A Ship Motion Prediction Method with Variable Orders of Hydrodynamic Derivatives

Abstract

A ship motion prediction method with variable hydrodynamic derivative orders according to the present invention includes the following steps: Based on the Taylor series expansion idea, establish a four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives; Based on the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, use the extended Kalman filter algorithm to identify the parameters of the hydrodynamic derivatives of different orders; According to the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, predict the ship trajectory deviation, and adaptively determine the dynamic order of the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives to achieve the prediction of the ship motion state. Compared with the fixed model structure, the ship motion prediction method based on the hydrodynamic derivative order adaptive ship maneuvering motion model proposed by the present invention can effectively improve the accuracy of motion prediction.

Description

Technical Field

[0001] The present invention belongs to the fields of ship and ocean engineering technology and motion prediction, and relates to a ship motion prediction method with variable orders of hydrodynamic derivatives. Background Technique

[0002] The prediction research on the motion performance of a ship when sailing in waves is a classic and important topic in the field of ship and ocean engineering. The ship's maneuvering motion is actually a complex process with multi-degree-of-freedom coupling, multi-factor interference, and random uncertainty. Traditional motion modeling methods include mechanism modeling and identification modeling. With the construction and development of large ships, it is very difficult to accurately predict the ship's sailing trajectory only by relying on empirical formula calculations. Model ship tests require high economic costs and time costs, and mechanism modeling consumes a large amount of manual experience. In contrast, the system identification method has become an important method for establishing the mathematical model of ship maneuvering motion.

[0003] Accurately determining the hydrodynamic derivatives in the mathematical model is the key to improving the accuracy of ship maneuvering motion. Conducting parameter identification research based on the ship maneuvering motion prediction model with a fixed structure can improve the accuracy of ship motion prediction to a certain extent. However, when the rudder angle is large and the course is unstable, it is very difficult to make accurate predictions only relying on linearized hydrodynamic derivatives. At this time, it is necessary to consider the nonlinear terms among them, but when the order of the hydrodynamic derivatives is too high, it will increase the computational complexity of the model. Summary of the Invention

[0004] In order to solve the above problems, the technical solution adopted by the present invention is: a ship motion prediction method with variable orders of hydrodynamic derivatives, which is characterized by including the following steps:

[0005] Based on the Taylor series expansion idea, establish a four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives;

[0006] Based on the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, adopt the extended Kalman filter algorithm to identify the parameters of the hydrodynamic derivatives of different orders;

[0007] According to the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, predict the ship trajectory deviation, and adaptively determine the dynamic order of the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives to achieve the prediction of the ship motion state.

[0008] Furthermore: The four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives established based on the Taylor series expansion idea is as follows:

[0009]

[0010] where: X(u) is the straight-ahead resistance of the ship; K is the order of the hydrodynamic expansion, which varies with the model and K = 2, 3, 4; u and v are the velocity components in the x and y directions respectively; p is the roll angular velocity; r is the yaw angular velocity; φ is the roll angle; X, Y, L, and N are the viscous hydrodynamic forces and moments in the longitudinal, lateral, roll, and yaw directions of the ship, and the subscript H represents the hull; X H (v0, r0, φ0), Y H (v0, r0, φ0), L H (v0, r0, φ0), N H (v0, r0, φ0) are the hydrodynamic forces and moments in the longitudinal, lateral, roll, and yaw directions at the initial state (v0, r0, φ0) respectively.

[0011] Considering the left-right symmetry of the ship's shape, the variation of X with respect to v, r, and φ is symmetric, and X is an even function of v, r, and φ. The variation of Y, L, and N with respect to v, r, and φ is antisymmetric, and Y, L, and N are odd functions of v, r, and φ. Therefore, each term of the first and third derivatives of X with respect to v, r, and φ is zero, and each term of the second and fourth derivatives of Y, L, and N with respect to v, r, and φ is zero, that is:

[0012]

[0013] where: Z H (v0, r0, φ0) = Y H (v0, r0, φ0), L H (v0, r0, φ0), N H (v0, r0, φ0) are the hydrodynamic forces and moments in the lateral, roll, and yaw directions at the initial state (v0, r0, φ0) respectively;

[0014] Only analyze the longitudinal force of the propeller, and calculate the propeller thrust using the following formula:

[0015]

