Bridge scouring single-phase flow calculation method based on physical information neural network

Abstract

Disclosed in the present invention is a bridge scouring single-phase flow calculation method based on a physical information neural network. The method comprises the following steps: selecting a training sample and a prediction sample, and obtaining corresponding coordinate data; using the coordinate data of the training sample as input and feeding same into a first neural network for training, outputting a sediment elevation change, and calculating a corresponding riverbed elevation; using the corresponding riverbed elevation as part of input and feeding same into a second neural network for training, and outputting corresponding flow field parameters; after training errors of the two networks are converged, obtaining two trained concatenated neural networks; inputting the coordinate data of the prediction sample into the trained first neural network, performing forward calculation to output a corresponding sediment elevation change, and calculating a corresponding riverbed elevation; and using the riverbed elevation of the prediction sample and randomly extracted points within a certain range above the riverbed elevation as input of the trained second neural network, and performing forward calculation to output corresponding flow field parameters. The present invention has wide applicability.

Description

A single-phase flow calculation method for bridge scour based on physical information neural network Technical Field

[0001] The present invention belongs to the technical field of bridge health monitoring, and in particular relates to a bridge scour single-phase flow calculation method based on physical information neural network. Background Art

[0002] Local scour of bridge foundations is attributed to the extremely complex interaction between the surrounding three-dimensional water flow, the pier foundation, and the sediment. For example, the submerged foundation strongly disturbs the incoming flow, generating complex turbulent flows such as undercurrent, horseshoe vortices, and wake vortex shedding. Turbulent flow forces sediment into motion, and the high concentration of suspended sediment particles reacts on the water flow. The mutual constraints and influences between the water flow and sediment result in a multifaceted and complex mechanism of local scour. These factors include pier characteristics, such as the transverse width or diameter, the downstream length, and the shape, number, and distribution of piers; flow factors, such as the average velocity and depth of the water flow in front of the piers, the incoming flow angle, and the turbulent characteristics of the water flow; and bed material characteristics, such as sediment particle size, gradation, and relative roughness. These factors can also interact with each other, further complicating the process.

[0003] Currently, local scour research methods primarily include field observations of real bridges, flume model tests, and computational fluid dynamics (CFD) simulations. CFD is currently one of the most popular methods for studying local scour. Increased computer speeds and improved numerical methods have facilitated the application of CFD, sediment kinematics, and terrain dynamics in scour numerical simulations. CFD scour simulations first use CFD to solve the flow field around a submerged foundation, obtaining velocity and pressure fields. From this, the bed shear stress is determined and compared with the critical shear stress of the sediment on the bed. If the sediment meets the critical shear stress, the bed load and suspended load transport rates are calculated, resulting in the scour volume and elevation change on the riverbed. The computational domain and mesh are then updated based on the elevation change, and the next round of CFD flow field solution and sediment transport calculations is performed. When the shear stress on the scour pit surface equals the critical shear stress, the scour pit ceases to develop, and the equilibrium (maximum) scour pit depth and morphology are determined.

[0004] However, CFD-based calculation methods take a long time to solve, and their accuracy is highly dependent on the number and precision of the meshes. In recent years, with the continuous development of deep learning algorithms, an increasing number of deep learning methods have been applied to scour depth prediction, such as masked attention neural networks, M5-Tree, gene expression programming (GEP), locally weighted linear regression (LWLR), support vector regression (SVR), and multivariate linear regression (MLR). Deep learning methods only require a few key parameters to obtain corresponding prediction results, resulting in high prediction efficiency. However, deep learning algorithms have high requirements for training data. If the training data is too small or the coverage is too narrow, the trained model will have poor generalization and cannot be effectively applied to scour depth prediction in various situations.

[0005] Summary of the Invention

[0006] Purpose of the invention: The purpose of the present invention is to provide a single-phase flow calculation method for bridge scour based on physical information neural network. The method has wide applicability and can quickly and accurately predict the underwater foundation scour depth and flow field distribution.

