Method and device for forecasting hydrodynamic force of submerged body under ice, medium and program product

Abstract

The invention provides an under-ice submerged body hydrodynamic forecasting method and device, a medium and a program product, and the method comprises the steps: obtaining an ice coverage Green function based on a coupling kinetic equation of an ice layer and water; performing dimensionless processing on the ice coverage Green function; predicting a value of a dimensionless deicing coverage Green function by using a neural network model; solving a speed potential based on a value of a dimensionless deicing coverage Green function; the hydrodynamic condition is calculated based on the speed potential. According to the method for forecasting the hydrodynamic force of the submerged body under the ice, machine learning and the potential flow theory are deeply fused, a novel hybrid forecasting model with a physical mechanism and data intelligence is constructed, and accurate and efficient forecasting of the hydrodynamic force condition of the submerged body under the ice is successfully achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of ship and ocean engineering, and in particular relates to a method, device, medium and program product for predicting hydrodynamics of an under-ice submerged body. Background Art

[0002] With global warming, the demand for Arctic shipping lane development, subglacial resource exploration, and submersible missions is growing. Research on the efficient design and performance optimization of submersibles beneath the ice has become a hot topic. The complexity and unique nature of the submersible environment place extremely high demands on the hydrodynamic characteristics of submersibles, exacerbating the conflict between accuracy and efficiency in traditional hydrodynamic assessment methods. Therefore, the need for new technological breakthroughs is urgent.

[0003] In recent years, the rapid development of artificial intelligence (AI) technology has provided innovative solutions to these problems. Machine learning algorithms, such as neural networks, have demonstrated significant advantages in processing high-dimensional data. However, neural network models that rely solely on data are often limited by the scope of training samples and the interpretability of physical laws, making it difficult to directly predict the hydrodynamics of submerged bodies beneath the ice. Summary of the Invention

[0004] In view of the deficiencies in the prior art, the present invention provides a method, device, medium, and program product for predicting the hydrodynamics of an under-ice submerged body, so as to solve the problem of efficient and accurate prediction of the hydrodynamics of an under-ice submerged body.

[0005] The present invention achieves the above technical objectives through the following technical means.

[0006] A method for predicting hydrodynamics of submerged bodies under ice:

[0007] Based on the coupled dynamic equations of ice and water, the ice cover Green's function is obtained;

[0008] Make the ice cover Green's function dimensionless;

[0009] The value of the dimensionless ice cover Green's function is predicted using a neural network model;

[0010] Based on the value of the dimensionless ice cover Green's function, the velocity potential is solved;

[0011] The hydrodynamic situation is obtained based on velocity potential calculation.

[0012] Furthermore, the ice cover Green's function for:

[0013]

[0014] Where x = (x0, y0, z0) and They represent the field and source position coordinates respectively. The origin of the o-xyz coordinate system is located at the ice-water interface, and the z axis is vertically upward. T, ρ I , L are the thickness, density and stiffness of the ice layer respectively, ρ W is the water density, g is the acceleration due to gravity, i is the imaginary unit, e is the natural constant, r(·) represents the distance between the field point and the source point, r1(·) represents the distance between the field point and the source point with respect to the ice surface, k0 = ω 2 / g is the wave number, k1 is the equation (L / (gρ W ))k 5 +(1-(Tρ I / ρ W )k0)k-k0=0, J0(·) represents the first kind of zero-order Bessel function, It represents the principal value integral of variable k, where k is the wave number variable.

[0015] Furthermore, the method for dimensionless treatment of ice cover Green's function is as follows:

[0016] Green's function for ice cover remember:

[0017]

[0018] The dimensionless expression of is:

[0019]

[0020] The partial derivatives of are:

[0021]

[0022] in:

[0023]

[0024] Where J1(·) represents the first-order Bessel function of the first kind.

[0025] Furthermore, the neural network model is a feedforward neural network model, and the input of the model is The output of the model is a number value.