[0016] where: w p 、t p 、n and D p are the wake fraction coefficient, thrust deduction coefficient, propeller revolution speed, and propeller diameter of the propeller respectively; J p is the advance coefficient; a0 and a1 are regression coefficients obtained from the open-water characteristic curve of the propeller;

[0017] Calculate the hydrodynamic forces and moments caused by the rudder using the following formula:

[0018]

[0019] where: FN is the normal force of the rudder; δ is the rudder angle; t R is the added mass coefficient of the rudder force; a H is the correction factor for the lateral force induced by steering on the hull; z R is the vertical height of the center of action of the rudder force; x H is the longitudinal coordinate of the point of action of the rudder interference force; x R is the longitudinal position of the point of action of the normal rudder force.

[0020] Furthermore, the process of parameter identification of hydrodynamic derivatives of different orders using the extended Kalman filter algorithm is as follows:

[0021] The extended Kalman filter algorithm is divided into two steps: state prediction and state update:

[0022] The predicted state estimation matrix and the prior covariance matrix of the error are:

[0023]

[0024] In the formula, is the Jacobian matrix; P(k|k) is the posterior covariance matrix of the estimation error; Q(k) is the process noise covariance matrix;

[0025] Update the Kalman gain matrix, the optimal estimated value of the state, and the posterior covariance matrix of the error:

[0026]

[0027] In the formula, R(k + 1) is the covariance matrix of the measurement noise.

[0028] Furthermore, the process of predicting the ship trajectory deviation according to the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, adaptively determining the dynamic order of the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, and realizing the prediction of the ship motion state is as follows:

[0029] Define the trajectory deviation index to adaptively adjust the order of the nonlinear terms of the ship maneuvering motion model. Define the sum of the distances between the motion trajectories generated by the ship motion prediction model with hydrodynamic derivatives expanded to the Kth order at each moment and the true trajectory as:

[0030]

[0031] In the formula, N is the number of samples; is the predicted value at the i-th sampling point, x i , y i is the true value at the i-th sampling point;

[0032] Define the trajectory deviation index as a threshold value, and the expression of the trajectory deviation index is as follows:

[0033]

[0034] When T K > 0, it indicates that the ship maneuvering prediction model with the hydrodynamic derivatives expanded to the Kth order is superior to the ship maneuvering prediction model with the hydrodynamic derivatives expanded to the 2nd order;

[0035] When T K < 0, it indicates that the ship maneuvering prediction model with the hydrodynamic derivatives expanded to the Kth order is inferior to the ship maneuvering prediction model with the hydrodynamic derivatives expanded to the 2nd order; the order of the nonlinear terms of the ship maneuvering motion prediction model takes the order corresponding to the maximum value of T K as the optimal choice of the model structure.

[0036] A ship motion prediction device with variable orders of hydrodynamic derivatives includes:

[0037] A building module: used to establish a four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives based on the Taylor series expansion idea;

[0038] An identification module: used to perform parameter identification on the hydrodynamic derivatives of different orders by adopting the extended Kalman filter algorithm based on the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives;

[0039] A determination module: used to predict the ship trajectory deviation according to the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, adaptively determine the dynamic order of the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, and realize the prediction of the ship motion state.

[0040] A ship motion prediction method with variable orders of hydrodynamic derivatives provided by the present invention has the following advantages:

[0041] Compared with the fixed model structure, the ship motion prediction method based on the ship maneuvering motion model with adaptive orders of hydrodynamic derivatives proposed by the present invention can effectively improve the accuracy of motion prediction;

[0042] The inventive method proposed by the present invention can improve the accuracy of ship motion prediction while taking into account the computational complexity. Description of the Drawings

[0043] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required in the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0044] Figure 1 is the flowchart of the method;

[0045] Figure 2 is a schematic diagram of the planar coordinate system adopted by the ship motion MMG model;

[0046] Figure 3 is the flowchart of ship motion prediction by the method proposed in the present invention. Detailed implementation manners

[0047] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other. The following will refer to the drawings and combine the embodiments to detail the present invention.

