A method and system for calculating multiphase flow scour of bridge piers based on physical information neural networks

Abstract

This invention discloses a method and system for calculating multiphase flow pier scour based on a physical information neural network, comprising the following steps: constructing a two-phase flow pier scour calculation equation based on the Euler-Euler method; constructing initial parameters and boundary conditions for a two-phase flow pier scour model, generating simulation data, and dividing the data into a test set and a training set; establishing a two-phase flow-based physical information neural network based on the constructed two-phase flow pier scour calculation equation and the given initial parameters and boundary conditions of the two-phase flow pier scour model; training the two-phase flow-based physical information neural network to obtain the prediction results of the multiphase flow pier scour physical information neural network. This invention overcomes the limitations of traditional prediction methods and significantly improves computational efficiency while ensuring accuracy.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering safety and hydraulics technology, and in particular relates to a method and system for calculating multiphase flow scour of bridge piers based on physical information neural networks. Background Technology

[0002] In bridge engineering, localized scour of bridge piers is a significant factor affecting bridge safety. Three-dimensional solid-liquid multiphase flow is a fundamental physical phenomenon in the process of localized scour of bridge piers, and its prediction and analysis are crucial for bridge design, maintenance, and safety assessment. Traditional methods for predicting pier scour are mainly based on empirical formulas or simplified physical models. While these methods can provide rapid predictions in some cases, they typically lack sufficient accuracy and generalization ability, especially under complex flow conditions.

[0003] In recent years, with the development of computational fluid dynamics (CFD) technology, it has become possible to predict bridge pier scour processes through numerical simulation. However, high-precision CFD simulations typically require substantial computational resources and time, and are highly sensitive to initial and boundary conditions, making them impractical for real-world engineering applications. Furthermore, traditional numerical simulation methods often require detailed topographic and flow velocity data as input, which is difficult to obtain in practice, limiting their application scope.

[0004] Therefore, it is urgent to solve the above problems. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a multiphase flow calculation method for bridge pier scour based on physical information neural networks, which overcomes the limitations of traditional prediction methods, significantly improves calculation efficiency while ensuring accuracy, and is suitable for real-time or near-real-time application scenarios.

[0006] Technical Solution: To achieve the above objectives, this invention discloses a method for calculating multiphase flow scour of bridge piers based on a physical information neural network, comprising the following steps:

[0007] (1) Construct the calculation equation for the scour of two-phase flow bridge piers based on the Euler-Euler method;

[0008] (2) Construct the initial parameters and boundary conditions of the two-phase flow pier scour model, generate simulation data, and divide the data into test set and training set;

[0009] (3) Based on the two-phase flow pier scour calculation equation constructed in step (1) and the initial parameters and boundary conditions of the two-phase flow pier scour model given in step (2), a physical information neural network based on two-phase flow is established; the physical information neural network based on two-phase flow is constructed by adopting the form of less data supervision and physical equation constraint, and introducing Fourier layers and dynamic weight strategy to form a weakly supervised physical information neural network.

[0010] (4) Train the physical information neural network based on two-phase flow to obtain the prediction results of the physical information neural network for scour of multiphase flow piers.

[0011] Step (1) specifically includes the following steps:

[0012] (1.1) Both the sediment phase and the water phase are treated as two fluids and described using the Euler method. The sediment phase is a non-Newtonian fluid and a dense particle rheological constitutive model is applied. The water phase is a Newtonian fluid and a turbulence model is applied.

[0013] (1.2) Construct the Euler-Euler method for calculating the governing equations of two-phase flow. The governing equations of two-phase flow are the mass conservation equation and the momentum conservation equation. The governing equations of two-phase flow include the mass conservation equations of the sediment phase and the momentum conservation equations of the sediment phase and the water phase.

[0014] Mass conservation equations for sediment and aqueous phases:

[0015]

[0016]

[0017] Where φ and 1-φ are the volume fractions of the sediment phase and the water phase, respectively. and The velocity of the sediment phase and the water phase is t, the time is t, and the subscripts i and j are the operation indicators. The subscripts i and j = 1, 2 and 3 respectively represent the components of the physical quantities in the flow direction, span direction and vertical direction in the rectangular coordinate system.

[0018] Momentum conservation equations for sediment and water phases:

[0019]

[0020]

[0021] Where ρ s and ρ f The densities of sediment and water are respectively, in g. i Let f be the acceleration due to gravity, p be the fluid pressure, and f be the acceleration due to gravity. i The external force that drives the flow The fluid stress is given by the constitutive equation of the water phase. and The normal and shear stresses of the sediment phase are given by the constitutive equation of the sediment phase. The eddy viscosity coefficient is calculated using the closed-loop turbulence equation, where K is the drag force parameter, and S is the eddy viscosity coefficient. c It is a Schmidt number;

[0022] The drag force parameter K is determined by the following equation:

[0023]

[0024]

[0025] Re p =(1-φ)||u f -u s ||d / v f

[0026] Where d is the particle diameter, C d Re is the drag coefficient. p v is the particle Reynolds number. f h is the kinematic viscosity of the fluid. Exp For depends on Re p The resistance exponent, under specific operating conditions, can be taken as a constant, ||u f -u s || represents the vector magnitude;

[0027] Schmidt number S c The following equation is used to determine:

[0028]

[0029] Where w fall0 U is the falling speed. * Bed friction velocity, u small A local minimum value can be chosen to prevent the equation from becoming singular;

[0030] (1.3) Construct the water phase constitutive equation and the turbulence closure equation. The turbulence closure equation includes the cross-diffusion effect of sediment phase and water phase. Both k-ω and k-ε turbulence closure equations can be used. k is the turbulence kinetic energy, ε is the turbulence energy dissipation rate, which represents the rate at which turbulence kinetic energy is converted into internal energy per unit time; ω is the turbulence frequency at a specific scale, which represents the speed of turbulent eddies.

[0031] Constitutive equation of water phase:

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] Where vmix φ is the viscosity of the mixture. max The maximum volume concentration can be taken as 1; k is the turbulent kinetic energy, calculated using the turbulence equation in a closed loop. The subscript k is the operational index, and k = 1, 2, and 3 represent the components of the physical quantities in the flow direction, spanwise direction, and vertical direction in the rectangular coordinate system, respectively.

[0039] k-ω turbulence closure equation:

[0040]

[0041] k-equation:

[0042]

[0043] equation:

[0044]

[0045]

[0046]

[0047]

[0048]

[0049] CD kω For the cross-diffusion term, C μ C lim σ k C 1ω C 2ω0 C 3ω C 4ω and σ ω All are constant terms and can be set according to specific environmental conditions; that is, the same as the k-ε model; parameter t mf Characterizing the correlation between particle and fluid velocity fluctuations, B is the only model calibration parameter, which is related to sediment flux and ranges from 0.1 to 2. It can be used as a machine parameter for machine learning.

[0050] Cross-diffusion term CD kω The following equation is used to determine:

[0051]

[0052]

[0053]

[0054] Where coefficient A is a smoothing term that gradually transitions between the activated and inactivated regions of the cross-diffusion term. It is a step function; its value is 1 when its independent variable is zero or positive, and 0 otherwise. d0 For constant terms;

[0055] k-ε turbulence closure equation:

[0056]

[0057] ε=C μ kω

[0058] The form of equation k remains unchanged. Replacing ω with ε in equation k using the above equation, we obtain equation ε:

[0059]

[0060] Where σ ε C 1ε C 2ε C 3ε C 4ε For constant terms;

[0061] (1.4) Construct the constitutive equation for the sediment phase in two-phase flow. The constitutive equation for the sediment phase is as follows:

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] in For particle pressure, p s p is the shear or collision component of particle pressure. ff C is the permanent contact component of particle pressure. t The ratio of the root-mean-square velocity fluctuations of sediment to fluid is a constant, ranging from 1 to 3; the constant coefficients of the equation. φ can be taken as 0.57. max2 The value can be taken as 0.635, which is related to the calibration of bedload and suspended mass; Fr, η0, and η1 are rheological empirical parameters, which can be taken as 0.05, 3, and 5, respectively; B represents the frictional viscosity of the sediment particles. φ 2 / 3 can be taken; ∥S s ∥for The norm of a matrix;

[0070] Friction viscosity of mud and sand particles The following equation is used to determine:

[0071]

[0072]

[0073]

[0074] Where v max For the maximum solid viscosity, D small A local minimum value can be chosen to prevent singularities in the equations, where I is the dimensionless inertia number, and μ... s is the static friction coefficient, μ2 is the empirical dynamic coefficient, and I0 is the rheological empirical constant;

[0075] (1.5) Determine the parameter and variable types of the established two-phase flow pier scour calculation equation. The parameter and variable types include constant parameters of the equation, general variables of the equation, and derived variables of the equation.

[0076] The constant parameters necessary for the equation calculation are determined through experiments or model inversion. These constant parameters include the density ρ of the sediment. s The density of water ρ f The external force f that drives the flow i gravitational acceleration g i Particle diameter d, resistance index h Exp kinematic viscosity of fluid v f Falling speed w fall0 Bed friction velocity y*, additional terms to prevent singularities in the equation u small and D small Constant coefficients in the constitutive equation of sediment phase φ max2 With B φ Rheological empirical parameters η0, η1 and Fr, and maximum volume concentration φ max The ratio of the root mean square velocity fluctuations of sediment to fluid, C t Maximum solid viscosity v max static friction coefficient μ s The empirical dynamic coefficient μ2, the rheological empirical constant I0, the model calibration parameter B, and the constant coefficient C in the turbulence closure equation. μ C 1ω C 2ω0 C 3ω C 4ω σ k σ ω σ d0 σ ε C 1ε C2ε C 3ε C 4ε and C lim The constant parameters of the equation include a freely definable kinematic parameter B; the required constant parameters of the equation can be obtained by regression prediction using conventional DNN neural networks based on experimental data sets or simulation results obtained by SPH particle flow simulation, lattice Boltzmann simulation, local DNS simulation, etc.

