Modelica-based modeling method for wind wave current coupling environment of FPSO system

Abstract

This invention discloses a modeling method for wind-wave-current coupled environment of an FPSO system based on Modelica, relating to the field of model convergence technology. By setting different time steps and running simulations, the responses of key physical quantities are recorded, and a time step sensitivity index is calculated. The model is then divided into different meshes and simulated, and a mesh independence index is calculated. The dynamic response of the FPSO platform is recorded, and an instability index of the simulation results is calculated. Combining the time step sensitivity index, mesh independence index, and simulation result instability index, a convergence anomaly coefficient is calculated and compared with a preset threshold to determine whether the model's convergence is acceptable. This process verifies the standardized convergence of the Modelica-based FPSO system wind-wave-current coupled model, ensuring timely detection of model convergence performance, avoiding error accumulation, improving the accuracy and reliability of simulation results, and thus reducing potential impacts on engineering decisions and safety assessments.

Description

Technical Field

[0001] This invention relates to the field of model convergence technology, specifically to a method for modeling the wind-wave-current coupled environment of an FPSO system based on Modelica. Background Technology

[0002] Modelica-based wind-wave-current coupled environment modeling of FPSO systems refers to using Modelica, a multi-domain modeling language, to simulate and analyze the dynamic behavior of Floating Production Storage and Offloading (FPSO) units under environmental conditions such as wind, waves, and currents. This model comprehensively simulates the FPSO's motion response, structural response, and fluid-solid interactions by coupling the dynamics of wind, wave, and current fields. It also incorporates various environmental factors (such as wave period, wind speed, and current direction) to predict the FPSO's stability, navigation performance, and operational safety. This modeling method, by accurately describing the interactions between fluid mechanics, structural mechanics, and control systems in the physical process, makes the simulation results more realistic and reliable.

[0003] The wind-wave-current coupling model is the core of this modeling method, involving the complex physical interactions between the wind-wave-current environment and the FPSO platform. These interactions are highly nonlinear, and the coupling effect between the platform and the fluid makes the system's dynamic response more complex. For example, different wave frequencies, amplitudes, and directions directly affect the FPSO platform's floating, tilting, and rolling behavior, while changes in wind speed significantly impact the platform's lateral moment and additional loads. Simultaneously, the influence of ocean currents on platform dynamics can lead to further stability issues. These factors combined result in a highly time-varying and sensitive system response.

[0004] This modeling approach allows for the accurate capture of the impact of changing environmental conditions on FPSO operational performance during simulations, providing a scientific basis for design, operation, and safety assessments. Specifically, Modelica-based wind-wave-current coupled environment modeling helps engineers evaluate FPSO response performance under different environmental conditions and optimize design schemes during the FPSO system design phase. During operation, it enables real-time simulation to predict FPSO behavior under various wind, wave, and current conditions, ensuring safe operation. Furthermore, in terms of fault detection and prediction, the model can support maintenance decisions by monitoring the platform's dynamic response to promptly identify potential anomalies.

[0005] However, due to the lack of a standardized convergence verification method for the wind-wave-current coupling model of the Modelica-based FPSO system, the convergence of the model is often not effectively detected in a timely manner in practical applications. This lack of verification may lead to numerical instability or error accumulation in the model, which affects the accuracy and reliability of the simulation results, and consequently the credibility of engineering decisions and safety assessments. Summary of the Invention

[0006] The purpose of this invention is to solve the problems mentioned above and provide a method for modeling the wind-wave-current coupled environment of an FPSO system based on Modelica.

[0007] This invention proposes a wind-wave-current coupled environment modeling method for FPSO systems based on Modelica, the method comprising:

[0008] Set multiple different time steps, and for each time step, run the simulation model and record the response of key physical quantities, and calculate the time step sensitivity index;

[0009] The fluid domain involved in the model is divided into different meshes, and the model is simulated separately. The key physical quantities of the response are recorded, and the mesh independence index is calculated.

[0010] The model was simulated and the dynamic response of the FPSO platform was recorded. The instability index of the simulation results of the model was calculated.

[0011] The convergence anomaly coefficient is calculated based on the time step sensitivity index, mesh independence index, and simulation result stability index. The convergence of the model is then judged to be qualified based on the preset convergence anomaly coefficient threshold.