[0048] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. The following description of at least one exemplary embodiment is actually only illustrative and in no way limits the present invention and its application or use. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0049] It should be noted that the terms used herein are only for describing specific implementation manners and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0050] Unless otherwise specifically stated, the relative arrangement of components and steps, numerical expressions, and numerical values set forth in these embodiments do not limit the scope of the present invention. At the same time, it should be clear that, for the sake of convenience of description, the dimensions of the various parts shown in the drawings are not drawn in actual proportional relationship. Technologies, methods, and devices known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, the said technologies, methods, and devices should be regarded as part of the authorization specification. In all the examples shown and discussed here, any specific values should be construed as merely exemplary and not as a limitation. Therefore, other examples of the exemplary embodiments may have different values. It should be noted that: like reference numerals and letters denote like items in the following drawings, and thus, once an item is defined in one drawing, it does not need to be further discussed in subsequent drawings.

[0051] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by orientation words such as "front, rear, upper, lower, left, right", "lateral, vertical, perpendicular, horizontal", and "top, bottom", etc. is usually based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description. Without contrary description, these orientation words do not indicate and imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation. Therefore, it should not be construed as limiting the protection scope of the present invention: the orientation words "inside, outside" refer to the inside and outside relative to the contour of each component itself.

[0052] For the convenience of description, spatial relative terms such as "above...", "over...", "on the upper surface of...", "upper...", etc. can be used here to describe the spatial positional relationship between a device or feature shown in the drawings and other devices or features. It should be understood that the spatial relative terms are intended to include different orientations in use or operation in addition to the orientation described in the drawings for the device. For example, if the device in the drawing is inverted, the device described as "above other devices or structures" or "over other devices or structures" will then be positioned as "below other devices or structures" or "under other devices or structures". Thus, the exemplary term "above..." can include both the orientations of "above..." and "below...". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and corresponding interpretations should be made for the spatial relative descriptions used here.

[0053] In addition, it should be noted that the use of words such as "first", "second", etc. to limit components is only for the convenience of differentiating the corresponding components. Without otherwise stating, the above words have no special meaning. Therefore, it should not be construed as limiting the protection scope of the present invention.

[0054] Figure 1It is the flow chart of the method;

[0055] A ship motion prediction method with variable hydrodynamic derivative orders, comprising the following steps:

[0056] S1: Based on the Taylor series expansion idea, establish a four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives;

[0057] S2: Based on the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, adopt the extended Kalman filter algorithm to identify the parameters of hydrodynamic derivatives of different orders;

[0058] S3: According to the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, predict the ship trajectory deviation, and adaptively determine the dynamic order of the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives to realize the prediction of the ship motion state.

[0059] Steps S1 / S2 / S3 are executed sequentially;

[0060] As Figure 2 shown is the planar coordinate system adopted by the ship motion MMG model referred to in the present invention. Assuming that the coordinate origin of the ship is at the center of gravity position, the hull is a rigid body, the heaving motion and pitching motion of the ship are ignored, and only the four degrees of freedom of surge, sway, roll and yaw are considered. The following ship motion equations are established:

[0061]

[0062] In the formula: u and v are the velocity components in the x-direction and y-direction respectively; p is the roll angular velocity; r is the yaw angular velocity; φ is the roll angle; m is the mass of the ship; m x , m y are the added masses of the ship in the x-axis and y-axis directions respectively; I x , J x , I z , J z are the moments of inertia and added moments of inertia of the ship about the x-axis and z-axis respectively; l x is the x-coordinate value of the center of the added mass m x ; W is the displacement of the ship; GM is the initial metacentric height of the ship; X, Y, L, N are the viscous fluid dynamic forces and moments of the ship in the longitudinal, lateral, roll and yaw directions respectively, and the subscripts H, P, R represent the hull, propeller and rudder respectively.

[0063] Figure 3 This is the flow chart for predicting ship motion by the method proposed in the present invention, and the specific content is as follows:

[0064] Based on the idea of Taylor series expansion, the hydrodynamic forces and moments acting on the hull are Taylor-expanded with respect to the lateral velocity, yaw angular velocity, and roll angle to calculate the viscous hydrodynamic forces of the hull:

[0065]

[0066] where: X(u) is the ship's straight-ahead resistance; K is the order of the hydrodynamic expansion, which varies with the model here and K = 2, 3, 4. X H (v0, r0, φ0), Y H (v0, r0, φ0), L H (v0, r0, φ0), N H (v0, r0, φ0) are the hydrodynamic forces and moments in the longitudinal, lateral, roll, and yaw directions at the initial state (v0, r0, φ0), respectively;

[0067] Considering the ship's shape is symmetric about the left and right, the variation of X with respect to v, r, and φ is symmetric, X is an even function of v, r, and φ, and the variation of Y, L, and N with respect to v, r, and φ is antisymmetric, Y, L, and N are odd functions of v, r, and φ. Therefore, each term of the first and third derivatives of X with respect to v, r, and φ is zero, and each term of the second and fourth derivatives of Y, L, and N with respect to v, r, and φ is zero, that is:

[0068]

[0069] where: Z H (v0, r0, φ0) = Y H (v0, r0, φ0).

