Pier scouring multiphase flow calculation method and system based on physical information neural network

Abstract

The invention discloses a bridge pier scouring multiphase flow calculation method and system based on a physical information neural network. The method comprises the following steps: constructing a two-phase flow bridge pier scouring calculation equation based on an Euler-Euler method; constructing initial parameters and boundary conditions of the two-phase flow pier scouring model, generating simulation data, and dividing the data into a test set and a training set; establishing a physical information neural network based on the two-phase flow according to the constructed two-phase flow-based pier scouring calculation equation and the given initial parameters and boundary conditions of the two-phase flow-based pier scouring model; and training the physical information neural network based on the two-phase flow to obtain a prediction result of the multiphase flow pier scouring physical information neural network. According to the method, the limitation of a traditional prediction method is overcome, and the calculation efficiency can be remarkably improved while the precision is ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridge engineering safety and hydraulics, and in particular relates to a method and system for calculating multiphase flow of bridge pier scour based on physical information neural network. Background Art

[0002] In bridge engineering, local scour of bridge piers is one of the important factors affecting bridge safety. Three-dimensional solid-liquid multiphase flow is the basic physical phenomenon in the process of local scour of bridge piers, and its prediction and analysis are crucial for bridge design, maintenance and safety assessment. Traditional pier scour prediction methods are mainly based on empirical formulas or simplified physical models. Although these methods can provide fast predictions in some cases, they usually 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 the scouring process of bridge piers through numerical simulation. However, high-precision CFD simulation usually requires a lot of computing resources and time, and is very sensitive to initial values ​​and boundary conditions, which is not very practical in actual engineering applications. In addition, traditional numerical simulation methods often require detailed terrain, flow velocity and other data as input, which are difficult to obtain in practice, limiting their scope of application.

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

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

[0006] Technical solution: To achieve the above purpose, the present invention discloses a method for calculating multiphase flow of bridge pier scour based on physical information neural network, which includes the following steps:

[0007] (1) Construct the two-phase flow pier scour calculation equation 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 a test set and a training set;

[0009] (3) According to the two-phase flow bridge pier scour calculation equation constructed in step (1) and the initial parameters and boundary conditions of the two-phase flow bridge 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 in the form of small data supervision and physical equation constraints, and Fourier layer and dynamic weight strategy are introduced 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 multiphase flow pier scour.

[0011] Wherein, step (1) specifically comprises the following steps:

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

[0013] (1.2) Constructing the Euler-Euler method two-phase flow calculation control equations, which are the mass conservation equation and the momentum conservation equation. The two-phase flow calculation control equations include the mass conservation equation of the sediment phase and the water phase, and the momentum conservation equation of the sediment phase and the water phase;

[0014] The mass conservation equations for the sediment phase and the water phase are:

[0015]

[0016]

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

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

[0019]

[0020]

[0021] where ρ s and ρ f are the densities of sediment and water, g i is the acceleration due to gravity, p is the fluid pressure, f i The external force driving the flow is is the fluid stress, given by the water phase constitutive equation, and is the normal stress and shear stress of the sediment phase, which is given by the constitutive equation of the sediment phase; is the eddy viscosity coefficient, which is calculated using the turbulence closed equation, K is the drag force parameter, S c is the Schmidt number;

[0022] The drag force parameter K is determined using 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 is the resistance coefficient, Re p is the particle Reynolds number, v f is the fluid kinematic viscosity, h Exp Depends on Re p The obstruction index can be taken as a constant under certain working conditions, ||u f -u s || is the vector modulus;

[0027] Schmidt number S c Determined using the following equation:

[0028]

[0029] where w fall0 is the falling speed, u * Bed friction velocity, u small A certain minimum value can be taken to prevent the equation from becoming singular;

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

[0031] Constitutive equation of water phase:

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

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

[0039] k-ω turbulence closed equation:

[0040]

[0041] k equation:

[0042]

[0043] equation:

[0044]

[0045]

[0046]

[0047]

[0048]

[0049] CD kω is the cross diffusion term, C μ , C lim , σ k , C 1ω , C 2ω0 , C 3ω , C 4ω and σ ω are all constant terms and can be set according to the specific environment conditions; that is, the k-ε model is the same as the parameter t mf Characterizes the degree of correlation between particles and fluid velocity fluctuations. B is the only model calibration parameter, which is related to sediment flux and has a value range of 0.1 to 2. It can be used as a maneuvering parameter for machine learning.

[0050] Cross diffusion term CD kω Determined using the following equation:

[0051]

[0052]

[0053]

[0054] The coefficient A is a smoothing term that gradually transitions between the activated and inactivated areas of the cross-diffusion term. is a step function. When the independent variable is zero or positive, the function value is 1; otherwise, it is 0. d0 is a constant term;

[0055] k-ε turbulence closed equation:

[0056]

[0057] ε=C μ kω

[0058] The form of the k equation remains unchanged. Use the above formula to replace ω in the k equation with ε, and the ε equation is:

[0059]

[0060] where σ ε , C 1ε , C 2ε , C 3ε , C 4ε is a constant term;

[0061] (1.4) Construct the two-phase flow sediment phase constitutive equation:

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] in is the particle pressure, p s is the shear or collision component of the particle pressure, p ff is the permanent contact component of the particle pressure, C t is the ratio of the root mean square velocity fluctuation of sediment to fluid, which is a constant between 1 and 3; the constant coefficient of the equation It can be 0.57, φ max2 It can be taken as 0.635, which is related to the calibration of bed load and suspended load; Fr, η0, η1 are rheological empirical parameters, which can be taken as 0.05, 3, 5 respectively; is the friction viscosity of the sediment particles, B φ 2 / 3 is acceptable; ∥S s ∥ Norm of a matrix;

[0070] Friction viscosity of sand particles Determined using the following equation:

[0071]

[0072]

[0073]

[0074] where v max is the maximum solid phase viscosity, D small A certain minimum value can be taken to prevent the equation from being singular, I is the dimensionless inertia number, 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 parameters and variable types of the established two-phase flow pier scour calculation equation, which include equation constant parameters, equation general variables, and equation derived variables;

[0076] The constant parameters required for the equation calculation are determined by experiments or model inversion. The constant parameters of the equation include the density of the sediment ρ s , water density ρ f , the external force driving the flow f i , gravitational acceleration g i , particle diameter d, barrier index h Exp 、Fluid kinematic viscosity v f , falling speed w fall0 , bed friction velocity y*, additional term u to prevent singularity in the equation small and D small , constant coefficients in the sediment phase constitutive equation φ max2 With B φ , rheological empirical parameters η0, η1 and Fr, maximum volume concentration φ max , the ratio of the root mean square velocity fluctuation of sediment to fluid C t , maximum solid phase viscosity v max , static friction coefficient μ s , empirical dynamic coefficient μ2, rheological empirical constant I0, model calibration parameter B and constant coefficient C in the turbulent closed 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 , there is a freely definable maneuvering parameter B in the equation constant parameters; some constant parameters required by the equation can be obtained by regression prediction using conventional DNN neural network based on the simulation results obtained by experimental measured data sets or SPH particle flow simulation, lattice Boltzmann simulation, local DNS simulation, etc.;

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

[0078] The derived variables of the equation include the sediment phase shear stress Fluid stress Schmidt number S c , eddy viscosity coefficient Particle Reynolds number Re p , drag coefficient C d , drag force parameter K, intermediate quantity used in calculation of water phase constitutive equation and Viscosity of the mixture v mix , the correlation between particles and fluid velocity fluctuations t mf , intermediate quantity C used in calculation of turbulent closed equation 2ω , χ ω ,Ω ij With σ d , smoothing term A, cross diffusion term CD kω , permanent contact component of particle pressure p ff , intermediate quantity used in calculation of sediment phase constitutive equation and μ(I), friction viscosity of sediment particles

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

[0080] (2.1) constructing a two-phase flow bridge pier scour model and defining the initial condition of the two-phase flow bridge pier scour model. The two-phase flow bridge pier scour model consists of upper clear water, lower sediment and bridge piers. According to the two-phase flow bridge pier scour calculation equation in step (1), the fluid area 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 size of the two-phase flow pier scour model. According to the size of the pier, the model defines a certain length of boundary in the three directions of length, width and height. The cross-section of the pier adopted is circular. The size of the model calculation domain can be defined according to the size of the pier cross section. 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. The water area height is 3 to 4 times the pier diameter, and the sediment domain height is 2 to 3 times the pier diameter.