[0012] Optionally, the calculation of the time step sensitivity index includes:

[0013] Set multiple different time step values, namely: coarse time step Medium time step Fine time step ;

[0014] For each time step, run the simulation and record the responses of key physical quantities; the recorded physical quantities are: the responses of physical quantities at coarse time steps. Physical quantity response at an average time step Physical quantity response at fine time steps ;

[0015] Calculate the error at each time step, for example, by calculating the relative error of platform displacement or acceleration: ; ; In the formula, , , These represent the errors under coarse time steps, medium time steps, and fine time steps, respectively. This is a pre-defined reference solution;

[0016] Calculate the error ratio for different time steps and combine it with the time step differences to obtain the time step sensitivity index: In the formula, This is the time step sensitivity index.

[0017] Optionally, the calculation of the grid independence index includes:

[0018] Within the fluid domain, select coarse and fine meshes, as follows: coarse mesh size... Fine mesh size ;

[0019] Simulations were performed separately for coarse and fine meshes, and the key physical quantities of the response were recorded. These key physical quantities represent the displacement values ​​under the coarse and fine meshes, respectively: displacement response under coarse mesh. Displacement response under fine mesh ; and ;

[0020] Calculate the relative error between the coarse and fine meshes based on their displacement responses. This reflects the impact of mesh generation on the results: the calculation formula is: ;

[0021] The grid independence index is calculated using the following formula: In the formula, The grid independence index, This is the grid convergence index.

[0022] Optionally, the instability index of the simulation results of the calculation model includes:

[0023] Simulate the model and record the dynamic response displacement of the FPSO platform. Calculate the mean of the response. and standard deviation The calculation formula is: , In the formula, In time Displacement at that point It is the number of time steps;

[0024] The instability index of the simulation results is calculated using the following formula: In the formula, This represents the instability index of the simulation results.

[0025] Optionally, the convergence anomaly coefficients calculated include:

[0026] ;

[0027] In the formula, The convergence anomaly coefficient, , , These are the time step sensitivity index, the mesh independence index, and the simulation result stability index, respectively. These are the preset scaling factors for the time step sensitivity index, the mesh independence index, and the simulation result stability index, respectively. All are greater than 0.

[0028] Optionally, determining whether the model's convergence is satisfactory, in conjunction with a preset convergence anomaly coefficient threshold, includes:

[0029] The convergence anomaly coefficient is compared with the preset convergence anomaly coefficient threshold. If the convergence anomaly coefficient is less than the preset convergence anomaly coefficient threshold, it means that the convergence of the model is qualified.

[0030] If the convergence anomaly coefficient is not less than the preset convergence anomaly coefficient threshold, it indicates that the model's convergence is unqualified and the model needs to be optimized until the convergence anomaly coefficient is less than the preset convergence anomaly coefficient threshold.

[0031] The beneficial effects of this invention are:

[0032] This invention proposes a modeling method for wind-wave-current coupled environment of FPSO systems based on Modelica. By setting multiple different time steps and running a simulation model at each time step, recording the responses of key physical quantities, and calculating the time step sensitivity index; by dividing the fluid domain involved in the model into different meshes, simulating the model separately, recording the key physical quantities of the response, and calculating the mesh independence index; by simulating the model and recording the dynamic response of the FPSO platform, and calculating the simulation result instability index; and by calculating the convergence anomaly coefficient based on the time step sensitivity index, mesh independence index, and simulation result stability index, and combining this with a preset convergence anomaly coefficient threshold to determine whether the model's convergence is acceptable, this method can verify the standardized convergence of the Modelica-based FPSO system wind-wave-current coupled model, enabling timely and effective detection of the model's convergence performance in practical applications. This ensures model numerical stability, prevents error accumulation, and guarantees the accuracy and reliability of simulation results, reducing the impact on the credibility of engineering decisions and safety assessments. Attached Figure Description

[0033] The present invention will now be further described with reference to the accompanying drawings.

[0034] Figure 1 A flowchart illustrating the wind-wave-current coupled environment modeling method for FPSO systems based on Modelica. Detailed Implementation

[0035] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] This invention provides a method for modeling the wind-wave-current coupled environment of an FPSO system based on Modelica. See also... Figure 1 , Figure 1 A flowchart illustrating a wind-wave-current coupled environment modeling method for an FPSO system based on Modelica, provided in an embodiment of the present invention. The method includes the following steps:

[0038] Set multiple different time steps, and for each time step, run the simulation model and record the response of key physical quantities, and calculate the time step sensitivity index;

[0039] The fluid domain involved in the model is divided into different meshes, and the model is simulated separately. The key physical quantities of the response are recorded, and the mesh independence index is calculated.