[0077] The general variables of the equation, i.e., the independent variables, include the volume fraction of sediment phase φ and the velocity of the sediment phase. The velocity of the water phase Fluid pressure o, turbulent kinetic energy k, turbulent frequency ω, turbulent energy dissipation rate ε, i = 1, 2, 3, a total of eleven;

[0078] The derived variables of the equation include sediment phase shear stress. Fluid stress Schmidt number S c Eddy viscosity coefficient Particle Reynolds number Re p Drag coefficient C d Dragging force parameter K, intermediate quantities used in the calculation of the water phase constitutive equation and Mixture viscosity v mix The correlation t between particle and fluid velocity fluctuations mf Intermediate quantity C used in the calculation of the turbulent closure equation 2ω , χ ω Ω ij With σ d Smoothing term A, Cross-diffusion term CD kω Particle pressure permanent contact component p ff Intermediate quantities used in the calculation of the constitutive equation of sediment phase Frictional viscosity with μ(I) and sediment particles

[0079] Preferably, step (2) specifically includes the following steps:

[0080] (2.1) Construct a two-phase flow pier scour model and define the initial conditions of the two-phase flow pier scour model. The two-phase flow pier scour model consists of upper clear water, lower sediment and pier. According to the two-phase flow pier scour calculation equation in step (1), the fluid region of the model is divided into two parts: the initial water area and the initial sediment area. The initial water area is the upper clear water with a water phase volume fraction of 1, and the initial sediment area is the riverbed sediment layer with a water phase volume fraction of 0.

[0081] (2.2) Define the dimensions of the two-phase flow pier scour model. Based on the pier dimensions, the model defines a certain length of boundary in the length, width and height directions. The pier cross-section is circular. The size of the model calculation domain can be defined according to the pier cross-section dimensions. The length direction can be 10 to 15 times the pier diameter, the width direction can be 8 to 10 times the pier diameter, and the height direction can be 5 to 7 times the pier diameter. Among them, the height of the water area is 3 to 4 times the pier diameter, and the height of the sediment domain is 2 to 3 times the pier diameter.

[0082] (2.3) Define the spatial distribution of calculation points for the two-phase flow pier scour model. Use an unstructured three-dimensional spatial mesh to establish the calculation points of the model and define an absolute spatial rectangular coordinate system. Use an unstructured three-dimensional spatial mesh to divide the model. Use a denser mesh for the water area and sediment area near the pier. From the pier to the model boundary, the mesh transitions from dense to sparse. Keep all corner points of the mesh as calculation points of the model and remove all edge lines of the mesh. Use the same mesh drawing method for the upper clear water and the lower sediment vertical planes. At the interface, the mesh is uniformly densified along the height direction.

[0083] (2.4) Define the boundary conditions for the two-phase flow pier scour model. Define corresponding boundary conditions at the inlet, outlet, top boundary, pier wall, and both sides of the model: at the inlet, for φ, Apply vertical profile boundaries to k and ω obtained from experiments, measurements, or finite element simulations; at the exit, specify zero gradient conditions for all variables; at the top boundary, apply zero gradient conditions to k and ω. Apply Newman boundary conditions, i.e., give the pressure gradient, to k and ω; at the pier wall, for and A no-slip boundary, i.e., a velocity of zero, is adopted; cyclic boundary conditions are applied to both sides of the boundary.

[0084] (2.5) Initialize the flow field parameters. Assign initial values ​​to all general variables listed in step (1.5) according to the definitions in steps (2.1) and (2.4) for all calculation points in the two-phase flow pier scour model, and initialize the flow field. The initial values ​​of all general variables in the model can also be provided by the results of the trained physical information neural network.

[0085] (2.6) Define the time discretization rules for model calculation points. Establish a fixed time interval or an adaptive and adjustable time step based on the model training results and the degree of disorder in the flow regime. The single step size shall not exceed 10. -6 s;

[0086] (2.7) Generate simulation data and divide the obtained simulation data into datasets to obtain the training set and test set of the physical information neural network.

[0087] Furthermore, step (3) specifically includes the following steps:

[0088] (3.1) Construct the main structure of the network. The main structure of the network adopts a fully connected network and a residual network. The network input is spatial coordinates X, Y, Z and time T. The nonlinear activation function is tanh. The output is all the general variables and equation kinematic parameters of the equation listed in step (1.5). The residual control term is jointly controlled by the training dataset and the physical information constructed in step (1), namely the two-phase flow pier scour calculation equation, to form a weakly supervised physical information neural network. Different nonlinear activation functions and network weight initialization schemes can be used, and the number of network layers and neurons can be optimized according to the network analysis results.

[0089] (3.2) Add a Fourier transform layer at the network input end, perform Fourier transform on the input term v and then input it into the main network. v contains spatial coordinates X, Y, Z and time T.

[0090]

[0091] Where a and b are the Fourier series coefficients and the Fourier fundamental frequency, respectively, and b follows a Gaussian distribution of N(0,1);

[0092] (3.3) Perform dimensionless and normalized processing on the dataset;

[0093] (3.4) Calculate the partial differential operators for each variable at the network output of step (3.1) using automatic differentiation (AD), and substitute them into the water phase constitutive equation, turbulent closure equation, and sediment phase constitutive equation established in steps (1.3) to (1.4) to obtain the derived variable values ​​of the equations listed in step (1.5); and calculate the initial and boundary errors loss by combining the initial and boundary conditions given in step (2). IC loss BC ;

[0094] (3.5) Perform the first differentiation operation on the network output data. Use the derived variables of the partial equations calculated in step (3.4) and the general variables of the network output equations in step (3.1) to calculate the partial differential operator again using automatic differentiation (AD). Substitute these variables into the mass conservation equation and momentum conservation equation established in step (1.2) to calculate the equation constraint error loss of the physical information neural network. PDE Simultaneously, combining the initial and boundary conditions given in step (2), the initial and boundary error losses are calculated again. IC′ loss BC′ ;

[0095] (3.6) Calculate the error loss of the entire neural network totalThe error is defined as a linear combination of the initial condition error, boundary condition error, and equation constraint error:

[0096] loss phy =αloss PDE +βloss IC +γloss BC +β′loss Ic ′+γ′loss BC′

[0097] loss total =loss phy +α′loss simulation data training set

[0098] Where: α, β, γ, α′, β′, γ′ are the weight coefficients of the loss function;

[0099] (3.7) A dynamic weighting strategy is adopted for the weight coefficients of the loss function. During the network training process, the coefficients are adaptively updated using the gradient statistics of backpropagation. The dynamic weighting strategy dynamically adjusts the weights of different parts of the loss function according to the performance of the loss function during the model training process.

[0100] (3.8) Initialize the parameters of the neural network. The parameters of the neural network are randomly initialized or randomly initialized using the Xavier scheme.

[0101] (3.9) A causal training strategy is adopted. The initial conditions used for training the physical information neural network are all the flow field parameters at a certain moment after the flow field calculation in step (2) has been initially stabilized. That is, the flow state initialized for the training set is not static. (3.10) Define the sampling strategy in the training process. When training the network, the spatiotemporal coordinates of the input end can be fixed coordinates or dynamic coordinates. The spatiotemporal coordinates include spatial coordinates X, Y, Z and time T. If fixed coordinates are used, random sampling can be used to select points, or the coordinates of the calculation points defined in step (2.3) can be sampled. The input end can use dynamic coordinates, and the coordinates of the calculation points defined in step (2.3) can be sampled in different ways at different times.

[0102] Furthermore, step (4) specifically includes the following steps:

[0103] (4.1) Train the physical information neural network, backpropagate the error, update the weights and biases, until the training error converges;

[0104] (4.2) Considering GPU acceleration and parallel computing, the neural network is deployed on a multi-core GPU for parallel operation. Each GPU can process a small batch of data, while different parts of the model are assigned to different GPUs.

[0105] (4.3) The trained neural network model is used for prediction. After the neural network error converges, the final values ​​of φ at each point are obtained. p, by observing the change of φ at each point of the model over time, the scour development law of the bridge piers calculated by the multiphase flow of bridge scour based on the physical information neural network can be obtained.

[0106] Based on the same inventive concept, this invention discloses a multiphase flow calculation system for bridge pier scour based on a physical information neural network, comprising:

[0107] A module for constructing computational equations is used to construct computational equations for two-phase flow pier scour based on the Euler-Euler method.

[0108] A simulation data module is constructed to build the initial parameters and boundary conditions of the two-phase flow pier scour model, generate simulation data, and divide the data into test set and training set;

[0109] A physical information neural network module is constructed to establish a physical information neural network based on two-phase flow, based on the constructed calculation equation for the scour of the two-phase flow pier and the given initial parameters and boundary conditions of the two-phase flow pier scour model. The construction of the physical information neural network based on two-phase flow adopts the form of limited data supervision and physical equation constraints, and introduces Fourier layers and dynamic weight strategies to form a weakly supervised physical information neural network.

[0110] A training neural network module is used to train a physical information neural network based on two-phase flow to obtain the prediction results of the physical information neural network for scour of multiphase flow bridge piers.

[0111] In the module for constructing computational equations, both the sediment phase and the water phase are treated as two different fluids and described using the Euler method. The sediment phase is a non-Newtonian fluid and is described using a dense particle rheological constitutive model, while the water phase is a Newtonian fluid and is described using a turbulence model.

[0112] The Euler-Euler method is used to construct the governing equations for two-phase flow calculation. The governing equations for two-phase flow calculation are the mass conservation equation and the momentum conservation equation. The governing equations for two-phase flow calculation include the mass conservation equations for the sediment phase and the momentum conservation equations for the sediment phase and the water phase.

[0113] Mass conservation equations for sediment and aqueous phases:

[0114]

[0115]

[0116] Where φ and 1-φ are the volume fractions of the sediment phase and the water phase, respectively. and The velocity of the sediment phase and the water phase is t, the time is t, and the subscripts i and j are the operation indicators. The subscripts i and j = 1, 2 and 3 respectively represent the components of the physical quantities in the flow direction, span direction and vertical direction in the rectangular coordinate system.

