An intelligent ship maneuvering motion prediction method based on mathematical equation-data driving fusion

Abstract

The application provides an intelligent ship maneuvering motion prediction method based on mathematical equation-data driving fusion, and comprises the following steps: on the basis of an MMG model, a four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives is established based on the Taylor series expansion thought; based on the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, an extended Kalman filtering algorithm is used to perform parameter identification on hydrodynamic derivatives of different orders; on the basis of the optimal order prediction model, real ship motion data are combined to construct a ship motion prediction residual; a least squares support vector machine algorithm is used for black box modeling to approximate the motion prediction residual; a BP neural network is built, the prediction residual of the least squares support vector machine black box model and the prediction result of the optimal model are used as input, and real ship navigation data are used as output to learn and train the neural network, so that the estimation of the ship motion state is realized.

Description

Technical Field

[0001] This invention relates to the fields of ship and marine engineering technology and ship motion prediction, specifically to an intelligent ship maneuvering motion prediction method based on mathematical equation-data-driven fusion. Background Technology

[0002] Ship maneuvering is a complex process involving multiple degrees of freedom, multiple factors, and random uncertainties. High-precision intelligent prediction technology for ship maneuvering is a key technology supporting future intelligent and unmanned ships. Its core challenge lies in determining the structure and identifying the parameters of the prediction model. Traditional mathematical equations for maneuvering can predict the basic motion laws of ships based on mechanical mechanisms, but this requires establishing complex equations. Because they do not fully consider relevant influencing factors and the cutoff order of hydrodynamic derivatives, traditional methods cannot cover all navigation conditions and marine environments, thus making it difficult to ensure the accuracy and adaptability of maneuvering prediction.

[0003] Advanced artificial intelligence methods can address this problem by fully mining navigation data. Various machine learning algorithms can fit a nonlinear mapping of the recursively evolving "black box" of ship maneuvering motion states. However, the complexity and generalization ability of ship maneuvering prediction models built using data-driven methods are entirely dependent on the diversity and richness of the data samples. Furthermore, data-driven modeling methods struggle to fundamentally explain the mechanisms of ship maneuvering motions, failing to guarantee the robustness and reliability of ship maneuvering motion predictions. Summary of the Invention

[0004] To address the aforementioned problems, the technical solution adopted in this invention is: an intelligent ship maneuvering motion prediction method based on mathematical equation-data-driven fusion, comprising the following steps:

[0005] First, based on the MMG model, and using the idea of ​​Taylor series expansion, a four-degree-of-freedom ship maneuvering motion prediction model with variable higher-order hydrodynamic derivatives is established.

[0006] Then, based on the four-degree-of-freedom ship maneuvering motion prediction model with variable higher-order hydrodynamic derivatives, the extended Kalman filter algorithm is used to identify the parameters of hydrodynamic derivatives of different orders, and the deterministic coefficients R are used to predict the parameters. 2 Obtain the optimal order prediction model; based on the optimal order prediction model, obtain preliminary prediction results of ship motion state;

[0007] Based on the optimal order prediction model, and combined with real ship motion data, ship motion prediction residuals are constructed; the least squares support vector machine algorithm is used for black box modeling to approximate the motion prediction residuals.

[0008] Finally, a BP neural network was constructed, using the prediction residuals of the least squares support vector machine black box model and the prediction results of the optimal model as inputs, and real ship navigation data as outputs to train the neural network and achieve the estimation of ship motion state.