[0082] (2.3) Define the spatial distribution of the calculation points of the two-phase flow bridge pier scour model, use unstructured three-dimensional spatial grids to establish the calculation points of the model, and define the absolute spatial rectangular coordinate system; use unstructured three-dimensional spatial grids to divide the model, use relatively dense grids for the water area and sediment domain near the bridge piers, and transition from dense to sparse grids from the bridge piers to the model boundary; retain all corner points of the grid as the calculation points of the model, and remove all edges of the grid; use the same grid drawing method between different vertical planes of the upper clear water and the lower sediment, and evenly encrypt the mesh along the height direction at the interface;

[0083] (2.4) Define the boundary conditions of 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, k and ω impose vertical profile boundaries obtained from experiments or measurements or finite element simulations; at the outlet, zero gradient conditions are specified for all variables; the top boundary, k and ω apply Newman boundary conditions, that is, a given pressure gradient; at the pier wall, and A no-slip boundary is used, i.e. the velocity is zero; cyclic boundary conditions are applied on both sides of the boundary;

[0084] (2.5) Initialize the flow field parameters. According to the definitions in steps (2.1) and (2.4), assign all the initial values ​​of the general variables listed in step (1.5) to all the calculation points in the two-phase flow pier scour model to initialize the flow field. The initial values ​​of all the 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 of the model calculation points, fix the time interval or establish an adaptive and adjustable time step according to the model training results and the degree of chaos of the flow development, and the single step size shall not exceed 10 -6 s;

[0086] (2.7) Generate simulation data and divide the obtained simulation data into data sets to obtain training sets and test sets 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 the spatial coordinates X, Y, Z and time T. The nonlinear activation function is tanh. The output is all the general variables and equation maneuvering parameters of the equation listed in step (1.5). The residual control term is jointly controlled by the training data set 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 item v and then input it into the main network. v contains spatial coordinates X, Y, Z and time T;

[0090]

[0091] Among them, a and b are the Fourier series coefficient and the Fourier fundamental frequency respectively, and b obeys the Gaussian distribution of N(0,1);

[0092] (3.3) Non-dimensionalize and normalize the data set;

[0093] (3.4) Use automatic differentiation AD to calculate the partial differential operator of each variable at the output end of the network in step (3.1), and substitute it into the water phase constitutive equation, turbulent closed equation, and sediment phase constitutive equation established in steps (1.3) to (1.4) to calculate the derived variable values ​​of the equation listed in step (1.5); and combine the initial conditions and boundary conditions given in step (2) to calculate the initial and boundary errors loss IC 、loss BC ;

[0094] (3.5) Perform the first differential operation on the network output data, use the automatic differentiation AD to calculate the partial differential operator again, substitute the mass conservation equation and momentum conservation equation established in step (1.2) into the partial equation derived variables calculated in step (3.4) and the general variables of the equation output by the network in step (3.1), and calculate to obtain the equation constraint error loss of the physical information neural network PDE , and combine the initial and boundary conditions given in step (2) to calculate the initial and boundary error loss again IC′ 、loss BC′ ;

[0095] (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, the boundary condition error, and the 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] Among them: α, β, γ, α′, β′, γ′ are the weight coefficients of the loss function;

[0099] (3.7) A dynamic weight strategy is used for the weight coefficients of the loss function. The coefficients are adaptively updated using the back-propagated gradient statistics during network training. The dynamic weight strategy dynamically adjusts the weights of different parts of the loss function according to the performance of the loss function during model training.

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

[0101] (3.9) A causal training strategy is adopted. The initial conditions used in the physical information neural network training are all the flow field parameters at a certain moment after the flow field calculation in step (2) is initially stabilized, that is, the flow state initialized for the training set rather than the static state; (3.10) The sampling strategy in the training process is defined. When training the network, the space-time coordinates of the input end can be fixed coordinates or dynamic coordinates. The space-time coordinates include the 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] Further, step (4) specifically includes the following steps:

[0103] (4.1) Train the physical information neural network, back propagate the error, and 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 multi-core GPUs for parallel computing. A small batch of data can be processed on each GPU, and different parts of the model can be assigned to different GPUs.

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

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

[0107] Construct a calculation equation module, which is used to construct a two-phase flow bridge pier scour calculation equation based on the Euler-Euler method;

[0108] Construct a simulation data module to construct 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;

[0109] Construct a physical information neural network module, which is used to establish a physical information neural network based on two-phase flow according to the constructed two-phase flow bridge pier scour calculation equation, as well as the given two-phase flow bridge pier scour model initial parameters and boundary conditions; construct a physical information neural network based on two-phase flow, adopt the form of small data supervision and physical equation constraints, and introduce Fourier layer and dynamic weight strategy to form a weakly supervised physical information neural network;

[0110] 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 of multiphase flow pier scour.

[0111] In the calculation equation module, the sediment phase and the water phase are treated as two fluids and described by the Euler method. The sediment phase is a non-Newtonian fluid and the dense particle rheological constitutive model is applied. The water phase is a Newtonian fluid and the turbulence model is applied.

[0112] Construct the Euler-Euler method two-phase flow calculation control equation, which is the mass conservation equation and momentum conservation equation. The two-phase flow calculation control equation includes the mass conservation equation of the sediment phase and the water phase, and the momentum conservation equation of the sediment phase and the water phase;

[0113] The mass conservation equations for the sediment phase and the water phase are:

[0114]

[0115]

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

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

[0118]

[0119]

[0120] where ρ s and ρ f are the densities of sediment and water, g i is the acceleration due to gravity, p is the fluid pressure, f i The external force driving the flow is is the fluid stress, given by the water phase constitutive equation, and is the normal stress and shear stress of the sediment phase, which is given by the constitutive equation of the sediment phase; is the eddy viscosity coefficient, which is calculated using the turbulence closed equation, K is the drag force parameter, S c is the Schmidt number;

[0121] The drag force parameter K is determined using 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 is the resistance coefficient, Re p is the particle Reynolds number, v f is the fluid kinematic viscosity, h Exp Depends on Re p The obstruction index can be taken as a constant under certain working conditions, ||u f -u s || is the vector modulus;

[0126] Schmidt number S c Determined using the following equation:

[0127]

[0128] where w fall0 is the falling speed, u *Bed friction velocity, u small A certain minimum value can be taken to prevent the equation from becoming singular;

[0129] Construct the water phase constitutive equation and turbulence closed equation, where the turbulence closed equation includes the cross-diffusion effect of the sediment phase and the water phase. Both k-ω and k-ε turbulence closed equations can be used, k is the turbulent kinetic energy, ε is the dissipation rate of turbulent energy, representing the rate of turbulent energy conversion into internal energy per unit time; ω is the turbulence frequency of a specific scale, representing the rate of turbulent eddies;

[0130] Constitutive equation of water phase:

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

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

[0138] k-ω turbulence closed equation:

[0139]

[0140] k equation:

[0141]

[0142] equation:

[0143]

[0144]

[0145]

[0146]

[0147]

[0148] CD kωis the cross diffusion term, C μ , C lim , σ k , C 1ω , C 2ω0 , C 3ω , C 4ω and σ ω are all constant terms and can be set according to the specific environment conditions; that is, the k-ε model is the same as the parameter t mf Characterizes the degree of correlation between particles and fluid velocity fluctuations. B is the only model calibration parameter, which is related to sediment flux and has a value range of 0.1 to 2. It can be used as a maneuvering parameter for machine learning.

