Identification method of ship nonlinear rolling parameters based on physical information neural network

Abstract

The present invention relates to the field of marine engineering technology, and provides a method for identifying nonlinear roll parameters of ships based on physical information neural networks. Determine the free decay data of the ship's roll angle and its norm, the initial conditions of the roll motion and its norm, and the physical equation of the roll motion and its norm; determine the feedforward neural network, and calculate to obtain the optimal network hyperparameters; based on the optimized network hyperparameters, determine the physical information neural network framework; based on the norm of the free decay data of the ship's roll angle, the norm of the initial conditions of the roll motion, and the norm of the physical equation of the roll motion, determine the total loss function of the network; minimize the total loss function, drive the neural network operation, obtain the unknown quantity of the neural network, and obtain the roll parameters to be identified. This method provides a neural network method with both high precision and high efficiency for the actual ship roll motion analysis.

Description

Technical Field

[0001] The invention relates to the technical field of marine engineering, and in particular to a method for identifying ship nonlinear rolling parameters based on a physical information neural network. Background Art

[0002] In the dynamic analysis of ship motion, the assessment of roll motion is particularly important because it has a significant correlation with ship capsizing. Among the many factors that affect roll motion, damping force and restoring force occupy a key position. In essence, the action mechanism of these forces is nonlinear, and the inducing factors of the forces are complex, affected by fluid viscosity, hull friction, and bilge keel resistance. In order to better describe the nonlinear characteristics of damping force and restoring force, predecessors have proposed a variety of parameterized models, but how to accurately calibrate the parameters of these models remains a challenge. To solve this problem, this study proposes a neural network-based parameter correction algorithm to identify these nonlinear parameters through a small amount of roll free decay motion data.

[0003] In terms of roll damping identification, Ikeda's semi-empirical method is the most famous and widely used method, which is also recommended by the ITTC Guidelines. However, some studies have found that it has inconsistent problems in the prediction of roll parameters. In recent years, many numerical or experimental methods have emerged, including asymptotic method, least squares method, support vector regression, homotopy perturbation method, Runge-Kutta method, Froude energy method and wavelet method, which give approximate solutions of damping parameters by analyzing free decay signals. These methods are increasingly favored because of their ability to solve nonlinear differential equations. In terms of roll restoring force identification, nonlinear effects related to hydrostatic moment and Froude-Krylov wave loads usually need to be considered. Although several analytical methods were proposed in the early days, the accuracy was difficult to achieve as expected. Among the numerical methods, the GZ curve method and the exact pressure integration method were developed to evaluate the hydrostatic moment and Froude-Krylov load. However, there are very limited studies on the simultaneous correction of roll damping force and restoring moment.

[0004] The essence of synchronously identifying the damping parameters and restoring force parameters of roll motion is a process of solving an inverse problem. In recent years, deep learning algorithms have shown superior performance in solving inverse problems. The core lies in training neural network models to effectively approximate large-scale data sets. This type of data-driven method can obviously greatly surpass traditional methods in terms of reconstruction accuracy and computational efficiency. In particular, the physical information neural network method encodes the physical control equations into the residual network, making the resulting solution physically interpretable. Given that the ship roll can be represented by nonlinear differential equations, it is expected that the roll motion equations can be embedded in the physical information neural network to solve the parameterization problems related to nonlinear roll motion. Summary of the invention

[0005] The purpose of the present invention is to solve the above technical problems and provide a method for identifying ship nonlinear rolling parameters based on physical information neural network.

[0006] In order to achieve the above object, in some embodiments of the present invention, the following technical solutions are provided:

[0007] A method for identifying ship nonlinear rolling parameters based on physical information neural network comprises the following steps:

[0008] S1: Determine the free decay data of the ship's roll angle and its norm, the initial conditions of the roll motion and its norm, and the physical equation of the roll motion and its norm;

[0009] S2: determining a feedforward neural network, taking physical time as input of the neural network, roll angle as output of the neural network, and roll parameter to be identified as unknown quantity of the neural network, and determining a total loss function of the neural network based on the norm of free decay data of the ship roll angle, the norm of initial condition of roll motion, and the norm of physical equation of roll motion;

[0010] S3: establishing a hyperparameter optimization objective function of the neural network, and optimizing the network hyperparameters of the neural network based on the hyperparameter optimization objective function to obtain optimized network hyperparameters;

[0011] S4: Based on the optimized network hyperparameters, determine the physical information neural network framework; minimize the total loss function, drive the neural network operation, obtain the unknown quantity of the neural network, and obtain the roll parameter to be identified.