[0117] Momentum conservation equations for sediment and water phases:

[0118]

[0119]

[0120] Where ρ s and ρ f The densities of sediment and water are respectively, in g. i Let f be the acceleration due to gravity, p be the fluid pressure, and f be the acceleration due to gravity. i The external force that drives the flow The fluid stress is given by the constitutive equation of the water phase. and The normal and shear stresses of the sediment phase are given by the constitutive equation of the sediment phase. The eddy viscosity coefficient is calculated using the closed-loop turbulence equation, where K is the drag force parameter, and S is the eddy viscosity coefficient. c It is a Schmidt number;

[0121] The drag force parameter K is determined by the following equation:

[0122]

[0123]

[0124] Re p =(1-φ)||u f -u s ||d / v f

[0125] Where d is the particle diameter, C d Re is the drag coefficient. p v is the particle Reynolds number. f h is the kinematic viscosity of the fluid. Exp For depends on Re p The resistance exponent, under specific operating conditions, can be taken as a constant, ||u f -u s || represents the vector magnitude;

[0126] Schmidt number S c The following equation is used to determine:

[0127]

[0128] Where w fall0 U is the falling speed. *Bed friction velocity, u small A local minimum value can be chosen to prevent the equation from becoming singular;

[0129] The constitutive equation for the water phase and the turbulent closure equation are constructed. The turbulent closure equation includes the cross-diffusion effect of the sediment phase and the water phase. Both k-ω and k-ε turbulent closure equations can be used. k is the turbulent kinetic energy, ε is the turbulent energy dissipation rate, which represents the rate at which turbulent kinetic energy is converted into internal energy per unit time; ω is the turbulent frequency at a specific scale, which represents the speed of turbulent eddies.

[0130] Constitutive equation of water phase:

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137] Where v mix φ is the viscosity of the mixture. max The maximum volume concentration can be taken as 1; k is the turbulent kinetic energy, calculated using the turbulence equation in a closed loop. The subscript k is the operational index, and k = 1, 2, and 3 represent the components of the physical quantities in the flow direction, spanwise direction, and vertical direction in the rectangular coordinate system, respectively.

[0138] k-ω turbulence closure equation:

[0139]

[0140] k-equation:

[0141]

[0142] equation:

[0143]

[0144]

[0145]

[0146]

[0147]

[0148] CD kωFor the cross-diffusion term, C μ C lim σ k C 1ω C 2ω0 C 3ω C 4ω and σ ω All are constant terms and can be set according to specific environmental conditions; that is, the same as the k-ε model; parameter t mf Characterizing the correlation between particle and fluid velocity fluctuations, B is the only model calibration parameter, which is related to sediment flux and ranges from 0.1 to 2. It can be used as a machine parameter for machine learning.

[0149] Cross-diffusion term CD kω The following equation is used to determine:

[0150]

[0151]

[0152]

[0153] Where coefficient A is a smoothing term that gradually transitions between the activated and inactivated regions of the cross-diffusion term. It is a step function; its value is 1 when its independent variable is zero or positive, and 0 otherwise. d0 For constant terms;

[0154] k-ε turbulence closure equation:

[0155]

[0156] ε=C μ kω

[0157] The form of equation k remains unchanged. Replacing ω with ε in equation k using the above equation, we obtain equation ε:

[0158]

[0159] Where σ ε C 1ε C 2ε C 3ε C 4ε For constant terms;

[0160] Constructing the constitutive equations for the sediment phase in two-phase flow: Sediment phase constitutive equations:

[0161]

[0162]

[0163]

[0164]

[0165]

[0166]

[0167]

[0168] in For particle pressure, p s p is the shear or collision component of particle pressure. ff C is the permanent contact component of particle pressure. t The ratio of the root-mean-square velocity fluctuations of sediment to fluid is a constant, ranging from 1 to 3; the constant coefficients of the equation. φ can be taken as 0.57. max2 The value can be taken as 0.635, which is related to the calibration of bedload and suspended mass; Fr, η0, and η1 are rheological empirical parameters, which can be taken as 0.05, 3, and 5, respectively; B represents the frictional viscosity of the sediment particles. φ 2 / 3 is acceptable; ||S s ||For The norm of a matrix;

[0169] Friction viscosity of mud and sand particles The following equation is used to determine:

[0170]

[0171]

[0172]

[0173] Where v max For the maximum solid viscosity, D small A local minimum value can be chosen to prevent singularities in the equations, where I is the dimensionless inertia number, and μ... s is the static friction coefficient, μ2 is the empirical dynamic coefficient, and I0 is the rheological empirical constant;

[0174] Determine the types of parameters and variables in the established two-phase flow pier scour calculation equations. The types of parameters and variables include constant parameters, general variables, and derived variables of the equations.

[0175] The constant parameters necessary for the equation calculation are determined through experiments or model inversion. These constant parameters include the density ρ of the sediment. s The density of water ρ f The external force f that drives the flow i gravitational acceleration gi Particle diameter d, resistance index h Exp kinematic viscosity of fluid v f Falling speed W fall0 Bed friction velocity u * Additional terms u to prevent singularities in equations small and D small Constant coefficients in the constitutive equation of sediment phase φ max2 With B φ Rheological empirical parameters η0, η1 and Fr, and maximum volume concentration φ max The ratio of the root mean square velocity fluctuations of sediment to fluid, C t Maximum solid viscosity v max static friction coefficient μ s The empirical dynamic coefficient μ2, the rheological empirical constant I0, the model calibration parameter B, and the constant coefficient C in the turbulence closure equation. μ C 1ω C 2ω0 C 3ω C 4ω σ k σ ω σ d0 σ ε C 1ε C 2ε C 3ε C 4ε and C lim The constant parameters of the equation include a freely definable kinematic parameter B; the required constant parameters of the equation can be obtained by regression prediction using conventional DNN neural networks based on experimental data sets or simulation results obtained by SPH particle flow simulation, lattice Boltzmann simulation, local DNS simulation, etc.

[0176] The general variables of the equation, i.e., the independent variables, include the volume fraction of sediment phase φ and the velocity of the sediment phase. The velocity of the water phase Fluid pressure p, turbulent kinetic energy k, turbulent frequency ω, turbulent energy dissipation rate ε, i = 1, 2, 3, a total of eleven;

[0177] The derived variables of the equation include sediment phase shear stress. Fluid stress Schmidt number S c Eddy viscosity coefficient Particle Reynolds number Re p Drag coefficient C d Dragging force parameter K, intermediate quantities used in the calculation of the water phase constitutive equation and Mixture viscosity v mixThe correlation t between particle and fluid velocity fluctuations mf Intermediate quantity C used in the calculation of the turbulent closure equation 2ω , χ ω Ω ij With σ d Smoothing term A, Cross-diffusion term CD kω Particle pressure permanent contact component p ff Intermediate quantities used in the calculation of the constitutive equation of sediment phase Frictional viscosity with μ(I) and sediment particles

[0178] Preferably, a two-phase flow pier scour model is constructed in the simulation data module. The initial state of the two-phase flow pier scour model is defined. The two-phase flow pier scour model consists of upper clear water, lower sediment and pier. According to the two-phase flow pier scour calculation equation, the fluid region of the model is divided into two parts: the initial water area and the initial sediment area. The initial water area is the upper clear water with a water phase volume fraction of 1, and the initial sediment area is the riverbed sediment layer with a water phase volume fraction of 0.

[0179] Define the dimensions of the two-phase flow pier scour model. Based on the pier dimensions, define a certain length boundary in the length, width, and height directions of the model. The pier cross-section is circular. The size of the computational domain of the model can be defined according to the cross-sectional dimensions of the pier. In the length direction, it can be 10 to 15 times the pier diameter; in the width direction, it can be 8 to 10 times the pier diameter; and in the height direction, it can be 5 to 7 times the pier diameter. Among them, the height of the water area is 3 to 4 times the pier diameter, and the height of the sediment domain is 2 to 3 times the pier diameter.

[0180] The spatial distribution of calculation points for the two-phase flow pier scour model is defined. An unstructured three-dimensional spatial mesh is used to establish the calculation points of the model, and an absolute spatial rectangular coordinate system is defined. The model is divided using an unstructured three-dimensional spatial mesh. A denser mesh is used for the water area and sediment domain near the pier, and the mesh gradually becomes sparser from the pier to the model boundary. All corner points of the mesh are retained as calculation points of the model, and all edge lines of the mesh are removed. The same meshing method is used for vertical planes between the upper clear water and the lower sediment, and the mesh is uniformly densified along the height direction at the interface.

[0181] Define boundary conditions for the two-phase flow pier scour model, defining corresponding boundary conditions at the inlet, outlet, top boundary, pier wall, and both sides of the model: at the inlet, for φ, Apply vertical profile boundaries to k and ω obtained from experiments, measurements, or finite element simulations; at the exit, specify zero gradient conditions for all variables; at the top boundary, apply zero gradient conditions to k and ω. Apply Newman boundary conditions, i.e., give the pressure gradient, to k and ω; at the pier wall, for and A no-slip boundary, i.e., a velocity of zero, is adopted; cyclic boundary conditions are applied to both sides of the boundary.

[0182] Initialize the flow field parameters by assigning initial values ​​to all the listed general variables at all calculation points in the two-phase flow pier scour model according to the definition, and initialize the flow field; the initial values ​​of all general variables in the model can also be provided by the results of a pre-trained physical information neural network;

[0183] Define the time discretization rules for model computation points, establishing a fixed time interval or an adaptively adjustable time step based on model training results and the degree of disorder in flow development, with a single step size not exceeding 10. -6 s;

[0184] Simulation data is generated, and the obtained simulation data is divided into datasets to obtain the training set and test set of the physical information neural network.

[0185] Furthermore, the physical information neural network module constructs the main network structure, which employs a fully connected network and a residual network. The network input consists of spatial coordinates X, Y, Z and time T, with tanh as the nonlinear activation function. The output includes all general variables and equation maneuvering parameters from the listed equations. The residual control term is jointly controlled by the training dataset and the constructed physical information, namely the two-phase flow pier scour calculation equations, forming a weakly supervised physical information neural network. Different nonlinear activation functions and network weight initialization schemes can be used, and the number of network layers and neurons can be optimized based on the network analysis results.

[0186] Add a Fourier transform layer at the network input end to perform a Fourier transform on the input term v before inputting it into the main network. v contains spatial coordinates X, Y, Z and time T.

