production and the safety of personnel and equipment.

[0003] Among the many critical systems of an FPSO, the riser locking system is a typical complex system spanning multiple domains, undertaking key functions such as supporting the riser's weight, absorbing wave loads, and maintaining riser stability. This system is highly integrated with multiple subsystems, including mechanical structure, hydraulic drive, and electrical control, involving multiple disciplines such as mechanical dynamics, fluid mechanics, and control theory. Complex energy, information, and material flows interact between these subsystems. For example, deformation of the mechanical structure affects the pressure distribution of the hydraulic system, while commands from the control system alter the hydraulic system's operating state, thus influencing the forces and displacements of the entire mechanical structure. This multi-physics coupling and multi-timescale characteristic presents significant challenges to the design and verification of the riser support system.

[0004] Traditional locking system designs primarily rely on simplified models or physical prototype testing within a single domain, which presents the following problems: Domain fragmentation: Different professional fields such as mechanical, hydraulic, and control use their own independent tools and methods for modeling, making it difficult to achieve system-level coupled analysis, which makes it difficult to detect design defects in the early stages; Poor model reusability: Existing modeling methods lack a unified architectural design, making it difficult to reuse model components across different projects, requiring a lot of repetitive work for each new design; High verification costs: Over-reliance on physical prototype testing is not only time-consuming and costly, but also makes it difficult to cover various extreme working conditions and poses safety hazards; Multi-physics coupling effects are difficult to describe accurately: The riser locking system involves coupling of multiple fields such as mechanical dynamics, fluid mechanics, and control theory, and traditional methods are difficult to accurately capture the interaction between these fields. Low design iteration efficiency: The lack of digital model support makes the design modification and verification process cumbersome and makes it difficult to respond quickly to changes in design requirements.

[0005] These problems severely restrict the design quality and development efficiency of complex FPSO equipment. At their root, traditional methods fundamentally lack a unified, multi-domain physical modeling language and system architecture that supports non-causal modeling, making it difficult to achieve true multi-domain collaboration, model reuse, and efficient verification. Therefore, there is an urgent need for a digital modeling method that can be based on such a unified architecture, achieve multi-domain collaboration, support model reuse, and reduce verification costs, in order to systematically solve the aforementioned engineering challenges. Summary of the Invention

[0006] The purpose of this invention is to address the problems of fragmented multi-domain models, poor model reusability, high verification costs, and difficulty in accurately describing multi-physics coupling effects in existing technologies. To address these issues, a multi-domain coupling modeling method for complex FPSO equipment based on Modelica is proposed. This method leverages the non-causal, object-oriented, and unified multi-domain modeling characteristics of the Modelica language, combined with the powerful simulation integration capabilities of the MWORDS platform, to construct a reusable and scalable unified multi-domain model library for complex marine engineering equipment. This enables digital design, integration, and verification from the component level to the system level, ultimately achieving digital design and verification of complex marine engineering systems throughout their entire lifecycle.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A multi-domain coupled modeling method for complex FPSO equipment based on Modelica, comprising: S1. System Decomposition and Architecture Design: Decompose the riser support system into control, hydraulic and mechanical subsystems and define standardized interface specifications for each model component; S2. Multi-domain component development: Based on the standardized interface specifications, develop corresponding control system model components, hydraulic system model components, and mechanical system model components using the Modelica language; S3. Coupling Mechanism Implementation: Based on the model components, design mechanical-hydraulic, control-hydraulic and control-mechanical coupling interfaces, integrate the equations of each component into a unified system of differential-algebraic equations, and handle multi-timescale problems; S4. System Integration and Verification: Integrate the model components through coupling interfaces to build a digital prototype of the system, and perform fully coupled simulation to verify the system performance.

[0008] As a further technical solution of the present invention, S1 specifically includes: For the FPSO riser support system, a top-down approach is adopted for hierarchical decomposition, which decomposes the system into three main subsystems: control system, hydraulic system and mechanical system. Each subsystem is further decomposed into functional modules. Based on the MWORKS platform, a unified hierarchical model library architecture is designed, and standardized interfaces and parameter specifications for each model component are defined.

[0009] As a further technical solution of the present invention, the unified hierarchical model library architecture has a top layer of riser support system assembly model, a middle layer of three subsystem models of control system, hydraulic system and mechanical system, and a bottom layer of basic model components corresponding to each functional module. All components follow a unified physical port and signal port interface specification.

[0010] As a further technical solution of the present invention, in S2, the control system model component includes at least a hydraulic controller model and a PID controller model; The hydraulic controller model is implemented using a tracking differentiator algorithm. Its discrete form is used to quickly track the input signal and extract the differential signal. The tracking speed is controlled by setting a speed factor to suppress the noise amplification effect.

[0011] As a further technical solution of the present invention, in S2, the hydraulic system model component includes at least a TSUDL system model component for top support and lateral pushing, and a BSDL system model component for bottom support; The TSUDL system model components include a top cone circuit and a transverse push circuit. The top cone circuit model is described by the pressure regulating equation of the pressure reducing valve, the flow equation of the control valve, the force balance equation of the hydraulic cylinder, and the flow continuity equation, and is used to simulate the driving and control of the rotating ring. The transverse push circuit model is described by the piston dynamics equation including contact force, hydraulic pressure, inertial force, and damping force, and is used to simulate the top jamming, retraction unlocking, and throttling buffering processes.