[0012] In some embodiments of the present invention, in step S1:

[0013] Roll angle free decay data Expressed as an equation ;

[0014] Initial conditions for rolling motion and Expressed as an equation ;

[0015] The physical equation for rolling motion is expressed as: ;in, represents a nonlinear rolling parameter; the physical equation of the rolling motion includes a damping term of the ship motion and a restoring moment term of the ship motion;

[0016] The physical equations of rolling motion are rewritten to include:

[0017] The linear-quadratic-cubic damping model is used to characterize the damping term of ship motion, namely:

[0018] ;

[0019] The linear-cubic restoring force model is used to characterize the restoring moment term of the ship motion, namely:

[0020] ;

[0021] Therefore, the physical equation of rolling motion can be rewritten as:

[0022] ;

[0023] Among them, the nonlinear roll parameter That is the vector , is the first-order damping parameter, represents the total roll inertia including the structural inertia and the added inertia of water, Representation and and The associated nonlinear damping forces; Representation and The associated nonlinear restoring moment, is the second-order damping parameter, is the third-order damping parameter; is the first-order restoring force parameter, is the second-order restoring force parameter, is the roll angular acceleration, represents the rolling angular velocity, Indicates the roll angle.

[0024] In some embodiments of the present invention, in step S2, the steps of calculating the norm of the free decay data of the ship's roll angle, the norm of the initial condition of the roll motion, and the norm of the physical equation of the roll motion include:

[0025] Roll angle attenuation data of Norm It is expressed as:

[0026] ;

[0027] Initial conditions for rolling motion and of The norm is expressed as :

[0028] ;

[0029] Physical equations for rolling motion of The norm is expressed as :

[0030] ;

[0031] in, , , They represent the physical constraints satisfying the free decay data, initial conditions, and physical equations respectively; Represents the coordinates of discrete data points; , Represent the number of free decay data and physical equation data respectively; the superscript “^” represents the estimated value of the variable in the current neural network iteration step.

[0032] In some embodiments of the present invention, the step of determining the total loss function of the neural network includes:

[0033] Determine the total network loss function :

[0034]

[0035] in, 、 、 They represent the weight distribution of the corresponding physical constraints respectively; is the parameter to be optimized in the neural network, including network weights , Network bias And the roll parameters , expressed as .

[0036] In some embodiments of the present invention, the step of optimizing the neural network hyperparameters in S3 includes:

[0037] Select the neural network hyperparameters to be optimized, including: learning rate , Network Layers , the number of neurons ;

[0038] Establish the hyperparameter optimization objective function:

[0039] ;

[0040] in, is the number of roll parameters, is the estimated value of the roll parameter, is the true value of the roll parameter, the estimated value is the calculation result obtained by the neural network in the current iteration step, and the true value is the true result set in advance. The Bayesian optimization method is used to minimize the objective function , optimize the neural network hyperparameters.

[0041] In some embodiments of the present invention, the step of minimizing the total network loss function in step S4 includes:

[0042] After determining the physical information neural network framework, the Adam optimization solver is used to minimize the total loss function of the network. :

[0043] ;

[0044] in, represents the equation minimization operator;

[0045] Obtain the network parameters to be optimized After finding the optimal solution, the nonlinear roll parameters are extracted. .