[0149] Cross diffusion term CD kω Determined using the following equation:

[0150]

[0151]

[0152]

[0153] The coefficient A is a smoothing term that gradually transitions between the activated and inactivated areas of the cross-diffusion term. is a step function. When the independent variable is zero or positive, the function value is 1; otherwise, it is 0. d0 is a constant term;

[0154] k-ε turbulence closed equation:

[0155]

[0156] ε=C μ kω

[0157] The form of the k equation remains unchanged. Use the above formula to replace ω in the k equation with ε, and the ε equation is:

[0158]

[0159] where σ ε , C 1ε , C 2ε , C 3ε , C 4ε is a constant term;

[0160] Construct the two-phase flow sediment phase constitutive equation, sediment phase constitutive equation:

[0161]

[0162]

[0163]

[0164]

[0165]

[0166]

[0167]

[0168] in is the particle pressure, p s is the shear or collision component of the particle pressure, p ff is the permanent contact component of the particle pressure, C t is the ratio of the root mean square velocity fluctuation of sediment to fluid, which is a constant between 1 and 3; the constant coefficient of the equation It can be 0.57, φ max2 It can be taken as 0.635, which is related to the calibration of bed load and suspended load; Fr, η0, η1 are rheological empirical parameters, which can be taken as 0.05, 3, 5 respectively; is the friction viscosity of the sediment particles, B φ 2 / 3 is acceptable; ||S s || for Norm of a matrix;

[0169] Friction viscosity of sand particles Determined using the following equation:

[0170]

[0171]

[0172]

[0173] where v max is the maximum solid phase viscosity, D small A certain minimum value can be taken to prevent the equation from being singular, I is the dimensionless inertia number, μ s is the static friction coefficient, μ2 is the empirical dynamic coefficient, and I0 is the rheological empirical constant;

[0174] Determine the parameters and variable types of the established two-phase flow bridge pier scour calculation equation, the parameter and variable types include equation constant parameters, equation general variables and equation derived variables;

[0175] The constant parameters required for the equation calculation are determined by experiments or model inversion. The constant parameters of the equation include the density of the sediment ρ s , water density ρ f , the external force driving the flow f i , gravitational acceleration gi , particle diameter d, barrier index h Exp 、Fluid kinematic viscosity v f , falling speed W fall0 , bed friction velocity u * , additional term u to prevent the equation from being singular small and D small , constant coefficients in the sediment phase constitutive equation φ max2 With B φ , rheological empirical parameters η0, η1 and Fr, maximum volume concentration φ max , the ratio of the root mean square velocity fluctuation of sediment to fluid C t , maximum solid phase viscosity v max , static friction coefficient μ s , empirical dynamic coefficient μ2, rheological empirical constant I0, model calibration parameter B and constant coefficient C in the turbulent closed 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 , there is a freely definable maneuvering parameter B in the equation constant parameters; some constant parameters required by the equation can be obtained by regression prediction using conventional DNN neural network based on the simulation results obtained by experimental measured data sets or SPH particle flow simulation, lattice Boltzmann simulation, local DNS simulation, etc.;

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

[0177] The derived variables of the equation include the sediment phase shear stress Fluid stress Schmidt number S c , eddy viscosity coefficient Particle Reynolds number Re p , drag coefficient C d , drag force parameter K, intermediate quantity used in calculation of water phase constitutive equation and Viscosity of the mixture v mix, the correlation between particles and fluid velocity fluctuations t mf , intermediate quantity C used in calculation of turbulent closed equation 2ω , χ ω ,Ω ij With σ d , smoothing term A, cross diffusion term CD kω , permanent contact component of particle pressure p ff , intermediate quantity used in calculation of sediment phase constitutive equation and μ(I), friction viscosity of sediment particles

[0178] Preferably, a two-phase flow bridge pier scour model is constructed in the simulation data module, and the initial condition of the two-phase flow bridge pier scour model is defined. The two-phase flow bridge pier scour model consists of upper clear water, lower sediment and bridge piers. According to the two-phase flow bridge pier scour calculation equation, the fluid area of ​​the model is divided into two parts, an initial water area and an 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 size of the two-phase flow pier scour model. According to the size of the pier, the model defines a certain length of boundary in the three directions of length, width and height. The adopted pier cross section is circular. The size of the model calculation domain can be defined according to the size of the pier cross section. 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. The water area height is 3 to 4 times the pier diameter, and the sediment domain height is 2 to 3 times the pier diameter.

[0180] Define the spatial distribution of the calculation points of the two-phase flow bridge pier scour model, use unstructured three-dimensional space grids to establish the calculation points of the model, and define the absolute spatial rectangular coordinate system; use unstructured three-dimensional space grids to divide the model, use relatively dense grids for the water area and sediment domain near the bridge piers, and the grid transitions from dense to sparse from the bridge piers to the model boundary; retain all corner points of the grid as the calculation points of the model, and remove all edges of the grid; use the same meshing method between different vertical planes of the upper clear water and the lower sediment, and evenly encrypt the interface along the height direction;

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

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

[0183] Define the time discrete rule of the model calculation point, fix the time interval or establish an adaptive and adjustable time step according to the model training results and the degree of chaos of flow development, and the single step size shall not exceed 10 -6 s;

[0184] Generate simulation data, and divide the obtained simulation data into data sets to obtain training sets and test sets of the physical information neural network.

[0185] Furthermore, the main structure of the network is constructed in the physical information neural network module. The main structure of the network adopts a fully connected network and a residual network. The network input is the spatial coordinates X, Y, Z and time T, the nonlinear activation function is tanh, and the output is all the general variables and equation maneuvering parameters of the listed equations; the residual control item is jointly controlled by the training data set and the constructed physical information, 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;

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

[0187]

[0188] Among them, a and b are the Fourier series coefficient and the Fourier fundamental frequency respectively, and b obeys the Gaussian distribution of N(0,1);

[0189] Non-dimensionalize and normalize the data set;

[0190] The variables at the output of the network are calculated using the automatic differential AD partial differential operator, and are substituted into the established water phase constitutive equation, turbulent closed equation, and sediment phase constitutive equation to obtain the values ​​of the variables derived from the listed equations; and the initial and boundary errors loss are calculated in combination with the given initial and boundary conditions. IC 、loss BC ;

[0191] Perform the first differential operation on the network output data, use the automatic differentiation AD to calculate the partial differential operator again, substitute the established mass conservation equation and momentum conservation equation for calculation, and obtain the equation constraint error liss of the physical information neural network. PDE , and combine the given initial and boundary conditions to calculate the initial and boundary errors loss 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, the boundary condition error, and the 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] Among them: α, β, γ, α′, β′, γ′ are the weight coefficients of the loss function;

[0196] A dynamic weight strategy is used for the weight coefficients of the loss function. The coefficients are adaptively updated using the gradient statistics of back propagation during network training. The dynamic weight strategy dynamically adjusts the weights of different parts of the loss function according to the performance of the loss function during model training.

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

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

[0199] Furthermore, in the training neural network module, the physical information neural network is trained, the error is back-propagated, and the weights and biases are updated until the training error converges;

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

[0201] The trained neural network model is used for prediction. After the neural network error converges, the φ, By observing the changes of φ at each point in the model over time, the development law of pier scour calculated by the bridge scour multiphase flow based on the physical information neural network can be obtained.

[0202] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: the present invention improves prediction accuracy, reduces data requirements, improves computing efficiency, and enhances model generalization ability; the present invention combines physical laws and deep learning methods to more accurately simulate and predict the scouring process around bridge piers, thereby improving prediction accuracy; the present invention reduces dependence on a large amount of experimental data through a training process guided by physical information, reduces the difficulty and cost of data acquisition, and compared with traditional numerical simulation methods, the present invention can significantly improve computing efficiency while ensuring accuracy, and is suitable for real-time or near real-time application scenarios; the present invention enhances the model's prediction ability for unseen data and improves the model's generalization ability by integrating physical laws; in the present invention, for bridge pier scouring, the multiphase flow model has significant advantages over the scouring model of single-phase flow combined with dynamic grid technology in simulating complex fluid dynamics problems, such as bridge pier scouring; multiphase flow can more accurately capture the interaction between fluid and solid particles, and provide a more realistic scouring process simulation; the present invention can greatly reduce computing costs and improve computing efficiency after using neural networks, give full play to the advantages of multiphase flow theory, and make the best use of its strengths and avoid its weaknesses, so that bridge pier scouring is easier to predict. BRIEF DESCRIPTION OF THE DRAWINGS

[0203] Figure 1 is a flow chart of the present invention;

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

[0205] Figure 3 It is a structural schematic diagram of the two-phase flow pier scour model in the present invention. DETAILED DESCRIPTION

[0206] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

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

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

[0209] The step (1) specifically comprises the following steps:

[0210] (1.1) The sediment phase and the water phase are treated as two fluids and described by the Euler method. The sediment phase is a non-Newtonian fluid and the dense particle rheological constitutive model is applied. The water phase is a Newtonian fluid and the turbulence model is applied. In computational fluid dynamics, the Euler method means that the grid is fixed, the fluid flows in the grid, and the flow parameters of the fluid at each grid point are calculated.