[0012] The BSDL system model component is described by a set of equations including valve orifice flow equation, cylinder force balance equation, and flow continuity equation, and is used to simulate the dynamic actuation process of the bottom support cylinder.

[0013] As a further technical solution of the present invention, in S2, the mechanical system model components include at least a frame model, a rotating ring model, a wedge model, a locking mechanism model, a transverse piston model, and an actuation mechanism model; The mechanical system model components are all constructed based on multibody dynamics theory. Among them, the rotating ring model is based on the dynamic equation of a rigid body rotating about a fixed axis; the wedge model is based on the dynamic equation of a constrained rigid body linear motion; the locking mechanism model is based on the Newton-Euler equations including a nonlinear contact force model; and the transverse piston model and the actuation mechanism model are based on the piston dynamics equations.

[0014] As a further technical solution of the present invention, S3 specifically includes: Based on the model components developed in step S2, a cross-domain coupling interface is designed and implemented, including: establishing an energy coupling interface between the mechanical system and the hydraulic system through the mapping relationship between the hydraulic cylinder piston displacement and hydraulic pressure and flow rate; establishing a signal coupling interface between the control system and the hydraulic system through the relationship between the control signal and the hydraulic valve opening; and establishing a feedback coupling interface between the control system and the mechanical system through sensor feedback signals. By leveraging the non-causal modeling characteristics of Modelica, physical equations from various fields are integrated into a unified system of differential-algebraic equations. Symbolic processing, BLT transformation, and adaptive variable step size solution strategies are employed to handle multi-timescale problems and discrete events.

[0015] As a further technical solution of the present invention, the integration of physical equations from various fields into a unified system of differential-algebraic equations specifically includes: The force balance equations and kinematic equations of mechanical systems, the fluid dynamics equations and flow continuity equations of hydraulic systems, and the control algorithm equations of control systems are uniformly expressed in a non-causal form as Modelica equations, and the compiler automatically generates a set of differential algebraic equations for the overall system.

[0016] As a further technical solution of the present invention, the adaptive variable step size solution strategy is specifically as follows: Based on the different dynamic response time scales of the control system, hydraulic system, and mechanical system, the integral step size is dynamically adjusted during the simulation solution process, and an event detection mechanism is introduced for discrete events such as hydraulic valve switching and mechanical contact collision.

[0017] As a further technical solution of the present invention, S4 specifically includes: The model components developed in step S2 are integrated into the whole system through the coupling interface implemented in step S3. The control system model, hydraulic system model, and mechanical system model are connected through standardized energy flow and information flow interfaces to form a closed-loop simulation system containing complete physical effects and logical control, thereby constructing a digital prototype of the FPSO riser support system. In a unified simulation environment, a fully coupled dynamic simulation is performed on typical working conditions of riser locking and releasing to obtain and analyze the system's action sequence, displacement, velocity, pressure, and flow performance indicators, thereby completing the functional and performance verification of the system design scheme.

[0018] The beneficial effects of this invention are as follows: 1. Enhanced multi-domain collaborative design capabilities: Through the unified Modelica modeling language and the MWORKS.Sysplorer platform, seamless coupling of multiple domains such as mechanical, hydraulic, and control is achieved, which can accurately describe the interaction between various physical domains in the FPSO riser support system, thereby improving the integrity and collaboration of the system design.

[0019] 2. Enhanced Model Reusability and Extensibility: The hierarchical model architecture and standardized interface design proposed in this invention enable model components to have good reusability and extensibility, significantly reducing development costs.

[0020] 3. Significantly reduced design verification costs: High-precision digital prototypes can identify and resolve potential problems in serial design early in the design process, reducing the number of physical prototype tests and lowering costs by more than 30%. At the same time, they can cover more extreme operating conditions and improve system safety. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the hydraulic controller model in Example 1; Figure 2 This is a schematic diagram of the PID controller model in Example 1; Figure 3 This is a topological diagram of the internal structure of the TSUDL model in Example 1; Figure 4 This is a topological diagram of the internal structure of the BSDL system model in Example 1; Figure 5 This is a diagram of the internal topology of the rotating ring model in Example 1; Figure 6 This is a diagram of the internal topology of the wedge block model in Example 1; Figure 7 This is a diagram showing the internal topology of the locking mechanism model in Example 1; Figure 8 This is a diagram of the internal topology of the transverse piston model in Example 1; Figure 9 This is a diagram showing the internal topology of the actuation mechanism model in Example 1; Figure 10 This is a graph showing the piston speed of the TopCone hydraulic cylinder in the virtual simulation performance indicators of Example 2; Figure 11This is a graph showing the piston displacement curve of the TopCone hydraulic cylinder in the virtual simulation performance indicators of Example 2; Figure 12 This is a graph showing the piston speed of the transverse thrust cylinder in the virtual simulation performance indicators of Example 2; Figure 13 This is a graph showing the piston displacement curve of the transverse thrust cylinder in the virtual simulation performance indicators of Example 2; Figure 14 This is a graph showing the pressure curves of the two chambers of the top cone hydraulic cylinder in the virtual simulation performance indicators of Example 2; Figure 15 This is the displacement curve of the top cone hydraulic cylinder in the virtual simulation performance indicators of Example 2. Detailed Implementation

[0022] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below in conjunction with specific embodiments.

