Hydrodynamic force action surface deformation calculation method based on deep neural network

Abstract

The invention provides a fluid dynamic action surface deformation calculation method based on a deep neural network, and the method comprises the steps: taking fluid characteristics and solid characteristic parameters as input data, taking surface deformation of a finite element calculation surface lift action as output data, and taking a constructed data set as a neural network training sample; and training a nonlinear high-order mapping relationship between corresponding input and output quantities of the neural network travel. According to the method, the mapping relation between fluid characteristics and solid characteristic parameters and fluid-solid coupling field physical parameters is established through machine learning, the difficulty of establishing a complex model can be reduced, the efficiency of establishing a unified design process can be improved, and the method can be popularized to different output physical quantities and has good application prospects. A new method is provided for solving a physical model which is high in nonlinearity and complex in equation form, and a new thought is provided for further analyzing the fluid mechanics law of the fluid-solid coupling phenomenon of complex fluid and complex surfaces.

Description

Technical Field

[0001] This invention belongs to the field of intelligent fluid dynamics calculation technology, specifically relating to a method for calculating surface deformation under fluid dynamic effects based on deep neural networks. Background Technology

[0002] Solving real-world fluid mechanics problems requires establishing corresponding physical models based on the Navier-Stokes equations and related equations. However, in complex real-world environments, the influence of various factors necessitates the enhancement of the equations' nonlinearity. Specifically, in production practices and natural environments, water is the main component of most liquids, but it contains many solutes, such as polyvinyl alcohol (PVA), polyacrylamide (PAA), poly(ethylene oxide) (PEO), polyvinylpyrrolidone (PVP), and polyacrylamide (PAM), which can transform the solution properties from viscous to viscoelastic. On the other hand, when fluid-solid interactions are significant and the Young's modulus of the solid surface is not very high, the solid surface will deform. Therefore, when a viscoelastic fluid is sheared at a surface, as the relative velocity increases, the fluid between the two surfaces generates a force perpendicular to the surface during the shearing process. Consequently, if the Young's modulus of the surface is small, the surface will deform under the action of this force. When the deformation can significantly alter the gap between the two surfaces, the flow field and pressure within the gap will also change. Analysis reveals that this process requires consideration of various physical changes in the fluid, such as viscoelasticity, surface deformation, and the forces acting on the fluid micro-elements, making direct analytical solutions virtually impossible. Even when using the finite element method, the problem of boundary layer mesh refinement remains. This drastically increases the number of meshes, limiting computational power and generally making it suitable only for micro- and nano-scale fluid calculations, remaining ineffective for macro-scale calculations. Furthermore, the increased difficulty of mesh generation due to deformable boundaries further narrows the solvable range.

[0003] With the development of GPU computing power, represented by NVIDIA, and the CUDA ecosystem, intelligence emerges when the amount of training data exceeds tens of billions; currently, the amount of data has surpassed trillions. Large-scale regression models driven by massive amounts of data possess excellent generalization intelligence, demonstrating performance comparable to or even surpassing that of outstanding humans in multiple fields. Machine learning methods can also be used to solve fluid dynamics problems. By using fluid properties and solid characteristic parameters as input data and force parameters as output data, a multi-layered neural network is built between the two. The network structure parameters are used as fitting parameters to fit the laws governing the input and output data, constructing a mapping that conforms to the input and output data. Summary of the Invention

[0004] (a) Technical problems to be solved

[0005] This invention proposes a method for calculating surface deformation under hydrodynamic effects based on deep neural networks, in order to solve the technical problem of how to solve physical models with strong nonlinearity and complex equations.

[0006] (II) Technical Solution

[0007] To address the aforementioned technical problems, this invention proposes a method for calculating surface deformation under hydrodynamic effects based on deep neural networks. This method includes the following steps:

[0008] S1. Establishing a finite element model of shear flow in a fluid-structure system.

[0009] S1-1. Formation of a fluid-structure system with shear flow.

[0010] The fluid-structure system includes plate A, plate B, and a viscoelastic fluid. Plate A is a deformable plate, and plate B is a rigid plate. Both plates are infinitely large, and the distance between them is H, which is sufficiently large and fixed. The fluid between the two plates is viscoelastic, and the contact points between the plates and the fluid are no-slip boundary conditions. Plate A is fixed, while plate B is movable, driving the fluid to move and thus causing shearing, forming a shear flow.

