Intelligent Prediction Method and System for Seakeeping Performance of Ships Based on Physics-Informed Neural Networks

Abstract

The present invention belongs to the technical field of ship and ocean engineering, and discloses an intelligent prediction method and system for ship seakeeping performance based on physics-informed neural networks. This method combines the CFD-RAO method with PINNs, and realizes the rapid and high-precision prediction of ship seakeeping performance by constructing a coupling model of physical equations and neural network loss functions. The present invention realizes the rapid and high-precision prediction of ship seakeeping performance. This method can not only effectively cope with the multi-degree-of-freedom coupling motion under complex sea conditions, but also has strong real-time performance and adaptability, providing more scientific and reliable technical support for ship design and navigation safety.

Description

Technical Field

[0001] The present invention belongs to the technical field of ship and ocean engineering, and particularly relates to an intelligent prediction method and system for ship seakeeping performance based on physics-informed neural networks. Background Art

[0002] Seakeeping performance is one of the key indicators of ship hydrodynamic performance, and has an important impact on the safety, comfort and economy of ships during navigation. In traditional hull design, designers usually pay more attention to the optimization of calm water resistance to improve the ship's speed. However, with the complexity of the ship navigation environment, the importance of seakeeping performance has been gradually recognized. Seakeeping performance not only affects the stability of ships in rough sea conditions, but also directly relates to the safety of crew and cargo, as well as the operating cost of ships.

[0003] Current seakeeping prediction technologies mainly rely on methods such as physical model experiments, computational fluid dynamics (CFD) simulations, and empirical formulas. Although these methods can reflect the seakeeping performance of ships to a certain extent, they are usually based on preset working conditions and conditions, which limit the coupling, accuracy, and fast performance prediction of complex models under complex conditions, making it difficult to cope with complex and changing actual sea conditions, and the calculation efficiency is low and it is difficult to quickly predict seakeeping performance. In addition, although methods such as the response amplitude operator (RAO) alone have relatively high calculation efficiency, they have limitations in dealing with multi-degree-of-freedom, nonlinear, and coupled motions, and cannot achieve high-precision and real-time prediction under complex conditions.

[0004] With the rapid development of artificial intelligence and deep learning technologies, physics-informed neural networks (PINNs) have gradually become an emerging tool for solving complex problems involving physical laws. Physics-informed neural networks are a hybrid method that combines physical equations with data-driven models. By embedding physical laws into the structure of neural networks, the generalization ability and prediction accuracy of the models are greatly improved. Compared with traditional neural networks, PINNs not only rely on data for learning, but also can constrain the models through physical equations, making the prediction results conform to physical laws, thereby effectively reducing the overfitting phenomenon and improving the prediction accuracy under unseen data conditions.

[0005] In the field of ship seakeeping prediction, the application of PINNs has gradually attracted attention. Although traditional deep learning models perform well in processing large amounts of data, in the prediction of complex sea conditions and nonlinear coupled motions, the lack of consideration of physical laws often leads to prediction deviations. By using the physical equations of ship motion as the loss function of the neural network, PINNs enables the model to not only learn data features during training but also follow physical laws, thus significantly improving the prediction accuracy of ship seakeeping in complex sea conditions. Therefore, a ship seakeeping prediction method based on physics-informed neural networks is proposed to ensure fast and accurate prediction.

[0006] The problems and defects of the existing technology are as follows: In the existing technology, the prediction accuracy of ship seakeeping is low, the real-time performance and adaptability to multi-degree-of-freedom coupled motions under complex sea conditions are poor, and it cannot provide a scientific basis for ship design and navigation safety. Summary of the Invention

[0007] To overcome the problems in the related technology, the disclosed embodiments of the present invention provide an intelligent ship seakeeping prediction method and system based on physics-informed neural networks. In particular, it relates to the cross-technology field of applying machine learning and deep learning technologies to physical process simulation. The method combines computational fluid dynamics (CFD) and response amplitude operator (RAO) technologies to construct an intelligent model that can quickly and accurately predict the motion response of a ship in waves and its seakeeping performance. By combining physical equations with actual data through the loss function of the neural network, the model can not only achieve high-precision prediction but also have higher adaptability and reliability, especially under complex sea conditions.

[0008] The technical solution is as follows: An intelligent ship seakeeping prediction method based on physics-informed neural networks, which combines the CFD-RAO method with PINNs. By constructing a coupled model of physical equations and the neural network loss function, it realizes fast and high-precision prediction of ship seakeeping, specifically including the following steps:

[0009] S1. Use computational fluid dynamics CFD and response amplitude operator RAO methods to obtain the dataset required for the physics-informed neural network, and preprocess the dataset;

[0010] S2. Use the prediction error equation and the physical equation of ship seakeeping to construct a loss function to constrain the neural network;

[0011] S3. Apply a combined optimizer for network training;

[0012] S4. Conduct network prediction and evaluation to achieve the prediction of ship seakeeping.

[0013] In step S1, a dataset required for the physics-informed neural network is obtained using the computational fluid dynamics (CFD) and the response amplitude operator (RAO) method, including:

[0014] (1.1) Construct a control model based on the CFD-RAO method;

[0015] (1.2) Establish a physical model of the ship and the flow field;

[0016] (1.3) Perform CFD-RAO coupled simulation.