[0040] The model was simulated and the dynamic response of the FPSO platform was recorded. The instability index of the simulation results of the model was calculated.

[0041] The convergence anomaly coefficient is calculated based on the time step sensitivity index, mesh independence index, and simulation result stability index. The convergence of the model is then judged to be qualified based on the preset convergence anomaly coefficient threshold.

[0042] Based on the modelica-based FPSO system wind-wave-current coupling environment modeling method provided in this invention embodiment, the above steps can verify the standardized convergence of the Modelica-based FPSO system wind-wave-current coupling model, so that the convergence performance of the model can be effectively detected in a timely manner in practical applications; the model numerical values ​​are stable, and there will be no error accumulation problem, ensuring the accuracy and reliability of simulation results and reducing the impact on the credibility of engineering decisions and safety assessments.

[0043] In one embodiment, multiple different time steps are set, and for each time step, a simulation model is run and the responses of key physical quantities are recorded. The time step sensitivity index is calculated, including:

[0044] Set multiple different time step values, namely: coarse time step (Larger time step); Medium time step (Moderate time step); Fine time step (Smaller time step);

[0045] For each time step, run the simulation and record the responses of key physical quantities (such as displacement and acceleration of the FPSO platform); the recorded physical quantities are the responses of physical quantities at coarse time steps. (e.g., platform displacement, acceleration, etc.); physical quantity response at medium time steps Physical quantity response at fine time steps ;

[0046] Calculate the error at each time step, for example, by calculating the relative error of platform displacement or acceleration: ; ; In the formula, , , These represent the errors under coarse time steps, medium time steps, and fine time steps, respectively. This is a preset reference solution (e.g., the result of the finest time step).

[0047] Calculate the error ratio for different time steps and combine it with the time step differences to obtain the time step sensitivity index: In the formula, This is the time step sensitivity index.

[0048] It should be noted that the data acquisition method for the above calculations mainly relies on the results of the simulation of the FPSO system wind-wave-current coupling model based on Modelica. First, different time steps (coarse, medium, and fine time steps) are set in the model, and multiple simulations are performed for each. In each simulation, key physical quantities related to the dynamic response of the FPSO platform, such as platform displacement, velocity, and acceleration, are recorded. Then, by comparing the simulation results under coarse, medium, and fine time steps, the relative errors of physical quantities such as platform displacement or acceleration are calculated, with the result of the finest time step used as the reference solution. Finally, by calculating the error ratio under different time steps and combining it with the time step differences, a time step sensitivity index is obtained, thereby evaluating the impact of the time step on simulation accuracy and stability, and providing a basis for further model optimization.

[0049] It's important to note that the time step sensitivity index is used to measure the sensitivity of a Modelica-based FPSO system wind-wave-current coupling simulation model to changes in the time step. Specifically, a larger time step sensitivity index indicates more significant differences in the model's response at different time steps, especially a larger error gap between coarse and fine time steps. This typically means that the model's numerical solution is highly sensitive to changes in the time step, potentially exhibiting significant numerical instability or error accumulation, leading to convergence anomalies. In other words, a large time step sensitivity index indicates that the model's dynamic response is significantly affected by the time step setting, potentially failing to accurately capture the system's true behavior, thus impacting the model's convergence and the reliability of the simulation results. Therefore, to ensure model convergence and obtain stable and accurate simulation results, it is necessary to optimize the time step setting, ensuring consistent and error-free responses across different time scales, and avoiding numerical instability caused by excessively large or small time steps.