[0011] S1-2. Establishing a finite element model of shear flow in a fluid-structure system.

[0012] Based on the Olydroyd-B viscoelastic constitutive model, viscoelastic fluid property parameters are set, including the viscosity η contributed by polymers in the fluid. p Relaxation time λ1 and lag time λ2;

[0013] Forces exerted by fluids on solid surfaces Modeling is performed, represented as:

[0014]

[0015] in, The fluid-solid boundary normal vector is η; η is the solution viscosity, derived from the solvent viscosity η. s With solute viscosity η p Together they constitute, that is, η = η s +η p .

[0016] The governing equations of the flow field are described by the incompressible Navier-Stokes equations and the continuity equation, and are expressed as follows:

[0017]

[0018] in, For velocity tensor; This refers to the elastic stress tensor in the constitutive model. It is a unit diagonal matrix; ρ is the solution density; p is the fluid pressure field;

[0019] The deformation control equation for plate B is expressed as:

[0020]

[0021] in, This represents the stress tensor of a solid. Represents the material displacement field; G and β represent the Lamé constants;

[0022] S2. Select the plate B's moving speed vm / s, Lamé constants G and β, solution density ρ, and solvent viscosity η. s and solute viscosity η p Relaxation time λ1 and lag time λ2 are used as key variables to generate sample data. The sample data is then substituted into the established fluid-structure interaction finite element model for shear flow. After removing outliers, the maximum deformation is obtained as the output data. Specifically, this includes:

[0023] S2-1. Design parameters: Plate B movement speed vm / s, Lamé constants G and β, solution density ρ, solvent viscosity η. s and solute viscosity η p Relaxation time λ1 and lag time λ2 are the key variables, totaling 8 parameters, represented as (v, G, β, ρ, η). s ,η p ,λ1,λ2) k , k represents the kth design point, and its range of variation is determined by giving the maximum and minimum values ​​of each key variable; the 8 design variables are grouped in a combination manner, and the design points of 5 parameters and 3 levels are designed in a central composite design to generate multiple sets of design points;

[0024] S2-2. Substitute the design points into the shear flow finite element model of the fluid-structure system established in step S1 to obtain the corresponding target response quantity—the deformation δ of plate B. i The data of the target response and corresponding design parameters are organized as (v,G,β,ρ,η). s ,η p ,λ1,λ2) k →(δ k );

[0025] S2-3. The calculated data is divided into two groups with a ratio of 9:1 by random sampling, thereby constructing the training samples and validation samples of the neural network;

[0026] S3. Construct a BP neural network and train it on the training samples.

[0027] Furthermore, in the fluid-solid system, the viscoelastic fluid between the two plates comprises one or more components.

[0028] Furthermore, in the finite element model of shear flow in a fluid-solid system, the mesh is set as a triangle.

[0029] Furthermore, in the finite element model of shear flow in the fluid-solid system, the number of mesh layers exceeds 10.

[0030] Furthermore, step S3 specifically includes:

[0031] S3-1. Constructing a Neural Network

[0032] A four-layer neural network is constructed, with eight neurons in the input layer corresponding to eight input variables; two hidden layers in the middle; and the final output layer outputting a single variable. All layers are fully connected. The weight between neuron i and neuron j is w. ij The threshold of neuron j is b j The output value of each neuron is represented as:

[0033]

[0034] Where f is the activation function;

[0035] S3-2. Neural Network Training

[0036] ① Randomly assign weights w ij The initial value, and the threshold b j The initial value;

[0037] ② Organize the training samples and validation samples to obtain the input sample data and expected output data, satisfying the conditions for random sample selection;

[0038] ③ Randomly select a training sample as the data for training the neural network, substitute the input sample data into the established neural network for forward calculation, calculate the predicted value O and the loss function Loss, and use the loss function Loss to calculate the network error E;

[0039] ④ Perform reverse calculation using the Adam method to adjust the weights;

[0040] ⑤ By sampling from the validation samples and substituting them into the trained neural network, the predicted value and network error are calculated. It is then determined whether the network error E meets the requirements. If it does, the process ends; otherwise, it returns to ③ to continue training the neural network.