[0070] Only analyze the longitudinal force of the propeller, and use the following formula to calculate the propeller thrust:

[0071]

[0072] where: w p , t p , n and D p are the wake fraction coefficient, thrust deduction coefficient, propeller revolution speed, and propeller diameter of the propeller, respectively; J p is the advance coefficient; a0, a1 are the regression coefficients obtained from the propeller open-water characteristic curve.

[0073] Use the following formula to calculate the hydrodynamic forces and moments caused by the rudder:

[0074]

[0075] where: F N is the normal force of the rudder; δ is the rudder angle; t R is the deduction coefficient of the rudder force; aH is the correction factor for the steering-induced lateral force of the hull; z R is the vertical height of the center of action of the rudder force; x H is the longitudinal coordinate of the action point of the rudder interference force; x R is the longitudinal position of the action point of the normal rudder force.

[0076] Based on the above formula (5), the state and measurement equations of the ship's maneuvering motion model are obtained:

[0077]

[0078] where w(t) is the process noise; v(t) is the measurement noise.

[0079]

[0080] where is the number of columns of matrix H, where a1 = X uu , X uu represents the second derivative of u in the X direction; 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 are the linear hydrodynamic derivatives to be identified; a 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 are the high-order non-linear hydrodynamic derivatives to be identified; is the number of hydrodynamic derivatives of each order; each high-order non-linear hydrodynamic derivative is respectively:​​​​​​​ K v i +K r i +K φ i = K, where K = 2, 3, 4.

[0081] Assuming that the ship's outer shape is symmetric about the left and right, according to Equation (3), a3, b2, b4, c2, c4, d2, and d4 are all zero vectors.

[0082]

[0083] In the formula, Each term is respectively expressed as h K = [h K, 1h K,2 …h K,n Τ ; Each term can be expressed as

[0084] According to Equation (7), the extended Kalman filter is divided into two steps: state prediction and state update:

[0085] The predicted state estimation matrix and the prior covariance matrix of the error are:

[0086]

[0087] In the formula, is the Jacobian matrix; P(k|k) is the posterior covariance matrix of the estimation error; Q(k) is the process noise covariance matrix;

[0088] Update the Kalman gain matrix, the optimal estimated value of the state, and the posterior covariance matrix of the error:

[0089]

[0090] In the formula, R(k + 1) is the covariance matrix of the measurement noise.

[0091] To improve the accuracy of the ship maneuvering prediction model and reduce the computational complexity, a trajectory deviation index is defined to adaptively adjust the order of the nonlinear terms of the ship maneuvering motion model. The sum of the distances between the motion trajectories generated by the ship motion prediction model with the hydrodynamic derivatives expanded to the Kth order at each moment and the true trajectory is defined as:

[0092]

[0093] In the formula, N is the number of samples; is the predicted value at the ith sampling point, x i , y​i is the true value of the i-th sampling point.

[0094] Define the trajectory deviation index as the threshold, and the expression of the trajectory deviation index is as follows:

[0095]

[0096] When T K > 0, it indicates that the ship maneuvering prediction model with the hydrodynamic derivatives expanded to the K-th order is superior to the ship maneuvering prediction model with the hydrodynamic derivatives expanded to the 2nd order;

[0097] When T K < 0, it indicates that the ship maneuvering prediction model with the hydrodynamic derivatives expanded to the K-th order is inferior to the ship maneuvering prediction model with the hydrodynamic derivatives expanded to the 2nd order. The order of the nonlinear terms in the ship maneuvering motion prediction model takes the order corresponding to the maximum value of T K as the optimal choice of the model structure.

[0098] Next, a specific embodiment will be used to illustrate in detail the ship motion prediction method provided in this embodiment.

[0099] The main parameters of a certain container ship are shown in Table 1.