[0009] Furthermore, the process of establishing a mathematical model of ship maneuvering motion with variable higher-order hydrodynamic derivatives based on the MMG model and the idea of ​​Taylor series expansion is as follows:

[0010] Based on the MMG model of ship maneuvering motion, assuming the ship's coordinate origin is at its center of gravity, the hull is a rigid body, and neglecting the ship's heave and pitch motions, considering only the four degrees of freedom of pitch, sway, roll, and bow, the following ship motion equations are established:

[0011]

[0012] In the formula: u and v are the velocity components of the ship in the x and y directions, respectively; p is the roll rate; r is the bow roll rate; φ is the roll angle; m is the mass of the ship; m x m y These are the ship's additional mass in the x-axis and y-axis directions, respectively; I x J x I z J z These are the moment of inertia and additional moment of inertia of the ship about the x-axis and z-axis, respectively; x For the added mass m x The x-coordinate of the center; W is the displacement of the ship; GM is the initial metacentric height of the ship; X, Y, L, and N are the viscous hydrodynamic forces and moments of the ship in the longitudinal, transverse, roll, and bow directions, respectively; and the subscripts H, P, and R represent the hull, propeller, and rudder, respectively.

[0013] Furthermore, the hydrodynamic and torque calculation formulas for the propeller and rudder are as follows:

[0014]

[0015] In the formula: t p , n and D p These are the thrust deduction factor, propeller speed, and propeller diameter, respectively; J p F is the advance coefficient; N δ is the normal force of the rudder; δ is the rudder angle; t R The factor for reducing rudder force; a H The correction factor for steering-induced lateral forces on the hull; z R The vertical height of the center of action of the rudder force; x H x is the longitudinal coordinate of the point of application of the rudder interference force; RThe longitudinal position of the point of application of the rudder normal force;

[0016] Based on the idea of ​​Taylor series expansion, the forces and moments acting on the hull can be written as functions of u, v, p, r, and φ:

[0017]

[0018] In the formula: X(u) is the straight-line resistance of the ship, i.e., X(u) = X uu u 2 K is the order of the hydrodynamic expansion, which varies with the model and K = 2, 3, 4.

[0019] Based on the symmetrical shape of the ship, the variation of X with respect to v, r, and φ is symmetrical, and X is an even function of v, r, and φ. The variations of Y, L, and N with respect to v, r, and φ are antisymmetric, and Y, L, and N are odd functions of v, r, and φ. Therefore, the first and third derivatives of X with respect to v, r, and φ are all zero, and the second and fourth derivatives of Y, L, and N with respect to v, r, and φ are all zero.

[0020]

[0021] In the formula: Z H (v0,r0,φ0)=Y H (v0,r0,φ0),L H (v0,r0,φ0), N H (v0, r0, φ0) represent the hydrodynamic forces and moments for lateral, roll, and bow motions in the initial state (v0, r0, φ0), respectively. Here, v0, r0, and φ0 represent the initial sway velocity, initial bow angular velocity, and initial roll angle of the ship's motion, respectively.

[0022] Furthermore, the four-degree-of-freedom ship maneuvering motion prediction model based on variable higher-order hydrodynamic derivatives employs an extended Kalman filter algorithm to identify parameters of hydrodynamic derivatives of different orders, and utilizes the coefficients of determination R... 2 The process of obtaining the optimal order prediction model is as follows:

[0023] The four-degree-of-freedom ship maneuvering motion prediction model with variable higher-order hydrodynamic derivatives is discretized, and the model parameters are used as state variables to establish the following state equations and measurement equations:

[0024]

[0025] in,

[0026]

[0027] In the formula: w(t) is the process noise; v(t) is the measurement noise; t is the time of ship motion; Let X be the column number of matrix H; a1 = X uu b1 = [Y v Y p Y r Y φ ] Τ c1 = [L v L p L r L φ ] Τ d1 = [N v N p N r N φ ] Τ Let X be the linear hydrodynamic derivative that needs to be identified, where X uu a represents the second derivative of u in the X direction; K =[a K,1 a K,2 … a K,n ] Τ b K =[b K,1 b K,2 … b K,n ] Τ c K =[c K,1 c K,2 … c K,n ] Τ d K =[d K,1 d K,2 … d K,n ] Τ For the higher-order nonlinear hydrodynamic derivatives that need to be identified; Let be the number of hydrodynamic derivatives of each order; the higher-order nonlinear hydrodynamic derivatives for each term are as follows: For the hydrodynamic derivatives in the four degrees of freedom of sway, roll, pitch, and bow roll; where K = 2, 3, 4;

[0028] Assuming the ship's shape is symmetrical from left to right, according to equation (3), a3, b2, b4, c2, c4, d2, and d4 are all zero vectors.