[0046] Compared with the prior art, the ship nonlinear rolling parameter identification method based on physical information neural network proposed in the present invention has the following beneficial effects:

[0047] The present invention proposes a high-precision identification method for nonlinear roll parameters based on a small amount of ship roll attenuation data. By adding a loss function containing physical information to the feedforward neural network, a neural network model that meets the physical laws of ship roll is constructed. This overcomes the technical defect that the solutions obtained by traditional data methods lack physical interpretability, and provides a neural network method with both high precision and high efficiency for the actual ship roll motion analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0049] Figure 1 To invent a logic schematic diagram of a ship nonlinear rolling parameter identification method based on physical information neural network;

[0050] Figure 2 Flowchart of the method for identifying ship nonlinear rolling parameters provided by the embodiment of the present invention

[0051] Figure 3 This is a numerical model diagram of a DTMB-5415 ship involved in an embodiment of the present invention;

[0052] Figure 4 This is a DTMB-5415 ship roll attenuation data diagram involved in an embodiment of the present invention;

[0053] Figure 5 Schematic diagram of neural network hyperparameter optimization according to an embodiment of the present invention; (a) is the learning rate Optimization diagram; (b) is the number of network layers Optimization diagram; (c) is the number of neurons Optimization schematic diagram;

[0054] Figure 6 Iteration graph of the loss function of the neural network training set and the validation set obtained in the embodiment of the present invention;

[0055] Figure 7 Iteration diagrams of nonlinear roll parameters obtained in the embodiment of the present invention; (a) is an iteration diagram of the damping parameter value loss function; (b) is an iteration diagram of the stiffness parameter value loss function;

[0056] Figure 8 This is a comparison chart of the roll signal reconstructed according to an embodiment of the present invention, the measurement data, and the verification data. DETAILED DESCRIPTION

[0057] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0058] In the embodiments of the present application, prefixes such as "first" and "second" are used only to distinguish different description objects, and have no limiting effect on the position, order, priority, quantity or content of the described objects. The use of prefixes such as ordinal numbers to distinguish description objects in the embodiments of the present application does not constitute a limitation on the described objects. For the statement of the described objects, please refer to the description in the context of the claims or embodiments, and no unnecessary limitation should be constituted due to the use of such prefixes. In addition, in the description of the present embodiment, unless otherwise specified, the meaning of "multiple" is two or more.

[0059] The technical solution in the embodiment of the present application will be described below in conjunction with the drawings in the embodiment of the present application. In the description of the embodiment of the present application, unless otherwise specified, " / " means or, for example, A / B can mean A or B; "and / or" in this article is only a description of the association relationship of associated objects, indicating that there can be three relationships, for example, A and / or B can mean: A exists alone, A and B exist at the same time, and B exists alone.

[0060] In the several embodiments provided in the embodiments of the present application, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be an indirect coupling or communication connection through some interfaces, devices or units, which can be electrical, mechanical or other forms.

[0061] Rolling parameters are used to determine the rolling motion equation and are the basis for ship modeling. In the prior art, the identification of ship rolling parameters has the problems of low accuracy and low efficiency. To solve the above problems, the present invention provides a ship nonlinear rolling parameter identification method based on physical information neural network. Figure 1 and Figure 2 The method provided by the present invention comprises the following steps.

[0062] S1: Determine the free decay data of the ship's roll angle and its norm, the initial conditions of the roll motion and its norm, and the physical equation of the roll motion and its norm.

[0063] Among them, the free decay data of the ship's roll angle represents the data of the roll angle changing over time when the ship gradually recovers from the initial roll state to the static state without the action of external forces (such as waves, wind, etc.), which characterizes the decay trend of the ship's roll angle. The free decay data reflects the natural characteristics of the ship's roll motion, mainly including: the stability characteristics and damping characteristics of the ship.

[0064] The initial condition of the rolling motion is The roll angle value at the moment and the rolling angular velocity value .

[0065] The physical equations of roll motion are dynamic models that describe the roll motion of a ship under the action of external forces (such as waves, wind, etc.). These equations are usually based on Newton's second law and Euler's equations, combined with factors such as the ship's inertia, damping, restoring torque, and external forces, to analyze the response characteristics of the ship's roll motion.

[0066] In some embodiments of the present invention:

[0067] Roll angle free decay data Expressed as an equation ;

[0068] Initial conditions for rolling motion and Expressed as an equation .