[0017] In step (1.1), constructing a control model based on the CFD-RAO method includes:

[0018] Use the volume of fluid (VOF) method to capture the free surface wave during ship navigation. The expression is:

[0019] ;

[0020] ;

[0021] Where: is the fluid density, is the fluid velocities in three directions, is the time series, is the fluid pressure, is the spatial coordinates in three directions, is the component of the fluid velocity in the -th direction, is the component of the spatial coordinate in the -th direction, is the -th direction of the gravitational acceleration, is the dynamic viscosity coefficient of the fluid, is the turbulent pulsation component of the fluid velocity, is the turbulent pulsation component of the fluid velocity in the -th direction;

[0022] Adopt turbulence model to close the RANS equation. In the simulation of ship resistance, position derivative, rudder derivative, and rotation derivative tests, the basic equations are:

[0023] ;

[0024] ;

[0025] Where, is the turbulent kinetic energy, is the fluid in The dynamic viscosity coefficient in the is the fluid velocity, and the fluid velocity component in the direction, are all diffusion coefficients, are all turbulence production terms, are all turbulence dissipation terms, are all user-defined source terms, is the specific dissipation rate, is the orthogonal divergence term;

[0026] The hull is a rigid body. Select the reference coordinate system , with the coordinate origin at the midship, pointing to the stern, pointing to the starboard, vertically upward; the hull navigation attitude motion equation is:

[0027] ;

[0028] ;

[0029] ;

[0030] ;

[0031] In the formula, is the structural mass matrix, is the moment of inertia of the hull about , are the heave acceleration, pitch, and roll acceleration of the ship respectively, are the resultant forces acting on the hull along the axis, the resultant moment about the rotation axis, and the resultant moment about the axis respectively. The resultant force is obtained by integrating the hull surface stress under the condition of real-time solving the hull motion and capturing the free surface, considering the coupling effect between degrees of freedom;

[0032] After obtaining the data by CFD calculation, the response amplitude operator RAO method is used to obtain the dynamic response characteristics. The 6-degree-of-freedom ship linear frequency-domain motion equation corresponding to regular waves is:

[0033] ;

[0034] In the formula, is the encounter frequency, is the mass coefficient, is the th directional added mass coefficient and damping coefficient induced by the motion mode, is the restoring force coefficient, is the complex motion amplitude of the mode, is the unit wave amplitude wave force in the direction of, the wave amplitude, are the 6 degrees of freedom of the ship, represents the corresponding degree of freedom coupled with the degree of freedom.

[0035] In step (1.2), a physical model of the ship and the flow field is established, including:

[0036] A virtual wave tank with water as the fluid, set the variable parameters of the wave, capture the free surface by the volume of fluid method VOF, and use the overlapping network technology to simulate the ship's navigation attitude in real time to complete the establishment of the ship's navigation model.

[0037] In step S2, a loss function is constructed to constrain the neural network using the prediction error equation and the physical equation of the ship's seakeeping performance, including:

[0038] According to the principle of energy conservation of the ship's motion in waves, a relationship function between energy loss and prediction error is constructed to physically constrain the network, and the total loss function under the degree of freedom is constructed:

[0039] ;

[0040] In the formula, is the total loss function under the degree of freedom, are the weight coefficients of the two loss terms respectively, is based on the energy loss equation between the ship and the wave, is the prediction error value of the motion response, and the expression is:

[0041] ;

[0042] ;

[0043] In the formula, is the number of data points in the seakeeping performance state data set of the ship in a short time, is the total energy of the ship at time, is the predicted value of the network, is the true motion response amplitude of the th sample, is the linear damping coefficient, is the angular velocity under the is the th time point, is the th time point, is the mean absolute error (MAE) under the th degree of freedom, used to evaluate the deviation between the network predicted value and the true value .

[0044] Furthermore, the energy method is adopted to derive the equation of energy loss, and the decay motion equation of the ship's degree of freedom is obtained. The expression is:

[0045] ;

[0046] In the formula, is the total moment of inertia of the ship, are respectively the angle, angular velocity and angular acceleration under the degree of freedom, is the restoring force coefficient, is the linear damping coefficient, describing the influence of the damping force proportional to on the system, is the nonlinear damping coefficient, describing the influence of the nonlinear damping force proportional to on the system;

[0047] Dividing both sides of the equation by the total moment of inertia of the ship , we get:

[0048] ;

[0049] In the formula, is the natural angular frequency of the system under the th degree of freedom;

[0050] The total energy during the decay process of the ship's free degree of freedom consists of two parts: the kinetic energy caused by free rotation and the potential energy caused by the work done by the hydrostatic restoring moment. The total energy at time

[0051] is:

[0052] According to the principle of energy conservation in hydrodynamics, the energy loss equation at different times is obtained:

[0053] ;

[0054] In the formula, is the total energy of the ship at time, is Total energy of the ship at a moment.

[0055] In step S3, a combined optimizer is applied for network training, including:

[0056] Obtain the seakeeping response data of the ship under different sea conditions through the CFD-RAO method. The seakeeping response data includes the pitching, rolling, and heaving dynamic characteristics of the ship in waves. Based on the above data, construct a fully connected neural network model with time series as the input, and perform segmentation processing on the data for training the fully connected neural network model.

[0057] During the training process, an optimizer combination strategy is adopted. First, use the Adam optimizer for rapid convergence in the initial stage to approach the global optimal solution. Then switch to the LBFGS optimizer for multiple iterations and adjust with an automatic learning rate.

[0058] In step S4, network prediction and evaluation are performed to achieve the prediction of the ship's seakeeping performance, including: Using the trained fully connected neural network model to predict the seakeeping response values of the ship's pitching, rolling, and heaving for a new data set.

[0059] Another object of the present invention is to provide an intelligent prediction system for ship seakeeping performance based on a physics-informed neural network. This system implements the intelligent prediction method for ship seakeeping performance based on a physics-informed neural network. The system includes:

[0060] An initialization network and data preprocessing module for obtaining the data set required for the physics-informed neural network using the computational fluid dynamics CFD and the response amplitude operator RAO method, and preprocessing the data set.