[0211] (1.2) Constructing the Euler-Euler method two-phase flow calculation control equations, which are the mass conservation equation and the momentum conservation equation. The two-phase flow calculation control equations include the mass conservation equation of the sediment phase and the water phase, and the momentum conservation equation of the sediment phase and the water phase. The momentum conservation equation of the sediment phase and the water phase can adopt different forms of multiphase flow equations, which can change the interphase force, interphase transfer mechanism and interphase resistance expression of the multiphase flow;

[0212] The mass conservation equations for the sediment phase and the water phase are:

[0213]

[0214]

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

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

[0217]

[0218]

[0219] where ρ s and ρ f are the densities of sediment and water, g i is the acceleration due to gravity, p is the fluid pressure, f i The external force driving the flow is is the fluid stress, given by the water phase constitutive equation, and is the normal stress and shear stress of the sediment phase, which is given by the constitutive equation of the sediment phase; is the eddy viscosity coefficient, which is calculated using the turbulence closed equation, K is the drag force parameter, S c is the Schmidt number;

[0220] The drag force parameter K is determined using 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 is the resistance coefficient, Re p is the particle Reynolds number, v f is the fluid kinematic viscosity, h Exp Depends on Re p The obstruction index can be taken as a constant under certain working conditions, ||u f -u s || is the vector modulus;

[0225] Schmidt number S c Determined using the following equation:

[0226]

[0227] where w fall0 is the falling speed, u * Bed friction velocity, u small A certain minimum value can be taken to prevent the equation from becoming singular;

[0228] (1.3) Construct the water phase constitutive equation and turbulence closed equation, where the turbulence closed equation includes the cross-diffusion effect of the sediment phase and the water phase. Both k-ω and k-ε turbulence closed equations can be used, k is the turbulence kinetic energy, ε is the dissipation rate of turbulence energy, representing the rate of turbulent energy conversion into internal energy per unit time; ω is the turbulence frequency of a specific scale, representing the rate of turbulent eddies; the multiphase flow turbulence closed equation can use different forms of closed equations to construct supplementary equations, which can be supplemented by one equation, zero equation, and three equations. It can also be processed by the SGS stress model of large eddy simulation and the supplementary equations of the detached eddy simulation related model;

[0229] Constitutive equation of water phase:

[0230]

[0231]

[0232]

[0233]

[0234]

[0235]

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

[0237] k-ω turbulence closed equation:

[0238]

[0239] k equation:

[0240]

[0241] equation:

[0242]

[0243]

[0244]

[0245]

[0246]

[0247] CD kω is the cross diffusion term, C μ , C lim , σ k , C 1ω , C 2ω0 , C 3ω , C 4ω and σ ω are all constant terms and can be set according to the specific environment conditions; that is, the k-ε model is the same as the parameter t mf Characterizes the degree of correlation between particles and fluid velocity fluctuations. B is the only model calibration parameter, which is related to the sediment flux and can be set manually according to the model results. The value range is 0.1 to 2. It can also be used as a maneuverable parameter for machine learning.

[0248] Cross diffusion term CD kω Determined using the following equation:

[0249]

[0250]

[0251]

[0252] The coefficient A is a smoothing term that gradually transitions between the activated and inactivated areas of the cross-diffusion term. is a step function. When the independent variable is zero or positive, the function value is 1; otherwise, it is 0. d0 is a constant term;

[0253] k-ε turbulence closed equation:

[0254]

[0255] ε=C μ kω

[0256] The form of the k equation remains unchanged. Use the above formula to replace ω in the k equation with ε, and the ε equation is:

[0257]

[0258] where σ ε , C 1ε , C 2ε , C 3ε , C 4ε is a constant term;

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

[0260] Sediment phase constitutive equation:

[0261]

[0262]

[0263]

[0264]

[0265]

[0266]

[0267]

[0268] in is the particle pressure, p s is the shear or collision component of the particle pressure, p ff is the permanent contact component of the particle pressure, C t is the ratio of the root mean square velocity fluctuation of sediment to fluid, which is a constant between 1 and 3 and can be 1; the constant coefficient of the equation It can be 0.57, φ max2 It can be taken as 0.635, which is related to the calibration of bed load and suspended load; Fr, η0, η1 are rheological empirical parameters, which can be taken as 0.05, 3, 5 respectively; is the friction viscosity of the sediment particles, B φ 2 / 3 is acceptable; ∥S s ∥ Norm of a matrix;

[0269] Friction viscosity of sand particles Determined using the following equation:

[0270]

[0271]

[0272]

[0273] where v max is the maximum solid phase viscosity, D small A certain minimum value can be taken to prevent the equation from being singular, I is the dimensionless inertia number, 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 parameters and variable types of the established two-phase flow pier scour calculation equation, which include equation constant parameters, equation general variables, and equation derived variables;

[0275] The constant parameters required for the equation calculation are determined by experiments or model inversion. The constant parameters of the equation include the density of the sediment ρ s , water density ρ f , the external force driving the flow f i , gravitational acceleration g i , particle diameter d, barrier index h Exp 、Fluid kinematic viscosity v f , falling speed W fall0 , bed friction velocity u * , additional term u to prevent the equation from being singular small and D small , constant coefficients in the sediment phase constitutive equation φ max2 With B φ , rheological empirical parameters η0, η1 and Fr, maximum volume concentration φ max , the ratio of the root mean square velocity fluctuation of sediment to fluid C t , maximum solid phase viscosity v max , static friction coefficient μ s , empirical dynamic coefficient μ2, rheological empirical constant I0, model calibration parameter B and constant coefficient C in the turbulent closed 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 , there is a freely definable maneuvering parameter B in the equation constant parameters; some constant parameters required by the equation can be obtained by regression prediction using conventional DNN neural network based on the simulation results obtained by experimental measured data sets or SPH particle flow simulation, lattice Boltzmann simulation, local DNS simulation, etc.;

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

[0277] The derived variables of the equation include the sediment phase shear stress Fluid stress Schmidt number S c , eddy viscosity coefficient Particle Reynolds number Re p , drag coefficient C d , drag force parameter K, intermediate quantity used in calculation of water phase constitutive equation and Viscosity of the mixture v mix , the correlation between particles and fluid velocity fluctuations t mf , intermediate quantity C used in calculation of turbulent closed equation 2ω , χ ω ,Ω ij With σ d , smoothing term A, cross diffusion term CD kω , permanent contact component of particle pressure p ff, intermediate quantity used in calculation of sediment phase constitutive equation and μ(I), friction viscosity of 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 a test set and a training set;

[0279] The step (2) specifically comprises the following steps:

[0280] (2.1) Figure 3 As shown in FIG. 1 , a two-phase flow bridge pier scour model is constructed, and the initial condition of the two-phase flow bridge pier scour model is defined. The two-phase flow bridge pier scour model consists of upper clear water, lower sediment and bridge piers. According to the two-phase flow bridge pier scour calculation equation in step (1), the fluid area 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 condition to be analyzed can be initialized according to the actual situation, such as the actual flow field distribution after partial scouring has occurred or the scouring has been partially artificially filled, so as to obtain a more realistic and universal scouring calculation and scouring development prediction.