[0069] Under still water conditions, the physical equation of rolling motion is Usually expressed as:

[0070] ;

[0071] in, represents the nonlinear roll parameter, , , are roll angle, roll angular velocity and roll angular acceleration respectively; It represents the total roll inertia including the structural inertia and the water added inertia; Representation and and The associated nonlinear damping forces; Representation and The associated nonlinear restoring moment

[0072] Among them, the equation , , can be obtained based on the ship design parameters, which belongs to the prior art and will not be described in detail.

[0073] Furthermore, the physical equation for rolling motion is expressed as: ;in, represents a nonlinear rolling parameter; the physical equation of the rolling motion includes a damping term of the ship motion and a restoring moment term of the ship motion;

[0074] The physical equations of rolling motion are rewritten to include:

[0075] The linear-quadratic-cubic damping model is used to characterize the nonlinear damping term of ship motion, namely:

[0076] ;

[0077] The linear-cubic restoring force model is used to characterize the nonlinear restoring moment term of ship motion, namely:

[0078] ;

[0079] Therefore, the physical equation of rolling motion can be rewritten as:

[0080]

[0081] Among them, the nonlinear roll parameter That is the vector , represents the total roll inertia including the structural inertia and the added inertia of water, Representation and and The associated nonlinear damping forces; Representation and The associated nonlinear restoring moment, is the first-order damping parameter, is the second-order damping parameter, is the third-order damping parameter; is the first-order restoring force parameter, is the second-order restoring force parameter, is the roll angular acceleration, represents the rolling angular velocity, Indicates the roll angle.

[0082] S2: Determine a feedforward neural network, take physical time as the input of the neural network, roll angle as the output of the neural network, and roll parameter to be identified as the unknown quantity of the neural network, and determine the total loss function of the neural network based on the norm of the free decay data of the ship's roll angle, the initial condition norm of the roll motion, and the norm of the physical equation of the roll motion.

[0083] In some embodiments of the present invention, in step S2, the steps of calculating the norm of the free decay data of the ship's roll angle, the norm of the initial condition of the roll motion, and the norm of the physical equation of the roll motion include:

[0084] Roll angle attenuation data of Norm It is expressed as:

[0085] ;

[0086] Initial conditions for rolling motion and of The norm is expressed as :

[0087] ;

[0088] Physical equations for rolling motion of The norm is expressed as :

[0089] ;

[0090] in, 、 、 They represent the physical constraints satisfying the free decay data, initial conditions, and physical equations respectively; Represents the coordinates of discrete data points; 、 Represent the number of free decay data and physical equation data respectively; the superscript “^” represents the estimated value of the variable in the current neural network iteration step.

[0091] It should be noted that: Its derivatives are calculated in the neural network iteration process. The data of its derivatives can be numerically solved by the Runge-Kutta method to obtain the physical equations of rolling motion. The corresponding discrete sampling points and its derivatives. Substituting these data into the neural network, driving the network to calculate, each iteration step and its derivative values ​​are calculated by physical neural network method (the calculation process is as follows Figure 1 ) iterative solution.

[0092] In some embodiments of the present invention, the step of determining the constraint conditions of the neural network includes:

[0093] Determine the total network loss function :

[0094] ;

[0095] in, 、 、 They represent the weight distribution of the corresponding physical constraints respectively; is the parameter to be optimized in the neural network, including network weights , Network bias And the roll parameters , expressed as .

[0096] S3: Establishing a hyperparameter optimization objective function of the neural network, and optimizing the network hyperparameters of the neural network based on the hyperparameter optimization objective function to obtain optimized network hyperparameters.

[0097] In some embodiments of the present invention, the step of optimizing the neural network hyperparameters in S3 includes:

[0098] Select the neural network hyperparameters to be optimized, including: learning rate , Network Layers , the number of neurons ;

[0099] Establish the hyperparameter optimization objective function:

[0100] ;

[0101] in, is the number of roll parameters, is the estimated value of the roll parameter, is the true value of the roll parameter, the estimated value is the calculation result obtained by the neural network at the current iteration step, that is, the solution obtained by the neural network corresponding to the current learning rate, number of network layers, and number of neurons; the true value is the true result set in advance, that is, the set value of network hyperparameters such as learning rate, number of network layers, number of neurons, etc.; the Bayesian optimization method is used to minimize the objective function , optimize the neural network hyperparameters.

