A ship swaying motion prediction method based on physical information neural network

Abstract

The present invention relates to the field of intelligent prediction of ship swaying motion and proposes a ship swaying motion prediction method based on a physical information neural network. The method comprises the following steps: using fluid mechanics to simulate the heaving motion of a ship in real waves, and collecting swaying motion data of the ship when moving in the waves; constructing a physical information neural network model, initializing the physical information neural network model and completing data preprocessing; constructing a wave excitation force function from the obtained motion data, integrating the wave excitation force function into the physical information neural network model, and training the physical information neural network model; and inputting real-time motion data into the trained physical information neural network model to predict the heaving displacement and pitch angle of the ship.

Description

Technical Field

[0001] The present invention relates to a method for predicting ship swaying motion based on a physical information neural network. Specifically, the present invention belongs to the interdisciplinary field of applying machine learning and deep learning techniques with physical process simulation. Background Art

[0002] In modern marine engineering and shipping, accurately predicting a ship's rolling motion in waves is crucial for ensuring safety and optimizing navigation paths. Traditional ship rolling motion prediction relies primarily on physical models and empirical methods. However, these methods often suffer from insufficient prediction accuracy in complex sea conditions, especially when faced with sudden large waves or complex sea conditions with multiple waves interfering with each other. These limitations become even more pronounced.

[0003] Limitations of traditional forecasting methods:

[0004] Physical modeling methods: Models based on precise physical equations, such as linear and nonlinear wave theory, can provide a certain degree of forecast accuracy. However, these models are computationally complex and typically require significant computing resources. Furthermore, physical models require precise initial and boundary conditions; otherwise, the forecast results may deviate from the actual situation.

[0005] Empirical methods: These rely on extensive historical data and empirical rules, using statistics or other methods to make predictions. While they offer faster calculation speeds in some cases, these methods are highly data-dependent and often lack accuracy when faced with atypical wave conditions.

[0006] Hybrid methods: Hybrid methods that combine physical models and empirical methods attempt to take advantage of the advantages of both. However, in practical applications, such methods still find it difficult to provide consistent high-precision predictions under various complex sea conditions.

[0007] With the development of deep learning and artificial intelligence technologies, physics-informed neural networks have become a powerful tool for solving problems with complex physical backgrounds. Physically-informed neural networks incorporate the laws of physics into their architectures. By combining data-driven learning with physical models, these networks not only perform well in data-rich environments but also effectively handle situations where data is scarce or incomplete.

[0008] Solving partial differential equations using traditional neural networks requires extensive training data. These networks, such as convolutional neural networks and long-short-term memory neural networks, rely on repeated training from a large amount of sample data to learn the inherent patterns within the data and approximate the function to be solved with arbitrary precision. These neural networks, for example, lack prior physical information about the system being solved and instead simply fit the neural network's input and output data. This results in poor interpretability and limited performance due to the limited number of training samples. Physics-Informed Neural Networks (PINNs), an emerging technology, combine machine learning with physical models, offering a solution that maintains predictive accuracy while significantly improving computational efficiency. The core advantage of physics-informed neural networks lies in their ability to leverage existing physical knowledge (such as partial differential equations) to guide neural network learning, enabling accurate predictions of the behavior of physical systems even without extensive data support. Summary of the Invention

[0009] In order to solve the above technical problems, the present invention proposes a ship sway motion prediction method based on physical information neural network, comprising the following steps:

[0010] Step 1: Use fluid mechanics to simulate the heaving motion of a ship in real waves and collect the swaying motion data of the ship when moving in the waves;

[0011] Step 2: Build a physical information neural network model, initialize the physical information neural network model and complete data preprocessing;

[0012] Step 3: construct a wave excitation force function using the swaying motion data obtained in step 1, and train the wave excitation force function using a physical information neural network model;

[0013] Step 4: Input the real-time motion data into the trained physical information neural network model to predict the heave displacement and pitch angle of the ship.