[0029]

[0030] In the formula: Each item is represented as follows: h K =[h K,1 hK,2 … h K,n ] Τ Each item can be represented as

[0031] The above parameters were identified, and ship maneuvering motion models incorporating hydrodynamic derivatives of different orders were constructed, using the coefficients of determination R. 2 The basis for selecting a four-degree-of-freedom ship maneuvering motion prediction model with variable higher-order hydrodynamic derivatives:

[0032]

[0033] In the formula: m refers to the number of samples, R i , These are the true value and the predicted value of the i-th sample, respectively. It refers to the sample mean, when R 2 The closer R is to 1, the better the predictive performance of the model of that order. Therefore, we choose R. 2 The model closest to 1 is selected as the ship motion prediction model with the best model order.

[0034] Furthermore: the process of constructing the ship motion prediction residuals and using the least squares support vector machine algorithm for black-box modeling to approximate the motion prediction residuals is as follows:

[0035] Ship motion prediction residuals are constructed based on the optimal order model and real navigation data;

[0036] The true value of the ship's motion state is represented as The prediction results of the optimal model are expressed as follows: The residual between the actual and predicted values ​​of the ship's motion state is expressed as:

[0037]

[0038] The least squares support vector machine (LS-SVM) algorithm is used for black-box modeling, and the neural network input is... The output is The motion prediction residuals are approximated by training a neural network.

[0039] Furthermore: A BP neural network is constructed, using the prediction results of the least squares support vector machine black-box model and the prediction results of the optimal model as input, and real ship navigation data as output to train the neural network, thus realizing the estimation of the ship's motion state. The process is as follows:

[0040] A BP neural network is constructed based on the prediction results of the optimal order model and the prediction residuals of LS-SVM.

[0041] The prediction residuals of LS-SVM and the prediction results of the optimal order model are used as inputs to the BP neural network, and real ship navigation data is used as the output of the BP neural network for training.

[0042] The LS-SVM prediction residuals and the prediction results of the optimal order model are respectively expressed as follows: The estimated value of the ship's motion state is expressed as w. * w = u, v, p, r, φ.

[0043] This invention provides an intelligent ship maneuvering motion prediction method based on the fusion of mathematical equations and data-driven approaches. The proposed "mathematical-data" fusion intelligent ship motion prediction method can comprehensively utilize the advantages of both "mathematical equations" and "data-driven approaches," effectively improving the accuracy of ship motion prediction and ensuring both accuracy and reliability of motion prediction.

[0044] This invention does not require measuring environmental factors such as wind and waves during ship navigation. It only requires the ship's own navigation data to predict the ship's future movement. The method is simple, easy to implement, and highly versatile. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 The flowchart illustrates the ship motion prediction method based on the "mathematical-data" fusion of intelligent ship maneuvering motion proposed in this invention.

[0047] Figure 2 This is a schematic diagram of the four-degree-of-freedom ship motion coordinate system;

[0048] Figure 3 This is a schematic diagram of the residual approximation method based on the LS-SVM black box.

[0049] Figure 4 The graph shows the predicted results for the lateral velocity u.

[0050] Figure 5 The graph shows the predicted results for the longitudinal velocity v.

[0051] Figure 6 The graph shows the predicted roll rate p.

[0052] Figure 7 The diagram shows the predicted results for the bow roll rate r.

[0053] Figure 8 This is a graph showing the predicted roll angle φ. Detailed Implementation

[0054] It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0055] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. 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.