[0061] A neural network loss function construction module for constructing a loss function to constrain the neural network using a prediction error equation and a physical equation related to ship seakeeping performance.

[0062] A network training module for applying a combined optimizer for network training.

[0063] A network prediction and evaluation module for performing network prediction and evaluation to achieve the prediction of the ship's seakeeping performance.

[0064] Combining all the above technical solutions, the beneficial effects of the present invention are as follows: The present invention combines the CFD-RAO method with PINNs, and realizes the rapid and high-precision prediction of ship seakeeping performance by constructing a coupled model of a physical equation and a neural network loss function. This method can not only effectively cope with the multi-degree-of-freedom coupled motion under complex sea conditions, but also has strong real-time performance and adaptability, providing more scientific and reliable technical support for ship design and navigation safety.

[0065] The present invention first proposes to obtain a dataset through the CFD-RAO method and train it in a physics-informed neural network, as well as a specific physics-informed neural network algorithm including a loss function. By introducing the RAO, the disadvantages of high computational cost and long time consumption of traditional CFD methods are overcome; combined with CFD, the adaptability to complex non-linear conditions and complex environments is ensured; the combination of the two achieves faster and more accurate prediction, meeting the needs of real-time decision-making. Secondly, by introducing the physics-informed neural network (PINN, which combines physical constraints and neural networks), high-precision prediction can be completed in a short time, providing feasible technical support for the real-time monitoring and prediction of ship seakeeping performance. The PINN method is applicable to fields such as ship design and navigation safety assessment. In addition, it can also be extended to the dynamic performance assessment of other offshore engineering structures such as offshore wind power platforms and floating production units. The proposal of the present invention not only realizes localization, breaks the monopoly of foreign ship industry simulation software, but also achieves further breakthroughs and innovations on the development level of foreign software systems, and proposes a system with better performance and the ability to be put into real-time experiments.

[0066] The present invention solves the contradiction between real-time performance and computational efficiency, proposes the CFD-RAO method, which not only reduces costs but also improves computational efficiency, achieving fast and high-precision prediction. It solves the problem of difficulty in maintaining high precision in real sea conditions. By using the data obtained by the CFD-RAO method for model training and using the trained physics-informed neural network, high-precision prediction can be maintained under complex non-linear and multi-degree-of-freedom conditions. It can not only fit the observed values driven by data, but also follow physical laws under complex sea conditions, making the prediction more reliable and accurate. The physics-informed neural network effectively integrates physical laws and a large amount of obtained data, enabling the model to maintain prediction accuracy even in data-scarce regions. This advantage solves the contradiction between data scarcity and high-precision requirements in ship engineering and meets the long-term technical needs of people.

[0067] By introducing the physics-informed neural network (PINN), the present invention effectively overcomes the technical biases of traditional methods in terms of data dependence, non-linear adaptability, computational cost, and generalization ability. The PINN method embeds physical equations into the loss function of the neural network, realizing the organic combination of physical laws and data-driven models, enabling the model to still have high-precision prediction ability under data-scarce or unseen conditions. In addition, this method significantly improves the adaptability under complex non-linear sea conditions and meets the real-time requirements at a low computational cost, breaking through the limitations of traditional prediction methods in terms of real-time performance and accuracy, and providing an efficient and reliable innovative solution for ship seakeeping performance prediction. Description of the Drawings

[0068] The accompanying drawings herein are incorporated into and constitute a part of this specification, showing embodiments consistent with the present disclosure, and are used together with the specification to explain the principles of the present disclosure;

[0069] Figure 1 It is a flowchart of the intelligent seakeeping prediction method for ships based on the physics-informed neural network provided by an embodiment of the present invention;

[0070] Figure 2 It is a schematic diagram of the ship wave sailing grid scene model provided by an embodiment of the present invention;

[0071] Figure 3 It is a structural diagram of the physics-informed neural network provided by an embodiment of the present invention;

[0072] Figure 4 It is a schematic diagram of the intelligent seakeeping prediction system for ships based on the physics-informed neural network provided by an embodiment of the present invention;

[0073] In the figure: 1. Initialization network and data preprocessing module; 2. Construction of neural network loss function module; 3. Network training module; 4. Network prediction and evaluation module. Detailed implementation manners

[0074] To make the above objects, features, and advantages of the present invention more apparent and understandable, the following detailed description of the specific implementation manners of the present invention will be made with reference to the accompanying drawings. Many specific details are set forth in the following description to fully understand the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the connotation of the present invention. Therefore, the present invention is not limited by the specific implementations disclosed below.

[0075] The novelty of the present invention lies in that: based on the physics-informed neural network (PINN) trained by obtaining a database through the CFD-RAO method, the physical laws are embedded into the neural network loss function, integrating data-driven and physical constraints to achieve real-time and high-precision prediction of ship seakeeping in complex non-linear sea conditions. This method combines high efficiency, generalization ability, and multi-domain applicability, providing an innovative solution for ship design and navigation safety.

[0076] The present invention includes simulating the navigation of a ship under the action of waves based on the CFD-RAO method, constructing a prediction equation for the ship's energy and motion response as the loss function of a neural network, and using the physics-informed neural network method to predict the seakeeping performance of the ship through time series. Among them, the CFD-RAO method is used to perform frequency-domain analysis on the ship's time-domain response data, including the fluid phase and turbulence equations and the ship's motion frequency-domain equation, constructing a physical model of the ship's wave navigation, and performing coupled calculation simulations. Predict the dynamic characteristics of the ship's hull in the next second, improve the prediction accuracy, and ensure the safety and comfort of the ship during navigation through a real-time detection system.