[0050] In one implementation, analyzing the time step sensitivity index is beneficial for assessing the convergence of a Modelica-based FPSO system wind-wave-current coupling simulation model. Firstly, the time step sensitivity index helps identify the model's response consistency across different time steps, revealing whether numerical errors or instabilities arise due to time discretization. A large time step sensitivity index indicates that the simulation results are highly sensitive to changes in the time step, potentially leading to poor convergence or even unstable numerical solutions. Analyzing this index allows for the timely detection of these potential problems and guides the optimization of time step selection, ensuring stable convergence and accurate reflection of the system's dynamic behavior across multiple time scales. Furthermore, time step sensitivity analysis helps balance computational efficiency and accuracy in simulations, avoiding excessively fine or coarse time steps that waste computational resources or cause accuracy loss. Therefore, this analytical method not only improves the reliability and accuracy of the model, but also provides a scientific basis for model optimization, which helps to ensure that the Modelica-based FPSO system wind-wave-current coupled simulation model can accurately and stably simulate the real marine environment.

[0051] In one embodiment, the fluid domain involved in the model is divided into different meshes, and the model is simulated separately for each mesh. Key physical quantities of the response are recorded, and the mesh independence index is calculated, including:

[0052] Within the fluid domain, select coarse and fine meshes, as follows: coarse mesh size... Fine mesh size ;

[0053] Simulations were performed for both coarse and fine meshes, and the key physical quantities of the response were recorded, including the displacement response under the coarse mesh. Displacement response under fine mesh ; and These represent the displacement values ​​under coarse and fine grids, respectively; they are the specific numerical values ​​of the physical response.

[0054] Calculate the relative error between the coarse and fine meshes based on their displacement responses. This reflects the impact of mesh generation on the results: the calculation formula is: ;

[0055] The grid independence index is calculated using the following formula: In the formula, The grid independence index, The grid convergence exponent is usually derived through empirical or numerical convergence theory.

[0056] It should be noted that mesh independence analysis compares the simulation results of the model under different mesh divisions, calculates the relative error, and combines the convergence index to evaluate the model's accuracy and the impact of mesh division. Data acquisition mainly relies on numerical simulations after fine mesh division, and records the physical response under different meshes to calculate the error, thereby determining whether the mesh has achieved sufficient accuracy.

[0057] It's important to note that the mesh independence index is a metric used to evaluate the impact of mesh refinement accuracy on simulation results. It reflects the difference in physical response between coarse and fine meshes, indicating the convergence of the model solution as the mesh becomes finer. A larger mesh independence index means a greater error difference between coarse and fine meshes, suggesting that the simulation results do not converge significantly with mesh refinement, potentially indicating numerical errors or model design issues. In the Modelica-based simulation model of a wind-wave-current coupled FPSO system, a large mesh independence index may indicate that the system's physical response (such as wind and wave loads, hydrodynamic response, etc.) is highly sensitive to mesh refinement and has not met sufficient accuracy requirements. This usually suggests that the numerical solution of the model may be unstable, and the convergence of the simulation results may be abnormal. Therefore, a larger mesh independence index may indicate that the mesh was not refined enough during numerical simulation, or other problems exist, such as improper solver settings or an incomplete physical model, leading to poor convergence. This necessitates further optimization of the mesh or adjustment of the simulation model to ensure the reliability and accuracy of the results.

[0058] In one implementation, the advantage of analyzing the grid independence index in measuring whether the convergence of the Modelica-based FPSO system wind-wave-current coupling simulation model is abnormal is as follows:

[0059] The mesh independence index (GCI) plays a crucial role in measuring the convergence of Modelica-based simulation models of wind-wave-current coupling in FPSO systems, particularly in ensuring the accuracy and reliability of simulation results. By calculating the GCI, the impact of mesh refinement on the physical response can be quantified, thereby determining whether the model solution has stabilized and met the expected accuracy requirements. A small GCI value indicates that the variation in simulation results gradually decreases with mesh refinement, suggesting that the model has converged and the influence of mesh refinement on the results is negligible, ensuring the reliability of the simulation results. Conversely, a large GCI value may indicate that the model solution has not yet fully converged, the mesh refinement is inaccurate, or there are problems with the numerical method, requiring further adjustments and optimization. Therefore, the GCI provides an effective evaluation criterion for the model, helping researchers identify potential convergence anomalies or numerical instabilities, guiding model optimization, and thus improving the accuracy of simulation results, providing a more precise basis for the analysis of wind-wave-current coupling effects.

[0060] In one embodiment, simulating the model and recording the dynamic response of the FPSO platform, and calculating the instability index of the model's simulation results, includes:

[0061] Simulate the model and record the dynamic response displacement of the FPSO platform. Calculate the mean of the response. and standard deviation The calculation formula is: , In the formula, In time Displacement at that point It is the number of time steps;

[0062] The instability index of the simulation results is calculated using the following formula: In the formula, This represents the instability index of the simulation results.