[0007] Technical solution: To achieve the above objectives, the present invention discloses a bridge scour single-phase flow calculation method based on physical information neural network, comprising the following steps:

[0008] (1) Selecting training samples and prediction samples, and obtaining the coordinate data of the training samples and the prediction samples, the coordinate data including the X coordinate, Y coordinate and the time T of the sample;

[0009] (2) The X coordinate, Y coordinate and time T of the training sample are input into the first neural network for training, and the sediment elevation change △H is output, and the corresponding riverbed elevation Z is calculated;

[0010] (3) The corresponding riverbed elevation Z calculated in step (2) is used as part of the input into the second neural network for training, and the output is the corresponding flow field parameters, which include the X-direction velocity u, the Y-direction velocity v, the Z-direction velocity w and the pressure magnitude P;

[0011] (4) After the training errors of the first neural network and the second neural network converge, the trained first neural network and the second neural network that are connected in series are obtained;

[0012] (5) Input the X coordinate, Y coordinate and time T of the predicted sample into the first trained neural network, and forward calculate the output as the corresponding sediment elevation change △H, and calculate the corresponding riverbed elevation Z;

[0013] (6) The riverbed elevation Z of the predicted sample and the randomly selected points within a certain range above the riverbed elevation Z are used as the input of the trained second neural network, and the corresponding flow field parameters are obtained by forward calculation output. The flow field parameters include the X-direction velocity u, the Y-direction velocity v, the Z-direction velocity w and the pressure magnitude P.

[0014] Wherein, step (1) specifically includes the following steps:

[0015] (1.1) Using a random sampling method, training samples are selected from the internal points of the flow field during the prediction period. The training samples include initial training points, boundary training points, and internal training points. Prediction samples are randomly selected within a circular area around the bridge pier within a radius of 4 to 6 times the bridge pier.

[0016] (1.2) Define the absolute space rectangular coordinate system;

[0017] (1.3) Calculate the X coordinates, Y coordinates, and time T of the training and prediction samples.

[0018] Preferably, step (2) specifically includes the following steps:

[0019] (2.1) The first neural network is a multilayer perceptron neural network model. The X coordinate, Y coordinate, and time T of the training sample are input into the first neural network, and the initial sediment elevation change △H is obtained by forward calculation.

[0020] (2.2) Calculate the riverbed elevation Z based on the output of the initial sediment elevation change △H;

[0021] (2.3) Calculate the error of the first neural network. The error is defined as the linear combination of the initial condition error of the first neural network and the constraint error of the sediment transport physical equation of the first neural network.

[0022] (2.4) Error backpropagation, update weights and biases until the training error converges.

[0023] Furthermore, the specific steps for forward calculation of the initial sediment elevation change △H in step (2.1) are as follows:

[0024] Define the activation function Swish function:

[0025] Where x is the input of the activation function;

[0026] Assume there are k hidden layers, each hidden layer has n neurons, and the input vector is P = [X, Y, T], where P∈R 3 ; The output H of the i-th neuron in the l-th layer of the hidden layer li is: H li =SiLU(Wli ·H l-1 +b li )

[0027] Among them H l-1 is the output of the previous hidden layer, W li is the weight matrix of hidden layer l, b li is the bias vector of hidden layer l;

[0028] Recursively, for the overall output vector H of the lth layer l is: H l =[H l1 ,H l2 ,H l3 ,....,H ln ]

[0029] Among them H ln is the output of the nth neuron in the lth layer;

[0030] The output △H of the output layer of each forward calculation is expressed as: △H=W o ·H k +b0

[0031] Where W o is the weight matrix of the output layer, b0 is the bias vector of the output layer, H k is the output matrix of the kth hidden layer;

[0032] The output △H of the entire neural network is expressed as: △H=W o ·SiLU(W k ·SiLU(...SiLU(W1·SiLU(P+b1)+b k-1 )...)

[0033] Where W k represents the weight matrix of the kth hidden layer, b k-1 is the bias vector of the k-1th hidden layer.

[0034] Furthermore, the formula for calculating the corresponding riverbed elevation Z is: Z = ΔH + Z0

[0035] Where △H is the elevation change output by the first neural network, and Z0 is the riverbed elevation at the initial moment.