[0077] The present invention innovatively proposes a method combining CFD and RAO. The CFD method is commonly known for its high accuracy but low computational efficiency; the RAO method has few applications and large limitations, but high computational efficiency.

[0078] Example 1, as Figure 1 shown, the intelligent seakeeping prediction method for ships based on the physics-informed neural network provided by the embodiment of the present invention includes:

[0079] S1. Use the computational fluid dynamics CFD and the response amplitude operator RAO method to obtain the data set required by the physics-informed neural network, and preprocess the data set;

[0080] In this step, the input parameters of the neural network are clarified, and these parameters include time series , the ship's moment of inertia , the wave frequency and the coordinate position of the ship and the mass matrix ; these parameters are closely related to the influence of waves on the seakeeping performance of the ship. In order to accurately capture the seakeeping response of the ship under specific wave conditions, a large amount of original data needs to be collected first. These data include, but are not limited to, the motion displacement, velocity and acceleration of the ship under different wave conditions and position characteristics. The data can be obtained by performing frequency-domain analysis on the response data obtained through CFD simulation or model tests to obtain the response amplitude operator (RAO) at each frequency, reflecting the dynamic response characteristics of the ship in waves, as model data. As Figure 2 shown in the ship wave navigation grid scene model, using the star ccm+ software as the model carrier and adopting the method of overlapping grid encryption ensures the accuracy and reliability of the calculation.

[0081] In the preprocessing stage, data augmentation, adversarial denoising, etc. are performed on time series data, resulting in better processing results for time series data to ensure the consistency and accuracy of data input. Based on this, a frequency domain response database is established to provide a reliable data basis for the subsequent neural network training. And in actual applications later, only by looking up or interpolating the RAO data in this database can the corresponding response results be quickly obtained, without the need to repeat CFD simulations, achieving fast and accurate prediction.

[0082] S2. Construct a loss function to constrain the neural network using the prediction error equation and the physical equation of ship seakeeping performance;

[0083] In this step, the output of the neural network model is set to the angular velocity, damping coefficient, and predicted motion response amplitude of a certain degree of freedom of the ship. The construction of the loss function takes into account two main constraints: one is the physical equation constraint of the ship's motion response, and the other is the prediction accuracy of the predicted motion response amplitude. The constraint of the physical equation is based on the energy conservation theory in ship seakeeping analysis to ensure that the prediction results of the network follow physical laws. At the same time, by internally predicting parameters such as the resistance coefficient, added mass, and damping coefficient of the ship, the model's understanding and simulation ability of ship motion under complex sea conditions are further enhanced.

[0084] S3. Apply a combined optimizer for network training;

[0085] During the training process of the neural network, an optimizer combination strategy is adopted to ensure the efficiency of training and the accuracy of the model. In the initial stage of training, the Adam optimizer is used. Through its momentum accumulation and adaptive learning rate adjustment mechanism, the model can quickly converge to a region close to the global optimal solution. The relatively large learning rate of the Adam optimizer in the initial stage helps the model quickly reduce the loss value, achieve fast convergence, and ensure that the model reaches good performance in a short time. As the training progresses, the optimization strategy switches to the LBFGS optimizer. LBFGS utilizes approximate second-order information, combined with fine step size control and dynamic learning rate adjustment, to further optimize the model parameters, reducing the prediction error under physical constraint conditions. Through more accurate gradient direction and learning rate adjustment, LBFGS not only improves the numerical accuracy of the model but also ensures that the prediction results conform to the physical laws of ship seakeeping performance, avoids overfitting, and maintains stability and reliability under complex sea conditions. This combination strategy effectively balances the training efficiency and the accuracy of the model.

[0086] S4. Conduct network prediction and evaluation to achieve the prediction of ship seakeeping performance;

[0087] After completing the neural network training, the trained model is used to predict a new dataset, and dynamic characteristics (such as pitch, roll, and heave) of the new dataset are predicted. It not only relies on data-driven but also incorporates physical equations (such as energy conservation) as constraints for the loss function to ensure that the prediction results conform to actual physical laws. In addition, the combined optimizer strategy (Adam and LBFGS) adopted during the training process achieves fast convergence in the initial stage and refined tuning in the later stage, enabling the model to have higher numerical accuracy and stability during prediction. Finally, by comparing with physical models or experimental data, the system verifies the superior prediction performance of the model under complex sea conditions, ensuring its reliability and accuracy in practical applications.

[0088] Exemplarily, the method for constructing the neural network loss function in step 2 is specifically as follows:

[0089] For the problem of ship seakeeping prediction, an advanced method combining physics-informed neural networks (PINNs) with ship motion responses is introduced. Among them, as Figure 3 shown in the structure diagram of the physics-informed neural network, from top to bottom are the input layer, hidden layer, output layer, loss function, and the mechanism of operation and output. Among the input parameters: is the time series, are the encounter frequency of the ship and the natural frequency of the wave, is the moment of inertia about the axis of rotation, is the ship's coordinate position, is the structural mass matrix. Among the output parameters: is the angular velocity of the ship in a certain degree of freedom, are the linear damping coefficient and the nonlinear damping coefficient respectively, is the amplitude of the motion response predicted by the neural network.