[0014] In a preferred embodiment, in step 1, the heave-pitch motion equation is established:

[0015] ;

[0016] in, are the first and second derivatives of the heave displacement with respect to time t, is the pitch angle, are the first and second derivatives of the pitch angle with respect to time t, is the transverse coordinate of the ship's center of gravity in the fixed coordinate system of the hull, is the additional mass of the heave, is the longitudinal moment of inertia of the hull, is the additional moment of inertia of pitch, is the additional mass caused by the pitch motion in the heave direction, is the additional inertia moment caused by the heave motion in the pitch direction, are the linear damping coefficients for heave and pitch, represents the damping coefficient of the mutual coupling between heave and pitch motion, are the restoring moment coefficients for heave and pitch, represents the restoring moment coefficient of the mutual coupling between heave and pitch motion, and is the wave excitation moment in the heave and pitch directions.

[0017] In a preferred embodiment, the heave-pitch coupled motion equation of a ship in waves is established:

[0018] ;

[0019] in, is the damped frequency of the ship's heaving motion in waves, is the damped frequency of the ship's pitching motion in waves, ()and () is the nonlinear hydrodynamic function to be determined in the heave and pitch directions, , is the wave excitation force in the heave and pitch directions.

[0020] In a preferred embodiment, the heave-pitch equation of a ship in still water is established:

[0021] ;

[0022] in, is the natural frequency of the ship's heaving motion in still water, is the natural frequency of the ship's pitching motion in still water.

[0023] In a preferred embodiment, when the vessel experiences heave-pitch coupled motion in waves, the damping frequency and the natural frequency thereof satisfy the following relationship:

[0024] ;

[0025] in, is the dimensionless damping coefficient of heave, is the dimensionless damping coefficient of pitch.

[0026] In a preferred embodiment, the wave excitation force , Calculated by the following formula:

[0027] ;

[0028] Among them, the wave number is k, the displacement of the ship in the corresponding direction is u, ω represents the frequency information of the ship, the time is t, and the density of water is , the wave acceleration g(t), x represents the x-coordinate of the calculated point in the ship coordinate system established with the coordinates of the hull's buoyancy center as the origin.

[0029] In a preferred embodiment, the physical loss function of the physical information neural network model is:

[0030] ;

[0031] ;

[0032] in, The loss function of the physical equation representing the heave direction; Loss function representing the physical equation of roll;

[0033] The prediction loss function of the physical information neural network model is:

[0034] ;

[0035] Among them, represents the predicted value of heave displacement; Indicates the actual value of the heave displacement; Indicates the predicted value of the roll angle Indicates the actual value of the roll angle;

[0036] The total loss function of the physical information neural network model is:

[0037] + .

[0038] Beneficial technical effects of the present invention:

[0039] The present invention introduces a physical information neural network, which is specially designed for predicting the coupled motion of the vertical swing and pitching of ships in waves, and has significant practical value and innovation. Compared with the existing technology, the present invention has the characteristics of simple structure and clear algorithm, and provides accurate and reliable technical support for ship state prediction. In addition, the present method classifies the loss functions under different wave conditions, effectively improving the accuracy and reliability of the prediction of the ship motion state under complex sea conditions, making the present method more widely applicable. In summary, the present invention provides an advanced method for predicting the swaying motion of ships in waves, and at the same time provides new ideas for related research, which has both theoretical significance and application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is the network framework of the physical information neural network method of the present invention;

[0041] Figure 2 It is the KCS ship model adopted by the present invention;

[0042] Figure 3 is the predicted ship heave distribution diagram;

[0043] Figure 4 is the free surface mesh distribution. DETAILED DESCRIPTION

[0044] To make the purpose, technical solutions, and advantages of the embodiments of this application more clear, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the drawings in the embodiments of this application. Obviously, the described embodiments are part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0045] In the drawings of the specific implementation of the present invention, in order to better and more clearly describe the working principles of each component in the system, the connection relationship of each part in the device is shown, which only clearly distinguishes the relative position relationship between the components, and does not constitute a limitation on the signal transmission direction, connection sequence and structural size, size and shape of each part within the component or structure.