[0056] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0057] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0058] In the description of this invention, it should be understood that the orientation or positional relationship indicated by directional terms such as "front, back, up, down, left, right", "horizontal, vertical, horizontal" and "top, bottom" is generally based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing this invention and simplifying the description. Unless otherwise stated, these directional terms do not indicate or imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the scope of protection of this invention. The directional terms "inner" and "outer" refer to the inner and outer contours relative to the outline of each component itself.

[0059] For ease of description, spatial relative terms such as "above," "over," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation besides the orientation of the device as described in the figures. For example, if the device in the figures is inverted, a device described as "above" or "above" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.

[0060] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.

[0061] Figure 1 This is a flowchart illustrating the ship motion prediction method based on mathematical-data fusion proposed in this invention.

[0062] A method for predicting intelligent ship maneuvering motions based on mathematical equations and data-driven fusion, characterized by the following steps:

[0063] First, based on the MMG model, and using the idea of ​​Taylor series expansion, a four-degree-of-freedom ship maneuvering motion prediction model with variable higher-order hydrodynamic derivatives is established.

[0064] Then, based on the four-degree-of-freedom ship maneuvering motion prediction model with variable higher-order hydrodynamic derivatives, the extended Kalman filter algorithm is used to identify the parameters of hydrodynamic derivatives of different orders, and the deterministic coefficients R are used to predict the parameters. 2Obtain the optimal order prediction model; based on the parameters of hydrodynamic derivatives of different orders combined with deterministic coefficients, obtain the optimal order prediction model and get the prediction results of ship motion state;

[0065] Based on the optimal order prediction model, and combined with real ship motion data, ship motion prediction residuals are constructed; the least squares support vector machine algorithm is used for black box modeling to approximate the motion prediction residuals.

[0066] Finally, a BP neural network was constructed, using the prediction results of the least squares support vector machine black box model and the prediction results of the optimal model as input, and real ship navigation data as output to train the neural network and achieve the estimation of ship motion state.

[0067] like Figure 2 The diagram shows the ship motion coordinate system used in this invention; O0x0y0z0 is a fixed coordinate system fixed on the Earth's surface, with "x0" pointing due north, "y0" pointing due east, and "z0" pointing to the Earth's center; Oxyz is an attached coordinate system, where x refers to the bow, y refers to the starboard side, and z refers to the keel. u, v, p, and r represent the pitch speed, sway speed, roll rate, and bow roll rate, respectively.

[0068] Based on the MMG model of ship maneuvering motion, assuming the ship's coordinate origin is at its center of gravity, the hull is a rigid body, and neglecting the ship's heave and pitch motions, considering only the four degrees of freedom of pitch, sway, roll, and bow, the following ship motion equations are established:

[0069]

[0070] In the formula: u and v are the velocity components in the x and y directions, respectively; p is the roll rate; r is the bow rate; φ is the roll angle; m is the mass of the ship; m x m y These are the ship's additional mass in the x-axis and y-axis directions, respectively; I x J x I z J z These are the moment of inertia and additional moment of inertia of the ship about the x-axis and z-axis, respectively; x For the added mass m x The x-coordinate of the center; W is the displacement of the ship; GM is the initial metacentric height of the ship; X, Y, L, and N are the viscous hydrodynamic forces and moments of the ship in the longitudinal, transverse, roll, and bow directions, respectively; and the subscripts H, P, and R represent the hull, propeller, and rudder, respectively.

[0071] The hydrodynamic forces and torques caused by the propeller and rudder are calculated using the following formulas:

[0072]

[0073] In the formula: t p , n and D p These are the thrust deduction factor, propeller speed, and propeller diameter, respectively; J p F is the advance coefficient; N δ is the normal force of the rudder; δ is the rudder angle; t R The factor for reducing rudder force; a H The correction factor for steering-induced lateral forces on the hull; z R The vertical height of the center of action of the rudder force; x H x is the longitudinal coordinate of the point of application of the rudder interference force; R This refers to the longitudinal position of the point of application of the rudder normal force.