[0036] Preferably, the specific steps of step (2.3) are:

[0037] Initial condition error loss of the first neural network IC Expressed as:

[0038] where N ICis the number of training points at the initial moment of the first neural network, △H is the initial sediment elevation change output by the first neural network;

[0039] The physical error constraint of the sediment transport equation of the first neural network is expressed as:

[0040] Where N phy is the number of internal training points of the first neural network, Z is the riverbed elevation, n is the riverbed sediment void ratio, which can be taken as 0.41; bx is the longitudinal single-width volume sediment transport rate, q by is the volumetric sediment transport rate per transverse width, q bx and q by The sum of the sediment transport rates per unit width q b Decompose it and get the sum of the single width volume sediment transport rate q b The calculation formula is: q0 is the volumetric sediment transport rate per unit width of the bed load in the plane, is the sediment repose angle, K0 is a constant related to q0;

[0041] Calculate the error loss of the first neural network total : loss total =αloss phy +βloss IC

[0042] Where α is the linear superposition coefficient of the physical error of the first neural network, and β is the linear superposition coefficient of the initial condition error of the first neural network. The sizes of the two are generally on the order of 10.

[0043] Furthermore, step (3) specifically includes the following steps:

[0044] (3.1) The second neural network uses a DEEPONET-type neural network model or a multilayer perceptron-type neural network model. The riverbed elevation Z and 10 randomly selected points within the sediment median size range above the riverbed elevation Z are used as inputs of the second neural network. The initial flow field parameters are obtained through forward calculation.

[0045] (3.2) Calculate the error of the second neural network, where the error is defined as a linear combination of the initial condition error of the second neural network, the boundary condition error of the second neural network, and the NS equation constraint error of the second neural network;

[0046] (3.3) Error backpropagation, update weights and biases until the training error converges.

[0047] Furthermore, when the second neural network uses a neural network model in the form of DEEPONET, the step (3.1) specifically includes the following steps:

[0048] The riverbed elevation Z and the median sediment particle size d 10 meters above the riverbed elevation Z are calculated. 50 Random points within the size range are used as the input of the second neural network Z to calculate the flow field parameters in a forward direction to adapt to the changing flow field boundary; X∈[Z,Z+10d 50 ]

[0049] Select N input functions:

[0050] Calculate the value matrix F of m evaluation points in N input functions:

[0051] Use F as branch (b k ) network input, Z as trunk(t k ) network input, the flow field parameter matrix Q (u, v, w, P) is calculated:

[0052] Furthermore, when the second neural network adopts a multilayer perceptron neural network model, the step (3.1) specifically includes the following steps:

[0053] The riverbed elevation Z and the median sediment particle size d 10 meters above the riverbed elevation Z are calculated. 50 Random points within the size range are used as the input Z of the second neural network to calculate the flow field parameters in a forward direction to adapt to the changing flow field boundary; Z∈[Z,Z+10d 50 ]

[0054] Define the activation function Swish function:

[0055] Where x is the input of the activation function;

[0056] Assume there are k hidden layers, each hidden layer has n neurons, and the input vector is Z, where Z∈[Z,Z+10d 50 ];

[0057] The output H of the i-th neuron in the l-th layer of the hidden layer li is: H li =SiLU(W li ·H l-1 +b li )

[0058] Among them H l-1 is the output of the previous hidden layer, W li is the weight matrix of hidden layer l, bli is the bias vector of hidden layer l;

[0059] Recursively, for the overall output vector H of the lth layer l is: H l =[H l1 ,H l2 ,H l3 ,....,H ln ]

[0060] Among them H ln is the output of the nth neuron in the lth layer;

[0061] The output matrix Q(u, v, w, P) of the output layer is expressed as: Q = W o ·H k +b0

[0062] Where W o is the weight matrix of the output layer, b0 is the bias vector of the output layer, H k is the output matrix of the kth hidden layer;

[0063] The output Q(u, v, w, P) of the entire neural network is expressed as: Q = W o ·SiLU(W k ·SiLU(...SiLU(W1·SiLU(P+b1)+b k-1 )...)

[0064] Where W k represents the weight matrix of the kth hidden layer, b k-1 is the bias vector of the k-1th hidden layer.