[0281] (2.2) Define the size 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; according to the size of the pier, the model defines a certain length of boundary in the three directions of length, width and height to fully display the scour characteristics; the commonly used pier cross-section is circular, and the model calculation domain size can be defined according to the size of the pier cross-section, which can be 10 to 15 times the pier diameter in the length direction, 8 to 10 times the pier diameter in the width direction, and 5 to 7 times the pier diameter in the height direction, of which the water area height is 3 to 4 times the pier diameter, and the sediment domain height is 2 to 3 times the pier diameter; the pier distribution can be arranged according to the actual situation (including the abutment and pile foundation, etc.) to obtain calculations and predictions that are more in line with the actual situation;

[0282] (2.3) Define the spatial distribution of the calculation points of the two-phase flow bridge pier scour model, use unstructured three-dimensional spatial grids to establish the calculation points of the model, and define the absolute spatial rectangular coordinate system; use unstructured three-dimensional spatial grids to divide the model, use relatively dense grids for the water area and sediment domain near the bridge piers, and transition from dense to sparse grids from the bridge piers to the model boundary; retain all corner points of the grid as the calculation points of the model, and remove all edges of the grid; use the same grid drawing method between different vertical planes of the upper clear water and the lower sediment, and evenly encrypt the mesh along the height direction at the interface;

[0283] (2.4) Define the boundary conditions of 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, k and ω impose vertical profile boundaries obtained from experiments or measurements or finite element simulations; at the outlet, zero gradient conditions are specified for all variables; the top boundary, k and ψ apply Newman boundary conditions, that is, a given pressure gradient; at the pier wall, and A no-slip boundary is used, i.e. the velocity is zero; cyclic boundary conditions are applied on both sides of the boundary;

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

[0285] (2.6) Define the time discretization rules of the model calculation points, fix the time interval or establish an adaptive and adjustable time step according to the model training results and the degree of chaos of the flow development, and the single step size shall not exceed 10 -6 s;

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

[0287] (3) establishing a physical information neural network based on two-phase flow according to the two-phase flow bridge pier scour calculation equation constructed in step (1) and the initial parameters and boundary conditions of the two-phase flow bridge pier scour model given in step (2);

[0288] Based on the physical information neural network of two-phase flow, a weakly supervised physical information neural network is constructed by adopting the form of small data supervision and physical equation constraints, and introducing Fourier layer and dynamic weight strategy;

[0289] like Figure 2 As shown, the 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 the spatial coordinates X, Y, Z and time T. The nonlinear activation function is tanh. The output is all the general variables and equation maneuvering parameters of the equation listed in step (1.5); the residual control term is jointly controlled by the training data set 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 adopt different initialization schemes 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 specially 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. Kaiming initialization also has two variants, 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 item v before inputting it into the main network, where v contains spatial coordinates X, Y, Z and time T), to increase the convergence speed of the neural network for the high-frequency part of the equation and data;

[0292]

[0293] Among them, a and b are the Fourier series coefficient and the Fourier fundamental frequency respectively, and b obeys the Gaussian distribution of N(0,1);

[0294] (3.3) Non-dimensionalize and normalize the data set to enhance the applicability of the initial network training process;

[0295] (3.4) Use automatic differentiation AD to calculate the partial differential operator of each variable at the output end of the network in step (3.1), and substitute it into the water phase constitutive equation, turbulent closed equation, and sediment phase constitutive equation established in steps (1.3) to (1.4) to calculate the derived variable values ​​of the equation listed in step (1.5); and combine the initial conditions and boundary conditions given in step (2) to calculate the initial and boundary errors loss IC 、loss BC ;

[0296] (3.5) Perform the first differential operation on the network output data to make it satisfy some physical equations; use the automatic differentiation AD to calculate the partial differential operator of the partial equation derived variables calculated in step (3.4) and the general variables of the equation output by the network in step (3.1), and substitute them into the mass conservation equation and momentum conservation equation established in step (1.2) for calculation to obtain the equation constraint error loss of the physical information neural network PDE , and combine the initial and boundary conditions given in step (2) to calculate the initial and boundary error loss 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, the boundary condition error, and the 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] Among them: α, β, γ, α′, β′, γ′ are the weight coefficients of the loss function;

[0301] (3.7) A dynamic weight strategy is used for the weight coefficients of the loss function. The coefficients are adaptively updated using the gradient statistics of back propagation during network training. The dynamic weight 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 randomly initialized using random initialization or the Xavier scheme. Xavier initialization is an initialization method designed specifically for neural networks with linear or Sigmoid activation functions. It determines the initialization range of parameters based on the number of inputs and outputs, so that the variance of the inputs and outputs remains consistent, thereby preventing the gradient from disappearing or exploding. There are two variants of Xavier initialization: Xavier Glorot initialization and Xavier He initialization. Xavier Glorot initialization is suitable for Sigmoid and Tanh activation functions, and Xavier He initialization is suitable for ReLU and its variant activation functions. This application adopts Xavier The Glorot scheme can be used for initialization. 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 adopt different initialization schemes 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 specially 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. Kaiming initialization also has two variants, suitable for different activation functions and network structures;

[0303] (3.9) Using a causal training strategy, the initial conditions used in the physical information neural network training are all the flow field parameters at a certain moment after the flow field calculation in step (2) is initially stabilized, that is, the flow state initialized for the training set rather than the static state, which increases the convergence speed of the network training and prevents gradient explosion; (3.10) Define the sampling strategy during the training process. When training the network, the space-time coordinates of the input end can be input using fixed coordinates or dynamic coordinates. The space-time coordinates include the 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, which can increase the affinity of the network to the data and accelerate 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] The step (4) specifically comprises the following steps:

[0306] (4.1) Train the physical information neural network, back propagate the error, and 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 multi-core GPUs for parallel computing. A small batch of data can be processed on each GPU, and different parts of the model can be assigned to different GPUs.

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

[0309] If the present invention modifies the equation and parameters of step (1), it is necessary to re-establish the constant parameters, independent general variables and related derived variables of the equation according to the modified equation, and modify the corresponding information in the subsequent steps. The method of the present invention can be applied not only to multiphase flow pier scouring, but also to multiphase flow submarine cable scouring, debris flow movement and other problems.

[0310] Example 2

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

[0312] Constructing a calculation equation module for constructing a two-phase flow pier scour calculation equation based on the Euler-Euler method; constructing the calculation equation module to execute the specific steps of step (1) in Example 1;

[0313] Constructing a simulation data module for constructing initial parameters and boundary conditions of a two-phase flow pier scour model, generating simulation data, and dividing the data into a test set and a training set; constructing a simulation data module to execute the specific steps of step (2) in Example 1;

[0314] Constructing a physical information neural network module, which is used to establish a physical information neural network based on two-phase flow according to the constructed two-phase flow bridge pier scour calculation equation, and the given two-phase flow bridge pier scour model initial parameters and boundary conditions; constructing a physical information neural network based on two-phase flow, using the form of small data supervision and physical equation constraints, and introducing Fourier layer and dynamic weight strategy to form a weakly supervised physical information neural network; constructing a physical information neural network module 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 of multiphase flow pier scour. The training neural network module executes the specific steps of step (4) in Example 1.

Claims

1. A method for calculating multiphase flow of bridge pier scour based on physical information neural network, characterized in that: The steps include: (1) Construct the two-phase flow pier scour calculation equation 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 a test set and a training set; (3) According to the two-phase flow bridge pier scour calculation equation constructed in step (1) and the initial parameters and boundary conditions of the two-phase flow bridge 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 in the form of small data supervision and physical equation constraints, and Fourier layer and dynamic weight strategy are introduced to form a weakly supervised physical information neural network; (4) Train the physical information neural network based on two-phase flow to obtain the prediction results of the physical information neural network for multiphase flow pier scour.