[0100] Table 1 Main parameters of a certain container ship

[0101] Parameter Value Parameter Value <![CDATA[Captain L pp / m]]> 175 <![CDATA[Block coefficient C B > 0.559 Beam B / m 25.40 <![CDATA[Coefficient of fineness C P > 0.580 Mean draft d / m 8.50 <![CDATA[Propeller diameter D P / m]]> 6.533 <![CDATA[Displacement volume V / m 3 > 21222 <![CDATA[Rudder area A R / m 2 > 33.0376 Initial metacentric height GM / m 10.39 Rudder height H / m 7.7583

[0102] Perform a 20° / 20° Z-shaped test numerical simulation on this container ship with a simulation step of 0.1 s to obtain data such as longitudinal speed, lateral speed, roll angular velocity, yaw angular velocity, roll angle, rotational speed, rudder angle, etc. Use the extended Kalman filter for parameter identification, and substitute the identification results into the original ship maneuvering motion prediction model to calculate the trajectory deviation of the ship motion, and select a suitable ship motion prediction model. Compare the ship motion trajectory deviations in the 20° / 20° Z-shaped test under different orders of expansion of the hydrodynamic derivatives, as shown in Table 2.

[0103] Table 2 Trajectory deviations of models with different orders

[0104] Order of hydrodynamic expansion <![CDATA[d K / m]]> <![CDATA[T K > K＝2 285359.6160 0 K＝3 21323.9000 0.9253 K＝4 21376.5581 0.9251

[0105] It can be seen that when different orders K of the expansion terms of the hydrodynamic derivatives are selected, the trajectory deviations of the ship motion are also different. By comparing the hydrodynamic derivative models of different orders, the ship motion prediction model can be adaptively selected through the trajectory deviation index, which preliminarily shows that the method proposed in the present invention can effectively improve the accuracy of ship motion prediction.

[0106] To further illustrate that the method proposed by the present invention can improve the accuracy of ship motion prediction, hydrodynamic derivatives obtained by the above-mentioned extended Kalman filter identification are used for 20° / 10° Z-shaped and 25° turning simulation experiments for verification. The simulation step size is 0.1 s, and prediction results of longitudinal velocity, lateral velocity, roll angular velocity, yaw angular velocity, heading angle, rudder angle, and motion trajectory are obtained. The prediction accuracy of 20° / 10° Z-shaped and 25° turning is measured by root mean square error. The trajectory deviations and root mean square errors of predictions of longitudinal velocity, lateral velocity, roll angular velocity, and yaw angular velocity of different-order models are shown in Table 3 and Table 4 respectively.

[0107] Table 3 Trajectory Deviations of Different-Order Models

[0108]

[0109] Table 4 Root Mean Square Errors of Different-Order Models

[0110]

[0111]

[0112] By comparing ship motion prediction models containing hydrodynamic derivatives of different orders, it can be seen that the prediction method proposed according to the present invention can adaptively select a ship motion prediction model with hydrodynamic derivatives expanded to the fourth order to improve the prediction accuracy.

[0113] A ship motion prediction device with variable orders of hydrodynamic derivatives includes:

[0114] A building module: used to build a four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives based on the Taylor series expansion idea;

[0115] An identification module: used to perform parameter identification on hydrodynamic derivatives of different orders by using the extended Kalman filter algorithm based on the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives;

[0116] A determination module: used to predict the ship trajectory deviation according to the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, and adaptively determine the dynamic order of the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives to achieve the prediction of ship motion states.

[0117] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements 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 ship motion prediction method with variable orders of hydrodynamic derivatives, characterized in that: It includes the following steps: Based on the Taylor series expansion idea, a four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives is established; Based on the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, the extended Kalman filter algorithm is used to identify the parameters of the hydrodynamic derivatives of different orders; According to the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, the ship trajectory deviation is predicted, and the dynamic order of the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives is adaptively determined to realize the prediction of the ship motion state.