[0065] Preferably, the step (3.2) specifically includes the following steps:

[0066] Calculate the initial condition error loss of the second neural network IC′ :

[0067] where N IC′ is the number of training points at the initial moment of the second neural network, u n A sample speed u output by the second neural network n ={u n , v n ,ω n} T ; The true value of a sample's initial condition;

[0068] Calculate the boundary condition error loss of the second neural network BC′ :

[0069] where N BC′ is the number of training points on the boundary of the two neural networks, u n A sample speed u output by the second neural network n ={u n , v n ,ω n} T ; is the true value of a sample boundary condition;

[0070] Calculate the NS equation constraint error loss of the second neural network phy′ :

[0071] where N phy′ is the number of training points inside the flow field of the second neural network, u i A sample speed u output by the second neural network i ={u i , v i ,ω i} T , p i is the pressure of a sample output by the second neural network, R e is the fluid Reynolds number;

[0072] Calculate the error loss of the second neural network total′ : loss total′ =α′loss phy′ +β′loss IC′ +γ′loss BC′

[0073] Among them, α′ is the linear superposition coefficient of the physical error of the second neural network, β′ is the linear superposition coefficient of the initial condition error of the second neural network, and γ′ is the linear superposition coefficient of the boundary condition error of the second neural network. The sizes of the three are generally on the order of 10.

[0074] Beneficial effects: Compared with the existing technology, the present invention has the following significant advantages: the present invention combines the first neural network with the second neural network, and by inputting the X-coordinates and Y-coordinates of the training samples of the flow field within the prediction time and the time T of the training samples, the X-direction velocity u, Y-direction velocity v, Z-direction velocity w, pressure magnitude P and sediment elevation Z of each point in the flow field are finally obtained, thereby quickly and accurately predicting the underwater foundation scour depth and flow field distribution; ultimately, the scour situation of the bridge foundation structure can be quickly judged, providing technical support for further underwater detection and regional bridge scour rapid screening, and providing important support for early warning of bridge structure safety; compared with conventional scour prediction methods, the present invention does not require underwater operations, direct observation of scour status, or time-consuming calculations. Only the coordinate values ​​of the calculation points within the flow field can be used to quickly predict the development of bridge foundation scour depth within the expected time; the learning and calculation speed of the neural network based on the present invention help to improve the accuracy and computing efficiency of dynamic simulation; at the same time, by embedding physical information, the dependence on training data is reduced, and the generalization ability of the model is enhanced. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] FIG1 is a flow chart of the present invention;

[0076] FIG2 is a network structure for a single working condition in Example 1 of the present invention;

[0077] FIG3 shows a network structure for multiple working conditions in Example 2 of the present invention. DETAILED DESCRIPTION

[0078] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0079] Example 1

[0080] As shown in Figures 1 and 2, a single operating condition refers to a scour condition under a specific operating condition, where parameters such as pier radius, pier shape, and flow field size remain constant. This invention introduces a mathematical-physical model related to scour depth into a deep learning algorithm for the first time, establishing a data-free scour simulation method. For a single operating condition, this invention provides a single-phase flow calculation method for bridge scour based on a physical information neural network, including the following steps:

[0081] (1) Selecting training samples and prediction samples to obtain coordinate data of the training samples and prediction samples, where the coordinate data includes the X coordinate, the Y coordinate, and the time T of the sample, specifically includes the following steps;

[0082] (1.1) Using a random sampling method, training samples are selected from the internal points of the flow field during the prediction period. The training samples include initial training points, boundary training points, and internal training points. Prediction samples are randomly selected within a circular area around the bridge pier within a radius of 4 to 6 times the bridge pier.

[0083] (1.2) Define the absolute space rectangular coordinate system;

[0084] (1.3) Calculate the X coordinates and Y coordinates of the training sample and the prediction sample, as well as the time T of the training sample;

[0085] (2) The X coordinate, Y coordinate and time T of the training sample are input into the first neural network for training, and the sediment elevation change △H is output, and the corresponding riverbed elevation Z is calculated;

[0086] The specific steps include:

[0087] (2.1) The first neural network is a multilayer perceptron neural network model. The X coordinate, Y coordinate, and time T of the training sample are input into the first neural network, and the initial sediment elevation change △H is obtained by forward calculation.