[0063] It should be noted that the data involved in the above calculations were mainly obtained through simulations of a Modelica-based FPSO system. During the simulation, the system performs time-step calculations based on the input conditions of the wind-wave-current coupling model (such as wind speed, wave height, and current velocity), and records the dynamic response displacement data of the FPSO platform at each time step. Using this dynamic response data, the displacement value at each time step can be calculated, thereby further calculating the mean and standard deviation of the response. The acquisition of this data typically relies on high-precision numerical simulation tools, such as Modelica, for numerical integration and solution processes, ensuring the accuracy of the response data and the validity of the simulation results.

[0064] It should be noted that the instability index in the simulation results is an indicator used to measure the volatility and instability of the dynamic response in the Modelica-based FPSO system wind-wave-current coupled simulation model. It assesses the dynamic characteristics of the system over a certain period by calculating the relationship between the mean and standard deviation of the platform's response. A large instability index indicates significant volatility in the platform's displacement response, which may suggest that the model cannot converge stably under certain conditions or that the model has significant sensitivity within a certain parameter range, leading to increased uncertainty in the prediction results. This instability may be caused by factors such as the complexity of the system's internal coupling, drastic changes in external excitation, and convergence issues of the numerical calculation method. In other words, a larger instability index in the simulation results often means that the system has failed to reach convergence during the simulation, and more refined adjustments or optimizations to the model may be needed to ensure its stability and the reliability of the prediction results.

[0065] In one implementation, the advantage of analyzing the instability index of the simulation results in measuring whether the convergence degree of the Modelica-based FPSO system wind-wave-current coupling simulation model is abnormal is as follows:

[0066] Analyzing the instability index of simulation results is crucial for assessing the convergence of Modelica-based FPSO system wind-wave-current coupling simulation models to determine if they exhibit abnormalities. By monitoring the instability index, potential numerical instabilities during simulation can be identified in real time, helping engineers determine if convergence problems or the accumulation of numerical errors exist. An excessively high instability index may indicate that the model fails to converge effectively under certain conditions or that the system's dynamic response exhibits excessive oscillations. This is typically caused by inappropriate simulation parameter selection, insufficient computational accuracy, or unreasonable model assumptions. Analyzing the instability index allows for the timely identification of these potential problems, enabling necessary adjustments and optimizations to the model to ensure the accuracy and stability of the simulation results. Therefore, the instability index is not only a quantitative indicator of system response fluctuations but also an effective tool for assessing the reliability of simulation models.

[0067] In one embodiment, the convergence anomaly coefficient, calculated based on the time step sensitivity index, the mesh independence index, and the simulation result stability index, includes:

[0068] ;

[0069] In the formula, The convergence anomaly coefficient, , , These are the time step sensitivity index, the mesh independence index, and the simulation result stability index, respectively. These are the preset scaling factors for the time step sensitivity index, the mesh independence index, and the simulation result stability index, respectively. All are greater than 0.

[0070] It should be noted that before calculating the convergence anomaly coefficient, the time step sensitivity index, the mesh independence index, and the simulation result stability index need to be normalized. Commonly used normalization methods include Min-Max normalization and Z-Score normalization. The settings can be made according to the actual situation. For example, the expert empowerment method can be adopted, which involves inviting experts in relevant fields to determine the preset ratio coefficients of each indicator through professional opinion surveys and comprehensive evaluations.

[0071] In one embodiment, determining whether the model's convergence is satisfactory, in conjunction with a preset convergence anomaly coefficient threshold, includes:

[0072] The convergence anomaly coefficient is compared with the preset convergence anomaly coefficient threshold. If the convergence anomaly coefficient is less than the preset convergence anomaly coefficient threshold, it means that the convergence of the model is qualified.

[0073] If the convergence anomaly coefficient is not less than the preset convergence anomaly coefficient threshold, it indicates that the model's convergence is unqualified and the model needs to be optimized until the convergence anomaly coefficient is less than the preset convergence anomaly coefficient threshold.