[0074] Based on the idea of ​​Taylor series expansion, the forces and moments acting on the hull can be written as functions of u, v, p, r, and φ, that is:

[0075]

[0076] In the formula: X(u) is the straight-line resistance of the ship, i.e., X(u) = X uu u 2 K is the order of the hydrodynamic expansion, which can take values ​​of K = 2, 3, 4.

[0077] Considering the ship's symmetrical shape, the variation of X with respect to v, r, and φ is symmetrical, meaning X is an even function of v, r, and φ. The variations of Y, L, and N with respect to v, r, and φ are antisymmetric, meaning Y, L, and N are odd functions of v, r, and φ. Therefore, the first and third derivatives of X with respect to v, r, and φ are all zero, and the second and fourth derivatives of Y, L, and N with respect to v, r, and φ are all zero. That is:

[0078]

[0079] In the formula: Z H (v0,r0,φ0)=Y H (v0,r0,φ0),L H (v0,r0,φ0), N H (v0,r0,φ0) represent the hydrodynamic forces and torques of the lateral, roll, and bow motions in the initial state (v0,r0,φ0), where v0, r0, and φ0 are the initial sway velocity, initial bow angular velocity, and initial roll angle of the ship, respectively.

[0080] The aforementioned variable-order ship motion prediction model is discretized, and the model parameters are used as state variables to establish the following state equations and measurement equations:

[0081]

[0082] in,

[0083]

[0084] In the formula: w(t) is the process noise; v(t) is the measurement noise; t is the time of ship motion; Let X be the column number of matrix H; a1 = X uu b1 = [Y v Y p Y r Y φ ] Τ c1 = [L v L p L r L φ ] Τ d1 = [N v N p N r N φ ] Τ Let X be the linear hydrodynamic derivative that needs to be identified, where X uu This represents the second derivative of u in the X direction. K =[a K,1 a K,2 … a K,n ] Τ b K =[b K,1 b K,2 … b K,n ] Τ c K =[c K,1 c K,2 … c K,n ] Τ d K =[d K,1 d K,2 … d K,n ] Τ For the higher-order nonlinear hydrodynamic derivatives that need to be identified; Let be the number of hydrodynamic derivatives of each order; the higher-order nonlinear hydrodynamic derivatives for each term are as follows: Let be the hydrodynamic derivatives in the four degrees of freedom: sway, roll, pitch, and bow roll; where K = 2, 3, 4;

[0085] Assuming the ship's shape is symmetrical, according to equation (3), a3, b2, b4, c2, c4, d2, and d4 are all zero vectors.

[0086]

[0087] In the formula: Each item is represented as follows: h K =[h K,1 h K,2 … h K,n ] Τ Each item is represented as

[0088] The above parameters were identified, and ship maneuvering motion models incorporating hydrodynamic derivatives of different orders were constructed, using the coefficients of determination R. 2 As the basis for selecting the order of the hydrodynamic derivative in the mathematical model of ship maneuvering motion, a mathematical model of ship maneuvering motion with variable higher-order hydrodynamic derivatives is constructed:

[0089]

[0090] In the formula: m refers to the number of samples, R i , These are the true value and the predicted value of the i-th sample, respectively. This refers to the sample mean. When R... 2 The closer the value is to 1, the better the predictive performance of the model of that order. Therefore, we choose R. 2 The model closest to 1 is selected as the ship motion prediction model with the best model order.

[0091] Based on the optimal order model and real navigation data, a ship motion prediction residual is constructed, representing the true value of the ship's motion state as... The prediction results of the optimal model are expressed as follows: The residual between the actual value and the predicted value of the ship's motion state can be expressed as:

[0092]

[0093] like Figure 3 As shown, the Least Squares Support Vector Machine (LS-SVM) algorithm is used for black-box modeling, and the neural network input is... The output is The motion prediction residuals are approximated by training a neural network.

[0094] The specific steps for black-box modeling based on LS-SVM are as follows:

[0095] Assume training sample (x) i ,y i There are N, where x i ∈R m ,y i ∈R m The general approximate equation is:

[0096]

[0097] In the formula: x is the input vector; y is the output vector; is the kernel function; w is the weight matrix; b is the bias term.