[0088] The specific steps for forward calculation of the initial sediment elevation change ΔH in step (2.1) are as follows:

[0089] Define the activation function Swish function:

[0090] Where x is the input of the activation function;

[0091] Assume there are k hidden layers, each hidden layer has n neurons, and the input vector is P = [X, Y, T], where P∈R 3 ; The output H of the i-th neuron in the l-th layer of the hidden layer li is: H li =SiLU(W li ·H l-1 +b li )

[0092] Among them H l-1 is the output of the previous hidden layer, W li is the weight matrix of hidden layer l, b li is the bias vector of hidden layer l;

[0093] Recursively, for the overall output vector H of the lth layer l is: H l =[H l1 ,H l2 ,H l2 ,....,H ln ]

[0094] Among them H ln is the output of the nth neuron in the lth layer;

[0095] The output △H of the output layer of each forward calculation is expressed as: △H=W o ·H k +b0

[0096] Where W o is the weight matrix of the output layer, b0 is the bias vector of the output layer, and Hk is the output matrix of the kth hidden layer;

[0097] The output △H of the entire neural network is expressed as: △H=W o ·SiLU(W k ·SiLU(...SiLU(W1·SiLU(P+b1)+b k-1 )...)

[0098] Where W k represents the weight matrix of the kth hidden layer, b k-1 is the bias vector of the k-1th hidden layer;

[0099] (2.2) Calculate the corresponding riverbed elevation Z based on the output sediment elevation change △H;

[0100] The formula for calculating the corresponding riverbed elevation Z is: Z=ΔH+Z0

[0101] Where △H is the elevation change output by the first neural network, and Z0 is the riverbed elevation at the initial moment;

[0102] (2.3) Calculate the error of the first neural network. The error is defined as the linear combination of the initial condition error of the first neural network and the constraint error of the sediment transport physical equation of the first neural network.

[0103] The specific steps of step (2.3) are:

[0104] Initial condition error loss of the first neural network IC Expressed as:

[0105] where N IC is the number of training points at the initial moment of the first neural network, △H is the initial sediment elevation change output by the first neural network;

[0106] The physical error constraint of the sediment transport equation of the first neural network is expressed as:

[0107] Where N phy is the number of internal training points of the first neural network, Z is the riverbed elevation, n is the riverbed sediment void ratio, which can be taken as 0.41; bx is the longitudinal single-width volume sediment transport rate, q by is the volumetric sediment transport rate per transverse width, qbx and q by The sum of the sediment transport rates per unit width q b Decompose it and get the sum of the single width volume sediment transport rate q b The calculation formula is: q0 is the volumetric sediment transport rate per unit width of the bed load in the plane, is the sediment repose angle, K0 is a constant related to q0;

[0108] Calculate the error loss of the first neural network total : loss total =αloss phy +βloss IC

[0109] Where α is the linear superposition coefficient of the physical error of the first neural network, and β is the linear superposition coefficient of the initial condition error of the first neural network. The magnitudes of the two are generally on the order of 10.

[0110] (2.4) Error back propagation, update weights and biases until the training error converges;

[0111] (3) The corresponding riverbed elevation Z calculated in step (2) is used as part of the input into the second neural network for training, and the output is the corresponding flow field parameters, which include the X-direction velocity u, the Y-direction velocity v, the Z-direction velocity w and the pressure magnitude P;

[0112] The specific steps include:

[0113] (3.1) The second neural network uses a multilayer perceptron neural network model. The riverbed elevation Z and 10 random points above the riverbed elevation Z within the median sediment particle size range are used as inputs of the second neural network. The initial flow field parameters are calculated in a forward manner.

[0114] The step (3.1) specifically includes the following steps:

[0115] The riverbed elevation Z and the median sediment particle size d 10 meters above the riverbed elevation Z are calculated. 50 Random points within the size range are used as the input Z of the second neural network to calculate the flow field parameters in a forward direction to adapt to the changing flow field boundary; Z∈[Z,Z+10d 50 ]

[0116] Define the activation function Swish function:

[0117] Where x is the input of the activation function;

[0118] Assume there are k hidden layers, each hidden layer has n neurons, and the input vector is Z, where Z∈[Z,Z+10d 50 ];

[0119] The output H of the i-th neuron in the l-th layer of the hidden layer li is: H li =SiLU(W li ·H l-1 +b li )

[0120] Among them H l-1 is the output of the previous hidden layer, W li is the weight matrix of hidden layer l, b li is the bias vector of hidden layer l;

[0121] Recursively, for the overall output vector H of the lth layer l is: H l =[H l1 ,H l2 ,H l3 ,....,H ln ]

[0122] Among them H ln is the output of the nth neuron in the lth layer;

[0123] The output matrix Q(u, v, w, P) of the output layer is expressed as: Q = W o ·H k +b0

[0124] Where W o is the weight matrix of the output layer, b0 is the bias vector of the output layer, H k is the output matrix of the kth hidden layer;

[0125] The output Q(u, v, w, P) of the entire neural network is expressed as: Q = W o ·SiLU(W k ·SiLU(...SiLU(W1·SiLU(P+b1)+b k-1 )...)