[0041] Furthermore, in step S3-1, each hidden layer has no fewer than 30 neurons.

[0042] Furthermore, in step S3-1, the activation function f is selected as 8-(ReLU)-50-(ReLU)-50-(actan)-1.

[0043] (III) Beneficial Effects

[0044] This invention proposes a method for calculating surface deformation under hydrodynamic effects based on deep neural networks. Fluid properties and solid characteristic parameters are used as input data, and surface deformation under lift effects calculated by finite element methods is used as output data. The constructed dataset serves as training samples for the neural network, training it to establish a nonlinear high-order mapping relationship between the corresponding inputs and outputs. This method utilizes machine learning to establish a mapping relationship between fluid properties and solid characteristic parameters and the physical parameters of the fluid-structure interaction field. This reduces the difficulty of building complex models, improves the efficiency of establishing a unified design process, and can be extended to different output physical quantities. It provides a new method for solving physical models with strong nonlinearity and complex equation forms, and offers new insights into the hydrodynamic laws governing fluid-structure interaction phenomena between complex fluids and complex surfaces. Attached Figure Description

[0045] Figure 1 This is the main flow of the method for calculating surface deformation under hydrodynamic effects according to the present invention;

[0046] Figure 2 This is a schematic diagram of the fluid-solid system in this invention;

[0047] Figure 3 This is a schematic diagram of the neural network in this invention. Detailed Implementation

[0048] To make the objectives, contents, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0049] This embodiment proposes a method for calculating surface deformation under hydrodynamic effects based on deep neural networks. The main process is as follows: Figure 1 As shown, the specific steps include the following:

[0050] S1. Establishing a finite element model of shear flow in a fluid-structure system.

[0051] S1-1. Formation of a fluid-structure system with shear flow.

[0052] like Figure 2 As shown, plate A is a deformable plate, and plate B is a rigid plate. Both plates are infinitely large, and the distance between them is H. The fluid between the two plates is a viscoelastic fluid, which can have various components. The contact points between the plates and the fluid are subject to no-slip boundary conditions. Plate A is fixed, while plate B moves at a velocity vm / s, causing the fluid to move and thus shearing occurs, forming a shear flow.

[0053] S1-2. Establishing a finite element model of shear flow in a fluid-structure system.

[0054] Based on the Olydroyd-B viscoelastic constitutive model, viscoelastic fluid property parameters are set, including the viscosity η contributed by polymers in the fluid. p The relaxation time (a parameter unique to viscoelastic fluids) λ1 and hysteresis time λ2; the Olympic-B viscoelastic constitutive model is:

[0055]

[0056] This is the Olydroyd derivative with the flow.

[0057] The Olydroyd-B viscoelastic constitutive model is currently the most commonly used viscoelastic constitutive model, which can be used to describe the rheological behavior of dilute solutions of polymers such as PEO, PVP, and PAM. This viscoelastic constitutive model incorporates the Olydroyd flow derivative, assuming that the local reference position is not fixed when the stress tensor of the fluid element changes with time, and that the fluid element undergoes translational, rotational, and deformable motions.

[0058] Forces exerted by fluids on solid surfaces Modeling is performed, represented as:

[0059]

[0060] in, Let η be the normal vector of the fluid-solid boundary; the direction of the force exerted by the fluid on the solid is along the normal direction of the solid boundary. The solid boundary is subjected to the combined action of fluid viscous shear force and pressure. η is the solution viscosity, derived from the solvent viscosity η. s With solute viscosity η p Together they constitute, that is, η = η s +η p .

[0061] The governing equations of the flow field are described by the incompressible Navier-Stokes equations and the continuity equation, and are expressed as follows:

[0062]

[0063] in, For velocity tensor; The elastic stress tensor in the constitutive model is used as a modification term in the Navier-Stokes equations to describe the elastic characteristics of viscoelastic fluids. ρ is a unit diagonal matrix; p is the solution density; and p is the fluid pressure field.

[0064] Plate B is rigid, therefore deformation occurs only on plate A. In principle, plate B is considered to undergo small deformation, and its deformation characteristics are assumed to be consistent with those of a linear elastic material. The small deformation theory is used to describe the deformation of this surface. The small deformation of a linear elastic material is represented by the Lamé constant; therefore, the deformation governing equation for plate B is expressed as:

[0065]

[0066] in, This represents the stress tensor of a solid. β represents the material displacement field; G and β represent the Lamé constants.