[0098] Based on the principle of minimizing structured empirical risk, the above evaluation problem can be transformed into the following optimization problem:

[0099]

[0100] In the formula: c is the penalty coefficient; ξ i It is the regression error of the output, i = 1…N;

[0101] We introduce the following Lagrange function to solve equation (12):

[0102]

[0103] In the formula: α i It is a Lagrange multiplier.

[0104] The following Karush-Kuhn-Tucker conditions are used to express w, b, ξ in equation (13). i ,α i :

[0105]

[0106] Formula (14) can be expressed in matrix form as follows:

[0107]

[0108] In the formula: Q = [1 1 … 1] Τ , α=[α1 α2 … α N ] Τ y = [y1 y2 … y N ] Τ I is an N×N identity matrix. The method of this invention selects a radial basis kernel function;

[0109] Solving the above system of equations using the least squares method yields the LS-SVM model:

[0110]

[0111] like Figure 3 As shown, a BP neural network is constructed based on the prediction results of the optimal order model and the prediction residuals of LS-SVM.

[0112] The prediction residuals of LS-SVM and the prediction results of the optimal order model are used as inputs to the BP neural network, and the estimated value of the ship's motion state is used as the output of the BP neural network for training.

[0113] The LS-SVM prediction residuals and the prediction results of the optimal order model can be expressed as follows: The estimated value of the ship's motion state can be expressed as w * , w = u, v, p, r, φ, ultimately forming a ship motion prediction method that integrates "mathematics and data".

[0114] The principle and specific steps of the constructed BP neural network are as follows:

[0115] First, initialize the network, initializing the weights V and W between neurons in the input, hidden, and output layers, initializing the output threshold of the hidden layers, and setting the learning rate and activation function. The initial number of nodes in the hidden layer is obtained using the following empirical formula:

[0116]

[0117] In the formula: h is the number of hidden layer nodes; m is the number of input layer nodes; n is the number of output layer nodes; a is the adjustment constant.

[0118] The hidden layer and output layer are calculated using the following formula:

[0119]

[0120] In the formula: x i This refers to the input variable; w ij b j These are the weights and the threshold, respectively; H j 'f' refers to the output of the hidden layer; 'f' refers to the activation function.

[0121] Calculate the total error between the actual output and the expected output:

[0122]

[0123] In the formula: m is the number of samples; e i This is the error of the i-th sample. If the error requirement is met, the iteration ends; otherwise, it continues.

[0124] Repeat steps two through four by repeatedly adjusting the weights of the neurons until the error requirement is met.

[0125] The intelligent ship maneuvering motion prediction method proposed in this invention will be verified by referring to a specific embodiment;

[0126] The main parameters of a certain container ship are shown in Table 1.

[0127] Table 1. Main parameters of a container ship

[0128]

[0129]

[0130] Data from a Z-shaped simulation experiment involving rudder angle changes on the ship (starting from 10° and decreasing until it reaches a constant 30°) was used as the training set for the neural network. The trained network was then used to validate the predictions of the ship's ±20° Z-shaped, 25° / 15° Z-shaped, and 25° turning experiments. The prediction results of the "mathematical-data" fusion ship motion prediction method were obtained and compared with the prediction results based on the optimal order model and the simulation experiment results. Taking the ±20° Z-shaped experiment as an example... Figure 4-8 These are the prediction results for u, v, p, r, and φ, respectively. Figure 4 The graph shows the predicted results for the lateral velocity u. Figure 5 The graph shows the predicted results for the longitudinal velocity v. Figure 6 The graph shows the predicted roll rate p. Figure 7 The diagram shows the predicted results for the bow roll rate r. Figure 8 This is a graph showing the predicted roll angle φ.

[0131] It is easy to see that, compared with the optimal order model, the prediction results obtained by the "mathematical-data" fusion ship motion prediction method proposed in this invention are closer to the simulation data.