[0126] Where W k represents the weight matrix of the kth hidden layer, b k-1 is the bias vector of the k-1th hidden layer;

[0127] (3.2) Calculate the error of the second neural network. The error is defined as the linear combination of the initial condition error of the second neural network, the boundary condition error of the second neural network, and the NS equation constraint error of the second neural network:

[0128] The step (3.2) specifically includes the following steps:

[0129] Calculate the initial condition error loss of the second neural network IC ′:

[0130] where N IC′ is the number of training points at the initial moment of the second neural network, u n A sample speed u output by the second neural network n ={u n , v n ,ω n} T ; The true value of a sample's initial condition;

[0131] Calculate the boundary condition error loss of the second neural network BC′ :

[0132] where N BC′ is the number of training points on the boundary of the two neural networks, u n A sample speed u output by the second neural network n ={u n , v n ,ω n} T ; is the true value of a sample boundary condition;

[0133] Calculate the NS equation constraint error loss of the second neural network phy′ :

[0134] where N phy′ is the number of training points inside the flow field of the second neural network, u i A sample speed u output by the second neural network i ={u i , v i ,ω i} T , p i is the pressure of a sample output by the second neural network, R e is the fluid Reynolds number;

[0135] Calculate the error loss of the second neural network total′ : loss totak′ =α′loss phy′ +β ′ loss IC′ +γ′lossBC′

[0136] Among them, α′ is the linear superposition coefficient of the physical error of the second neural network, β′ is the linear superposition coefficient of the initial condition error of the second neural network, and γ′ is the linear superposition coefficient of the boundary condition error of the second neural network. The sizes of the three are generally on the order of 10;

[0137] (3.3) Error back propagation, update weights and biases until the training error converges;

[0138] (4) After the training errors of the first neural network and the second neural network converge, the trained first neural network and the second neural network that are connected in series are obtained;

[0139] (5) Input the X coordinate, Y coordinate and time T of the predicted sample into the first trained neural network, and output the corresponding sediment elevation change △H in the forward calculation; calculate the final corresponding riverbed elevation Z based on the output sediment elevation change △H;

[0140] The formula for calculating the final corresponding riverbed elevation Z is: Z=ΔH+Z0

[0141] Where △H is the final elevation change output by the first neural network, and Z0 is the riverbed elevation at the initial moment;

[0142] (6) The riverbed elevation Z of the predicted sample and the randomly selected points within a certain range above the riverbed elevation Z are used as the input of the trained second neural network, and the corresponding flow field parameters are obtained by forward calculation output. The flow field parameters include the X-direction velocity u, the Y-direction velocity v, the Z-direction velocity w and the pressure magnitude P.

[0143] This invention uses a multilayer perceptron neural network model and a multilayer perceptron neural network model in series for a single operating condition. This method simulates the scour process using a series physical information neural network architecture, Physics-Informed Scour Net, to achieve a foundation scour depth prediction method. This method can quickly and accurately predict underwater foundation scour depth and flow field distribution.

[0144] Example 2

[0145] As shown in Figures 1 and 3, multi-conditions refer to general conditions, such as scour conditions where parameters such as pier radius, pier shape, and flow field size are uncertain and can be modified according to different requirements. This invention introduces a mathematical-physical model related to scour depth into a deep learning algorithm for the first time, establishing a data-free scour simulation method. For multi-conditions, this invention provides a single-phase flow calculation method for bridge scour based on a physical information neural network, including the following steps:

[0146] (1) Selecting training samples and prediction samples to obtain coordinate data of the training samples and prediction samples, where the coordinate data includes the X coordinate, the Y coordinate, and the time T of the sample, specifically includes the following steps;

[0147] (1.1) Using a random sampling method, training samples are selected from the internal points of the flow field during the prediction period. The training samples include initial training points, boundary training points, and internal training points. Prediction samples are randomly selected within a circular area around the bridge pier within a radius of 4 to 6 times the bridge pier.