[0026] Furthermore, the feedforward neural network model includes an input layer, two hidden layers and an output layer, wherein data transfer between the layers is as follows:

[0027] Γ (l) =f(Γ (l-1) W (l)+B (l) ), l=1,2,3

[0028] Where Γ (l) and Γ (l-1) Represent the data vectors of the lth layer and the l-1th layer in the model, respectively. The 0th layer is the input layer of the model, the 1st and 2nd layers are hidden layers, the 3rd layer is the output layer, f(·) is the ReLU activation function, and W (l) and B (l) are the connection weight and bias of the lth layer respectively;

[0029] When the model is trained, the error back propagation algorithm is used to optimize the parameters.

[0030] Furthermore, the velocity potential is solved based on the following boundary integral equation:

[0031]

[0032] Where, and denote the velocity potential at the field point and the source point, respectively. represents the normal partial derivative, n is x or y or z, represents the surface S along the submerged body B The surface integral of .

[0033] Furthermore, based on the kinematic boundary conditions of the ice surface and Bernoulli's equation, the ice surface deformation and the hydrodynamic force of the submerged body caused by the motion of the submerged body are calculated:

[0034]

[0035] Where η(x,y,t) represents the deformation of the ice surface at coordinate (x,y) at time t, Re{·} represents the real part, i and j are 1, 2, and 3, respectively, along the x-axis, y-axis, and z-axis, and 4, 5, and 6, respectively, around the x-axis, y-axis, and z-axis. represents the generalized normal vector, μ ij and λ ij are the added mass and damping coefficient, respectively.

[0036] A computer device comprising a memory and a processor;

[0037] The memory is used to store computer programs;

[0038] The processor is used to execute the computer program and implement the above-mentioned method for predicting hydrodynamics of submerged bodies under ice when executing the computer program.

[0039] A computer-readable storage medium stores a computer program, which, when executed by a processor, causes the processor to execute the above-mentioned method for predicting the hydrodynamics of an underwater body under ice.

[0040] A computer program product includes a computer program, which implements the above-mentioned method for predicting hydrodynamics of submerged bodies under ice when executed by a processor.

[0041] The beneficial effects of the present invention are:

[0042] (1) The present invention provides a method for predicting the hydrodynamics of submerged bodies under ice. By deeply integrating machine learning with potential flow theory, a new hybrid prediction model with both physical mechanism and data intelligence is constructed, which successfully achieves accurate and efficient prediction of the hydrodynamic conditions of submerged bodies under ice.

[0043] (2) The present invention performs dimensionless processing on the ice cover Green's function, and then uses the feedforward neural network model to predict the value of the dimensionless ice cover Green's function, so as to calculate the corresponding ice cover Green's function and its partial derivatives, and finally realize the solution of the velocity potential, which makes it possible to calculate the hydrodynamic conditions of the submerged body under the ice.

[0044] (3) The computational efficiency of the method for predicting the hydrodynamics of submerged bodies under ice in the present invention is higher than that of the traditional potential flow theory hydrodynamic calculation method. When the calculation amount is 20,000, the average calculation time of the present invention is 1 / 20 of that of the traditional method. When the calculation amount is 2,000,000, the calculation time is approximately 1 / 60 of that of the traditional method. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 This is a schematic diagram of the spatial coordinate system where the submerged body under the ice is located;

[0046] Figure 2 This is a flow chart of the forecasting method of the present invention;

[0047] Figure 3 This is a diagram showing the ice surface deformation caused by the submersible at a depth of 1.25 times the maximum diameter in the test case;

[0048] Figure 4 This is a diagram showing the ice surface deformation caused by the submerged body at a diving depth of 5.0 times the maximum diameter in the test case;

[0049] Figure 5 This is the hydrodynamic curve caused by different diving depths in the test case. DETAILED DESCRIPTION

[0050] The embodiments of the present invention are described in detail below. Examples of the illustrated embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and are not to be construed as limiting the present invention.