2. The ship motion prediction method with variable hydrodynamic derivative order according to claim 1, characterized in that: The method for establishing a four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives based on the Taylor series expansion idea is as follows: where: X(u) is the straight-ahead resistance of the ship; K is the order of the hydrodynamic expansion, which varies with the model and K = 2, 3, 4; u and v are the velocity components in the x and y directions respectively; p is the roll angular velocity; r is the yaw angular velocity; φ is the roll angle; X, Y, L, and N are the viscous hydrodynamic forces and moments in the longitudinal, lateral, roll, and yaw directions of the ship, and the subscript H represents the hull; X H (v0, r0, φ0), Y H (v0, r0, φ0), L H (v0, r0, φ0), N H (v0, r0, φ0) are the hydrodynamic forces and moments in the longitudinal, lateral, roll, and yaw directions at the initial state (v0, r0, φ0) respectively; Considering the left-right symmetry of the ship's shape, the variation of X with respect to v, r, and φ is symmetric, X is an even function of v, r, and φ, and the variations of Y, L, and N with respect to v, r, and φ are antisymmetric, Y, L, and N are odd functions of v, r, and φ. Therefore, each term of the first-order and third-order derivatives of X with respect to v, r, and φ is zero, and each term of the second-order and fourth-order derivatives of Y, L, and N with respect to v, r, and φ is zero, that is: where: Z H (v0, r0, φ0) = Y H (v0, r0, φ0), L H (v0, r0, φ0), N H (v0, r0, φ0) are the hydrodynamic forces and moments of sway, roll, and yaw at the initial state (v0, r0, φ0), respectively; Only analyze the longitudinal force of the propeller, and calculate the propeller thrust using the following formula: where: w p , t p , n and D p are respectively the wake fraction coefficient, the thrust deduction coefficient, the propeller revolution speed and the propeller diameter of the propeller; J p is the advance coefficient; a0 and a1 are regression coefficients obtained according to the open water characteristic curve of the propeller; Calculate the hydrodynamic force and moment caused by the rudder using the following formula: where: F N is the normal force of the rudder; δ is the rudder angle; t R is the added mass coefficient of the rudder force; a H is the correction factor of the lateral force induced by steering; z R is the vertical height of the center of action of the rudder force; x H is the longitudinal coordinate of the action point of the rudder interference force; x R is the longitudinal position of the action point of the rudder normal force.

3. A ship motion prediction method with variable hydrodynamic derivative order according to claim 1, characterized in that: The process of using the extended Kalman filter algorithm to identify the parameters of the hydrodynamic derivatives of different orders is as follows: The extended Kalman filter algorithm is divided into two steps: state prediction and state update: Predict the state estimation matrix and the prior covariance matrix of the error: In the formula, is the Jacobian matrix; P(k|k) is the posterior covariance matrix of the estimation error; Q(k) is the process noise covariance matrix; Update the Kalman gain matrix, the optimal estimated value of the state, and the posterior covariance matrix of the error: In the formula, R(k + 1) is the covariance matrix of the measurement noise.

4. A ship motion prediction method with variable hydrodynamic derivative order according to claim 1, characterized in that: The process of predicting the ship trajectory deviation according to the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, adaptively determining the dynamic order of the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, and realizing the prediction of the ship motion state is as follows: Define the trajectory deviation index to adaptively adjust the order of the nonlinear terms of the ship maneuvering motion model. Define the sum of the distances between the motion trajectories generated by the ship motion prediction model with the hydrodynamic derivatives expanded to the Kth order and the true trajectory at each moment as: Where N is the number of samples; is the predicted value of the i-th sampling point, x i , y i is the true value of the i-th sampling point; Define the trajectory deviation index as the threshold, and the expression of the trajectory deviation index is as follows: When T K > 0, it indicates that the ship maneuvering prediction model with the hydrodynamic derivatives expanded to the K-th order is superior to the ship maneuvering prediction model with the hydrodynamic derivatives expanded to the 2nd order; When T K < 0, it indicates that the ship maneuvering prediction model with the hydrodynamic derivatives expanded to the K-th order is inferior to the ship maneuvering prediction model with the hydrodynamic derivatives expanded to the 2nd order; the order of the non-linear term of the ship maneuvering motion prediction model is taken as the optimal choice of the model structure with the order corresponding to the maximum value of T K ​ 5. A ship motion prediction device with variable orders of hydrodynamic derivatives, characterized in that: It includes: A building module: used to establish a four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives based on the Taylor series expansion idea; An identification module: used to identify the parameters of the hydrodynamic derivatives of different orders based on the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives by using the extended Kalman filter algorithm; A determination module: used to predict the ship trajectory deviation according to the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, adaptively determine the dynamic order of the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, and realize the prediction of the ship motion state.

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