[0046] Secondly, the term "one embodiment" or "embodiment" herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in various places throughout this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive of other embodiments.

[0047] The ship swaying motion prediction method based on physical information neural network of the present invention specifically comprises the following steps:

[0048] Step 1: Use fluid mechanics to simulate the heaving motion of a ship in real waves and collect the swaying motion data of the ship when it moves in the waves.

[0049] Specifically, by changing the wave amplitude, wave steepness and other related data, while paying attention to the heave displacement and pitch angle of the ship, the swaying motion data of the ship when moving in the waves is collected.

[0050] The specific steps include:

[0051] A control model is constructed based on the CFD method, which includes the heave-pitch equation in still water, the heave-pitch equation in small waves, and the heave-pitch equation in large waves.

[0052] This method only considers the two degrees of freedom of motion of the ship, heave and pitch. In the case of small amplitude sway, the effect of fluid viscosity is small and can be ignored. Therefore, the heave-pitch motion equation of the ship can be expressed as:

[0053] ;

[0054] The meanings of the parameters are shown in Table 1.

[0055] Table 1 Parameter meaning:

[0056]

[0057] In order to use the above formula to predict the small-amplitude heave-pitch coupled motion of a ship in waves, it is necessary to determine the unknown additional mass and additional moment of inertia, damping coefficient and wave excitation force (torque), and normalize the above formula:

[0058] ;

[0059] ;

[0060] In the case of large-scale swaying, the viscosity of the fluid cannot be ignored. Viscosity has an important influence on the swaying of the ship. The heave-pitch coupled motion of the ship is a periodic reciprocating motion. In the case of large-scale swaying, the heave-pitch coupled motion equation of the ship in the waves can be expressed as:

[0061] (1);

[0062] The meanings of the parameters are shown in Table 2.

[0063] Table 2 Parameter meaning:

[0064]

[0065] In still water motion, the wave excitation is 0, so the heave-pitch equation of the ship in still water is:

[0066] (2);

[0067] The meanings of the parameters are shown in Table 3.

[0068] Table 3 Parameter meaning:

[0069]

[0070] In addition, when a ship experiences heave-pitch coupled motion in waves, the damping frequency and natural frequency satisfy the following relationship:

[0071] (3);

[0072] The meanings of the parameters are shown in Table 4.

[0073] Table 4 Parameter meaning:

[0074]

[0075] Combining the above equations (1), (2), and (3), we can get:

[0076] (4);

[0077] A physical model of the ship and propeller is established to simulate the heave and pitch motion of the ship and propeller in still water, small waves, and large waves, obtaining the heave amplitude and pitch angle under different operating conditions. This data can be divided into training and test sets to train the neural network.

[0078] like Figure 2 The figure shows the KCS ship model used in this paper. This paper uses the KCS ship model entity as an example to study the swaying motion of a ship in waves. This figure shows the geometric scene where the ship model is located in the CFD coupled simulation.

[0079] The hull model uses the Kriso Container Ship model with a rudder, with a scaling ratio of 31.599. Detailed parameters are shown in Table 5.

[0080] Table 5 Ship model parameters:

[0081]

[0082] CFD coupled simulation utilizes finite element simulation software, employing a semi-computational domain symmetry approach to conserve computing resources. The mesh is locally refined in the following areas: the bow and stern, the free surface, and the fore and aft Kelvin waves. To eliminate invalid results caused by wave reflections at boundaries, a wave damping method is employed. Based on the above pre-processing, the KCS vessel's navigation under various operating conditions is simulated, monitoring the resistance, torque, and pitch and heave motions experienced by the hull. Key models include the volume of fluid (VOF) for water and air, and the dynamic fluid-solid interaction (DFBI) model, which is used to calculate the vessel's motion under fluid influence, simulating its forward and backward motion, free heave, and pitch.