[0074] It is important to note that comparing the convergence anomaly coefficient with a preset threshold is a crucial step in ensuring the stability and accuracy of the simulation model. When the calculated convergence anomaly coefficient is less than the preset threshold, it indicates that the simulation results demonstrate good convergence under the given time step and mesh division, and the error is within an acceptable range. This means that the simulation process has not experienced significant instability or excessive fluctuations, and the model's solution tends to be accurate and stable; therefore, the simulation result can be considered acceptable. Conversely, if the convergence anomaly coefficient is not less than the preset threshold, it indicates that there are significant errors or instabilities in the simulation process, possibly due to inappropriate mesh division, numerical inaccuracies, improper boundary condition settings, or unreasonable physical model assumptions. In this case, model optimization is necessary. This can be achieved by adjusting parameters, refining the mesh, and improving the numerical solution accuracy until the convergence anomaly coefficient meets the preset threshold, ensuring stable convergence and providing more reliable and accurate simulation results. Therefore, the convergence anomaly coefficient, as an important indicator for model validation, plays a vital role in model optimization and improving simulation accuracy.

[0075] It should be noted that when optimizing the model, the accuracy and stability of the simulation results can be improved in various ways. For example:

[0076] 1. Adjusting Model Parameters: Adjusting model parameters is a crucial method for optimizing simulation results. For a Modelica-based FPSO system wind-wave-current coupled simulation model, the following operations can be considered: Adjusting physical parameters: Parameters such as fluid density, viscosity, and wave frequency directly affect the model's dynamic response and stability. Determining a reasonable range of physical parameters through experiments or theoretical analysis and making appropriate adjustments can prevent the model from calculating in unstable regions. Optimizing numerical parameters: Such as time step and maximum number of iterations. An excessively large time step may lead to the accumulation of numerical errors, while an excessively small time step may increase the computational burden and cause numerical instability. By gradually adjusting the time step, the most suitable numerical solution scheme can be found, improving the model's convergence.

[0077] 2. Refining the Mesh: The mesh generation significantly impacts the accuracy and stability of simulation results. For wind-wave-flow coupled simulations of FPSO systems, refining the mesh can improve computational accuracy and convergence. Local Mesh Refinement: In regions with complex flows in fluid dynamics simulations, such as areas with drastic velocity changes or turbulent effects, local mesh refinement can improve computational accuracy. For these regions, higher resolution meshes can be used to capture more detailed physical phenomena and reduce computational errors.

[0078] Global mesh refinement: Appropriately reducing the mesh size throughout the model, especially in regions sensitive to computational results, can effectively reduce numerical errors. However, excessive mesh refinement can significantly increase computational costs, so a balance between accuracy and computational efficiency needs to be struck based on the specific problem.

[0079] 3. Improve the accuracy of numerical solutions:

[0080] In simulation, the accuracy of the numerical solution directly affects the convergence speed and stability of the model. The accuracy of the numerical solution can be improved through the following methods:

[0081] Choosing an appropriate solver: Different numerical solvers are suitable for different types of equations. For most physical models, choosing a solver suitable for nonlinear dynamic systems, such as an implicit solver, can improve the model's stability and convergence. Through experimentation and experience, select the most suitable numerical solution method.

[0082] Optimizing the solution algorithm: During model optimization, it may be necessary to adjust the convergence criteria of the solution algorithm or increase the number of iterations to ensure that the solver can work stably within the convergence error range. This can be achieved by increasing the number of iterations, adjusting the solver's convergence criteria, or applying methods to accelerate convergence.

[0083] Add a precision control mechanism: During the simulation process, an error control mechanism can be added to monitor various errors (such as relative and absolute errors) and adjust the solution precision in real time. When the error reaches a set threshold, an adaptive adjustment strategy can be triggered to improve the numerical stability and accuracy of the model.

[0084] 4. Check the physical model assumptions:

[0085] Simulation models are often simplified based on certain assumptions, such as ignoring certain physical phenomena or simplifying fluid dynamics models. To improve the convergence of the model, it is sometimes necessary to re-examine these assumptions:

[0086] Verify the applicability of the model: Ensure that the physical assumptions in the model are applicable to the current engineering problem. For example, can certain higher-order effects be ignored, or is it necessary to introduce more fluid dynamics details?