[0102] S4: Based on the optimized network hyperparameters, determine the physical information neural network framework; minimize the total loss function, drive the neural network operation, obtain the unknown quantity of the neural network, and obtain the roll parameter to be identified.

[0103] In some embodiments of the present invention, the step of minimizing the total network loss function in step S4 includes:

[0104] After determining the physical information neural network framework, the Adam optimization solver is used to minimize the total loss function of the network. :

[0105] ;

[0106] in, represents the equation minimization operator;

[0107] Obtain the network parameters to be optimized After finding the optimal solution, the nonlinear roll parameters are extracted. .

[0108] The following takes a ship-type floating marine structure as an example to illustrate the specific implementation effect of the method provided by the present invention.

[0109] The embodiment of the present invention selects the DTMB5415 destroyer standard model as a numerical example, see Figure 3 The ship has a full-size length of 142m, a waterline length of 142.18m, a molded width of 19.06m, a draft of 6.15m, and a displacement volume of 8424.4m3. In the numerical simulation, a scaled ship model of 1:35.48 is selected, and the calculation domain is a square box area of ​​20m*20m*8m, where the coordinate system 𝑥-𝑦 plane is located on the still water surface, and the 𝑧 axis is positive upward. This embodiment will calculate the roll attenuation motion signal of the ship rotating around the 𝑥 axis.

[0110] Release the ship model with an initial rotation angle of 10° and sample the time step , simulate the roll decay signal within 20 seconds Figure 4 The roll physical equation used in this embodiment is , the initial conditions are and .

[0111] based on Figure 1 In the physical neural network framework, the first step is to define the physical constraints related to the physical equations, initial conditions and measurement data. The loss weights are distributed in equal proportions. , the total loss function associated with the physical constraints Can be written.

[0112] After defining the loss function, the next step is to optimize the hyperparameters to determine the structure of the neural network. The optimization range of the hyperparameters is , , , 400 trials were conducted using the Bayesian optimization method, with each trial iteration The optimization results are as follows: Figure 5 As shown, the optimal hyperparameters are , , .

[0113] Based on the physical constraints and optimization hyperparameters given above, the Adam optimization solver is used to minimize the total loss function , which can drive the physical information neural network to solve the unknown parameters of the network Before network training begins, the linear damping parameter can be roughly estimated by the logarithmic decay rate method. ,in is the rolling period, and The amplitude corresponding to two consecutive cycles; the linear restoring force parameters can be roughly estimated by the resonance method , the remaining three parameters The initial value of is 0. After the network iteration optimization, the loss function iteration of the training set and the validation set is plotted in Figure 6 , the nonlinear roll parameter iteration process is plotted in Figure 7 , it can be seen that the identification parameters are approximately After the step, it has converged, and the final identification values ​​are .

[0114] Next, the identified roll parameters are substituted back into the roll physical equation, and the reconstructed roll signal is plotted and compared with the measured signal (first 20 seconds) and the predicted signal (20-40 seconds), as shown in Figure 2. Figure 8 The reconstructed signal not only agrees well with the measured signal in the first 20 seconds, but also maintains good consistency in the validation segment of 20-40 seconds, demonstrating the superior performance of the developed method.

[0115] The present invention proposes a high-precision identification method for nonlinear roll parameters based on a small amount of ship roll attenuation data. By embedding multiple loss functions containing physical equations, initial conditions, and measurement data in a feedforward neural network, a neural network model that meets the physical laws of ship roll is constructed. The optimization parameters in the network training stage automatically meet the physical equations, thereby achieving synchronous and efficient identification of nonlinear damping and recovery parameters.

[0116] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. It should be pointed out that for those skilled in the art, any modification, equivalent replacement and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the patent application shall be based on the protection scope of the attached claims.