[0148] (1.2) Define the absolute space rectangular coordinate system;

[0149] (1.3) Calculate the X coordinates and Y coordinates of the training sample and the prediction sample, as well as the time T of the training sample;

[0150] (2) The X coordinate, Y coordinate and time T of the training sample are input into the first neural network for training, and the sediment elevation change △H is output, and the corresponding riverbed elevation Z is calculated;

[0151] The specific steps include:

[0152] (2.1) The first neural network is a multilayer perceptron neural network model. The X-coordinate, Y-coordinate and time T of the training sample are input into the first neural network, and the initial sediment elevation change △H is obtained by forward calculation.

[0153] The specific steps for forward calculation of the initial sediment elevation change ΔH in step (2.1) are as follows:

[0154] Define the activation function Swish function:

[0155] Where x is the input of the activation function;

[0156] Assume there are k hidden layers, each hidden layer has n neurons, and the input vector is P = [X, Y, T], where P∈R 3 ; The output H of the i-th neuron in the l-th layer of the hidden layer li is: H li =SiLU(W li ·H l-1 +b li )

[0157] Among them H l-1 is the output of the previous hidden layer, W li is the weight matrix of hidden layer l, b li is the bias vector of hidden layer l;

[0158] Recursively, for the overall output vector H of the lth layerl is: H l =[H l1 ,H l2 ,H l3 ,....,H ln ]

[0159] Among them H ln is the output of the nth neuron in the lth layer;

[0160] The output △H of the output layer of each forward calculation is expressed as: △H=W o ·H k +b0

[0161] Where W o is the weight matrix of the output layer, b0 is the bias vector of the output layer, H k is the output matrix of the kth hidden layer;

[0162] The output △H of the entire neural network is expressed as: △H=W o ·SiLU(W k ·SiLU(...SiLU(W1·SiLU(P+b1)+b k-1 )...)

[0163] Where W k represents the weight matrix of the kth hidden layer, b k-1 is the bias vector of the k-1th hidden layer;

[0164] (2.2) Calculate the corresponding riverbed elevation Z based on the output sediment elevation change △H;

[0165] The formula for calculating the corresponding riverbed elevation Z is: Z=ΔH+X0

[0166] Where △H is the elevation change output by the first neural network, and Z0 is the riverbed elevation at the initial moment;

[0167] (2.3) Calculate the error of the first neural network. The error is defined as the linear combination of the initial condition error of the first neural network and the constraint error of the sediment transport physical equation of the first neural network.

[0168] The specific steps of step (2.3) are:

[0169] Initial condition error loss of the first neural network IC Expressed as:

[0170] where N IC is the number of training points at the initial moment of the first neural network, △H is the initial sediment elevation change output by the first neural network;

[0171] The physical error constraint of the sediment transport equation of the first neural network is expressed as:

[0172] Where N phy is the number of internal training points of the first neural network, Z is the riverbed elevation, n is the riverbed sediment void ratio, which can be taken as 0.41; bx is the longitudinal single-width volume sediment transport rate, q by is the volumetric sediment transport rate per transverse width, q bx and q by The sum of the sediment transport rates per unit width q b Decompose it and get the sum of the single width volume sediment transport rate q b The calculation formula is: q0 is the volumetric sediment transport rate per unit width of the bed load in the plane, is the sediment repose angle, K0 is a constant related to q0;

[0173] Calculate the error loss of the first neural network total : loss total =αloss phy +βloss IC

[0174] Where α is the linear superposition coefficient of the physical error of the first neural network, and β is the linear superposition coefficient of the initial condition error of the first neural network. The magnitudes of the two are generally on the order of 10.

[0175] (2.4) Error back propagation, update weights and biases until the training error converges;

[0176] (3) The corresponding riverbed elevation Z calculated in step (2) is used as input into the second neural network for training, and the output is the corresponding flow field parameters, which include the X-direction velocity u, the Y-direction velocity v, the Z-direction velocity w, and the pressure magnitude P;

[0177] The specific steps include:

[0178] (3.1) The second neural network uses a DEEPONET neural network model. The riverbed elevation Z and 10 random points above the riverbed elevation Z within the median sediment particle size range are used as inputs of the second neural network. The initial flow field parameters are obtained through forward calculation.