[0051] 1. Technical Solution

[0052] like Figure 1 As shown in Figure 1, in order to predict the hydrodynamics of a submerged body under ice, a three-dimensional rectangular coordinate system o-xyz is established, where the origin of the coordinate is located at the ice-water interface and the z-axis is vertically upward.

[0053] 1. Coupled dynamic equations of ice and water

[0054] Reference Figure 2 As shown in the above-established coordinate system, the movement of the submerged body will cause the bending deformation of the ice surface. If the ice layer is regarded as an elastic thin plate and it is assumed that there is no gap between the ice layer and the water during the elastic deformation process, the ice-water coupling dynamic equation (Formula 1) under the potential flow theory framework can be obtained as follows:

[0055]

[0056] Where, T, ρ I , L are the thickness, density and stiffness of the ice layer respectively, ρ W is the water density, g is the acceleration due to gravity, x, y, z represent the x-axis, y-axis, and z-axis variables in the o-xyz coordinate system, respectively, j = 1, 2, ..., 6, where They represent the velocity potential generated when the submerged body oscillates along the x-axis, y-axis, and z-axis at unit speed, respectively. They represent the velocity potential generated when the submerged body rotates around the x-axis, y-axis, and z-axis at unit speed; k0 = ω 2 / g is the wave number, ω is the oscillation frequency of the latent body, and the gradient operator The expression is as follows:

[0057]

[0058] 2. Ice Cover Green's Function

[0059] Velocity potential This can be solved using the following boundary integral equation (Formula 2):

[0060]

[0061] Where x = (x0, y0, z0) and Represent the field and source position coordinates respectively, and denote the velocity potential at the field point and the source point, respectively. represents the normal partial derivative, n is x or y or z, represents the surface S along the submerged body B The surface integral of To satisfy the ice cover Green's function of Formula 1, its expression (Formula 3) is:

[0062]

[0063] Where i is an imaginary unit, e is a natural constant, r(·) represents the distance between the field point and the source point, r1(·) represents the distance between the field point and the source point on the ice surface, and k1 is the equation (L / (gρ W ))k 5 +(1-(Tρ I / ρ W )k0)k-k0=0(variable k) zero point, J0(·) represents the first kind of zero-order Bessel function, It represents the principal value integral of variable k, where k is the wave number variable.

[0064] 3. Dimensionless processing

[0065] The last term on the right side of the ice cover Green's function in Formula 3 above is recorded as

[0066]

[0067] Perform the following dimensionless processing on it:

[0068]

[0069] Where, for The dimensionless expression of the variable The expressions are:

[0070]

[0071] Similar, yes The partial derivatives of are dimensionless and can be obtained as follows:

[0072]

[0073] in:

[0074]

[0075] Where J1(·) represents the first-order Bessel function of the first kind.

[0076] 4. Solving Green's function

[0077] The key to solving the boundary integral equation (Formula 2) is to calculate the ice cover Green's function and its partial derivatives To this end, this embodiment specifically uses a feedforward neural network model to calculate the dimensionless ice cover Green's function. The feedforward neural network model includes an input layer, two hidden layers and an output layer, where the data of the input layer is the independent variable The output data of the corresponding output layer is the dimensionless ice cover Green's function In the feedforward neural network model, the data transfer between two adjacent layers is as follows:

[0078] Γ (l) =f(Γ (l-1) W (l) +B (l) ), l=1,2,3

[0079] Where Γ (l) and Γ (l-1) Respectively represent the data vectors of the lth layer and the l-1th layer in the model, where the 0th layer is the input layer of the model, the 1st and 2nd layers are hidden layers, and the 3rd layer is the output layer. f(·) represents the activation function. In this embodiment, the ReLU activation function is specifically used. W (l) and B (l) are the connection weight and bias of the lth layer respectively.

[0080] The feedforward neural network model is first trained with a data set before use. This embodiment uses an error back propagation algorithm to optimize relevant parameters in the model during training.