[0067] The control parameters in the calculation process of the finite element model of shear flow in a fluid-structure interaction system include: calculation step size, number of iterations, and maximum number of loops. The mesh is set as triangular, and the number of mesh layers exceeds 10.

[0068] S2. Select the plate B's moving speed vm / s, Lamé constants G and β, solution density ρ, and solvent viscosity η. s and solute viscosity η p Relaxation time λ1 and lag time λ2 are used as key variables to generate a certain number of sample data. Substituting the sample data into the established finite element model, and removing outliers, the maximum deformation is obtained as the output data. Specifically, this includes:

[0069] S2-1. Design parameters: Plate B movement speed vm / s, Lamé constants G and β, solution density ρ, solvent viscosity η. s and solute viscosity η p Relaxation time λ1 and lag time λ2 are the key variables, totaling 8 parameters, represented as (v, G, β, ρ, η). s ,η p ,λ1,λ2) k 'k' represents the k-th design point, and its range of variation is determined by providing the maximum and minimum values ​​of each key variable. The eight design variables are grouped in a combined manner, and a 5-parameter, 3-level design point design is performed using a central composite design, generating a total of... Group design points.

[0070] S2-2. Substitute the design points into the shear flow finite element model of the fluid-structure system established in step S1 to obtain the corresponding target response quantity—the deformation δ of plate B. i The target response and corresponding design parameters are then compiled into data as (v, G, β, ρ, η). s ,η p ,λ1,λ2) k →(δ k ).

[0071] S2-3. The calculated data is divided into two groups with a ratio of 9:1 by random sampling, thereby constructing the training samples and validation samples of the neural network.

[0072] S3. Construct a BP neural network and train it on the training samples.

[0073] S3-1. Constructing a Neural Network

[0074] Construct a 4-layer neural network, such as Figure 3 As shown, the input layer has 8 neurons, corresponding to 8 input variables; the middle two hidden layers each have no fewer than 30 neurons (50 neurons are used in this embodiment); the final output layer outputs one variable; and all layers are fully connected. The weight between neuron i and neuron j is w. ij The threshold of neuron j is b j The output value of each neuron is represented as:

[0075]

[0076] Where f is the activation function, which is chosen as 8-(ReLU)-50-(ReLU)-50-(actan)-1.

[0077] S3-2. Neural Network Training

[0078] ① Randomly assign weights w ij The initial value, and the threshold b j The initial value.

[0079] ② Organize the training samples and validation samples to obtain the input sample data and expected output data, satisfying the conditions for random sample selection;

[0080] ③ Randomly select a training sample as the data for training the neural network, substitute the input sample data into the established neural network for forward calculation, calculate the predicted value O and the loss function Loss, and use the loss function Loss to calculate the network error E (the network error is determined by the calculated predicted value O and the true value).

[0081] ④ Perform reverse calculation using the Adam method to adjust the weights;

[0082] ⑤ By sampling from the validation samples and substituting them into the trained neural network, the predicted value and network error are calculated. It is then determined whether the network error E meets the requirements. If it does, the process ends; otherwise, it returns to ③ to continue training the neural network.