2. The method for calculating multiphase flow of bridge pier scour based on physical information neural network according to claim 1 is characterized by: The step (1) specifically comprises the following steps: (1.1) The sediment phase and the water phase are treated as two fluids and described by the Euler method. The sediment phase is a non-Newtonian fluid and the dense particle rheological constitutive model is applied. The water phase is a Newtonian fluid and the turbulence model is applied. (1.2) Constructing the Euler-Euler method two-phase flow calculation control equations, which are the mass conservation equation and the momentum conservation equation. The two-phase flow calculation control equations include the mass conservation equation of the sediment phase and the water phase, and the momentum conservation equation of the sediment phase and the water phase; The mass conservation equations for the sediment phase and the water phase are: Where φ and 1-φ are the volume fractions of the sediment phase and the water phase, and are the velocities of the sediment phase and the water phase, t is the time, subscripts i and j are operation indicators, and subscripts i, j = 1, 2, and 3 represent the components of the corresponding physical quantities in the flow direction, span direction, and vertical direction in the rectangular coordinate system, respectively; Momentum conservation equations for sediment and water phases: where ρ s and ρ f are the densities of sediment and water, g i is the acceleration due to gravity, p is the fluid pressure, f i The external force driving the flow is is the fluid stress, given by the water phase constitutive equation, and is the normal stress and shear stress of the sediment phase, which is given by the constitutive equation of the sediment phase; is the eddy viscosity coefficient, which is calculated using the turbulence closed equation, K is the drag force parameter, S c is the Schmidt number; The drag force parameter K is determined using the following equation: R ep =(1-φ)||u f -u s ||d / v f Where d is the particle diameter, C d is the resistance coefficient, Re p is the particle Reynolds number, v f is the fluid kinematic viscosity, h Exp Depends on Re p The obstruction index can be taken as a constant under certain working conditions, ||u f -u s || is the vector modulus; Schmidt number S c Determined using the following equation: where w fall0 is the falling speed, u * Bed friction velocity, u small A certain minimum value can be taken to prevent the equation from becoming singular; (1.3) Construct the water phase constitutive equation and the turbulence closed equation. The turbulence closed equation includes the cross-diffusion effect of the sediment phase and the water phase. Both the k-ω and k-ε turbulence closed equations can be used. k is the turbulent kinetic energy, ε is the dissipation rate of turbulent energy, representing the rate at which turbulent energy is converted into internal energy per unit time; ω is the turbulence frequency at a specific scale, representing the rate of turbulent eddies. Constitutive equation of water phase: where v mix is the viscosity of the mixture, φ max is the maximum volume concentration, which can be taken as 1; k is the turbulent kinetic energy, which is calculated using the closed turbulence equation. The subscript k is the operation index, and k = 1, 2, and 3 represent the components of the corresponding physical quantities in the stream direction, span direction, and vertical direction in the rectangular coordinate system, respectively; k-ω turbulence closed equation: k equation: Omega equation: CD kω is the cross diffusion term, C μ , C lim , σ k , C 1ω , C 2ω0 , C 3ω , C 4ω and σ ω are all constant terms and can be set according to the specific environment conditions; that is, the k-ε model is the same as the parameter t mf Characterizes the degree of correlation between particles and fluid velocity fluctuations. B is the only model calibration parameter, which is related to sediment flux and has a value range of 0.1 to 2. It can be used as a maneuvering parameter for machine learning. Cross diffusion term CD kω Determined using the following equation: The coefficient A is a smoothing term that gradually transitions between the activated and inactivated areas of the cross-diffusion term. is a step function. When the independent variable is zero or positive, the function value is 1; otherwise, it is 0. d0 is a constant term; k-ε turbulence closed equation: e=e=C μ yes The form of the k equation remains unchanged. Use the above formula to replace ω in the k equation with ε, and the ε equation is: where σ ε , C 1ε , C 2ε , C 3ε , C 4ε is a constant term; (1.4) Construct the two-phase flow sediment phase constitutive equation: in is the particle pressure, p s is the shear or collision component of the particle pressure, p ff is the permanent contact component of the particle pressure, C t is the ratio of the root mean square velocity fluctuation of sediment to fluid, which is a constant between 1 and 3; the constant coefficient of the equation It can be 0.57, φ max2 It can be taken as 0.635, which is related to the calibration of bed load and suspended load; Fr, η0, η1 are rheological empirical parameters, which can be taken as 0.05, 3, 5 respectively; is the friction viscosity of the sediment particles, B φ 2 / 3 is acceptable; ||S s || for Norm of a matrix; Friction viscosity of sand particles Determined using the following equation: where v max is the maximum solid phase viscosity, D small A certain minimum value can be taken to prevent the equation from being singular, I is the dimensionless inertia number, μ s is the static friction coefficient, s2 is the empirical dynamic coefficient, and I0 is the rheological empirical constant; (1.5) Determine the parameters and variable types of the established two-phase flow pier scour calculation equation, which include equation constant parameters, equation general variables, and equation derived variables; The constant parameters required for the equation calculation are determined by experiments or model inversion. The constant parameters of the equation include the density of the sediment ρ s , water density ρ f , the external force driving the flow f i , gravitational acceleration g i , particle diameter d, barrier index h Exp 、Fluid kinematic viscosity v f , falling speed w fall0 , bed friction velocity u * , additional term u to prevent the equation from being singular small and D small , constant coefficients in the sediment phase constitutive equation φ max2 With B φ , rheological empirical parameters η0, η1 and Fr, maximum volume concentration φ max , the ratio of the root mean square velocity fluctuation of sediment to fluid C t , maximum solid phase viscosity v max , static friction coefficient μ s , empirical dynamic coefficient μ2, rheological empirical constant I0, model calibration parameter B and constant coefficient C in turbulent closed 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 , there is a freely definable maneuvering parameter B in the equation constant parameters; some constant parameters required by the equation can be obtained by regression prediction using conventional DNN neural network based on the simulation results obtained by experimental measured data sets or SPH particle flow simulation, lattice Boltzmann simulation, local DNS simulation, etc.; The general variables of the equation, that is, the independent variables include the volume fraction of the sediment phase φ, the velocity of the sediment phase The speed of the water phase Fluid pressure p, turbulent kinetic energy k, turbulence frequency ω, turbulence energy dissipation rate ε, i = 1, 2, 3, a total of eleven; The derived variables of the equation include the sediment phase shear stress Fluid stress Schmidt number S c , eddy viscosity coefficient Particle Reynolds number Re p , drag coefficient C d , drag force parameter K, intermediate quantity used in calculation of water phase constitutive equation and Viscosity of the mixture v mix , the correlation between particles and fluid velocity fluctuations t mf , intermediate quantity C used in calculation of turbulent closed equation 2ω , χ ω ,Ω ij With σ d , smoothing term A, cross diffusion term CD kω , permanent contact component of particle pressure p ff , intermediate quantity used in calculation of sediment phase constitutive equation and μ(I), friction viscosity of sediment particles 3. The method for calculating multiphase flow of bridge pier scour based on physical information neural network according to claim 2 is characterized by: The step (2) specifically comprises the following steps: (2.1) constructing a two-phase flow bridge pier scour model and defining the initial condition of the two-phase flow bridge pier scour model. The two-phase flow bridge pier scour model consists of upper clear water, lower sediment and bridge piers. According to the two-phase flow bridge pier scour calculation equation in step (1), the fluid area 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 size of the two-phase flow pier scour model. According to the size of the pier, the model defines a certain length of boundary in the three directions of length, width and height. The cross-section of the pier adopted is circular. The size of the model calculation domain can be defined according to the size of the pier cross section. 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. The water area height is 3 to 4 times the pier diameter, and the sediment domain height is 2 to 3 times the pier diameter. (2.3) Define the spatial distribution of the calculation points of the two-phase flow bridge pier scour model, use unstructured three-dimensional spatial grids to establish the calculation points of the model, and define the absolute spatial rectangular coordinate system; use unstructured three-dimensional spatial grids to divide the model, use relatively dense grids for the water area and sediment domain near the bridge piers, and transition from dense to sparse grids from the bridge piers to the model boundary; retain all corner points of the grid as the calculation points of the model, and remove all edges of the grid; use the same grid drawing method between different vertical planes of the upper clear water and the lower sediment, and evenly encrypt the mesh along the height direction at the interface; (2.4) Define the boundary conditions of 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, k and ω impose vertical profile boundaries obtained from experiments or measurements or finite element simulations; at the outlet, zero gradient conditions are specified for all variables; the top boundary, k and ω apply Newman boundary conditions, that is, a given pressure gradient; at the pier wall, and A no-slip boundary is used, i.e. the velocity is zero; cyclic boundary conditions are applied on both sides of the boundary; (2.5) Initialize the flow field parameters. According to the definitions in steps (2.1) and (2.4), assign all the initial values ​​of the general variables listed in step (1.5) to all the calculation points in the two-phase flow pier scour model to initialize the flow field. The initial values ​​of all the 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 of the model calculation points, fix the time interval or establish an adaptive and adjustable time step according to the model training results and the degree of chaos of the flow development, and the single step size shall not exceed 10 -6 s; (2.7) Generate simulation data and divide the obtained simulation data into data sets to obtain training sets and test sets of the physical information neural network.