[0187]

[0188] Where a and b are the Fourier series coefficients and the Fourier fundamental frequency, respectively, and b follows a Gaussian distribution of N(0,1);

[0189] Perform dimensionless and normalized transformation on the dataset;

[0190] The partial differential operators of each variable at the network output are calculated using automatic differential (AD) calculations, and then substituted into the established constitutive equations for the water phase, turbulent closure, and sediment phase to obtain the derived variable values. Finally, the initial and boundary errors (losses) are calculated based on the given initial and boundary conditions. IC loss BC ;

[0191] The network output data is subjected to the first differential operation. The derived variables of the calculated partial equations and the general variables of the network output equations are then used again to calculate the partial differential operator using automatic differentiation (AD). Substituting these into the established mass conservation equation and momentum conservation equation, the constraint error LIS of the physical information neural network equation is obtained. PDE Simultaneously, combining the given initial and boundary conditions, the initial and boundary error losses are calculated again. IC′ loss BC′ ;

[0192] Calculate the error loss of the entire neural network total The error is defined as a linear combination of the initial condition error, boundary condition error, and equation constraint error:

[0193] loss phy =αloss PDE +βloss IC +γloss BC +β′loss IC′ +γ′loss BC′

[0194] loss total =loss phy +α′loss 仿真数据训练集

[0195] Where: α, β, γ, α′, β′, γ′ are the weight coefficients of the loss function;

[0196] A dynamic weighting strategy is adopted for the weight coefficients of the loss function. During network training, the coefficients are adaptively updated using the gradient statistics of backpropagation. The dynamic weighting strategy dynamically adjusts the weights of different parts of the loss function based on the performance of the loss function during model training.

[0197] The parameters of the neural network are initialized using either random initialization or the Xavier scheme.

[0198] A causal training strategy is adopted. The initial conditions used for training the physical information neural network are all the flow field parameters at a certain moment after the initial stabilization of the flow field calculation, that is, the flow state initialized for the training set rather than static. A sampling strategy is defined in the training process. When training the network, the spatiotemporal coordinates of the input end can be fixed coordinates or dynamic coordinates. The spatiotemporal coordinates include spatial coordinates X, Y, Z and time T. If fixed coordinates are used, random sampling can be used to select points, or the coordinates of the defined calculation points can be sampled. The input end can use dynamic coordinates, and the coordinates of the defined calculation points can be sampled in different ways at different times.

[0199] Furthermore, the physical information neural network is trained in the training neural network module, and the error is backpropagated to update the weights and biases until the training error converges.

[0200] Considering GPU acceleration and parallel computing, the neural network can be deployed on multi-core GPUs for parallel operation, allowing each GPU to process a small batch of data, while different parts of the model can be assigned to different GPUs.

[0201] Prediction is performed using a trained neural network model. After the neural network error converges, the final values ​​φ at each point are obtained. p, by observing the change of φ at each point of the model over time, the scour development law of the bridge piers calculated by the multiphase flow of bridge scour based on the physical information neural network can be obtained.

[0202] Beneficial Effects: Compared with existing technologies, this invention has the following significant advantages: It improves prediction accuracy, reduces data requirements, enhances computational efficiency, and strengthens model generalization ability; combining physical laws and deep learning methods, it can more accurately simulate and predict the scour process around bridge piers, improving prediction accuracy; the training process guided by physical information reduces reliance on large amounts of experimental data, lowering the difficulty and cost of data acquisition. Compared with traditional numerical simulation methods, this invention significantly improves computational efficiency while maintaining accuracy, making it suitable for real-time or near-real-time applications; by integrating physical laws, it enhances the model's predictive ability for unseen data, improving model generalization ability; for bridge pier scour, the multiphase flow model, compared to the single-phase flow combined with dynamic mesh technology, has significant advantages in simulating complex fluid dynamics problems such as bridge pier scour; multiphase flow can more accurately capture the interaction between fluid and solid particles, providing a more realistic simulation of the scour process; the use of neural networks in this invention can greatly reduce computational costs and improve computational efficiency, fully leveraging the advantages of multiphase flow theory while avoiding its disadvantages, making bridge pier scour easier to predict. Attached Figure Description

[0203] Figure 1 This is a flowchart of the present invention;

[0204] Figure 2 This is a schematic diagram of the physical information neural network structure in this invention;

[0205] Figure 3 This is a schematic diagram of the two-phase flow pier scour model in this invention. Detailed Implementation

[0206] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0207] like Figure 1As shown, a method for calculating multiphase flow scour of bridge piers based on a physical information neural network includes the following steps:

[0208] (1) Construct the calculation equation for the scour of two-phase flow bridge piers based on the Euler-Euler method;

[0209] Step (1) specifically includes the following steps:

[0210] (1.1) Both the sediment phase and the water phase are treated as two different fluids and described using the Eulerian method. The sediment phase is a non-Newtonian fluid and a dense particle rheological constitutive model is applied, while the water phase is a Newtonian fluid and a turbulence model is applied. In computational fluid dynamics, the Eulerian method is: the grid is stationary, the fluid flows within the grid, and the flow parameters of the fluid at each grid point are calculated.

[0211] (1.2) Construct the Euler-Euler method for calculating the governing equations of two-phase flow. The governing equations of two-phase flow are the mass conservation equation and the momentum conservation equation. The governing equations of two-phase flow include the mass conservation equations of the sediment phase and the momentum conservation equations of the sediment phase and the water phase. The momentum conservation equations of the sediment phase and the water phase can adopt different forms of multiphase flow equations, which can change the interphase interaction force, interphase transmission mechanism and interphase resistance expression form of multiphase flow.

[0212] Mass conservation equations for sediment and aqueous phases:

[0213]

[0214]

[0215] Where φ and 1-φ are the volume fractions of the sediment phase and the water phase, respectively. and The velocity of the sediment phase and the water phase is t, the time is t, and the subscripts i and j are the operation indicators. The subscripts i and j = 1, 2 and 3 respectively represent the components of the physical quantities in the flow direction, span direction and vertical direction in the rectangular coordinate system.

[0216] Momentum conservation equations for sediment and water phases:

[0217]

[0218]

[0219] Where ρ s and ρ f The densities of sediment and water are respectively, in g. i Let f be the acceleration due to gravity, p be the fluid pressure, and f be the acceleration due to gravity. i The external force that drives the flow The fluid stress is given by the constitutive equation of the water phase. and The normal and shear stresses of the sediment phase are given by the constitutive equation of the sediment phase. The eddy viscosity coefficient is calculated using the closed-loop turbulence equation, where K is the drag force parameter, and S is the eddy viscosity coefficient. c It is a Schmidt number;

[0220] The drag force parameter K is determined by the following equation:

[0221]

[0222]

[0223] Re p =(1-φ)||u f -u s ||d / v f

[0224] Where d is the particle diameter, C d Re is the drag coefficient. p v is the particle Reynolds number. f h is the kinematic viscosity of the fluid. Exp For depends on Re p The resistance exponent, under specific operating conditions, can be taken as a constant, ||u f -u s || represents the vector magnitude;

[0225] Schmidt number S c The following equation is used to determine:

[0226]

[0227] Where w fall0 U is the falling speed. * Bed friction velocity, u small A local minimum value can be chosen to prevent the equation from becoming singular;

[0228] (1.3) Construct the water phase constitutive equation and the turbulence closure equation. The turbulence closure equation includes the cross-diffusion effect of sediment phase and water phase. Both k-ω and k-ε turbulence closure equations can be used. k is the turbulence kinetic energy, ε is the turbulence energy dissipation rate, which represents the rate at which turbulence energy is converted into internal energy per unit time; ω is the turbulence frequency at a specific scale, which represents the speed of turbulent eddies. The multiphase flow turbulence closure equation can be supplemented by constructing supplementary equations in different forms. One-equation, zero-equation, and three-equation supplementary equations can be used, or the supplementary equations of the SGS stress model of large eddy simulation and the related models of separated eddy simulation can be used.

[0229] Constitutive equation of water phase:

[0230]

[0231]

[0232]

[0233]

[0234]

[0235]

[0236] Where v mix φ is the viscosity of the mixture. max The maximum volume concentration can be taken as 1; k is the turbulent kinetic energy, calculated using the turbulence equation in a closed loop. The subscript k is the operational index, and k = 1, 2, and 3 represent the components of the physical quantities in the flow direction, spanwise direction, and vertical direction in the rectangular coordinate system, respectively.

[0237] k-ω turbulence closure equation:

[0238]

[0239] k-equation:

[0240]

[0241] equation:

[0242]

[0243]

[0244]

[0245]

[0246]

[0247] CD kω For the cross-diffusion term, C μ C lim σ k C 1ω C 2ω0 C 3ω C 4ω and σ ω All are constant terms and can be set according to specific environmental conditions; that is, the same as the k-ε model; parameter t mf Characterizing the correlation between particle and fluid velocity fluctuations, B is the only model calibration parameter, which is related to sediment flux and can be set manually according to the model results. Its value ranges from 0.1 to 2. It can also be used as a flexible parameter for machine learning.

[0248] Cross-diffusion term CD kω The following equation is used to determine:

[0249]

[0250]

[0251]

[0252] Where coefficient A is a smoothing term that gradually transitions between the activated and inactivated regions of the cross-diffusion term. It is a step function; its value is 1 when its independent variable is zero or positive, and 0 otherwise. d0 For constant terms;

[0253] k-ε turbulence closure equation:

[0254]

[0255] ε=C μ kω

[0256] The form of equation k remains unchanged. Replacing ω with ε in equation k using the above equation, we obtain equation ε:

[0257]

[0258] Where σ ε C 1ε C 2ε C 3ε C 4ε For constant terms;

[0259] (1.4) Construct the constitutive equations for the sediment phase of two-phase flow. The constitutive equations for the sediment phase can be established using different rheological models. As long as the multiphase flow differential equation set is complete and closed, subsequent methods can be used for calculation and prediction.

[0260] Constitutive equation of sediment phase:

[0261]

[0262]

[0263]

[0264]

[0265]

[0266]

[0267]

[0268] in For particle pressure, p s p is the shear or collision component of particle pressure. ff C is the permanent contact component of particle pressure. t The ratio of the root-mean-square velocity fluctuations of sediment to fluid is a constant, ranging from 1 to 3, and can be taken as 1; the constant coefficient of the equation. φ can be taken as 0.57. max2 The value can be taken as 0.635, which is related to the calibration of bedload and suspended mass; Fr, η0, and η1 are rheological empirical parameters, which can be taken as 0.05, 3, and 5, respectively; B represents the frictional viscosity of the sediment particles. φ 2 / 3 can be taken; ∥S s ∥for The norm of a matrix;

[0269] Friction viscosity of mud and sand particles The following equation is used to determine:

[0270]

[0271]

[0272]

[0273] Where v max For the maximum solid viscosity, D small A local minimum value can be chosen to prevent singularities in the equations, where I is the dimensionless inertia number, and μ... s is the static friction coefficient, μ2 is the empirical dynamic coefficient, and I0 is the rheological empirical constant;

[0274] (1.5) Determine the parameter and variable types of the established two-phase flow pier scour calculation equation. The parameter and variable types include constant parameters of the equation, general variables of the equation, and derived variables of the equation.