[0083] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating surface deformation under hydrodynamic effects based on deep neural networks, characterized in that, The method for calculating surface deformation under hydrodynamic effects includes the following steps: S1. Establishing a finite element model of shear flow in a fluid-structure system. S1-1. Formation of a fluid-structure system with shear flow. The fluid-structure system includes plate A, plate B, and a viscoelastic fluid. Plate A is a deformable plate, and plate B is a rigid plate. Both plates are infinitely large, and the distance between them is H, which is sufficiently large and fixed. The fluid between the two plates is viscoelastic, and the contact points between the plates and the fluid are no-slip boundary conditions. Plate A is fixed, while plate B is movable, driving the fluid to move and thus causing shearing, forming a shear flow. S1-2. Establishing a finite element model of shear flow in a fluid-structure system. Based on the Olydroyd-B viscoelastic constitutive model, viscoelastic fluid property parameters are set, including the viscosity η contributed by polymers in the fluid. p Relaxation time λ1 and lag time λ2; Forces exerted by fluids on solid surfaces Modeling is performed, represented as: in, The fluid-solid boundary normal vector is η; η is the solution viscosity, derived from the solvent viscosity η. s With solute viscosity η p Together they constitute, that is, η = η s +η p . The governing equations of the flow field are described by the incompressible Navier-Stokes equations and the continuity equation, and are expressed as follows: in, For velocity tensor; This refers to the elastic stress tensor in the constitutive model. The matrix is ​​a unit diagonal matrix; ρ is the solution density; p is the fluid pressure field. The deformation control equation for plate B is expressed as: in, This represents the stress tensor of a solid. Represents the material displacement field; G and β represent the Lamé constants; S2. Select the plate B's moving speed vm / s, Lamé constants G and β, solution density ρ, and solvent viscosity η. s and solute viscosity η p Relaxation time λ1 and lag time λ2 are used as key variables to generate sample data. The sample data is then substituted into the established fluid-structure interaction finite element model for shear flow. After removing outliers, the maximum deformation is obtained as the output data. Specifically, this includes: S2-1. Design parameters: Plate B movement speed vm / s, Lamé constants G and β, solution density ρ, solvent viscosity η. s and solute viscosity η p Relaxation time λ1 and lag time λ2 are the key variables, totaling 8 parameters, represented as (v, G, β, ρ, η). s ,η p ,λ1,λ2) k , k represents the kth design point, and its range of variation is determined by giving the maximum and minimum values ​​of each key variable; the 8 design variables are grouped in a combination manner, and the design points of 5 parameters and 3 levels are designed in a central composite design to generate multiple sets of design points; S2-2. Substitute the design points into the shear flow finite element model of the fluid-structure system established in step S1 to obtain the corresponding target response quantity—the deformation δ of plate B. i The data of the target response and corresponding design parameters are organized as (v,G,β,ρ,η). s ,η p ,λ1,λ2) k →(δ k ); S2-3. The calculated data is divided into two groups with a ratio of 9:1 by random sampling, thereby constructing the training samples and validation samples of the neural network; S3. Construct a BP neural network and train it on the training samples.

2. The method for calculating surface deformation under hydrodynamic effects based on deep neural networks as described in claim 1, characterized in that, In a fluid-solid system, the viscoelastic fluid between the two plates comprises one or more components.

3. The method for calculating surface deformation under hydrodynamic effects based on deep neural networks as described in claim 1, characterized in that, In the finite element model of shear flow in a fluid-structure system, the mesh is set as triangles.

4. The method for calculating surface deformation under hydrodynamic effects based on deep neural networks as described in claim 1, characterized in that, In the finite element model of shear flow in a fluid-structure system, the number of mesh layers exceeds 10.

5. The method for calculating surface deformation under hydrodynamic effects based on deep neural networks as described in claim 1, characterized in that, Step S3 specifically includes: S3-1. Constructing a Neural Network A four-layer neural network is constructed, with eight neurons in the input layer corresponding to eight input variables; two hidden layers in the middle; and the final output layer outputting a single variable. All layers are fully connected. The weight between neuron i and neuron j is w. ij The threshold of neuron j is b j The output value of each neuron is represented as: Where f is the activation function; S3-2. Neural Network Training ① Randomly assign weights w ij The initial value, and the threshold b j The initial value; ② Organize the training samples and validation samples to obtain the input sample data and expected output data, satisfying the conditions for random sample selection; ③ Randomly select a training sample as the data for training the neural network, substitute the input sample data into the established neural network for forward calculation, calculate the predicted value O and the loss function Loss, and use the loss function Loss to calculate the network error E; ④ Perform reverse calculation using the Adam method to adjust the weights; ⑤ By sampling from the validation samples and substituting them into the trained neural network, the predicted value and network error are calculated. It is then determined whether the network error E meets the requirements. If it does, the process ends; otherwise, it returns to ③ to continue training the neural network.

6. The method for calculating surface deformation under hydrodynamic effects based on deep neural networks as described in claim 5, characterized in that, In step S3-1, each hidden layer has no fewer than 30 neurons.

7. The method for calculating surface deformation under hydrodynamic effects based on deep neural networks as described in claim 5, characterized in that, In step S3-1, the activation function f is selected as 8-(ReLU)-50-(ReLU)-50-(actan)-1.

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