[0090] For seakeeping indexes such as the longitudinal motion (such as heave and pitch) and heave response of the ship, the model comprehensively considers multi-dimensional input variables such as time series, wave characteristics, and mass matrix, and innovatively embeds physical equations into the loss function to ensure that the neural network can not only learn the characteristics of the data but also strictly follow the physical laws in ship dynamics during the training process. In the specific design of the loss function, the model not only considers data errors but also further adds constraints based on physical factors of energy conservation. These physical constraints are incorporated into the loss function of the neural network through a formulated energy term, enabling the model to not only fit the data distribution but also continuously adjust the output to conform to the real physical response during the process of minimizing the loss. This method effectively solves the overfitting and instability problems of conventional neural networks in nonlinear coupling systems.

[0091] Exemplarily, the construction of the total loss function:

[0092] The total loss function of the PINNs model proposed by the present invention consists of two parts, and the specific expression is as follows:

[0093] The data prediction loss part quantifies the error between the predicted ship attitude of the model and the experimental data.

[0094] ;

[0095] The energy loss is constructed based on the principle of energy conservation between the ship and the wave, which further ensures the physical rationality of the model prediction.

[0096] ;

[0097] In the formula, is the total loss function under the degrees of freedom, are the weight coefficients of the two loss terms respectively, is based on the energy loss equation between the ship and the wave, is the predicted error value of the motion response, and the expression is:

[0098] ;

[0099] By adjusting the values of the weight coefficients, the physical error and the data error are reduced, so that the total loss function reaches the minimum value. The minimization process of the total loss function can prompt the neural network to accurately fit the data on the premise of satisfying the physical constraints, enabling the PINN to handle complex problems with physical constraints. It can not only fit the training data well, but also ensure that the prediction results of the model conform to the physical laws, and are more reliable and accurate in complex practical applications.

[0100] Example 2, as another implementation manner of the present invention, the ship seakeeping intelligent prediction method provided by the embodiment of the present invention includes:

[0101] Step 1. Use the computational fluid dynamics (CFD) and response amplitude operator (RAO) methods to obtain the data set required for the physics-informed neural network, including:

[0102] (1.1) Construct a control model based on the CFD-RAO method.

[0103] When using the fluid phase for simulation, it is considered that the fluid phase is an incompressible viscous fluid and follows the mass conservation law and the momentum conservation law when flowing in the flow field. The basic equations are selected as the continuity equation and the Navier-Stokes equation, and the volume of fluid method (VOF) is used to capture the free surface wave during the ship's navigation.

[0104] ;

[0105] ;

[0106] wherein: is the fluid density, is the fluid velocities in three directions, is the fluid pressure, is the spatial coordinates in three directions, is the component of the fluid velocity in the th direction, is the component of the spatial coordinate in the th direction, is the gravitational acceleration in the th direction, is the dynamic viscosity coefficient of the fluid, is the turbulent pulsation component of the fluid velocity, is the turbulent pulsation component of the fluid velocity in the th direction;

[0107] Adopting the turbulence model to close the RANS equations, in the simulations of ship resistance, position derivatives, rudder derivatives, and rotational derivatives tests, the basic equations are:

[0108] ;

[0109] ;

[0110] wherein, is the turbulent kinetic energy, is the dynamic viscosity coefficient of the fluid in the direction, is the fluid velocity, is the velocity component of the fluid in the direction, are all diffusion coefficients, are all turbulence production terms, are all turbulence dissipation terms, are all user-defined source terms, is the specific dissipation rate, is the orthogonal divergence term;

[0111] Assume that the hull is a rigid body, and select the reference coordinate system with the origin of coordinates at the midship, pointing to the stern, pointing to the starboard, vertically upward; the motion equations of the hull navigation attitude (heave, pitch, roll, etc.) are as follows:

[0112] ;

[0113] ;

[0114] ;

[0115] ;

[0116] In the formula, is the structural mass matrix, is the moment of inertia of the hull about ; are the heave acceleration, pitch, and roll acceleration of the ship respectively, are the resultant forces acting on the hull along the axis, the resultant moment about the rotation axis, and the resultant moment about the axis respectively. The resultant force is obtained by integrating the hull surface stress under the condition of real-time solving the hull motion and capturing the free surface, considering the coupling effect between degrees of freedom;

[0117] The core of ship seakeeping performance calculation is to accurately predict the motion of the ship in waves. The dynamic characteristics of the hull under wave action can be described by the frequency response method in the frequency range. After obtaining the data by CFD calculation, the response amplitude operator (RAO) method is used to obtain the dynamic response characteristics. The 6-degree-of-freedom ship linear frequency-domain motion equation corresponding to regular waves is:

[0118] ;

[0119] In the formula, is the encounter frequency, is the mass coefficient, is the th kind of added mass coefficient and damping coefficient induced by the direction of motion mode, is the restoring force coefficient, is the modal complex motion amplitude, is the direction unit wave amplitude wave force, is the wave amplitude, are the 6 degrees of freedom of the ship, represents the corresponding degree of freedom coupled with the degree of freedom.

[0120] (1.2) Establish the physical model of the ship and the flow field.

[0121] The hull model calculates data using various ship types and scales. Taking the MOERI Container Ship (KCS) model with a scale ratio of 31.599 as an example, the remaining parameters are shown in Table 1.

[0122] Table 1 Ship model parameters

[0123]

[0124] Ship navigation model: In a virtual wave tank with water as the fluid, variable parameters of waves are set, and the VOF (Volume of Fluid) method is used to capture the free surface, and the overlapping network technology is used to simulate the ship navigation attitude in real time. The density of the water in the model is 997.561 kg / m³. The properties of water and waves are defined in the Eulerian phase, and the relative motion between the ship and the flow field is defined. As Figure 2 shown.

[0125] (1.3) CFD-RAO coupled simulation.