[0275] The constant parameters necessary for the equation calculation are determined through experiments or model inversion. These constant parameters include the density ρ of the sediment. s The density of water ρ f The external force f that drives the flow i gravitational acceleration g i Particle diameter d, resistance index h Exp kinematic viscosity of fluid v f Falling speed W fall0 Bed friction velocity u * Additional terms u to prevent singularities in equations small and D small Constant coefficients in the constitutive equation of sediment phase φ max2 With B φ Rheological empirical parameters η0, η1 and Fr, and maximum volume concentration φ max The ratio of the root mean square velocity fluctuations of sediment to fluid, C t Maximum solid viscosity v max static friction coefficient μ s The empirical dynamic coefficient μ2, the rheological empirical constant I0, the model calibration parameter B, and the constant coefficient C in the turbulence closure equation. μ C 1ω C 2ω0 C 3ω C 4ω σ k σ ω σ d0 σ ε C 1ε C 2ε C 3ε C 4ε and C lim The constant parameters of the equation include a freely definable kinematic parameter B; the required constant parameters of the equation can be obtained by regression prediction using conventional DNN neural networks based on experimental data sets or simulation results obtained by SPH particle flow simulation, lattice Boltzmann simulation, local DNS simulation, etc.

[0276] The general variables of the equation, i.e., the independent variables, include the volume fraction of sediment phase φ and the velocity of the sediment phase. The velocity of the water phase Fluid pressure p, turbulent kinetic energy k, turbulent frequency ω, turbulent energy dissipation rate ε, i = 1, 2, 3, a total of eleven;

[0277] The derived variables of the equation include sediment phase shear stress. Fluid stress Schmidt number S c Eddy viscosity coefficient Particle Reynolds number Re p Drag coefficient C d Dragging force parameter K, intermediate quantities used in the calculation of the water phase constitutive equation and Mixture viscosity v mix The correlation t between particle and fluid velocity fluctuations mf Intermediate quantity C used in the calculation of the turbulent closure equation 2ω , χ ω Ω ij With σ d Smoothing term A, Cross-diffusion term CD kω Particle pressure permanent contact component p ffIntermediate quantities used in the calculation of the constitutive equation of sediment phase Frictional viscosity with μ(I) and sediment particles

[0278] (2) Construct the initial parameters and boundary conditions of the two-phase flow pier scour model, generate simulation data, and divide the data into test set and training set;

[0279] Step (2) specifically includes the following steps:

[0280] (2.1) As Figure 3 As shown, a two-phase flow pier scour model is constructed. The initial conditions of the two-phase flow pier scour model are defined. The two-phase flow pier scour model consists of upper clear water, lower sediment and pier. According to the two-phase flow pier scour calculation equation in step (1), the fluid region of the model is divided into two parts: the initial water area and the initial sediment area. The initial water area is the upper clear water with a water phase volume fraction of 1, and the initial sediment area is the riverbed sediment layer with a water phase volume fraction of 0. The model working conditions to be analyzed can be initialized according to the actual situation, such as the actual flow field distribution after partial scour or partial artificial filling of scour, so as to obtain a more realistic and universal scour calculation and scour development prediction.

[0281] (2.2) Define the dimensions of the two-phase flow pier scour model to ensure that the defined area can effectively reflect the scour characteristics and describe the final scour and sedimentation conditions; based on the pier dimensions, define a certain length of boundary in the length, width, and height directions of the model to fully demonstrate the scour characteristics; the commonly used pier cross-section is circular, and the size of the model's computational domain can be defined according to the pier cross-section dimensions. In the length direction, it can be 10 to 15 times the pier diameter, in the width direction, it can be 8 to 10 times the pier diameter, and in the height direction, it can be 5 to 7 times the pier diameter, of which the height of the water area is 3 to 4 times the pier diameter, and the height of the sediment area is 2 to 3 times the pier diameter; the pier distribution can be arranged according to the actual situation (including the inclusion of abutments and pile foundations, etc.) to obtain calculations and predictions that are more consistent with the actual situation;

[0282] (2.3) Define the spatial distribution of calculation points for the two-phase flow pier scour model. Use an unstructured three-dimensional spatial mesh to establish the calculation points of the model and define an absolute spatial rectangular coordinate system. Use an unstructured three-dimensional spatial mesh to divide the model. Use a denser mesh for the water area and sediment area near the pier. From the pier to the model boundary, the mesh transitions from dense to sparse. Keep all corner points of the mesh as calculation points of the model and remove all edge lines of the mesh. Use the same mesh drawing method for the upper clear water and the lower sediment vertical planes. At the interface, the mesh is uniformly densified along the height direction.

[0283] (2.4) Define the boundary conditions for the two-phase flow pier scour model. Define corresponding boundary conditions at the inlet, outlet, top boundary, pier wall, and both sides of the model: at the inlet, for φ, Apply vertical profile boundaries to k and ω obtained from experiments, measurements, or finite element simulations; at the exit, specify zero gradient conditions for all variables; at the top boundary, apply zero gradient conditions to k and ω. Apply Newman boundary conditions to k and ψ, i.e., give a pressure gradient; at the pier wall, for and A no-slip boundary, i.e., a velocity of zero, is adopted; cyclic boundary conditions are applied to both sides of the boundary.

[0284] (2.5) Initialize the flow field parameters. Assign initial values ​​to all general variables listed in step (1.5) according to the definitions in steps (2.1) and (2.4) for all calculation points in the two-phase flow pier scour model. The initial values ​​of all general variables in the model can also be provided by the results of the trained PINN network.

[0285] (2.6) Define the time discretization rules for model calculation points. Establish a fixed time interval or an adaptive and adjustable time step based on the model training results and the degree of disorder in the flow regime. The single step size shall not exceed 10. -6 s;

[0286] (2.7) Generate simulation data and divide the obtained simulation data into datasets to obtain the training set and test set of the neural network;

[0287] (3) Based on the two-phase flow pier scour calculation equation constructed in step (1) and the initial parameters and boundary conditions of the two-phase flow pier scour model given in step (2), establish a physical information neural network based on two-phase flow.

[0288] A physical information neural network based on two-phase flow is constructed, which adopts the form of limited data supervision and physical equation constraints, and introduces Fourier layers and dynamic weight strategy to form a weakly supervised physical information neural network.

[0289] like Figure 2 As shown, step (3) specifically includes the following steps:

[0290] (3.1) Construct the main structure of the network. The main structure of the network adopts a fully connected network and a residual network. The network input is spatial coordinates X, Y, Z and time T. The nonlinear activation function is tanh. The output is all the general variables and equation kinematic parameters of the equation listed in step (1.5). The residual control term is jointly controlled by the training dataset and the physical information constructed in step (1), namely the two-phase flow pier scour calculation equation, to form a weakly supervised physical information neural network. Different nonlinear activation functions and network weight initialization schemes can be used, and the number of network layers and neurons can be optimized according to the network analysis results. The parameter initialization scheme of the neural network can be different according to different activation functions. Generally, the zero initialization scheme is not used, so as not to break the symmetry problem. In addition, schemes such as Kaiming initialization can be used. Kaiming initialization is an initialization method specifically designed for the ReLU activation function. It adjusts the initialization variance according to the characteristics of ReLU so that the output variance of the neural network remains unchanged. There are also two variations of Kaiming initialization, which are suitable for different activation functions and network structures.

[0291] (3.2) Add a Fourier transform layer at the network input end, perform Fourier transform on the input term v and then input it into the main network. v contains spatial coordinates X, Y, Z and time T), which increases the convergence speed of the neural network for the high-frequency part of the equation and data.

[0292]

[0293] Where a and b are the Fourier series coefficients and the Fourier fundamental frequency, respectively, and b follows a Gaussian distribution of N(0,1);

[0294] (3.3) Dimensionless and normalized data in the dataset to enhance the applicability of the initial training process of the network;

[0295] (3.4) Calculate the partial differential operators for each variable at the network output of step (3.1) using automatic differentiation (AD), and substitute them into the water phase constitutive equation, turbulent closure equation, and sediment phase constitutive equation established in steps (1.3) to (1.4) to obtain the derived variable values ​​of the equations listed in step (1.5); and calculate the initial and boundary errors loss by combining the initial and boundary conditions given in step (2). IC loss BC ;

[0296] (3.5) Perform the first differential operation on the network output data to satisfy some physical equations; use the derived variables of the partial equations calculated in step (3.4) and the general variables of the equations output by the network in step (3.1) to calculate the partial differential operator again using automatic differentiation (AD), and substitute them into the mass conservation equation and momentum conservation equation established in step (1.2) to calculate the equation constraint error loss of the physical information neural network. PDE Simultaneously, combining the initial and boundary conditions given in step (2), the initial and boundary error losses are calculated again. IC′ loss BC′ ;

[0297] (3.6) Calculate the error loss of the entire neural network total The error is defined as a linear combination of the initial condition error, boundary condition error, and equation constraint error:

[0298] loss phy =αloss PDE +βloss IC +γloss BC +β′loss IC′ +γ′loss BC′

[0299] loss total =loss phy +α′loss simulation data training set

[0300] Where: α, β, γ, α′, β′, γ′ are the weight coefficients of the loss function;

[0301] (3.7) A dynamic weighting strategy is adopted for the weight coefficients of the loss function. During the network training process, the coefficients are adaptively updated using the gradient statistics of backpropagation. The dynamic weighting strategy dynamically adjusts the weights of different parts of the loss function according to the performance of the loss function during model training, thereby improving the training effect and performance of the model.

[0302] (3.8) Initialize the parameters of the neural network. The parameters of the neural network are initialized randomly or using the Xavier scheme. Xavier initialization is an initialization method specifically designed for neural networks with linear or sigmoid activation functions. It determines the initialization range of parameters based on the number of inputs and outputs, ensuring that the variance of inputs and outputs remains consistent, thereby preventing gradient vanishing or exploding problems. There are two variations of Xavier initialization: Xavier Glorot initialization and Xavier He initialization. Xavier Glorot initialization is suitable for sigmoid and tanh activation functions, while Xavier He initialization is suitable for ReLU and its variant activation functions. This application uses Xavier... The Glorot scheme is used for initialization, employing different nonlinear activation functions and network weight initialization schemes. The number of network layers and neurons is optimized based on network analysis results. The parameter initialization scheme for the neural network can vary depending on the activation function; generally, zero initialization is avoided to prevent breaking symmetry. Other schemes include Kaiming initialization, a method specifically designed for the ReLU activation function. Kaiming initialization adjusts the initial variance based on the characteristics of ReLU, ensuring the output variance of the neural network remains constant. Kaiming initialization also has two variations suitable for different activation functions and network structures.