4. The method for calculating multiphase flow of bridge pier scour based on physical information neural network according to claim 3 is characterized by: The step (3) specifically comprises 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 the spatial coordinates X, Y, Z and time T. The nonlinear activation function is tanh. The output is all the general variables and equation maneuvering parameters of the equation listed in step (1.5). The residual control term is jointly controlled by the training data set 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 end, perform Fourier transform on the input item v and then input it into the main network. v contains spatial coordinates X, Y, Z and time T; Among them, a and b are the Fourier series coefficient and the Fourier fundamental frequency respectively, and b obeys the Gaussian distribution of N(0,1); (3.3) Non-dimensionalize and normalize the data set; (3.4) Use automatic differentiation AD to calculate the partial differential operator of each variable at the output end of the network in step (3.1), and substitute it into the water phase constitutive equation, turbulent closed equation, and sediment phase constitutive equation established in steps (1.3) to (1.4) to calculate the derived variable values ​​of the equation listed in step (1.5); and combine the initial conditions and boundary conditions given in step (2) to calculate the initial and boundary errors loss IC 、loss BC ; (3.5) Perform the first differential operation on the network output data, use the automatic differentiation AD to calculate the partial differential operator again, substitute the mass conservation equation and momentum conservation equation established in step (1.2) into the partial equation derived variables calculated in step (3.4) and the general variables of the equation output by the network in step (3.1), and calculate to obtain the equation constraint error loss of the physical information neural network PDE , and combine the initial and boundary conditions given in step (2) to calculate the initial and boundary error loss again IC′ 、loss BC′ ; (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, the boundary condition error, and the equation constraint error: loss phy =a loss PDE +βloss IC +gloss BC +β′loss IC′ +γ′loss BC′ loss total =loss phy +α′loss 仿真数据训练集 Among them: α, β, γ, α′, β′, γ′ are the weight coefficients of the loss function; (3.7) A dynamic weight strategy is used for the weight coefficients of the loss function. The coefficients are adaptively updated using the back-propagated gradient statistics during network training. The dynamic weight strategy dynamically adjusts the weights of different parts of the loss function according to the performance of the loss function during model training. (3.8) Initializing the parameters of the neural network. The parameters of the neural network are randomly initialized using random initialization or the Xavier scheme; (3.9) A causal training strategy is adopted. The initial conditions used in the physical information neural network training are all the flow field parameters at a certain moment after the flow field calculation in step (2) is initially stabilized, that is, the flow state initialized for the training set rather than the static state; (3.10) The sampling strategy in the training process is defined. When training the network, the space-time coordinates of the input end can be fixed coordinates or dynamic coordinates. The space-time coordinates include the 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 of bridge pier scour based on physical information neural network according to claim 4 is characterized by: The step (4) specifically comprises the following steps: (4.1) Train the physical information neural network, back propagate the error, and update the weights and biases until the training error converges; (4.2) Considering GPU acceleration and parallel computing, the neural network is deployed on multi-core GPUs for parallel computing. A small batch of data can be processed on each GPU, and different parts of the model can be assigned to different GPUs. (4.3) The trained neural network model is used for prediction. After the neural network error converges, the final result is φ, By observing the changes of φ at each point in the model over time, the development law of pier scour calculated by the bridge scour multiphase flow based on the physical information neural network can be obtained.

6. A bridge pier scour multiphase flow calculation system based on physical information neural network, characterized in that: include: Construct a calculation equation module, which is used to construct a two-phase flow bridge pier scour calculation equation based on the Euler-Euler method; Construct a simulation data module to construct 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; Construct a physical information neural network module, which is used to establish a physical information neural network based on two-phase flow according to the constructed two-phase flow bridge pier scour calculation equation, as well as the given two-phase flow bridge pier scour model initial parameters and boundary conditions; construct a physical information neural network based on two-phase flow, adopt the form of small data supervision and physical equation constraints, and introduce Fourier layer and dynamic weight strategy to form a weakly supervised physical information neural network; 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 of multiphase flow pier scour.