[0081] 5. Ice surface deformation and submerged hydrodynamic calculations

[0082] Based on the actual sensed data (thickness T of ice layer, density ρ I , stiffness L, water density ρ W , field, source coordinates, etc.), and the dimensionless ice cover Green’s function is obtained through the feedforward neural network model Then, substitute into formula 2 to obtain the velocity potential of the flow field Then, based on the kinematic boundary conditions of the ice surface and Bernoulli's equation, the corresponding ice surface deformation and hydrodynamic conditions caused by the motion of the submerged body can be obtained:

[0083]

[0084] Where η(x,y,t) represents the deformation of the ice surface at coordinate (x,y) at time t, Re{·} represents the real part, and the value of i is the same as j. When the value is 1, 2, or 3, it represents the direction along the x-axis, y-axis, and z-axis, respectively. When the value is 4, 5, or 6, it represents the direction around the x-axis, y-axis, and z-axis, respectively. represents the generalized normal vector, μ ij and λ ij are the added mass and damping coefficient, respectively.

[0085] 2. Test and Verification

[0086] The ice deformation and hydrodynamic forces caused by the movement of a SUBOFF submarine under ice are predicted. The vertical length of this submarine is 4.261m and the maximum diameter is 0.508m. The ice layer has a Young's modulus of 6GPa, a Poisson's ratio of 0.3, a thickness of 2cm, and a density of 922.5kg / m3. 3 .

[0087] like Figure 3 and Figure 4 As shown in FIG, based on the prediction method of the present invention, the ice surface deformation caused by the vertical oscillation of the submarine at different diving depths is given; Figure 3 Corresponding to a diving depth of 1.25 times the maximum diameter, Figure 4 Corresponding to a diving depth of 5.0 times the maximum diameter.

[0088] like Figure 5 The figure shows the hydrodynamic conditions caused by the vertical oscillation of the submarine at different diving depths based on the prediction method of the present invention, where (a) is the curve of the change of additional mass caused by the different oscillation frequencies of the submarine body, and (b) is the curve of the change of damping coefficient caused by the different oscillation frequencies of the submarine body.

[0089] III. Devices, Storage Media, and Program Products

[0090] 1. Based on the same inventive concept as the above-mentioned method for predicting the hydrodynamics of submerged underwater bodies, the present application also provides an electronic device, which includes a processor and a memory, in which a computer-readable code is stored. When the computer-readable code is executed by the processor, the method for predicting the hydrodynamics of submerged underwater bodies of the present invention is implemented.

[0091] The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium can store an operating system and computer-readable code. The computer-readable code includes program instructions that, when executed, cause the processor to execute the method for predicting the hydrodynamics of a submerged submerged body under ice. The processor provides computing and control capabilities, supporting the operation of the entire electronic device. The memory provides an environment for the computer-readable code in the non-volatile storage medium to run. When executed by the processor, the computer-readable code causes the processor to execute the method for predicting the hydrodynamics of a submerged submerged body under ice.

[0092] It should be understood that the processor may be a central processing unit, other general-purpose processors, digital signal processors, application-specific integrated circuits, field programmable gate arrays or other programmable logic devices, transistor logic devices, discrete hardware components, etc. Among them, the general-purpose processor may be a microprocessor or any conventional processor.

[0093] 2. This application also provides a readable storage medium, which can be the internal storage unit of the electronic device described in the aforementioned embodiment, such as the hard disk or memory of the computer device. The readable storage medium can also be an external storage device of the electronic device, such as a plug-in hard disk, smart memory card, secure digital card, etc. equipped with the electronic device.

[0094] 3. The present application also provides a computer program product, comprising a computer program or instructions, which, when executed by a processor, implements the method for predicting the hydrodynamics of submerged bodies under ice of the present invention.

[0095] In the description of the present invention, it should be understood that the terms "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as limiting the present invention.

[0096] The present invention is not limited to the above-mentioned embodiments. Any obvious improvement, replacement or modification that can be made by those skilled in the art without departing from the essence of the present invention shall fall within the scope of protection of the present invention.