[0303] (3.9) A causal training strategy is adopted. The initial conditions used for training the physical information neural network are all the flow field parameters at a certain moment after the flow field calculation in step (2) has been initially stabilized. That is, the flow state initialized for the training set is not static, which increases the convergence speed of the network training and prevents gradient explosion. (3.10) A sampling strategy is defined in the training process. When training the network, the spatiotemporal coordinates of the input end can be fixed or dynamic. The spatiotemporal coordinates include spatial coordinates X, Y, Z and time T. If fixed coordinates are used, random sampling can be used to select points, or the coordinates of the calculation points defined in step (2.3) can be sampled. The input end can use dynamic coordinates. The coordinates of the calculation points defined in step (2.3) can be sampled in different ways at different times, which can increase the network's affinity to the data and speed up the convergence speed.

[0304] (4) Train a physical information neural network based on two-phase flow to obtain the PINN prediction results of multiphase flow pier scour; distributed training can also be used to distribute different parts of the model on multiple machines for calculation.

[0305] Step (4) specifically includes the following steps:

[0306] (4.1) Train the physical information neural network, backpropagate the error, update the weights and biases, until the training error converges;

[0307] (4.2) Considering GPU acceleration and parallel computing, the neural network is deployed on a multi-core GPU for parallel operation. Each GPU can process a small batch of data, while different parts of the model are assigned to different GPUs.

[0308] (4.3) The trained neural network model is used for prediction. After the neural network error converges, the final values ​​of φ at each point are obtained. p, by observing the change of φ at each point of the model over time, the scour development law of the bridge piers calculated by the multiphase flow of bridge scour based on the physical information neural network can be obtained.

[0309] If the equations and parameters in step (1) of this invention are modified, the constant parameters, independent general variables, and related derived variables of the equations need to be re-established based on the modified equations, and the corresponding information needs to be modified in subsequent steps. The method of this invention can be applied not only to the scouring of multiphase flow bridge piers, but also to the scouring of multiphase flow submarine cables, debris flow, and other problems.

[0310] Example 2

[0311] like Figure 1 As shown, a multiphase flow calculation system for bridge pier scour based on a physical information neural network includes:

[0312] The calculation equation construction module is used to construct the calculation equation for the scour of the two-phase flow bridge pier based on the Euler-Euler method; the calculation equation construction module executes the specific steps of step (1) in Example 1;

[0313] A simulation data module is constructed to build the initial parameters and boundary conditions of the two-phase flow pier scour model, generate simulation data, and divide the data into a test set and a training set; the specific steps of step (2) in Example 1 are executed in the construction of the simulation data module.

[0314] A physical information neural network module is constructed to establish a physical information neural network based on two-phase flow, based on the constructed two-phase flow pier scour calculation equation and the given initial parameters and boundary conditions of the two-phase flow pier scour model. The physical information neural network based on two-phase flow is constructed by adopting a form of low data supervision and physical equation constraint, and introducing Fourier layers and dynamic weight strategies to form a weakly supervised physical information neural network. The physical information neural network module is constructed to execute the specific steps of step (3) in Example 1.

[0315] The training neural network module is used to train the physical information neural network based on two-phase flow to obtain the prediction results of the physical information neural network for scour of multiphase flow piers. The training neural network module executes the specific steps of step (4) in Example 1.

Claims

1. A method for calculating multiphase flow scour of bridge piers based on a physical information neural network, characterized in that, Includes the following steps: (1) Construct the calculation equation for the scour of two-phase flow bridge piers based on the Euler-Euler method; (2) Construct the initial parameters and boundary conditions of the two-phase flow pier scour model, generate simulation data, and divide the data into test set and training set; (3) Based on the two-phase flow pier scour calculation equation constructed in step (1) and the initial parameters and boundary conditions of the two-phase flow pier scour model given in step (2), a physical information neural network based on two-phase flow is established; the physical information neural network based on two-phase flow is constructed by adopting a form of less data supervision and physical equation constraint, and Fourier layers and dynamic weight strategy are introduced to form a weakly supervised physical information neural network; among them, a dynamic weight strategy is adopted for the weight coefficients of the loss function, and the coefficients are adaptively updated by using the gradient statistics of backpropagation during the network training process. The dynamic weight strategy dynamically adjusts the weights of different parts of the loss function according to the performance of the loss function during the model training process; the error of the neural network is defined as a linear combination of initial condition error, boundary condition error and equation constraint error: ， in: These are the weighting coefficients of the loss function. The equation constraint error of the physical information neural network. These are the initial condition error and the boundary condition error. The initial condition error and boundary condition error are recalculated. (4) Train the physical information neural network based on two-phase flow to obtain the prediction results of the physical information neural network for scour of multiphase flow piers.

2. The method for calculating multiphase flow scour of bridge piers based on a physical information neural network according to claim 1, characterized in that: Step (1) specifically includes the following steps: (1.1) Both the sediment phase and the water phase are treated as two fluids and described using the Eulerian method. The sediment phase is a non-Newtonian fluid and a dense particle rheological constitutive model is applied, while the water phase is a Newtonian fluid and a turbulence model is applied. (1.2) Construct the Eulerian-Eulerian method for calculating the governing equations of two-phase flow. The governing equations of two-phase flow are the mass conservation equation and the momentum conservation equation. The governing equations of two-phase flow include the mass conservation equations of the sediment phase and the momentum conservation equations of the sediment phase and the water phase. Mass conservation equations for sediment and aqueous phases: ， in and The volume fractions of the sediment and aqueous phases. and Let be the velocity of the sediment phase and the water phase in the i-th direction. For time, subscript For calculation indicators, subscript These represent the components of the physical quantities in the flow direction, span direction, and vertical direction in a rectangular coordinate system, respectively. Momentum conservation equations for sediment and water phases: , in and The densities of sediment and water are respectively. It is the acceleration due to gravity. For fluid pressure, The external force that drives the flow The fluid stress is given by the constitutive equation of the water phase. and The normal and shear stresses of the sediment phase are given by the constitutive equation of the sediment phase. The eddy viscosity is calculated using the turbulence closure equation. This refers to the drag force parameter. It is a Schmidt number; Drag force parameters The following equation is used to determine: ， in The particle diameter, The drag coefficient, The particle Reynolds number, For fluid kinematic viscosity, For depends on The resistance index, under specific operating conditions, can be taken as a constant. The vector magnitude; Schmidt number The following equation is used to determine: ， in For the falling speed, The bed friction velocity, A local minimum value can be chosen to prevent the equation from becoming singular; (1.3) Construct the constitutive equation for the water phase and the turbulent closure equation, wherein the turbulent closure equation includes the cross-diffusion effects of the sediment phase and the water phase. and Both turbulent closure equations can be used. For turbulent kinetic energy, The dissipation rate of turbulent energy represents the rate at which turbulent energy is converted into internal energy per unit time. The turbulence frequency is a scale, representing the speed of the turbulent eddies; Constitutive equation of water phase: ， ， ， in The viscosity of the mixture, For the maximum volume concentration, we can take a value of 1; For turbulent kinetic energy, use the turbulence equation closed-loop calculation, subscript... For calculation indicators, These represent the components of the physical quantities in the flow direction, span direction, and vertical direction in a rectangular coordinate system, respectively. Turbulent closure equation: ， equation: ， equation: , ， ， in For cross-diffusion terms, , , , , , , and These are all constant terms and can be set according to specific environmental conditions; that is... Same model; parameters Characterizes the degree of correlation between particle and fluid velocity fluctuations. It is the only model calibration parameter, related to sediment flux, and has a value range of 0.1 to 2. It can be used as a machine parameter for machine learning. Cross-diffusion term The following equation is used to determine: ， Where the coefficient This is a smooth term that gradually transitions between the activated and inactive regions of the cross-diffusion term. It is a step function, whose value is 1 when its independent variable is zero or positive, and 0 otherwise. For constant terms; Turbulent closure equation: ， The equation remains unchanged; the above formula is used for substitution. In the equation for , equation: , in , , , , For constant terms; (1.4) Construct the constitutive equation for the sediment phase in two-phase flow. The constitutive equation for the sediment phase is as follows: ， ， ， ， in For sediment phase normal stress, This refers to the shear or impact component of particle pressure. This represents the permanent contact component of particle pressure. The ratio of the root-mean-square velocity fluctuations of sediment to fluid is a constant, ranging from 1 to 3; the constant coefficients of the equation. 0.57 is acceptable. A value of 0.635 is acceptable, depending on the calibration of bedload and suspended mass. These are rheological empirical parameters, which can be taken as 0.05, 3, and 5 respectively; The frictional viscosity of mud and sand particles. 2 / 3 is acceptable; for The norm of a matrix; Friction viscosity of mud and sand particles The following equation is used to determine: ， in The maximum solid-phase viscosity, A local minimum value can be chosen to prevent singularities in the equation. The inertial number is a dimensionless number. The static friction coefficient is For empirical dynamic coefficients, These are rheological empirical constants; (1.5) Determine the parameter and variable types of the established two-phase flow pier scour calculation equation. The parameter and variable types include constant parameters of the equation, general variables of the equation, and derived variables of the equation. The constant parameters necessary for the equation calculations are determined through experiments or model inversion. These constant parameters include the density of sediment. The density of water External forces driving the flow Gravitational acceleration Particle diameter Obstacle Index kinematic viscosity of fluids Falling speed Bed friction velocity To prevent singular additional terms in equations and Constant coefficients in the constitutive equation of sediment phase , and Rheological empirical parameters , and Maximum volume concentration The ratio of the root mean square velocity fluctuations of sediment to those of fluid Maximum solid viscosity static friction coefficient Empirical dynamic coefficient Rheological empirical constants Model calibration parameters and the constant coefficients in the turbulence closure equation , , , , , , , , , , , , and The constant parameters of the equation include a freely definable kinematic parameter B; the required constant parameters of the equation can be obtained by regression prediction using conventional DNN neural networks based on experimental data sets or simulation results obtained by SPH particle flow simulation, lattice Boltzmann simulation, and local DNS simulation. The general variables of the equation, i.e., the independent variables, include the volume fraction of sediment phase. The velocity of sediment phase The velocity of the water phase Fluid pressure Turbulent kinetic energy turbulence frequency Turbulent energy dissipation rate , There are eleven in total; The derived variables of the equation include sediment phase shear stress. Fluid stress Schmidt number Eddy viscosity coefficient Particle Reynolds number drag coefficient Dragging force parameters Intermediate quantities used in the calculation of the constitutive equation of the water phase , and Viscosity of mixture The correlation between particle and fluid velocity fluctuations Intermediate quantities used in the calculation of turbulent closure equations , , and Smoothing terms Cross-diffusion term Permanent contact component of particle pressure Intermediate quantities used in the calculation of the constitutive equation of sediment phase , , and Friction viscosity of mud and sand particles .