[0126] To accurately simulate the hydrodynamic performance of the ship during navigation, the longitudinal and transverse lengths of the computational domain are set to 6.0 times the ship length, and the vertical height is set to 4.0 times the ship length. The ship is kept at a fixed position. The upstream inlet boundary is the wave generation area, and the wave height, period, wavelength, wave direction, etc. of the waves are defined at the inlet. The Froude number is used to perform the calculation. The outlet boundary is set as the wave absorption area, and the lateral boundary is set as the symmetry plane. The hull surface is configured with an anti-slip wall condition. The physical model is wave-dissipated to prevent waves from generating reflections, interference, or other adverse effects in unnecessary areas. The motion model is connected to the flow solver, and the spatial position and boundary condition function of the control grid are updated at each time step, and local grid refinement is performed in areas such as the free surface, ship model, and Kelvin waves on the hull to ensure the calculation accuracy of the flow field; six layers of prism grids are generated near the hull surface to simulate the boundary layer flow. The dynamic characteristics of the ship collected over time are subjected to frequency domain transformation analysis to calculate the response amplitude of the ship when the wave frequency changes, obtain the motion response of the hull, and thus study the seakeeping performance of the hull. Multiple simulations are performed according to different working conditions to evaluate the seakeeping performance of the hull under different conditions.

[0127] Step 2: Construct a loss function to constrain the neural network using physical equations related to waves and ship seakeeping;

[0128] Due to the principle of energy conservation of the ship's motion in waves, a relationship function between energy loss and prediction error is constructed to physically constrain the network, and a loss function in degrees of freedom is constructed:

[0129] ;

[0130] Wherein, is the total loss function under degrees of freedom, are the weight coefficients of the two loss terms respectively, is the energy loss equation based on the energy loss between the ship and the waves, is the predicted error value of the motion response, and the expression is:

[0131] ;

[0132] ;

[0133] Wherein, is the number of data points in the seakeeping state dataset of the ship in a short period of time, is the total energy of the ship at time, is the predicted value of the network, is the true motion response amplitude of the th sample, is the linear damping coefficient, is the angular velocity under the th degree of freedom, is the th time point, is the th time point, is the mean absolute error under the th degree of freedom, used to evaluate the deviation between the network predicted value and the true value.

[0134] During the training process, the neural network not only considers the prediction error, but also ensures the compliance of physical laws, making the model have higher credibility and reliability in practical applications.

[0135] Exemplarily, in step 2, the energy method is used to deduce the energy loss equation. Further research is carried out according to the ship's degree-of-freedom decay motion equation given by Jiang Yin et al. The innovative ship's degree-of-freedom decay motion equation given by the present invention is:

[0136] ;

[0137] Wherein, is the total moment of inertia of the ship, are respectively the angle, angular velocity and angular acceleration under the degree of freedom, is the restoring force coefficient, is the linear damping coefficient, describing the influence of the damping force proportional to is the non - linear damping coefficient, describing the influence of the non - linear damping force proportional to on the system;

[0138] Dividing both sides of the equation by the total inertia moment of the ship , we get:

[0139] ;

[0140] In the formula, is the natural angular frequency of the system in the degree of freedom;

[0141] The total energy of the ship's free - degree decay process consists of two parts: the kinetic energy caused by free rotation and the potential energy caused by the work done by the hydrostatic restoring moment. The total energy at time

[0142] is:

[0143] According to the principle of energy conservation in hydrodynamics, the energy loss equation at different times is obtained:

[0144] ;

[0145] In the formula, is the total energy of the ship at time, is the total energy of the ship at time.

[0146] In this way, the physical constraints in the prediction of the physical neural information network are ensured, which is of great significance for the authenticity and reliability of the prediction results.

[0147] In step 3 and step 4, the ship's seakeeping performance is predicted, optimized and evaluated through the physical - informed neural network method in time series.

[0148] First, the seakeeping response data of the ship under different sea conditions are obtained through the CFD - RAO method. These data include the dynamic characteristics such as the pitch, roll and heave of the ship in waves. Based on these data, a fully - connected neural network model is constructed with time series as the input, and the data are segmented and then the model training starts.

[0149] During the training process, an optimizer combination strategy is adopted. First, the Adam optimizer is used for rapid convergence in the initial stage to ensure that the model quickly approaches the global optimal solution. As the training progresses, it is switched to the LBFGS optimizer for fine - tuning to further improve the prediction accuracy of the model. The training process includes tens of thousands of iterative steps and an automatic learning rate is used for adjustment to ensure that the model can adapt to the complexity of different sea conditions.

[0150] After the model training is completed, the trained neural network model is used to predict a new data set, with a focus on the model's performance in predicting seakeeping response values such as ship pitch, roll, and heave. By comparing the model's prediction results with existing physical models or experimental data, its prediction accuracy and reliability are evaluated.

[0151] Exemplarily, since the seakeeping performance of ships under different sea conditions is complex and variable, each small batch of data cannot fully represent the distribution of hull characteristics during the entire navigation process, which may lead to oscillations in the loss value at the end of training. However, the final neural network model can still effectively predict the seakeeping performance of the ship at the next moment, providing reliable technical support for ship design and navigation safety.

[0152] During the training process of the deep learning model, using a large number of iterative steps and an automatic learning rate adjustment strategy is an effective method to improve the model's performance. By adopting a higher learning rate at the initial stage to quickly converge, and then fine-tuning by adjusting the learning rate at the later stage, the model can show stronger adaptability in complex and variable environments. This method is particularly suitable for complex tasks such as ship seakeeping prediction, because it can ensure that the model can effectively learn data features and follow physical laws when processing data under different sea conditions, providing reliable prediction results.