[0083] Step 2: Build a physical information neural network model, initialize the physical information neural network model and complete data preprocessing.

[0084] The input parameters of the neural network are wave frequency, amplitude, wave steepness and other related parameters as well as the ship's speed. The output of the network is the ship's heave displacement and pitch angle. The training internal parameter of the network is the wave damping coefficient when the ship is sailing.

[0085] First, computational fluid dynamics (CFD) methods are used to obtain sufficient raw data to improve the accuracy of neural network predictions. Second, the raw data must be preprocessed to ensure consistency of the input data. The main methods include but are not limited to normalization and data denoising.

[0086] Step 3: construct a wave excitation force function using the swaying motion data obtained in step 1, and train the wave excitation force function using a physical information neural network model.

[0087] The following motion data have been obtained in step 1: the damping frequency of the ship's heaving motion in waves, the damping frequency of the ship's pitching motion in waves, the natural frequency of the ship's heaving motion in still water, the natural frequency of the ship's pitching motion in still water, the wave excitation force, the pitch angle, the heaving displacement, and the relationship between the various motion data is:

[0088] ;

[0089] Among them, the wave excitation force , It can be calculated by the following formula:

[0090] ;

[0091] Where x represents the x-coordinate of the calculated point in the ship-borne coordinate system established with the coordinates of the hull's buoyancy center as the origin.

[0092] The input of the physical information neural network model is the characteristic parameters of the wave, which include: k represents the wave number, u represents the displacement of the ship in the corresponding direction, ω represents the frequency information of the ship, t represents the time, represents the density of water, and g(t) represents the acceleration of the wave.

[0093] The output of the physical information neural network model is the heave displacement z and pitch angle , the internal parameters of the training are and .in, is the damped frequency of the ship's heaving motion in waves, is the damped frequency of the ship's pitching motion in waves, is the natural frequency of the ship's heaving motion in still water, The natural frequency of the ship's pitching motion in still water, the physical loss function of the physical information neural network model is:

[0094] ;

[0095] in, The loss function of the physical equation representing the heave direction; Loss function representing the physical equation of roll.

[0096] The prediction loss function of the physical information neural network model is:

[0097] ;

[0098] Among them, represents the predicted value of heave displacement; Indicates the actual value of the heave displacement; Indicates the predicted value of the roll angle

[0099] Indicates the actual value of the roll angle

[0100] The total loss function of the physical information neural network model is:

[0101] + ;

[0102] like Figure 4 The grid distribution of the free surface is shown in Figure 1. The grid in the figure is the grid distribution of the free surface. Local refinement can simulate the distribution of waves on the free surface in a more detailed manner while reducing the waste of computing resources.

[0103] like Figure 3 The following figure shows the predicted heave distribution of the ship. The wave height distribution of the water surface waves observed vertically downward from the top of the ship along the negative direction of the coordinate system's z-axis is shown in Figure 1. Different colors represent different wave heights.

[0104] Step 4: Input the real-time motion data into the trained physical information neural network model to predict the heave displacement and pitch angle of the ship.

[0105] The prediction results of the physical information neural network are compared with the experimental data to prove the feasibility of this method.

[0106] A comprehensive analysis of the prediction results from the physical information neural network (PINN) and computational fluid dynamics (CFD) revealed that the two methods offer comparable accuracy. However, PINN is more applicable to more complex wave conditions, maintaining high accuracy in calm water, small waves, and large waves. Furthermore, PINN offers a significant advantage over CFD in terms of prediction speed.

[0107] like Figure 1 The figure shows the network framework of the physical information neural network method of the present invention. The entire neural network is divided into an input layer, a hidden layer, and an output layer. The input parameters of the input layer include wave characteristics such as wave steepness, frequency, and amplitude, as well as the ship's speed. The output parameters of the output layer include the ship's heave displacement, pitch angle, heave frequency, and other parameters. The neural network's prediction results are incorporated into the ship's heave and pitch equations, and the error values ​​are fed into the Adam and L-FBGS optimizers to minimize the loss until the loss falls within the allowable range.