[0023] Example 1 Please see the appendix Figure 1 - Appendix Figure 15 This paper presents a multi-domain coupled modeling method for complex FPSO equipment based on Modelica. It is primarily applied to the digital design, simulation, and verification of complex marine engineering equipment, such as FPSO riser locking systems, which involve coupling across mechanical, hydraulic, and control domains. The core of this method lies in leveraging the non-causal, object-oriented, and multi-domain unified modeling characteristics of the Modelica language, combined with the MWORKS.Sysplorer simulation platform, to construct a reusable and scalable unified model library. A standardized coupling mechanism is then used to achieve full-system simulation. The method mainly includes four aspects: model library architecture design for locking devices, development of multi-domain components, implementation of the coupling mechanism, and simulation verification. The specific implementation steps are as follows: S1. System Decomposition and Model Library Architecture Design S11. For the specific object of the FPSO riser support system, a top-down analysis method is used for hierarchical decomposition. At the top level, the entire system is identified as three interrelated core subsystems: the control system responsible for logical operations and instruction generation, the hydraulic system responsible for providing power and executing actions, and the mechanical system responsible for load bearing and transmission.

[0024] S12. Further decompose each subsystem into functional modules. For example, the control system can be decomposed into modules such as hydraulic controller and PID controller; the hydraulic system can be decomposed into modules such as TSUDL (top locking device) system, BSDL (bottom locking device) system, top cone circuit, and horizontal push circuit; the mechanical system can be decomposed into modules such as frame, rotating ring, wedge, locking mechanism, horizontal push piston, and actuation mechanism.

[0025] S13. Based on the MWORKS platform, design a hierarchical model library architecture. This architecture clarifies the organizational relationship from the top-level system assembly to the bottom-level basic components. More importantly, it defines the unified interface specifications (including physical connection ports such as mechanical flanges and hydraulic ports, as well as signal ports such as control commands and sensor feedback) and parameter standards (such as mass, moment of inertia, damping coefficient, PID parameters, etc.) that all model components must follow.

[0026] The output of this step is a complete and standardized model library architecture blueprint and interface definition, which lays the foundation for compatibility and composability for subsequent component development.

[0027] S2. Development of Multi-Domain Component Model Library Based on the architecture blueprint and interface specifications output in step S1, model component libraries for the three major domains are developed using the non-causal equation modeling capabilities of the Modelica language.

[0028] S21. Control System Model Component Development: S211. Hydraulic controller model (hydraulic controller model as follows) Figure 1 (as shown) Using differential approximation formula To achieve differentiation, the noise amplification effect is so severe that it becomes unusable. To eliminate or reduce the noise amplification effect, consider replacing the inertial element in the classic differentiator with the following second-order form, achieving approximate differentiation through the difference between the outputs of the two inertial elements: , in: For true differential, For input signal, For output signal, is the time constant.

[0029] Let the second-order system be: , The fast optimal control synthesis system of the above formula is: , So, variables In acceleration The fastest way to track the input signal under the constraints , yes The differential can be regarded as The derivative of the above equation. Since the above equation is prone to high-frequency chattering when it reaches steady state, the discrete form of the tracking differentiator is given below: , Directly calculate the above formula To quickly control the optimal synthesis function, we obtain... , The acceleration given in this system does not need to be filtered, so , For the integration step size, The speed at which the tracking is determined is called the speed factor. These are intermediate variables in the calculation process.

[0030] S212. PID controller model (PID controller model as follows) Figure 2 (as shown) To implement the classic proportional-integral-derivative control algorithm, the calculation formula is as follows: , in: These are the proportional, integral, and differential coefficients, respectively. For error signals, For integration variables, This is the integral term of the error signal (cumulative error). The first derivative of the error signal (error rate of change); Error signal for: , in: Let r(t) be the error signal at time t, r(t) be the system setpoint (target value) at time t, and y(t) be the actual output value of the system at time t.

[0031] S22. Hydraulic System Model Component Development: For the riser support hydraulic system model, based on the riser support hydraulic system diagram, a hydraulic system model library is established, including TSUDL system model components and BSDL system model components: The S221.TSUDL system model is primarily used for simulation calculations of the hydraulic systems of the top cone circuit and the lateral thrust section related to TSUDL; it includes the top cone circuit and the lateral thrust circuit, realizing the functions of top support and lateral thrust. The internal structure topology diagram of the TSUDL model is shown below. Figure 3 As shown.

[0032] The basic hydraulic system dynamics equations of TSUDL include, but are not limited to: , in: The hydraulic pressure of the control chamber in the TSUDL system. For time, The rate of change of pressure with respect to time, The bulk modulus of hydraulic oil (reflecting the compressibility of hydraulic oil). For the volume of the hydraulic control chamber, The flow rate into the control chamber. The flow rate out of the control chamber is given by A, where A is the effective area of ​​the hydraulic cylinder piston. For piston displacement, This represents the piston's speed.

[0033] The TSUDL model includes a physical interface and a control interface, where the hydraulic system physical interface port is located. B and port B1 The external hydraulic circuit is supplied with pressure interfaces; the pressure and flow from the hydraulic source flow into two circuits through these two interfaces. TopCone Cmd and MTL Cmd The two loops are given command signal inputs, and the two loop models calculate the corresponding displacement outputs based on the command inputs, using TSUDL. TC＿Position and MTL Position The model is transmitted.

[0034] I. To enable the jacking cone circuit to precisely control the displacement of the hydraulic cylinder, thereby driving the rotating ring to achieve reliable locking or releasing actions, a jacking cone circuit system model was designed, including core components such as a pressure reducing valve, a control valve, a hydraulic cylinder, and a displacement sensor. This model is mainly responsible for dynamically simulating the pressure distribution, flow changes, and real-time output position of the hydraulic cylinder within the circuit under given pump station pressure supply and control commands.