[0132] To further illustrate the effectiveness of the method of the present invention, the root mean square error between the prediction results and the simulation results is used to measure the prediction accuracy. The prediction results of the above three experiments based on a single optimal order mathematical model and a "mathematical-data" fusion model are shown in Tables 2, 3 and 4.

[0133] Table 2. Predicted results of ±20° Z-shaped experiments

[0134]

[0135]

[0136] Table 3. Predicted results of the 25° / 15° Z-shaped experiment.

[0137]

[0138] Table 4. Predicted results of the 25° rotation experiment

[0139]

[0140] Note: Add 20° and 30° rotation experiments as part of the training set based on the above training set.

[0141] As can be seen from the root mean square error of prediction based on the two models, the root mean square error of prediction is reduced after introducing the data-driven method compared to a single optimal order mathematical model. This further demonstrates that the intelligent ship maneuvering motion prediction method based on the fusion of mathematical equations and data-driven methods proposed in this invention can effectively improve the prediction accuracy.

[0142] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting intelligent ship maneuvering motions based on mathematical equations and data-driven fusion, characterized in that, Includes the following steps: First, based on the MMG model, and using the idea of ​​Taylor series expansion, a four-degree-of-freedom ship maneuvering motion prediction model with variable higher-order hydrodynamic derivatives is established. Then, based on the four-degree-of-freedom ship maneuvering motion prediction model with variable higher-order hydrodynamic derivatives, the extended Kalman filter algorithm is used to identify the parameters of hydrodynamic derivatives of different orders, and the deterministic coefficients are used to... Obtain the optimal order prediction model; based on the optimal order prediction model, obtain preliminary prediction results of ship motion state; Based on the optimal order prediction model, and combined with real ship motion data, ship motion prediction residuals are constructed; the least squares support vector machine algorithm is used for black box modeling to approximate the motion prediction residuals. Finally, a BP neural network was constructed, using the prediction results of the least squares support vector machine black box model and the prediction results of the optimal model as input, and real ship navigation data as output to train the neural network, thereby achieving accurate estimation of the ship's motion state.

2. The intelligent ship maneuvering motion prediction method based on mathematical equation-data-driven fusion according to claim 1, characterized in that, The process of establishing a mathematical model of ship maneuvering motion with variable higher-order hydrodynamic derivatives based on the MMG model and the idea of ​​Taylor series expansion is as follows: Based on the MMG model of ship maneuvering motion, assuming the ship's coordinate origin is at its center of gravity, the hull is a rigid body, and neglecting the ship's heave and pitch motions, considering only the four degrees of freedom of pitch, sway, roll, and bow, the following ship motion equations are established: （1） In the formula: , The ships are respectively in direction and Velocity component in the direction; This refers to the roll angular velocity; The bow roll angular velocity; This refers to the roll angle; For the quality of the ship; , The ships are respectively in shaft and Additional mass in the axial direction; , , , Ships around shaft and Moment of inertia and additional moment of inertia of the shaft; For added mass Center Coordinate values; The displacement of the ship; This is the initial metacentric height of the ship; , , , These refer to the viscous hydrodynamics and moments of the ship in the longitudinal, lateral, roll, and bow directions, respectively, with subscripts... , , These represent the hull, propeller, and rudder, respectively.