[0153] This seakeeping prediction method based on physics-informed neural networks significantly improves the speed, accuracy, and practicality of prediction by combining computational fluid dynamics (CFD) and response amplitude operator (RAO) techniques. Using a combined optimizer and an automatic learning rate adjustment strategy not only improves the model's convergence speed but also ensures reliability and stability under complex sea conditions. These advantages make this method have important technical value in practical applications, providing more scientific and reliable support for ship design and navigation safety.

[0154] The present invention combines CFD, RAO, and physics-informed neural networks (PINNs) methods to predict the dynamic characteristics of ships under complex sea conditions through efficient and accurate frequency-domain response analysis, and verifies its superior performance in different application scenarios (such as ship stability under high-frequency waves, safety of deep-sea drilling platforms, seakeeping performance of military ships, attitude control of autonomous ships, etc.). In the simulation experiment, the sea conditions are set to include complex conditions such as large-amplitude long-period waves, high-frequency irregular waves, and multi-directional coupled wave conditions to comprehensively evaluate the adaptability and reliability of the model. The experimental results show that the prediction error of the PINNs model under these complex sea conditions is less than 9.5%, and it can capture the dynamic response of ships more quickly and accurately than traditional methods, providing efficient and low-error technical support for practical applications.

[0155] The present invention has important social value, enhancing the safety and stability of ships in complex sea conditions, contributing to energy conservation and emission reduction, and supporting the development of intelligent shipping. At the same time, this technology can be extended to other industries, such as the safety assessment of offshore wind farms and offshore oil platforms, to ensure the operational stability of facilities in harsh environments. In addition, in the fields of autonomous driving and intelligent control, the precise prediction ability of this technology can provide efficient and real-time safety guarantees for automated systems such as unmanned ships and unmanned platforms, conduct fatigue prediction and sea condition analysis, promote the application of intelligent technologies in water transportation and resource development, drive industrial transformation and upgrading, and achieve the sustainable development of society and higher resource utilization efficiency.

[0156] Example 3, as Figure 4 shown, the embodiment of the present invention provides an intelligent prediction system for ship seakeeping performance based on a physics-informed neural network, including:

[0157] An initialization network and data preprocessing module 1, which is used to obtain the data set required for the physics-informed neural network by using computational fluid dynamics (CFD) and the response amplitude operator (RAO) method, and preprocess the data set.

[0158] A neural network loss function construction module 2, which is used to construct a loss function to constrain the neural network by using physical equations related to waves and ship seakeeping performance.

[0159] A network training module 3, which is used to train the network by applying a combined optimizer.

[0160] A network prediction and evaluation module 4, which is used to perform network prediction and evaluation to achieve the prediction of ship seakeeping performance.

[0161] As mentioned above, the above is only a relatively optimal specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for intelligent prediction of ship seakeeping performance based on physical information neural network, characterized in that: This method combines the CFD-RAO method with PINNs, and realizes fast and high-precision prediction of ship seakeeping by constructing a coupling model of physical equations and neural network loss functions. The specific steps include: S1. Use computational fluid dynamics (CFD) and response amplitude operator (RAO) method to obtain the data set required by the physical information neural network and pre-process the data set; S2, constructing a loss function constrained neural network using the prediction error equation and the physical equation of ship seakeeping; S3, apply the combinatorial optimizer to perform network training; S4. Conduct network prediction and evaluation to predict the seakeeping performance of ships; In step S1, the method of using computational fluid dynamics (CFD) and response amplitude operator (RAO) to obtain the data set required by the physical information neural network includes: (1.1) Construct control model based on CFD-RAO method; (1.2) Establish physical models of ships and flow fields; (1.3) CFD-RAO coupling simulation; In step (1.1), the control model is constructed based on the CFD-RAO method, including: The free surface waves during the ship's navigation are captured using the volume of fluid method VOF, and the expression is: Where: ρ is the fluid density, U i is the velocity of the fluid in the i direction, where the i direction is any one of the three directions x, y, and z, i = 1, 2, 3, x points to the stern, y points to the starboard, z is vertically upward, t is the time series, P is the fluid pressure, x i is the spatial coordinate of the fluid in the i direction, H j is the fluid velocity U i The component in the direction of the jth degree of freedom of the ship, j = 1, 2...6; h j is the spatial coordinate x i The component in the direction of the jth degree of freedom of the ship, g i is the gravitational acceleration in the i-th direction, μ is the dynamic viscosity coefficient of the fluid, U′ i is the fluid velocity U i The turbulent fluctuation component, H′ j is the fluid velocity U i Turbulent fluctuation component in the direction of the jth ship degree of freedom; The SSTK-ω turbulence model is used to close the RANS equations to simulate the ship resistance, position derivative, rudder derivative and rotation derivative tests. The basic equation is: Where k is the turbulent kinetic energy, μ i is the dynamic viscosity coefficient of the fluid in the i direction, u is the fluid velocity, u i is the velocity component of the fluid in the i direction, Γ k , Γ ω are diffusion coefficients, are all turbulence generation terms, Y k , Y ω are turbulent dissipation terms, S k ,s ω are user-defined source terms, ω is the specific dissipation rate, D ω is an orthogonal divergence term; The hull is a rigid body. The reference coordinate system oxyz is selected, and the origin of the coordinate system is located in the middle of the ship. The motion equation of the hull's sailing attitude is: Where M S is the structural mass matrix, I2, I3 are the moments of inertia of the hull around y, x, are the heave acceleration, pitch acceleration and roll acceleration of the ship respectively. F1, F2 and F3 are the resultant force acting on the hull along the z-axis, the resultant moment around the y-axis and the resultant moment around the x-axis respectively. The resultant force is obtained by integrating the stress on the hull surface while solving the hull motion in real time and capturing the free liquid surface, taking into account the coupling effect between the degrees of freedom. After obtaining the data using CFD calculation, the response amplitude operator RAO method is used to obtain the dynamic response characteristics. The linear frequency domain motion equation of the 6-DOF ship in the regular wave is: Where ω′ is the encounter frequency, m ij is the quality coefficient, A ij , B ij is the additional mass coefficient and damping coefficient in the i direction induced by the motion mode of the j-th ship degree of freedom, C ij is the restoring force coefficient, R j is the complex motion amplitude of the motion mode under the j degrees of freedom of the ship, F i is the unit amplitude wave force in the ith direction, ξ a is the wave amplitude, j is the 6 degrees of freedom of the ship, and the 6 degrees of freedom of the ship represent the corresponding degrees of freedom coupled with the i direction; In step S2, the loss function constraint neural network is constructed by using the prediction error equation and the physical equation of the ship's seakeeping, including: According to the energy conservation principle of the ship moving in the waves, the relationship function between energy loss and prediction error is constructed to physically constrain the network and construct the total loss function under j degrees of freedom: In the formula, is the total loss function under j degrees of freedom, α1 and α2 are the weight coefficients of the two loss terms, is the energy loss equation between the ship and the waves, is the prediction error value of the motion response, expressed as: Where N is the number of data points in the ship seakeeping state data set in a short period of time, E is the total energy of the ship at time t, is the predicted value of the network, Y j is the true motion response amplitude of the j-degree-of-freedom sample, v is the linear damping coefficient, β is the nonlinear damping coefficient, is the angular velocity of the jth degree of freedom, t j+1 is the time point of the j+1th degree of freedom, t j is the time point of the j-th degree of freedom, MAE j is the mean absolute error under the jth degree of freedom, used to evaluate the network prediction value and the true value Y j The deviation between .