3. The method for calculating multiphase flow scour of bridge piers based on a physical information neural network according to claim 2, characterized in that: Step (2) specifically includes the following steps: (2.1) Construct a two-phase flow pier scour model and define the initial conditions of the two-phase flow pier scour model. The two-phase flow pier scour model consists of upper clear water, lower sediment and pier. According to the two-phase flow pier scour calculation equation in step (1), the fluid region of the model is divided into two parts: the initial water area and the initial sediment area. The initial water area is the upper clear water with a water phase volume fraction of 1, and the initial sediment area is the riverbed sediment layer with a water phase volume fraction of 0. (2.2) Define the dimensions of the two-phase flow pier scour model. Based on the pier dimensions, the model defines a certain length of boundary in the length, width and height directions. The pier cross-section is circular. The size of the model calculation domain can be defined according to the pier cross-section dimensions. The length direction can be 10 to 15 times the pier diameter, the width direction can be 8 to 10 times the pier diameter, and the height direction can be 5 to 7 times the pier diameter. Among them, the height of the water area is 3 to 4 times the pier diameter, and the height of the sediment domain is 2 to 3 times the pier diameter. (2.3) Define the spatial distribution of calculation points for the two-phase flow pier scour model. Use an unstructured three-dimensional spatial mesh to establish the calculation points of the model and define an absolute spatial rectangular coordinate system. Use an unstructured three-dimensional spatial mesh to divide the model. Use a denser mesh for the water area and sediment area near the pier. From the pier to the model boundary, the mesh transitions from dense to sparse. Keep all corner points of the mesh as calculation points of the model and remove all edge lines of the mesh. Use the same mesh drawing method for the upper clear water and the lower sediment vertical planes. At the interface, the mesh is uniformly densified along the height direction. (2.4) Define the boundary conditions for the two-phase flow pier scour model. Define corresponding boundary conditions at the inlet, outlet, top boundary, pier wall, and both sides of the model: at the inlet, for , , , and Apply a vertical profile boundary obtained from experiments, measurements, or finite element simulations; at the exit, specify a zero gradient condition for all variables; at the top boundary, for... , and Apply the Newman boundary condition, i.e., give the pressure gradient; at the pier wall, for and A no-slip boundary, i.e., a velocity of zero, is adopted; cyclic boundary conditions are applied to both sides of the boundary. (2.5) Initialize the flow field parameters. Assign initial values ​​to all general variables listed in step (1.5) according to the definitions in steps (2.1) and (2.4) for all calculation points in the two-phase flow pier scour model, and initialize the flow field. The initial values ​​of all general variables in the model can also be provided by the results of the trained physical information neural network. (2.6) Define the time discretization rules for model calculation points. Establish an adaptive and adjustable time step based on the model training results and the degree of disorder in the flow regime. The single step size shall not exceed 10. -6 s; (2.7) Generate simulation data and divide the obtained simulation data into datasets to obtain the training set and test set of the physical information neural network.

4. The method for calculating multiphase flow scour of bridge piers based on a physical information neural network according to claim 3, characterized in that: Step (3) specifically includes the following steps: (3.1) Construct the main structure of the network. The main structure of the network adopts a fully connected network and a residual network. The network input is spatial coordinates X, Y, Z and time T. The nonlinear activation function is tanh. The output is all the general variables and equation kinematic parameters of the equation listed in step (1.5). The residual control term is jointly controlled by the training dataset and the physical information constructed in step (1), namely the two-phase flow pier scour calculation equation, to form a weakly supervised physical information neural network. Different nonlinear activation functions and network weight initialization schemes can be used, and the number of network layers and neurons can be optimized according to the network analysis results. (3.2) Add a Fourier transform layer at the network input to process the input terms. After performing a Fourier transform, it is then input into the main network. It includes spatial coordinates X, Y, Z and time T; , in, and These are the Fourier series coefficients and the Fourier fundamental frequency, respectively. obey Gaussian distribution; (3.3) Perform dimensionless and normalized processing on the dataset; (3.4) Calculate the partial differential operators of each variable at the network output of step (3.1) using automatic differentiation AD, and substitute them into the water phase constitutive equation, turbulent closure equation, and sediment phase constitutive equation established in steps (1.3) to (1.4) to obtain the derived variable values ​​of the equations listed in step (1.5); and calculate the initial condition and boundary condition errors in combination with the initial conditions and boundary conditions given in step (2). ; (3.5) Perform the first differential operation on the network output data. Use the derived variables of the partial equations calculated in step (3.4) and the general variables of the network output equations in step (3.1) to calculate the partial differential operator again using automatic differentiation (AD). Substitute them into the mass conservation equation and momentum conservation equation established in step (1.2) to calculate the equation constraint error of the physical information neural network. In addition, based on the initial and boundary conditions given in step (2), the errors of the initial and boundary conditions are calculated again. ; (3.6) Calculate the error of the entire neural network ; (3.7) A dynamic weighting strategy is adopted for the weight coefficients of the loss function. During the network training process, the coefficients are adaptively updated using the gradient statistics of backpropagation. The dynamic weighting strategy dynamically adjusts the weights of different parts of the loss function according to the performance of the loss function during the model training process. (3.8) Initialize the parameters of the neural network. The parameters of the neural network are randomly initialized or randomly initialized using the Xavier scheme. (3.9) The causal training strategy is adopted. The initial conditions used for training the physical information neural network are all the flow field parameters at a certain moment after the flow field calculation in step (2) has been initially stabilized, that is, the flow state initialized for the training set rather than the static state. (3.10) Define the sampling strategy during the training process. When training the network, the spatiotemporal coordinates of the input end can be fixed or dynamic. The spatiotemporal coordinates include spatial coordinates X, Y, Z and time T. If fixed coordinates are used, random sampling can be used to select points, or the coordinates of the calculation points defined in step (2.3) can be sampled. The input end can use dynamic coordinates, and the coordinates of the calculation points defined in step (2.3) can be sampled in different ways at different times.

5. The method for calculating multiphase flow scour of bridge piers based on a physical information neural network according to claim 4, characterized in that: Step (4) specifically includes the following steps: (4.1) Train the physical information neural network, backpropagate the error, update the weights and biases, until the training error converges; (4.2) Considering GPU acceleration and parallel computing, the neural network is deployed on a multi-core GPU for parallel operation. Each GPU can process a small batch of data, while different parts of the model are assigned to different GPUs. (4.3) Prediction is performed using a trained neural network model. After the neural network error converges, the final result for each point is obtained. By observing each point of the model The scour development law of bridge piers can be obtained by calculating the multiphase flow of bridge scour based on physical information neural network over time.

6. A multiphase flow calculation system for bridge pier scour based on a physical information neural network, characterized in that, include: A module for constructing computational equations is used to construct computational equations for two-phase flow pier scour based on the Euler-Euler method. A simulation data module is constructed to build the initial parameters and boundary conditions of the two-phase flow pier scour model, generate simulation data, and divide the data into test set and training set; A physical information neural network module is constructed to establish a two-phase flow-based physical information neural network based on the constructed two-phase flow pier scour calculation equations and the given initial parameters and boundary conditions of the two-phase flow pier scour model. The construction of the two-phase flow-based physical information neural network adopts a form of limited data supervision and physical equation constraints, and introduces Fourier layers and a dynamic weighting strategy to form a weakly supervised physical information neural network. Specifically, a dynamic weighting strategy is used for the weight coefficients of the loss function. During network training, the coefficients are adaptively updated using the gradient statistics of backpropagation. The dynamic weighting strategy dynamically adjusts the weights of different parts of the loss function based on the performance of the loss function during model training. The error of the neural network is defined as a linear combination of initial condition error, boundary condition error, and equation constraint error. ， in: These are the weighting coefficients of the loss function. The equation constraint error of the physical information neural network. These are the initial condition error and the boundary condition error. The initial condition error and boundary condition error are recalculated. A training neural network module is used to train a physical information neural network based on two-phase flow to obtain the prediction results of the physical information neural network for scour of multiphase flow bridge piers.