3. The intelligent ship maneuvering motion prediction method based on mathematical equation-data-driven fusion according to claim 2, characterized in that, The formulas for calculating the hydrodynamic forces and torques of the propeller and rudder are as follows: （2） In the formula: , and These are the thrust deduction factor, propeller speed, and propeller diameter, respectively. This is the advance coefficient; The normal force acting as the rudder; For rudder angle; The factor for reducing rudder force; The correction factor for steering-induced lateral forces on the hull; The vertical height of the center of action of the rudder force; The longitudinal coordinate of the point of application of the rudder interference force; The longitudinal position of the point of application of the rudder normal force; Based on the idea of ​​Taylor series expansion, the forces and moments acting on the hull are written as... , , , , The function is: （3） In the formula: It is the direct resistance of the ship, that is ; The order of the hydrodynamic expansion varies with the model here. ; Based on the ship's symmetrical shape. about , , The changes are symmetrical. for , , even functions, , , about , , The change is antisymmetric. , , for , , Therefore, it is an odd function. about , , The first and third derivatives are both zero. , , about , , The second and fourth derivatives are all zero, that is: （4） In the formula: , , These represent the initial states of lateral, roll, and bow roll, respectively. The fluid dynamics and torques under these conditions, among which , , These are the initial sway speed, initial bow roll rate, and initial roll angle of the ship, respectively.

4. The intelligent ship maneuvering motion prediction method based on mathematical equation-data-driven fusion according to claim 3, characterized in that: The four-degree-of-freedom ship maneuvering motion prediction model based on variable higher-order hydrodynamic derivatives employs an extended Kalman filter algorithm to identify parameters of different orders of hydrodynamic derivatives and utilizes deterministic coefficients. The process of obtaining the optimal order prediction model is as follows: The four-degree-of-freedom ship maneuvering motion prediction model with variable higher-order hydrodynamic derivatives is discretized, and the model parameters are used as state variables to establish the following state equations and measurement equations: （5） in, （6） In the formula: This is process noise; For measuring noise; The time of the ship's movement; For matrix The number of columns; , , , For the linear hydrodynamic derivative that needs to be identified, where represent exist The second derivative in the direction; , , , For the higher-order nonlinear hydrodynamic derivatives that need to be identified; Let be the number of hydrodynamic derivatives of each order; the higher-order nonlinear hydrodynamic derivatives for each term are as follows: , , , For the hydrodynamic derivatives in the four degrees of freedom of sway, roll, pitch, and bow roll; where , ; Assuming the ship's shape is symmetrical from left to right, according to equation (3), we get All are zero vectors (7) In the formula: Each item is represented as ; Each item can be represented as ; The above parameters are identified, and ship maneuvering motion models containing hydrodynamic derivatives of different orders are constructed, using deterministic coefficients. The basis for selecting a four-degree-of-freedom ship maneuvering motion prediction model with variable higher-order hydrodynamic derivatives: （8） In the formula: This refers to the number of samples. , The first The true and predicted values ​​of each sample It refers to the average value of the sample. The closer the value is to 1, the better the predictive performance of the model of that order. Therefore, we should choose... The model closest to 1 is selected as the ship motion prediction model with the best model order.

5. The intelligent ship maneuvering motion prediction method based on mathematical equation-data-driven fusion according to claim 2, characterized in that: The process of constructing ship motion prediction residuals and approximating them using a least squares support vector machine algorithm for black-box modeling is as follows: Ship motion prediction residuals are constructed based on the optimal order model and real navigation data; The true value of the ship's motion state is represented as The prediction results of the optimal model are expressed as follows: The residual between the actual value and the predicted value of the ship's motion state is expressed as: （9） The least squares support vector machine (LS-SVM) algorithm is used for black-box modeling, and the neural network input is... The output is By training a neural network, the residual of motion prediction can be approximated.

6. The intelligent ship maneuvering motion prediction method based on mathematical equation-data-driven fusion according to claim 2, characterized in that: The process of building a BP neural network, using the prediction residuals of the least squares support vector machine black-box model and the prediction results of the optimal model as input, and real ship navigation data as output, to train the neural network and achieve the estimation of ship motion state is as follows: A BP neural network is constructed based on the prediction results of the optimal order model and the prediction residuals of LS-SVM. The prediction residuals of LS-SVM and the prediction results of the optimal order model are used as inputs to the BP neural network, and real ship navigation data is used as the output of the BP neural network for training. The LS-SVM prediction residuals and the prediction results of the optimal order model are respectively expressed as follows: , The estimated value of the ship's motion state is expressed as: ,in .

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