[0087] Verify the rationality of boundary conditions: During the modeling process, ensure that the set boundary conditions (such as inflow / outflow conditions, fixed or free boundary conditions) are reasonable and conform to actual engineering conditions. Incorrect or unreasonable boundary conditions will lead to unstable simulation results, thereby affecting the convergence of the model.

[0088] 5. Conduct sensitivity analysis:

[0089] Sensitivity analysis of the model is an effective means of identifying and resolving convergence problems. By systematically varying the model's input parameters and observing the changes in the output response, we can identify which parameters have a significant impact on model stability. We should focus on the key parameters that affect system stability and accuracy, and then perform detailed optimization on these parameters.

[0090] By adjusting model parameters, refining the mesh, improving numerical solution accuracy, verifying physical model assumptions, and conducting sensitivity analysis, the Modelica-based FPSO system wind-wave-current coupling simulation model can be effectively optimized, improving its convergence and stability. These measures complement each other, not only ensuring the accuracy of simulation results but also reducing the waste of computational resources, ultimately improving the reliability and practicality of the model in engineering applications.

[0091] The foregoing has provided a detailed description of one embodiment of the present invention, but this description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and modifications made within the scope of the claims of this invention should still fall within the patent coverage of this invention.

Claims

1. A wind-wave-current coupled environment modeling method for FPSO systems based on Modelica, characterized in that, Includes the following steps: Set multiple different time steps, and for each time step, run the simulation model and record the response of key physical quantities, and calculate the time step sensitivity index; The fluid domain involved in the model is divided into different meshes, and the model is simulated separately. The key physical quantities of the response are recorded, and the mesh independence index is calculated. The model was simulated and the dynamic response of the FPSO platform was recorded. The instability index of the simulation results of the model was calculated. The convergence anomaly coefficient is calculated based on the time step sensitivity index, mesh independence index, and simulation result instability index. The convergence of the model is then judged to be qualified based on the preset convergence anomaly coefficient threshold. The calculation of the time step sensitivity index includes: Set multiple different time step values, namely: coarse time step Medium time step Fine time step ; For each time step, run the simulation and record the responses of key physical quantities; the recorded physical quantities are: the responses of physical quantities at coarse time steps. Physical quantity response at an average time step Physical quantity response at fine time steps ; Calculate the error at each time step, for example, by calculating the relative error of platform displacement or acceleration: ; ; In the formula, , , These represent the errors under coarse time steps, medium time steps, and fine time steps, respectively. This is a pre-defined reference solution; Calculate the error ratio for different time steps and combine it with the time step difference to obtain the time step sensitivity index: In the formula, For time step sensitivity index; The calculation of grid independence indices includes: Within the fluid domain, select coarse and fine meshes, as follows: coarse mesh size... Fine mesh size ; Simulations were performed separately for coarse and fine meshes, and the key physical quantities of the response were recorded. These key physical quantities represent the displacement values ​​under the coarse and fine meshes, respectively: displacement response under coarse mesh. Displacement response under fine mesh ; and ; Calculate the relative error between the coarse and fine meshes based on their displacement responses. This reflects the impact of mesh generation on the results: the calculation formula is: ; The grid independence index is calculated using the following formula: In the formula, The grid independence index, The grid convergence index; The instability index of the simulation results of the computational model includes: Simulate the model and record the dynamic response displacement of the FPSO platform. Calculate the mean of the response. and standard deviation The calculation formula is: , In the formula, In time Displacement at that point It is the number of time steps; The instability index of the simulation results is calculated using the following formula: In the formula, The instability index of the simulation results; The calculated convergence anomaly coefficients include: ； In the formula, The convergence anomaly coefficient, , , These are the time step sensitivity index, the mesh independence index, and the simulation result instability index, respectively. These are the preset scaling factors for the time step sensitivity index, the mesh independence index, and the simulation result instability index, respectively. All are greater than 0; Judging whether the convergence of the model is qualified by combining the preset convergence anomaly coefficient threshold includes: The convergence anomaly coefficient is compared with the preset convergence anomaly coefficient threshold. If the convergence anomaly coefficient is less than the preset convergence anomaly coefficient threshold, it means that the convergence of the model is qualified. If the convergence anomaly coefficient is not less than the preset convergence anomaly coefficient threshold, it indicates that the model's convergence is unqualified and the model needs to be optimized until the convergence anomaly coefficient is less than the preset convergence anomaly coefficient threshold.

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