[0108] A combination of the Adam and LBFGS optimizers is used to train the neural network, ensuring both training efficiency and model accuracy. The Adam optimizer can generate adaptive learning rates for different parameters, quickly approaching the global optimal solution, while the LBFGS optimizer offers the advantages of fast convergence and low memory usage.

[0109] The trained neural network model was used to predict data from the test set, focusing on the model's performance in predicting flow field velocity and pressure. The model's predictions were compared with those obtained from computational fluid dynamics (CFD) to verify the effectiveness and superiority of the physical information neural network in predicting ship rolling motion.

[0110] Finally, based on the prediction and evaluation results, the model is iteratively optimized, including but not limited to adjusting the network structure, optimizing the loss function, and selecting the optimization algorithm, to further improve the model's prediction accuracy and generalization capabilities. Ultimately, the optimized model is applied to the prediction of real-world ship rolling motion, providing decision support for ship performance evaluation and navigation status prediction.

[0111] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0112] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.

Claims

1. A ship swaying motion prediction method based on physical information neural network, characterized in that: The following steps are involved: Step 1: Use fluid mechanics to simulate the heave motion of a ship in real waves, collect the heave motion data of the ship in waves, and establish the heave-pitch coupled motion equation of the ship in waves; Step 2: Build a physical information neural network model, initialize the physical information neural network model and complete data preprocessing; Step 3: Construct a wave excitation force function using the swaying motion data obtained in step 1, and train the wave excitation force function using a physical information neural network model; the wave excitation forces f3 and f5 are calculated using the following formula: Where, the wave number is k, the displacement of the ship in the corresponding direction is u, ω represents the frequency information of the ship, time is t, the density of water is ρ, the acceleration of the wave is g(t), and x represents the x-coordinate of the calculated point in the ship coordinate system established with the coordinates of the buoyancy center of the hull as the origin; The physical loss function of the physical information neural network model is: Among them, ω 3,d is the damped frequency of the ship's heaving motion in waves, ω 5,d is the damped frequency of the ship's pitching motion in waves, f3 and f5 are the wave excitation forces in the heave and pitch directions, and Loss functionz Loss function of the physical equation representing the heave direction; functionθ Loss function representing the physical equation of roll; The prediction loss function of the physical information neural network model is: Among them, represents the predicted value of heave displacement; z n Indicates the actual value of the heave displacement; The predicted value of the roll angle θ n Indicates the actual value of the roll angle; The total loss function of the physical information neural network model is: Loss total =ω1L data +ω2Loss functionz +ω3Loss functionθ ; Step 4: Input the real-time motion data into the trained physical information neural network model to predict the heave displacement and pitch angle of the ship.

2. The ship swaying motion prediction method based on physical information neural network according to claim 1 is characterized in that: In step 1, the heave-pitch motion equation is established: in, are the first and second derivatives of the heave displacement with respect to time t, θ is the pitch angle, is the first and second derivative of the pitch angle with respect to time t, x G is the transverse coordinate of the ship's center of gravity in the fixed coordinate system of the hull, m 33 is the additional mass of the heave, J yy is the longitudinal moment of inertia of the hull, m 55 is the additional moment of inertia of pitching, m 35 is the additional mass caused by the pitch motion in the heave direction, m 53 is the additional inertia moment caused by the heave motion in the pitch direction, N 33 ,B 55 are the linear damping coefficients of heave and pitch, B 35 ,B 53 The damping coefficient for the coupling between heave and pitch motion, R 33 ,R 55 are the restoring moment coefficients of heave and pitch, R 35 ,R 53 represents the restoring moment coefficient of the mutual coupling between heave and pitch motions, τ3 and τ5 are the wave excitation moments in the heave and pitch directions.

Images