[0035] To more accurately describe the multi-physics coupling behavior of the top cone circuit, the hydraulic cylinder force balance equation, the flow continuity equation, and the valve port pressure-flow relationship can be used to characterize the system's dynamic response.

[0036] Its main functions include: reducing the pressure of the high-pressure oil provided by the pump station to the safe working pressure of the system; switching the direction of the oil circuit according to the control command to control the extension and retraction of the hydraulic cylinder; monitoring and feeding back the position of the hydraulic cylinder in real time to form a closed-loop control basis and ensure the accuracy and stability of the rotating ring rotation process.

[0037] 1. Pressure regulating equation for pressure reducing valve: , in: To set pressure, For the valve's pressure regulation gain, For inbound traffic, For rated flow rate, This is to reduce the workload on the system.

[0038] 2. Flow equation for electro-hydraulic proportional control valve: The control valve flows according to the input signal. Adjust valve core displacement This controls the flow rate through the valve port. The relationship is usually described by the valve's flow equation: , in: For flow coefficient, The flow area varies with the valve core displacement. The pressure difference across the valve port. For the density of the oil, The dynamic response time constant of the valve is denoted as . For the valve gain, This represents the valve core displacement.

[0039] 3. Force Balance and Motion Equations of Hydraulic Cylinders: The motion of the piston in a hydraulic cylinder is determined by the force balance: , in: The equivalent mass of the piston and load. For piston displacement, The viscous damping coefficient is... The external load force (from mechanical parts such as rotating rings) is the load. These refer to the pressures in the rodless and rod-side chambers of the hydraulic cylinder, respectively. These are the effective working areas of the two cavities, This refers to nonlinear frictional forces such as Coulomb friction.

[0040] 4. Dynamic equation for hydraulic chamber pressure (continuity equation): The pressure change in each hydraulic chamber is determined by the inflow and outflow rates and the change in chamber volume. , , in: The chamber volume (which varies with piston displacement). The effective bulk modulus of the oil. The net flow rate into and out of the cavity. This refers to the internal leakage flow rate.

[0041] The top cone circuit model mainly includes component models such as oil supply lines, safety valves, control valves, pressure reducing valves, sensors, and cylinders. The model includes physical interfaces and control interfaces, with the hydraulic system physical interface port... BThe external hydraulic circuit pressure supply interface receives pressure and flow from the hydraulic power source. The high-pressure oil supplied by the pump station is reduced to the working pressure by the pressure reducing valve before flowing into the control valve. The control valve switches the circuit state according to the corresponding control command, controlling the extension or retraction of the cylinder to achieve rotation of the rotating ring. Signal is the corresponding command signal input. The control valve model switches the corresponding circuit according to the command input, controlling the on / off connection from the oil supply interface to the cylinder, thereby achieving cylinder actuation control. The displacement sensor transmits the cylinder position signal through TSUDL. TC＿Position The interface outputs data.

[0042] II. To enable the transverse thrust circuit system model to accurately simulate the dynamic characteristics of the hydraulic cylinder during the locking and retraction processes, this model focuses on the core coupling effect of the control valve, the throttling hydraulic circuit, and the transverse thrust cylinder. Its key physical relationships are described by the following set of equations: 1. Control valve flow equation: The control valve flows according to the command signal Signal ( Switch the oil circuit direction to control the flow rate: , in: The flow coefficient of the valve. The pressure before the valve, 1. Pressure in the working chamber of the hydraulic cylinder. 2. Force balance equation for the transverse thrust hydraulic cylinder: The piston dynamics of the hydraulic cylinder are described by the following equation: , In the formula: For piston equivalent mass, For displacement, For piston area, The contact force (increases nonlinearly after being crushed).

[0043] 3. Dynamic equation for working chamber pressure: Pressure changes are determined by both the inflow rate and piston motion. , in: The cavity volume varies with displacement. This refers to the elastic modulus of the oil.

[0044] The transverse push circuit model ultimately achieves three functions: top locking, retraction unlocking, and interception buffering, providing a quantitative analysis basis for evaluating the dynamic performance and reliability of the locking mechanism.

[0045] Tightly clamped: When After the design gap is reached, Nonlinear increase, simulated locking force.

[0046] Back: When In reverse, the hydraulic circuit switches, and the hydraulic cylinder retracts under pressure and load.

[0047] Throttling buffer: through pipeline liquid resistance ( Adjust the speed and impact of the movement.

[0048] S222.BSDL System Model: This model describes the bottom support hydraulic circuit, comprising four main parts: oil supply lines, control valves, and BSDL cylinders. Its core dynamics are described by the following set of equations: 1. Flow distribution equation for control valve group: based on command signal BSDL Cmd (can be a set of signals) ), To control the flow rate of the corresponding hydraulic cylinder for each valve: , in: For the first The flow coefficient of each valve, For the system oil supply pressure, To correspond to the pressure in the working chamber of the hydraulic cylinder, This is the valve switching function.

[0049] 2. BSDL Cylinder Force Balance Equations: The dynamic equation for each cylinder is as follows: , In the formula: The first The equivalent mass, displacement, and piston area of ​​each cylinder. The damping coefficient is... This refers to the external load (such as locking reaction force) experienced by the cylinder.