Claims

1. A method for identifying ship nonlinear rolling parameters based on physical information neural network, characterized in that: The following steps are involved: S1: Determine the free decay data of the ship's roll angle and its norm, the initial conditions of the roll motion and its norm, and the physical equation of the roll motion and its norm; S2: determining a feedforward neural network, taking physical time as input of the neural network, roll angle as output of the neural network, and roll parameter to be identified as unknown quantity of the neural network, and determining a total loss function of the neural network based on the norm of free decay data of the ship roll angle, the norm of initial condition of roll motion, and the norm of physical equation of roll motion; S3: establishing a hyperparameter optimization objective function of the neural network, and optimizing the network hyperparameters of the neural network based on the hyperparameter optimization objective function to obtain optimized network hyperparameters; S4: Based on the optimized network hyperparameters, determine the physical information neural network framework; minimize the total loss function, drive the neural network operation, obtain the unknown quantity of the neural network, and obtain the roll parameter to be identified.

2. The method for identifying ship nonlinear rolling parameters based on physical information neural network according to claim 1, characterized in that: In step S1: Roll angle free decay data Expressed as an equation ; Initial conditions for rolling motion and Expressed as an equation ; The physical equation for rolling motion is expressed as: ;in, represents a nonlinear rolling parameter; the physical equation of the rolling motion includes a nonlinear damping term of the ship motion and a nonlinear restoring moment term of the ship motion; The physical equations of rolling motion are rewritten to include: The linear-quadratic-cubic damping model is used to characterize the nonlinear damping term of ship motion, namely: ； The linear-cubic restoring force model is used to characterize the nonlinear restoring moment term of ship motion, namely: ； Therefore, the physical equation of rolling motion can be rewritten as: ； Among them, the nonlinear roll parameter That is the vector , represents the total roll inertia including the structural inertia and the added inertia of water, Representation and and The associated nonlinear damping forces; Representation and The associated nonlinear restoring moment, is the first-order damping parameter, is the second-order damping parameter, is the third-order damping parameter; is the first-order restoring force parameter, is the second-order restoring force parameter, is the roll angular acceleration, represents the rolling angular velocity, Indicates the roll angle.

3. The method for identifying ship nonlinear rolling parameters based on physical information neural network according to claim 2, characterized in that: In step S2, the steps of calculating the norm of the free decay data of the ship's roll angle, the norm of the initial condition of the roll motion, and the norm of the physical equation of the roll motion include: Roll angle attenuation data of Norm It is expressed as: ； Initial conditions for rolling motion and of The norm is expressed as : ； Physical equations for rolling motion of The norm is expressed as : ； in, , , They represent the physical constraints satisfying the free decay data, initial conditions, and physical equations respectively; Represents the coordinates of discrete data points; , Represent the number of data for free decay data and physical equations respectively; is the parameter to be optimized in the neural network, including network weights , Network bias And the roll parameters , expressed as ; The superscript "^" represents the estimated value of the variable at the current neural network iteration step.

4. The method for identifying ship nonlinear rolling parameters based on physical information neural network according to claim 3, characterized in that: The steps of determining the total loss function of the neural network include: Determine the total network loss function : in, , , They represent the weight distribution of the corresponding physical constraints.

5. The method for identifying ship nonlinear rolling parameters based on physical information neural network according to claim 1, characterized in that: The steps for optimizing the neural network hyperparameters in S3 include: Select the neural network hyperparameters to be optimized, including: learning rate , Network Layers , the number of neurons ; Establish the hyperparameter optimization objective function: ； in, is the number of roll parameters, is the estimated value of the roll parameter, is the true value of the roll parameter, and the Bayesian optimization method is used to minimize the objective function , optimize the neural network hyperparameters.

6. The method for identifying ship nonlinear rolling parameters based on physical information neural network according to claim 1 or 4, characterized in that: The steps in S4 to minimize the total network loss function include: After determining the physical information neural network framework, the Adam optimization solver is used to minimize the total loss function of the network. : ； in, represents the equation minimization operator; Obtain the network parameters to be optimized After finding the optimal solution, extract the nonlinear roll parameters .

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