2. The ship seakeeping intelligent prediction method based on physical information neural network according to claim 1 is characterized in that: In step (1.2), the physical model of the ship and the flow field is established, including: A virtual wave pool with water as the fluid is built. The variable parameters of the wave are set, the free liquid surface is captured by the volume of fluid method VOF, and the overlapping network technology is used to simulate the ship's navigation posture in real time to complete the establishment of the ship's navigation model.

3. The ship seakeeping intelligent prediction method based on physical information neural network according to claim 1 is characterized in that: The energy method is used to derive the equation of energy loss, and the ship's freedom attenuation motion equation is obtained, which is expressed as follows: In the formula, I o is the total moment of inertia of the ship, are the angular acceleration, angular velocity and angle in the j degree of freedom, respectively, C s is the restoring force coefficient, N1 is the linear damping coefficient, describing the The influence of the damping force on the system is proportional to the nonlinear damping coefficient, N2 is the nonlinear damping coefficient, which describes the The influence of nonlinear damping force on the system is proportional to the Divide both sides of the equation by the total moment of inertia of the ship I o ,get: In the formula, ω j is the natural angular frequency of the system in the j degree of freedom; The total energy of the ship's freedom decay process consists of two parts: the kinetic energy caused by free rotation and the potential energy caused by the work done by the hydrostatic restoring torque. The total energy E(t) at time t is: According to the principle of energy conservation in fluid dynamics, the energy loss equation at different times is obtained: In the formula, E(t j+1 ) is t j+1 Total energy of the ship at the moment, E(t j ) is t j Total energy of the ship at the moment.

4. The method for intelligent prediction of ship seakeeping performance based on physical information neural network according to claim 1 is characterized in that: In step S3, the application combination optimizer performs network training, including: The seakeeping response data of the ship under different sea conditions are obtained by CFD-RAO method. The seakeeping response data includes the dynamic characteristics of pitch, roll and heave of the ship in waves. Based on the above data, a fully connected neural network model is constructed with time series as input, and the data is segmented and processed to train the fully connected neural network model. During the training process, an optimizer combination strategy is adopted. First, the Adam optimizer is used to converge quickly in the early stage and approach the global optimal solution; then it is switched to the LBFGS optimizer for multiple iterations and the automatic learning rate is used for adjustment.

5. The method for intelligent prediction of ship seakeeping performance based on physical information neural network according to claim 1 is characterized in that: In step S4, the network prediction and evaluation are performed to realize the prediction of the ship's seakeeping performance, including: using the trained fully connected neural network model to predict the seakeeping performance response values ​​of the ship's pitch, roll and heave for the new data set.

6. An intelligent prediction system for ship seakeeping based on physical information neural network, characterized in that: The system implements the ship seakeeping intelligent prediction method based on physical information neural network according to any one of claims 1 to 5, and the system comprises: Initializing the network and data preprocessing module (1), used to obtain the data set required by the physical information neural network by using computational fluid dynamics CFD and response amplitude operator RAO method, and preprocessing the data set; Constructing a neural network loss function module (2), which is used to construct a loss function constraint neural network using a prediction error equation and a physical equation related to the ship's seakeeping performance; A network training module (3), used for applying a combinatorial optimizer to perform network training; The network prediction and evaluation module (4) is used to perform network prediction and evaluation to achieve the prediction of the ship's seakeeping performance.

7. The ship seakeeping intelligent prediction system based on physical information neural network according to claim 6 is characterized in that: The system is mounted on a computer device, which includes: at least one processor, a memory, and a computer program stored in the memory and running on the at least one processor. When the processor executes the computer program, the functions of the above-mentioned ship seakeeping intelligent prediction system based on physical information neural network are realized.

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