[0050] The internal structure topology diagram of the BSDL system model is as follows: Figure 4 As shown. The model includes a physical interface and a control interface, where the hydraulic system physical interface port... B This is the pressure supply interface for the external hydraulic circuit. The pressure and flow from the hydraulic power source flow into the circuit through this interface, passing through corresponding pipes and control valves, and finally reaching each BSDL cylinder to actuate it. BSDL Cmd The control valve model switches the corresponding circuit according to the command input, controlling the on / off of the oil supply interface to the BSDL cylinder, thereby realizing the actuation control of the cylinder.

[0051] S23. Development of Mechanical System Model Components: The mechanical system model is responsible for the dynamic simulation of key structural components in the FPSO riser support system. Its core is the use of multibody dynamics to physically model the mechanical components. This model includes a frame model, a rotating ring model, a wedge block model, a locking mechanism model, a transverse piston model, and an actuation mechanism model. Each model is connected through a standardized multibody dynamics interface (transmitting variables such as force, torque, displacement, and velocity) to achieve coupled simulation with the hydraulic system and control system.

[0052] The physical principles and core equations of each model are as follows: S231. Frame Model: This is the main support structure of the FPSO riser support system. This model has a multibody dynamics interface, which can provide corresponding boundaries to other models connected to it.

[0053] The frame model mainly consists of a body and the coordinate transformation model connected to it. The body model calculates the corresponding force, torque, position vector, and attitude vector variables based on the provided parameters such as mass, moment of inertia, and initial coordinate vector, and interacts with other models through the multibody dynamics interface.

[0054] S232. Rotating Ring Model: Used for accurate simulation of the rotational motion of a rotating ring driven by a hydraulic actuator, it is the core moving component in the locking and releasing process of the riser. This model is based on the dynamic theory of rigid body rotation about a fixed axis and is coupled with the hydraulic system, control system and other mechanical components for simulation through a multibody dynamics interface.

[0055] Its core dynamic behavior is described by the following set of equations: 1. Kinematic description: Rotation around a fixed axis (usually The axis undergoes a one-dimensional rotational motion, and its angular displacement is denoted as . angular velocity is angular acceleration is

[0056] 2. Rotational dynamics equations: The rotation of the rotating ring is simplified from Euler's rotation equations (for the case about a fixed axis): , in: For the moment of inertia of rotation about the axis of rotation, This is the rotational damping coefficient (including bearing friction, etc.). The driving torque applied to the hydraulic actuator, This refers to nonlinear frictional torque (such as Coulomb friction). The constraint or frictional torque generated by contact with wedges, locking mechanisms, etc.

[0057] The internal topology diagram of the rotating ring model is as follows: Figure 5As shown, the model mainly consists of a rotating ring multibody module and a coordinate transformation model connected to it. The rotating ring multibody model calculates the corresponding force, torque, position vector, and attitude vector variables based on the provided parameters such as mass, moment of inertia, and initial coordinate vectors, as well as the force and torque variables provided by other models through the interface. It interacts with other models through the multibody dynamics interface. Ultimately, this is reflected in the rotating ring rotating under the thrust and torque of the hydraulic cylinder, outputting the corresponding angular velocity and angle.

[0058] S233. Wedge Model: Used for accurate simulation of the linear motion of the wedge under the combined action of the frame guide rail constraint and hydraulic driving force. It is a key moving component for realizing the radial locking or releasing function of the locking mechanism. This model is based on the constrained rigid body motion theory in multibody dynamics and is coupled with models of the frame, rotating ring, locking mechanism, etc. through a multibody dynamics interface for simulation.

[0059] Its core dynamic behavior is described by the following set of equations: 1. Kinematic Description: The wedge typically undergoes one-dimensional or two-dimensional constrained motion along a guide surface on the frame. Let its displacement along the guide direction be... The speed is acceleration is .

[0060] 2. Equations of motion (along the guiding direction): The motion of the wedge is described by Newton's second law: , in: The mass of the wedge; It is driven by external force (usually from the hydraulic thrust of the transverse piston). ; The normal constraint force (perpendicular to the direction of movement) applied to the frame guide rail ensures that the wedge moves along the predetermined trajectory; The frictional resistance of the guide rail can be modeled as a combination of Coulomb friction and viscous friction: , in: The coefficient of kinetic friction is . For the guide rail normal pressure, is the viscous damping coefficient.

[0061] The normal contact force generated when the wedge contacts the rotating ring (or other locking components) can be represented by the Hertzian contact model or a simplified stiffness-damping model: , in: For contact penetration depth, These are the contact stiffness and damping coefficient, respectively.

[0062] The internal topology diagram of the wedge model is as follows: Figure 6 As shown, the model mainly consists of a multibody module and a coordinate transformation model connected to it. The wedge multibody model calculates the corresponding force, torque, position vector, and attitude vector variables based on the provided parameters such as mass, moment of inertia, and initial coordinate vector, as well as the force and torque (including forces and torques generated in contact with the body) variables provided by other models through the interface. It interacts with other models through the multibody dynamics interface. Ultimately, this is reflected in the wedge moving under the constraints of the frame model, outputting the corresponding velocity and displacement.

[0063] S234. Locking Mechanism Model: Used for accurate simulation of the mechanical behavior of key locking components in the riser support system, it is the core functional module for achieving reliable locking and safe release of the riser. Based on multibody dynamics theory, this model describes the entire process of contact-locking-unlocking between the locking mechanism and the riser (or rotating ring). Through the coupling calculation of nonlinear contact force and friction force, it evaluates the static and dynamic characteristics in the locking state.