7. The multiphase flow calculation system for bridge pier scour based on a physical information neural network according to claim 6, characterized in that: In the module for constructing computational equations, both the sediment phase and the water phase are treated as two different fluids and described using the Eulerian method. The sediment phase is a non-Newtonian fluid and is described using a dense particle rheological constitutive model, while the water phase is a Newtonian fluid and is described using a turbulence model. The Euler-Euler method is used to construct the governing equations for two-phase flow calculation. The governing equations for two-phase flow calculation are the mass conservation equation and the momentum conservation equation. The governing equations for two-phase flow calculation include the mass conservation equations for the sediment phase and the momentum conservation equations for the sediment phase and the water phase. Mass conservation equations for sediment and aqueous phases: ， in and The volume fractions of the sediment and aqueous phases. and Let be the velocity of the sediment phase and the water phase in the i-th direction. For time, subscript For calculation indicators, subscript These represent the components of the physical quantities in the flow direction, span direction, and vertical direction in a rectangular coordinate system, respectively. Momentum conservation equations for sediment and water phases: , in and The densities of sediment and water are respectively. It is the acceleration due to gravity. For fluid pressure, The external force that drives the flow The fluid stress is given by the constitutive equation of the water phase. and The normal and shear stresses of the sediment phase are given by the constitutive equation of the sediment phase. The eddy viscosity is calculated using the turbulence closure equation. This refers to the drag force parameter. It is a Schmidt number; Drag force parameters The following equation is used to determine: ， in The particle diameter, The drag coefficient, The particle Reynolds number, For fluid kinematic viscosity, For depends on The resistance index, under specific operating conditions, can be taken as a constant. The vector magnitude; Schmidt number The following equation is used to determine: ， in For the falling speed, The bed friction velocity, A local minimum value can be chosen to prevent the equation from becoming singular; A constitutive equation for the aqueous phase and a turbulent closure equation were constructed, with the turbulent closure equation incorporating the cross-diffusion effects of the sediment and aqueous phases. and Both turbulent closure equations can be used. For turbulent kinetic energy, The dissipation rate of turbulent energy represents the rate at which turbulent energy is converted into internal energy per unit time. The turbulence frequency is a scale, representing the speed of the turbulent eddies; Constitutive equation of water phase: ， ， ， in The viscosity of the mixture, For the maximum volume concentration, we can take a value of 1; For turbulent kinetic energy, use the turbulence equation closed-loop calculation, subscript... For calculation indicators, These represent the components of the physical quantities in the flow direction, span direction, and vertical direction in a rectangular coordinate system, respectively. Turbulent closure equation: ， equation: ， equation: ， ， ， in For cross-diffusion terms, , , , , , , and These are all constant terms and can be set according to specific environmental conditions; that is... Same model; parameters Characterizes the degree of correlation between particle and fluid velocity fluctuations. It is the only model calibration parameter, related to sediment flux, and has a value range of 0.1 to 2. It can be used as a machine parameter for machine learning. Cross-diffusion term The following equation is used to determine: ， Where the coefficient This is a smooth term that gradually transitions between the activated and inactive regions of the cross-diffusion term. It is a step function, whose value is 1 when its independent variable is zero or positive, and 0 otherwise. For constant terms; Turbulent closure equation: ， The equation remains unchanged; the above formula is used for substitution. In the equation for , equation: , in , , , , For constant terms; Constructing the constitutive equations for the sediment phase in two-phase flow: Sediment phase constitutive equations: ， ， ， ， in For sediment phase normal stress, This refers to the shear or impact component of particle pressure. This represents the permanent contact component of particle pressure. The ratio of the root-mean-square velocity fluctuations of sediment to fluid is a constant, ranging from 1 to 3; the constant coefficients of the equation. 0.57 is acceptable. A value of 0.635 is acceptable, depending on the calibration of bedload and suspended mass. These are rheological empirical parameters, which can be taken as 0.05, 3, and 5 respectively; The frictional viscosity of mud and sand particles. 2 / 3 is acceptable; for The norm of a matrix; Friction viscosity of mud and sand particles The following equation is used to determine: ， in The maximum solid-phase viscosity, A local minimum value can be chosen to prevent singularities in the equation. The inertial number is a dimensionless number. The static friction coefficient is For empirical dynamic coefficients, These are rheological empirical constants; Determine the types of parameters and variables in the established two-phase flow pier scour calculation equations. The types of parameters and variables include constant parameters, general variables, and derived variables of the equations. The constant parameters necessary for the equation calculations are determined through experiments or model inversion. These constant parameters include the density of sediment. The density of water External forces driving the flow Gravitational acceleration Particle diameter Obstacle Index kinematic viscosity of fluids Falling speed Bed friction velocity To prevent singular additional terms in equations and Constant coefficients in the constitutive equation of sediment phase , and Rheological empirical parameters , and Maximum volume concentration The ratio of the root mean square velocity fluctuations of sediment to those of fluid Maximum solid viscosity static friction coefficient Empirical dynamic coefficient Rheological empirical constants Model calibration parameters and the constant coefficients in the turbulence closure equation , , , , , , , , , , , , and The constant parameters of the equation include a freely definable kinematic parameter B; the required constant parameters of the equation can be obtained by regression prediction using conventional DNN neural networks based on experimental data sets or simulation results obtained by SPH particle flow simulation, lattice Boltzmann simulation, and local DNS simulation. The general variables of the equation, i.e., the independent variables, include the volume fraction of sediment phase. The velocity of sediment phase The velocity of the water phase Fluid pressure Turbulent kinetic energy turbulence frequency Turbulent energy dissipation rate , There are eleven in total; The derived variables of the equation include sediment phase shear stress. Fluid stress Schmidt number Eddy viscosity coefficient Particle Reynolds number drag coefficient Dragging force parameters Intermediate quantities used in the calculation of the constitutive equation of the water phase , and Viscosity of mixture The correlation between particle and fluid velocity fluctuations Intermediate quantities used in the calculation of turbulent closure equations , , and Smoothing terms Cross-diffusion term Permanent contact component of particle pressure Intermediate quantities used in the calculation of the constitutive equation of sediment phase , , and Friction viscosity of mud and sand particles .

8. The multiphase flow calculation system for bridge pier scour based on a physical information neural network according to claim 7, characterized in that: The simulation data construction module constructs a two-phase flow pier scour model and defines the initial state of the two-phase flow pier scour model. The two-phase flow pier scour model consists of upper clear water, lower sediment and pier. According to the two-phase flow pier scour calculation equation, the fluid region of the model is divided into two parts: the initial water area and the initial sediment area. The initial water area is the upper clear water with a water phase volume fraction of 1, and the initial sediment area is the riverbed sediment layer with a water phase volume fraction of 0. Define the dimensions of the two-phase flow pier scour model. Based on the pier dimensions, define a certain length of boundary in the length, width, and height directions of the model. The pier cross-section is circular. The size of the computational domain of the model can be defined according to the cross-sectional dimensions of the pier. In the length direction, it can be 10 to 15 times the pier diameter; in the width direction, it can be 8 to 10 times the pier diameter; and in the height direction, it can be 5 to 7 times the pier diameter. Among them, the height of the water area is 3 to 4 times the pier diameter, and the height of the sediment domain is 2 to 3 times the pier diameter. The spatial distribution of calculation points for the two-phase flow pier scour model is defined. The calculation points of the model are established using an unstructured three-dimensional spatial mesh, and an absolute spatial rectangular coordinate system is defined. The model is divided using an unstructured three-dimensional spatial mesh. The water area and sediment domain near the pier are divided into a relatively dense mesh, and the mesh transitions from dense to sparse from the pier to the model boundary. All corner points of the mesh are retained as calculation points of the model, and all edge lines of the mesh are removed; the same mesh drawing method is used between the upper clear water and the lower mud and sand vertical planes, and the mesh is uniformly densified along the height direction at the interface; Define boundary conditions for the two-phase flow pier scour model, defining corresponding boundary conditions at the inlet, outlet, top boundary, pier wall, and both sides of the model: at the inlet, for , , , and Apply a vertical profile boundary obtained from experiments, measurements, or finite element simulations; at the exit, specify a zero gradient condition for all variables; at the top boundary, for... , and Apply the Newman boundary condition, i.e., give the pressure gradient; at the pier wall, for and A no-slip boundary, i.e., a velocity of zero, is adopted; cyclic boundary conditions are applied to both sides of the boundary. Initialize the flow field parameters by assigning initial values ​​to all the listed general variables at all calculation points in the two-phase flow pier scour model according to the definition, and initialize the flow field. The initial values ​​of all general variables in the model can also be provided by the results of a pre-trained physical information neural network; Define the time discretization rules for model computation points, establishing a fixed time interval or an adaptively adjustable time step based on model training results and the degree of disorder in flow development, with a single step size not exceeding 10. -6 s; Simulation data is generated, and the obtained simulation data is divided into datasets to obtain the training set and test set of the physical information neural network.

9. A multiphase flow calculation system for bridge pier scour based on a physical information neural network according to claim 8, characterized in that: The physical information neural network module constructs the main network structure, which adopts a fully connected network and a residual network. The network input consists of spatial coordinates X, Y, Z and time T, with tanh as the nonlinear activation function. The output consists of all general variables and equation maneuvering parameters of the listed equations. The residual control term is jointly controlled by the training dataset and the constructed physical information, namely the two-phase flow pier scour calculation equation, forming a weakly supervised physical information neural network. Different nonlinear activation functions and network weight initialization schemes can be used, and the number of network layers and neurons can be optimized based on the network analysis results. Add a Fourier transform layer at the network input to process the input items. After performing a Fourier transform, it is then input into the main network. It includes spatial coordinates X, Y, Z and time T; , in, and These are the Fourier series coefficients and the Fourier fundamental frequency, respectively. obey Gaussian distribution; Perform dimensionless and normalized transformation on the dataset; The partial differential operators of each variable at the network output are calculated using automatic differential (AD) calculations, and then substituted into the established constitutive equations for the water phase, turbulent closure, and sediment phase to obtain the derived variable values. Furthermore, the errors of the initial and boundary conditions are calculated in conjunction with the given initial and boundary conditions. ; The network output data is subjected to the first differential operation. The derived variables of the calculated partial equations and the general variables of the network output equations are then used again to calculate the partial differential operator using automatic differentiation (AD). Substituting these into the established mass conservation equation and momentum conservation equation, the equation constraint error of the physical information neural network is obtained. In addition, based on the given initial and boundary conditions, the errors of the initial and boundary conditions are calculated again. ; Calculate the error of the entire neural network , A dynamic weighting strategy is adopted for the weight coefficients of the loss function. During network training, the coefficients are adaptively updated using the gradient statistics of backpropagation. The dynamic weighting strategy dynamically adjusts the weights of different parts of the loss function based on the performance of the loss function during model training. The parameters of the neural network are initialized using either random initialization or the Xavier scheme. The causal training strategy is adopted. The initial conditions used for training the physical information neural network are all the flow field parameters at a certain moment after the flow field calculation has been initially stabilized, that is, the flow state initialized for the training set rather than static. Define the sampling strategy during the training process. When training the network, the spatiotemporal coordinates at the input end can be either fixed coordinates or dynamic coordinates. The spatiotemporal coordinates include spatial coordinates X, Y, Z and time T. If fixed coordinates are used, random sampling can be used to select points, or the coordinates of the defined calculation points can be sampled. If dynamic coordinates are used at the input end, the coordinates of the defined calculation points can be sampled in different ways at different times.

10. A multiphase flow calculation system for bridge pier scour based on a physical information neural network according to claim 9, characterized in that: The training neural network module trains a physical information neural network, backpropagates the error, updates the weights and biases, until the training error converges. Considering GPU acceleration and parallel computing, the neural network can be deployed on multi-core GPUs for parallel operation, allowing each GPU to process a small batch of data, while different parts of the model can be assigned to different GPUs. Prediction is performed using a trained neural network model. After the neural network error converges, the final result for each point is obtained. By observing each point of the model The scour development law of bridge piers can be obtained by calculating the multiphase flow of bridge scour based on physical information neural network over time.

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