Claims

1. A method for predicting hydrodynamics of an under-ice submerged body, characterized by: Based on the coupled dynamic equations of ice and water, the ice cover Green's function is obtained; Make the ice cover Green's function dimensionless; The value of the dimensionless ice cover Green's function is predicted using a neural network model; Based on the value of the dimensionless ice cover Green's function, the velocity potential is solved; The hydrodynamic situation is obtained based on velocity potential calculation.

2. The method for predicting hydrodynamics of an underwater body under ice according to claim 1, characterized in that: The ice cover Green's function for: Where x = (x0, y0, z0) and They represent the field and source position coordinates respectively. The origin of the o-xyz coordinate system is located at the ice-water interface, and the z axis is vertically upward. T, ρ I , L are the thickness, density and stiffness of the ice layer respectively, ρ W is the water density, g is the acceleration due to gravity, i is the imaginary unit, e is the natural constant, r(·) represents the distance between the field point and the source point, r1(·) represents the distance between the field point and the source point with respect to the ice surface, k0 = ω 2 / g is the wave number, k1 is the equation (L / (gρ W ))k 5 +(1-(Tρ I / ρ W )k0)k-k0=0, J0(·) represents the first kind of zero-order Bessel function, It represents the principal value integral of variable k, where k is the wave number variable.

3. The method for predicting hydrodynamics of an underwater body under ice according to claim 2, characterized in that: The method for dimensionless treatment of ice cover Green's function is: Green's function for ice cover remember: The dimensionless expression of is: The partial derivatives of are: in: Where J1(·) represents the first-order Bessel function of the first kind.

4. The method for predicting hydrodynamics of an underwater body under ice according to claim 3, characterized in that: The neural network model is a feedforward neural network model, and the input of the model is The output of the model is a number value.

5. The method for predicting hydrodynamics of an underwater body under ice according to claim 4, characterized in that: The feedforward neural network model includes an input layer, two hidden layers and an output layer, wherein the data transmission between the layers is as follows: C (l) =f(Γ (l-1) W (l) +B (l) ),l=1,2,3 Where Γ (l) and Γ (l-1) Represent the data vectors of the lth layer and the l-1th layer in the model, respectively. The 0th layer is the input layer of the model, the 1st and 2nd layers are hidden layers, the 3rd layer is the output layer, f(·) is the ReLU activation function, and W (l) and B (l) are the connection weight and bias of the lth layer respectively; When the model is trained, the error back propagation algorithm is used to optimize the parameters.

6. The method for predicting hydrodynamics of an underwater body under ice according to claim 4, characterized in that: The velocity potential is solved based on the following boundary integral equation: Where, and denote the velocity potential at the field point and the source point, respectively. represents the normal partial derivative, n is x or y or z, represents the surface S along the submerged body B The surface integral of .

7. The method for predicting hydrodynamics of an underwater body under ice according to claim 6, characterized in that: Based on the kinematic boundary conditions of the ice surface and Bernoulli's equation, the ice surface deformation and the hydrodynamic force of the submerged body caused by the motion of the submerged body are calculated: Where η(x,y,t) represents the deformation of the ice surface at coordinate (x,y) at time t, Re{·} represents the real part, i and j are 1, 2, and 3, respectively, along the x-axis, y-axis, and z-axis, and 4, 5, and 6, respectively, around the x-axis, y-axis, and z-axis. represents the generalized normal vector, μ ij and λ ij are the added mass and damping coefficient, respectively.

8. A computer device, characterized in that: including memory and processor; The memory is used to store computer programs; The processor is used to execute the computer program and implement the method for predicting hydrodynamics of an under-ice submerged body according to any one of claims 1 to 7 when executing the computer program.

9. A computer-readable storage medium, characterized in that: A computer program is stored, and when the computer program is executed by a processor, the processor executes the method for predicting the hydrodynamics of an under-ice submerged body according to any one of claims 1 to 7.

10. A computer program product, characterized in that: The method comprises a computer program, which, when executed by a processor, implements the method for predicting the hydrodynamics of an under-ice submerged body according to any one of claims 1 to 7.

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