[0064] Its core mechanical model is described by the following set of equations: The motion of the locking mechanism as a rigid body is described by the Newton-Euler equations. , , in: For the mass and inertia tensor of the locking mechanism, Forces and torques originating from hydraulic systems or other mechanical components.

[0065] The internal topology diagram of the locking mechanism model is as follows: Figure 7 As shown. Similar to the wedge model, this model mainly consists of a multibody module and a coordinate transformation model connected to it. The locking mechanism multibody model calculates corresponding force, torque, position vector, and attitude vector variables based on provided parameters such as mass, moment of inertia, and initial coordinate vectors, as well as force and torque (including forces and torques generated in contact with the body) variables provided by other models through the interface. It interacts with other models through the multibody dynamics interface. Ultimately, this is reflected in the relative displacement, force, and torque between the locking mechanism and the locked module.

[0066] S235. Lateral Piston Model: Used for accurate simulation of the one-dimensional linear motion of a hydraulically driven piston and its clamping force and displacement on a target mechanism (such as a wedge). It is a key power conversion component for realizing the radial locking function of the riser support system. This model is based on the piston dynamics equations, describing the dynamic response of the piston under the combined action of hydraulic pressure and external load. The piston's motion along the cylinder axis (assumed to be the x-axis) is described by Newton's second law: , in: For the mass of the piston and connecting rod; For piston displacement (measured from the initial position); It is the viscous damping coefficient; Hydraulic driving force; This refers to the contact reaction force generated after the piston comes into contact with the target mechanism (such as a wedge). The frictional resistance between the piston and the seals and cylinder can be described using the Stribeck friction model.

[0067] The internal topology diagram of the transverse piston model is as follows: Figure 8 As shown, the model mainly consists of a multibody module and a coordinate transformation model connected to it. The transverse piston multibody model calculates corresponding force, torque, position vector, and attitude vector variables based on provided parameters such as mass, moment of inertia, and initial coordinate vectors, as well as force and torque (including forces and torques generated in contact with the machine body) variables provided by other models through the interface. It interacts with other models through the multibody dynamics interface. Ultimately, this is reflected in the wedge moving under the constraints of the frame model, outputting corresponding velocity and displacement.

[0068] S235. Actuation Mechanism Model: Includes the actuating piston and actuating cylinder models, mainly used to simulate the rotational speed and displacement variables under the drive of the actuation mechanism. This model is based on the piston dynamics equation, and the actuation mechanism outputs the corresponding piston displacement and piston speed.

[0069] The internal topology diagram of the actuator model is as follows: Figure 9 As shown, the model mainly consists of a multibody module and a coordinate transformation model connected to it. The actuation mechanism multibody model calculates corresponding force, torque, position vector, and attitude vector variables based on provided parameters such as mass, moment of inertia, and initial coordinate vectors, as well as force and torque (including forces and torques generated in contact with the machine body) variables provided by other models through the interface. It interacts with other models through the multibody dynamics interface. Ultimately, this is reflected in the wedge moving under the constraints of the frame model, outputting corresponding velocity and displacement.

[0070] All mechanical model components are interconnected and coupled to external systems through standardized multibody dynamics interfaces (transmitting force, torque, displacement, velocity, etc.).

[0071] S3. Implementation of Multi-Domain Coupling Mechanism This step aims to effectively connect the independent multi-domain model components developed in step S2 into an organic whole, which is accomplished by designing and implementing three types of core coupling interfaces.

[0072] S31. Energy Coupling Interface Design: S311. Mechanical-Hydraulic Energy Coupling Interface: This interface establishes a coupling relationship between the mechanical and hydraulic systems through the mapping relationship between piston displacement, force, flow rate, and pressure in a hydraulic cylinder. For example, the piston displacement in the hydraulic cylinder model serves as the motion input to the mechanical system, while the force generated by the hydraulic cylinder acts as the load input to the mechanical system; conversely, the load force of the mechanical system affects the pressure of the hydraulic cylinder. This bidirectional energy exchange is naturally achieved by connecting the mechanical port (displacement / force) and the hydraulic port (pressure / flow rate) of the hydraulic cylinder.

[0073] S312. Control-Hydraulic Signal Coupling Interface: This interface establishes a coupling between the control system and the hydraulic system by establishing the relationship between the control signal and the hydraulic valve opening. For example, the electrical signals (such as current and voltage) output by the PID controller or hydraulic controller in the control system are connected as input signals to the control port of the hydraulic valve model (such as a proportional valve or servo valve) to determine the valve opening, thereby regulating the flow and pressure of the hydraulic system.

[0074] S313. Control-Mechanical Feedback Coupling Interface: This interface establishes a coupling between the control system and the mechanical system through sensor feedback signals. For example, sensor models in the mechanical system (such as displacement sensors and pressure sensors) convert the detected physical quantities (displacement, force) into electrical signals, which are then fed back to the control system through the signal interface to form a closed-loop control.

[0075] S32. Cross-domain equation integration: Based on Modelica's non-causal modeling characteristics, all the above coupling relationships are not signal flows with predefined input and output directions as in traditional causal modeling. Instead, they are formed by listing the equations of each component (including the connection constraint equations at the coupling interface) in an equal and natural form, together constituting a complete system of differential algebraic equations.