7. The bridge pier scour multiphase flow calculation system based on physical information neural network according to claim 6 is characterized by: In the calculation equation construction module, the sediment phase and the water phase are regarded as two fluids and described by the Euler method, wherein the sediment phase is a non-Newtonian fluid and a dense particle rheological constitutive model is applied, and the water phase is a Newtonian fluid and a turbulence model is applied; Construct the Euler-Euler method two-phase flow calculation control equation, which is the mass conservation equation and momentum conservation equation. The two-phase flow calculation control equation includes the mass conservation equation of the sediment phase and the water phase, and the momentum conservation equation of the sediment phase and the water phase; The mass conservation equations for the sediment phase and the water phase are: Where φ and 1-φ are the volume fractions of the sediment phase and the water phase, and are the velocities of the sediment phase and the water phase, t is the time, subscripts i and j are operation indicators, and subscripts i, j = 1, 2, and 3 represent the components of the corresponding physical quantities in the flow direction, span direction, and vertical direction in the rectangular coordinate system, respectively; Momentum conservation equations for sediment and water phases: where ρ s and ρ f are the densities of sediment and water, g i is the acceleration due to gravity, p is the fluid pressure, f i The external force driving the flow is is the fluid stress, given by the water phase constitutive equation, and is the normal stress and shear stress of the sediment phase, which is given by the constitutive equation of the sediment phase; is the eddy viscosity coefficient, which is calculated using the turbulence closed equation, K is the drag force parameter, S c is the Schmidt number; The drag force parameter K is determined using the following equation: Bid p (1-φ)||u f -u s ||d / v f Where d is the particle diameter, C d is the resistance coefficient, Re p is the particle Reynolds number, v f is the fluid kinematic viscosity, h Exp Depends on Re p The obstruction index can be taken as a constant under certain working conditions, ||u f -u s || is the vector modulus; Schmidt number S c Determined using the following equation: where w fall0 is the falling speed, u * Bed friction velocity, u small A certain minimum value can be taken to prevent the equation from becoming singular; Construct the water phase constitutive equation and turbulence closed equation, where the turbulence closed equation includes the cross-diffusion effect of the sediment phase and the water phase. Both k-ω and k-ε turbulence closed equations can be used, k is the turbulent kinetic energy, ε is the dissipation rate of turbulent energy, representing the rate of turbulent energy conversion into internal energy per unit time; ω is the turbulence frequency of a specific scale, representing the rate of turbulent eddies; Constitutive equation of water phase: where v mix is the viscosity of the mixture, φ max is the maximum volume concentration, which can be taken as 1; k is the turbulent kinetic energy, which is calculated using the closed turbulence equation. The subscript k is the operation index, and k = 1, 2, and 3 represent the components of the corresponding physical quantities in the stream direction, span direction, and vertical direction in the rectangular coordinate system, respectively; k-ω turbulence closed equation: k equation: equation: CD kω is the cross diffusion term, C μ , C lim , σ k , C 1ω , C 2ω0 , C 3ω , C 4ω and σ ω are all constant terms and can be set according to the specific environment conditions; that is, the k-ε model is the same as the parameter t mf Characterizes the degree of correlation between particles and fluid velocity fluctuations. B is the only model calibration parameter, which is related to sediment flux and has a value range of 0.1 to 2. It can be used as a maneuvering parameter for machine learning. Cross diffusion term CD kω Determined using the following equation: The coefficient A is a smoothing term that gradually transitions between the activated and inactivated areas of the cross-diffusion term. is a step function. When the independent variable is zero or positive, the function value is 1; otherwise, it is 0. d0 is a constant term; k-ε turbulence closed equation: e=e=C μ yes The form of the k equation remains unchanged. Use the above formula to replace ω in the k equation with ε, and the ε equation is: where σ ε , C 1ε , C 2ε , C 3ε , C 4ε is a constant term; Construct the two-phase flow sediment phase constitutive equation, sediment phase constitutive equation: in is the particle pressure, p s is the shear or collision component of the particle pressure, p ff is the permanent contact component of the particle pressure, C t is the ratio of the root mean square velocity fluctuation of sediment to fluid, which is a constant between 1 and 3; the constant coefficient of the equation It can be 0.57, φ max2 It can be taken as 0.635, which is related to the calibration of bed load and suspended load; Fr, η0, η1 are rheological empirical parameters, which can be taken as 0.05, 3, 5 respectively; is the friction viscosity of the sediment particles, B φ 2 / 3 is acceptable; ||S s || for Norm of a matrix; Friction viscosity of sand particles Determined using the following equation: where v max is the maximum solid phase viscosity, D small A certain minimum value can be taken to prevent the equation from being singular, I is the dimensionless inertia number, μ s is the static friction coefficient, μ2 is the empirical dynamic coefficient, and I0 is the rheological empirical constant; Determine the parameters and variable types of the established two-phase flow bridge pier scour calculation equation, the parameter and variable types include equation constant parameters, equation general variables and equation derived variables; The constant parameters required for the equation calculation are determined by experiments or model inversion. The constant parameters of the equation include the density of the sediment ρ s , water density ρ f , the external force driving the flow f i , gravitational acceleration g i , particle diameter d, barrier index h Exp 、Fluid kinematic viscosity v f , falling speed w fall0 , bed friction velocity u * , additional term u to prevent the equation from being singular small and D small , constant coefficients in the sediment phase constitutive equation φ max2 With B φ , rheological empirical parameters η0, η1 and Fr, maximum volume concentration φ max , the ratio of the root mean square velocity fluctuation of sediment to fluid C t , maximum solid phase viscosity v max , static friction coefficient μ s , empirical dynamic coefficient μ2, rheological empirical constant I0, model calibration parameter B and constant coefficient C in the turbulent closed 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 , there is a freely definable maneuvering parameter B in the equation constant parameters; some constant parameters required by the equation can be obtained by regression prediction using conventional DNN neural network based on the simulation results obtained by experimental measured data sets or SPH particle flow simulation, lattice Boltzmann simulation, local DNS simulation, etc.; The general variables of the equation, that is, the independent variables include the volume fraction of the sediment phase φ, the velocity of the sediment phase The speed of the water phase Fluid pressure p, turbulent kinetic energy k, turbulence frequency ω, turbulence energy dissipation rate ε, i = 1, 2, 3, a total of eleven; The derived variables of the equation include the sediment phase shear stress Fluid stress Schmidt number S c , eddy viscosity coefficient Particle Reynolds number Re p , drag coefficient C d , drag force parameter K, intermediate quantity used in calculation of water phase constitutive equation and Viscosity of the mixture v mix , the correlation between particles and fluid velocity fluctuations t mf , intermediate quantity C used in calculation of turbulent closed equation 2ω , χ ω ,Ω ij With σ d , smoothing term A, cross diffusion term CD kω , permanent contact component of particle pressure p ff , intermediate quantity used in calculation of sediment phase constitutive equation and μ(I), friction viscosity of sediment particles 8. The bridge pier scour multiphase flow calculation system based on physical information neural network according to claim 7 is characterized by: In the simulation data building module, a two-phase flow bridge pier scour model is built, and the initial condition of the two-phase flow bridge pier scour model is defined. The two-phase flow bridge pier scour model consists of upper clear water, lower sediment and bridge piers. According to the two-phase flow bridge pier scour calculation equation, the fluid area of ​​the model is divided into two parts, an initial water area and an 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 size of the two-phase flow pier scour model. According to the size of the pier, the model defines a certain length of boundary in the three directions of length, width and height. The adopted pier cross section is circular. The size of the model calculation domain can be defined according to the size of the pier cross section. 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. The water area height is 3 to 4 times the pier diameter, and the sediment domain height is 2 to 3 times the pier diameter. Define the spatial distribution of the calculation points of the two-phase flow bridge pier scour model, use unstructured three-dimensional spatial grids to establish the calculation points of the model, and define the absolute spatial rectangular coordinate system; use unstructured three-dimensional spatial grids to divide the model, use relatively dense grids for the water area and sediment domain near the bridge piers, and transition from dense to sparse grids from the bridge piers to the model boundary; All corner points of the grid are retained as calculation points of the model, and all edges of the grid are removed; the same mesh drawing method is used between different vertical planes of the upper clear water and the lower sediment, and the interface is evenly encrypted along the height direction; Define the boundary conditions of the two-phase flow pier scour model, and define corresponding boundary conditions at the inlet, outlet, top boundary, pier wall, and both sides of the model: at the inlet, for φ, k and ω impose vertical profile boundaries obtained from experiments or measurements or finite element simulations; at the outlet, zero gradient conditions are specified for all variables; the top boundary, k and ω apply Newman boundary conditions, that is, a given pressure gradient; at the pier wall, and A no-slip boundary is used, i.e. the velocity is zero; cyclic boundary conditions are applied on both sides of the boundary; Initialize the flow field parameters, assign all the listed general variables initial values ​​to all the 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 the trained physical information neural network; Define the time discrete rule of the model calculation point, fix the time interval or establish an adaptive and adjustable time step according to the model training results and the degree of chaos of flow development, and the single step size shall not exceed 10 -6 s; Generate simulation data, and divide the obtained simulation data into data sets to obtain training sets and test sets of the physical information neural network.

9. The bridge pier scour multiphase flow calculation system based on physical information neural network according to claim 8, characterized in that: The physical information neural network module is used to 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 the spatial coordinates X, Y, Z and time T. The nonlinear activation function is tanh. The output end is all the general variables and equation maneuvering parameters of the listed equations. The φ difference control item is jointly controlled by the training data set and the constructed physical information, i.e., the two-phase flow bridge 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. Add a Fourier transform layer at the network input end, perform Fourier transform on the input vertex v before inputting it into the main network, where v contains the spatial coordinates X, Y, Z and time T; Among them, a and b are the Fourier series coefficient and the Fourier fundamental frequency respectively, and b obeys the Gaussian distribution of N(0,1); Non-dimensionalize and normalize the data set; The variables at the output of the network are calculated using the automatic differential AD partial differential operator, and are substituted into the established water phase constitutive equation, turbulent closed equation, and sediment phase constitutive equation to obtain the values ​​of the variables derived from the listed equations; and the initial and boundary errors loss are calculated in combination with the given initial and boundary conditions. IC 、loss BC ; Perform the first differential operation on the network output data, use the automatic differentiation AD to calculate the partial differential operator of the derived variables of the partial equation and the general variables of the equation output by the network, substitute them into the established mass conservation equation and momentum conservation equation for calculation, and obtain the equation constraint error loss of the physical information neural network PDE , and combine the given initial and boundary conditions to calculate the initial and boundary errors loss again IC ′、loss BC′ ; Calculate the error loss of the entire neural network total , the error is defined as a linear combination of the initial condition error, the boundary condition error, and the equation constraint error: loss phy =a loss PDE +βloss IC +gloss BC +β′loss IC′ +γ′loss BC′ loss total =loss phy +α′loss 仿真数据训练集 Among them: α, β, γ, α′, β′, γ′ are the weight coefficients of the loss function; A dynamic weight strategy is used for the weight coefficients of the loss function. The coefficients are adaptively updated using the gradient statistics of back propagation during network training. The dynamic weight strategy dynamically adjusts the weights of different parts of the loss function according to the performance of the loss function during model training. Initialize the parameters of the neural network. The parameters of the neural network are randomly initialized using random initialization or the Xavier scheme. A causal training strategy is adopted, and the initial conditions used in the physical information neural network training are all flow field parameters at a certain moment after the flow field calculation is initially stabilized, that is, the flow state initialized for the training set rather than the static state; the sampling strategy in the training process is defined, and when training the network, the space-time coordinates of the input end can be input using fixed coordinates or dynamic coordinates, and the space-time coordinates include spatial coordinates X, Y, Z and time T; if fixed coordinates are used for input, random sampling can be used to select points, or the defined calculation point coordinates can be sampled; the input end can use dynamic coordinates for input, and the defined calculation point coordinates can be sampled in different ways at different times.

10. The bridge pier scour multiphase flow calculation system based on physical information neural network according to claim 9, characterized in that: The training neural network module trains the physical information neural network, back propagates the error, and updates the weights and biases until the training error converges; Considering GPU acceleration and parallel computing, the neural network is deployed on multi-core GPUs for parallel computing. A small batch of data can be processed on each GPU, and different parts of the model can be assigned to different GPUs. The trained neural network model is used for prediction. After the neural network error converges, the φ, By observing the changes of φ at each point in the model over time, the development law of pier scour calculated by the bridge scour multiphase flow based on the physical information neural network can be obtained.

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