[0076] Compared to traditional causal modeling, non-causal modeling offers significant advantages in handling multi-domain coupled systems. In causal modeling, the modeler must pre-define explicit causal relationships (i.e., inputs and outputs) for each module. For example, in a hydraulic system model, it must be determined beforehand whether it's "given flow rate, calculate pressure" or "given pressure, calculate flow rate." Once the system topology or interface relationships change, the original model must be reconstructed to reconstruct the causal relationships, resulting in poor adaptability and hindering system reconfiguration and reuse. However, in the Modelica non-causal modeling used in this invention, it is only necessary to directly describe the constraint relationships between variables based on physical laws (e.g., describing the physical relationship between pressure, flow rate, and piston displacement in a hydraulic system through equations), without manually specifying the causal direction. The simulation solver automatically derives the implicit causal relationships based on the structure of the overall equation set, thereby supporting flexible configuration of system structures, plug-and-play multi-domain models, and unified description and solution of complex coupling relationships, greatly enhancing the model's reconfigurability and applicability to multiple scenarios.

[0077] S33. Multi-timescale collaboration: To address the multi-timescale characteristics of the system—control system (fast, millisecond-level), hydraulic system (medium, second-level), and mechanical system (slow, minute-level)—the solver employs an adaptive variable step size strategy to improve simulation efficiency. Simultaneously, an event detection mechanism is introduced to handle the impact of discrete events such as hydraulic valve opening / closing and mechanical contact separation / collision on the continuous system state.

[0078] S4. System Integration and Simulation Verification All model components developed in step S2 are integrated into the MWORKS.Sysplorer platform according to the physical connections and logical relationships of the actual system, using the coupling mechanism implemented in step S3. Through a unified multi-domain modeling environment, seamless connections and data exchange between models are achieved, supporting fully coupled simulation analysis at the system level. During the integration process, special attention is paid to the conservation of physical quantities and the consistency of signal transmission at domain interfaces to ensure the physical realism of the overall system behavior. The final result is a system like... Figures 10-13 The image shows a complete digital prototype of the FPSO riser support system. This digital prototype is a virtual prototype that includes the complete mechanical structure, hydraulic piping, and control logic.

[0079] Example 2 The full-system digital prototype of the FPSO riser support system, constructed using the method of this invention, can perform high-fidelity virtual tests on typical working conditions such as "riser locking" and "riser release".

[0080] During the simulation, the system's action sequence, displacement, speed, and hydraulic system pressure and flow rate, among other performance indicators, were verified during the clamping process. Figure 14 - Figure 15As shown. By analyzing these performance indicators, the correctness of the system's action sequence, the stability of its dynamic response, the adequacy of the locking force, and the existence of potential problems such as pressure shocks can be verified. This process replaces or reduces expensive physical prototype testing, enabling the identification and correction of defects in the early stages of design, and significantly supporting the verification and optimization decisions of the entire system. By using high-precision digital prototypes to identify and resolve most design problems in advance, the number of physical prototype testing rounds is reduced by 2-3 rounds, and the overall verification cost is reduced by more than 30%.

[0081] By applying the method of this invention, the problem of domain fragmentation pointed out in the background art can be effectively solved, and multi-domain collaborative design can be realized; the development cycle can be greatly shortened by model reuse; and the dependence on physical prototypes and verification costs can be reduced by high-precision digital prototype simulation, thereby comprehensively improving the design quality and efficiency of complex marine engineering equipment such as FPSO.

[0082] As can be seen from the above description, the embodiments of the present invention achieve the following technical effects: Enhanced Multi-Domain Collaborative Design Capabilities: This invention achieves seamless coupling of multiple domains, including mechanical, hydraulic, and control, through the unified Modelica modeling language and the MWORKS.Sysplorer platform. It can accurately describe the interactions between various physical domains in the FPSO riser support system, thereby improving the integrity and synergy of the system design.

[0083] Enhanced Model Reusability and Extensibility: The hierarchical model architecture and standardized interface design proposed in this invention enable model components to have good reusability and extensibility, significantly reducing development costs.

[0084] Design verification costs are significantly reduced: High-precision digital prototypes can identify and resolve potential problems in serial design early in the design process, reducing the number of physical prototype tests and lowering costs by more than 30%. At the same time, they can cover more extreme operating conditions and improve system safety.

[0085] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of the invention is limited to these examples; within the framework of the invention, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of the different aspects of the invention as described above, which are not provided in detail for the sake of brevity.

[0086] This invention is intended to cover all such substitutions, modifications, and variations that fall within the broad scope of this specification. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A multi-domain coupled modeling method for complex FPSO equipment based on Modelica, characterized in that, include: S1. System Decomposition and Architecture Design: Decompose the riser support system into control, hydraulic and mechanical subsystems and define standardized interface specifications for each model component; S2. Multi-domain component development: Based on the standardized interface specifications, develop corresponding control system model components, hydraulic system model components, and mechanical system model components using the Modelica language; S3. Coupling Mechanism Implementation: Based on the model components, design mechanical-hydraulic, control-hydraulic and control-mechanical coupling interfaces, integrate the equations of each component into a unified system of differential-algebraic equations, and handle multi-timescale problems; S4. System Integration and Verification: Integrate the model components through coupling interfaces to build a digital prototype of the system, and perform fully coupled simulation to verify the system performance.

2. The multi-domain coupled modeling method for complex FPSO equipment based on Modelica according to claim 1, characterized in that, The process of decomposing the riser support system into control, hydraulic, and mechanical subsystems and defining standardized interface specifications for each model component specifically includes: For the FPSO riser support system, a top-down approach is adopted for hierarchical decomposition, which decomposes the system into three main subsystems: control system, hydraulic system and mechanical system. Each subsystem is further decomposed into functional modules. Based on the MWORKS platform, a unified hierarchical model library architecture is designed, and standardized interfaces and parameter specifications for each model component are defined.

3. The multi-domain coupled modeling method for complex FPSO equipment based on Modelica according to claim 2, characterized in that, The unified hierarchical model library architecture has a top layer of riser support system assembly model, a middle layer of three subsystem models of control system, hydraulic system and mechanical system, and a bottom layer of basic model components corresponding to each functional module. All components follow a unified physical port and signal port interface specification.

4. The multi-domain coupled modeling method for complex FPSO equipment based on Modelica according to claim 1, characterized in that, The control system model components include at least a hydraulic controller model and a PID controller model; The hydraulic controller model is implemented using a tracking differentiator algorithm. Its discrete form is used to quickly track the input signal and extract the differential signal. The tracking speed is controlled by setting a speed factor to suppress the noise amplification effect.

5. The multi-domain coupled modeling method for complex FPSO equipment based on Modelica according to claim 4, characterized in that, The hydraulic system model assembly includes at least a TSUDL system model assembly for top support and lateral thrust, and a BSDL system model assembly for bottom support; The TSUDL system model components include a top cone circuit and a transverse push circuit. The top cone circuit model is described by the pressure regulating equation of the pressure reducing valve, the flow equation of the control valve, the force balance equation of the hydraulic cylinder, and the flow continuity equation, and is used to simulate the driving and control of the rotating ring. The transverse push circuit model is described by the piston dynamics equation including contact force, hydraulic pressure, inertial force, and damping force, and is used to simulate the top jamming, retraction unlocking, and throttling buffering processes. The BSDL system model component is described by a set of equations including valve orifice flow equation, cylinder force balance equation, and flow continuity equation, and is used to simulate the dynamic actuation process of the bottom support cylinder.

6. The multi-domain coupled modeling method for complex FPSO equipment based on Modelica according to claim 5, characterized in that, The mechanical system model components include at least a frame model, a rotating ring model, a wedge model, a locking mechanism model, a transverse piston model, and an actuation mechanism model; The mechanical system model components are all constructed based on multibody dynamics theory. Among them, the rotating ring model is based on the dynamic equation of a rigid body rotating about a fixed axis; the wedge model is based on the dynamic equation of a constrained rigid body linear motion; the locking mechanism model is based on the Newton-Euler equations including a nonlinear contact force model; and the transverse piston model and the actuation mechanism model are based on the piston dynamics equations.

7. The multi-domain coupled modeling method for complex FPSO equipment based on Modelica according to claim 1, characterized in that, Based on the aforementioned model components, mechanical-hydraulic, control-hydraulic, and control-mechanical coupling interfaces are designed to integrate the equations of each component into a unified system of differential-algebraic equations, and to handle multi-timescale problems, specifically including: Based on the model components developed in step S2, a cross-domain coupling interface is designed and implemented, including: establishing an energy coupling interface between the mechanical system and the hydraulic system through the mapping relationship between the hydraulic cylinder piston displacement and hydraulic pressure and flow rate; establishing a signal coupling interface between the control system and the hydraulic system through the relationship between the control signal and the hydraulic valve opening; and establishing a feedback coupling interface between the control system and the mechanical system through sensor feedback signals. By leveraging the non-causal modeling characteristics of Modelica, physical equations from various fields are integrated into a unified system of differential-algebraic equations. Symbolic processing, BLT transformation, and adaptive variable step size solution strategies are employed to handle multi-timescale problems and discrete events.

8. The multi-domain coupled modeling method for complex FPSO equipment based on Modelica according to claim 7, characterized in that, The process of integrating physical equations from various fields into a unified system of differential-algebraic equations specifically includes the following steps: The force balance equations and kinematic equations of mechanical systems, the fluid dynamics equations and flow continuity equations of hydraulic systems, and the control algorithm equations of control systems are uniformly expressed in a non-causal form as Modelica equations, and the compiler automatically generates a set of differential algebraic equations for the overall system.

9. A multi-domain coupled modeling method for complex FPSO equipment based on Modelica according to claim 7, characterized in that, The adaptive variable step size solution strategy specifically includes the following steps: Based on the different dynamic response time scales of the control system, hydraulic system, and mechanical system, the integral step size is dynamically adjusted during the simulation solution process, and an event detection mechanism is introduced for discrete events such as hydraulic valve switching and mechanical contact collision.

10. A multi-domain coupled modeling method for complex FPSO equipment based on Modelica according to claim 1, characterized in that, The model components are integrated through a coupling interface to construct a digital prototype of the system. Fully coupled simulation is then performed to verify the system performance, specifically including: The model components developed in step S2 are integrated into the whole system through the coupling interface implemented in step S3. The control system model, hydraulic system model, and mechanical system model are connected through standardized energy flow and information flow interfaces to form a closed-loop simulation system containing complete physical effects and logical control, thereby constructing a digital prototype of the FPSO riser support system. In a unified simulation environment, a fully coupled dynamic simulation is performed on typical working conditions of riser locking and releasing to obtain and analyze the system's action sequence, displacement, velocity, pressure, and flow performance indicators, thereby completing the functional and performance verification of the system design scheme.

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