[0179] The step (3.1) specifically includes the following steps:

[0180] The riverbed elevation Z and the median sediment particle size d 10 meters above the riverbed elevation Z are calculated. 50Random points within the size range are used as the input Z of the second neural network to calculate the flow field parameters in a forward direction to adapt to the changing flow field boundary; Z∈[Z,Z+10d 50 ]

[0181] Select N input functions:

[0182] Calculate the value matrix F of m evaluation points in N input functions:

[0183] Use F as branch (b k ) network input, Z as trunk(t k ) network input, the flow field parameter matrix Q (u, v, w, P) is calculated:

[0184] (3.2) Calculate the error of the second neural network. The error is defined as the linear combination of the initial condition error of the second neural network, the boundary condition error of the second neural network, and the NS equation constraint error of the second neural network:

[0185] The step (3.2) specifically includes the following steps:

[0186] Calculate the initial condition error loss of the second neural network IC′ :

[0187] where N IC′ is the number of training points at the initial moment of the second neural network, u n A sample speed u output by the second neural network n ={u n , v n ,ω n} T ; The true value of a sample's initial condition;

[0188] Calculate the boundary condition error loss of the second neural network BC′ :

[0189] where N BC′ is the number of training points on the boundary of the two neural networks, u n A sample speed u output by the second neural network n ={u n , v n ,ω n} T ; is the true value of a sample boundary condition;

[0190] Calculate the NS equation constraint error loss of the second neural network phy′ :

[0191] where N phy′ is the number of training points inside the flow field of the second neural network, u i A sample speed u output by the second neural network i ={u i , v i ,ω i} T , p i is the pressure of a sample output by the second neural network, R e is the fluid Reynolds number;

[0192] Calculate the error loss of the second neural network total′ : loss total′ =α′loss phy′ +β′loss IC′ +γ′loss BC′

[0193] Among them, α′ is the linear superposition coefficient of the physical error of the second neural network, β′ is the linear superposition coefficient of the initial condition error of the second neural network, and γ′ is the linear superposition coefficient of the boundary condition error of the second neural network. The sizes of the three are generally on the order of 10;

[0194] (3.3) Error back propagation, update weights and biases until the training error converges;

[0195] (4) After the training errors of the first neural network and the second neural network converge, the trained first neural network and the second neural network that are connected in series are obtained;

[0196] (5) Input the X coordinate, Y coordinate and time T of the predicted sample into the first trained neural network, and output the corresponding sediment elevation change △H in the forward calculation; calculate the final corresponding riverbed elevation Z based on the output sediment elevation change △H;

[0197] The formula for calculating the final corresponding riverbed elevation Z is: Z=ΔH+Z0

[0198] Where △H is the final elevation change output by the first neural network, and Z0 is the riverbed elevation at the initial moment;

[0199] (6) The riverbed elevation Z of the predicted sample and the randomly selected points within a certain range above the riverbed elevation Z are used as the input of the trained second neural network, and the corresponding flow field parameters are obtained by forward calculation output. The flow field parameters include the X-direction velocity u, the Y-direction velocity v, the Z-direction velocity w and the pressure magnitude P.

[0200] This invention utilizes a multi-layer perceptron neural network model and a Deeponet-style neural network model in series for multiple operating conditions, which is a generalization and improvement of a single operating condition. This method simulates the scour process using a series physical information neural network architecture, Physics-Informed Scour Net, to achieve a foundation scour depth prediction method. This method can quickly and accurately predict underwater foundation scour depth and flow field distribution.

Claims

1. A bridge scour single-phase flow calculation method based on physical information neural network, characterized in that: The steps include: (1) Select training samples and prediction samples, and obtain the coordinate data of the training samples and the prediction samples. The coordinate data includes the X coordinate, the Y coordinate, and the time T of the sample; (2) The X coordinate, Y coordinate and time T of the training sample are input into the first neural network for training, and the sediment elevation change △H is output, and the corresponding riverbed elevation Z is calculated; (3) The corresponding riverbed elevation Z calculated in step (2) is used as part of the input into the second neural network for training, and the output is the corresponding flow field parameters, which include the X-direction velocity u, the Y-direction velocity v, the Z-direction velocity w and the pressure magnitude P; (4) After the training errors of the first neural network and the second neural network converge, the trained first neural network and the second neural network that are connected in series are obtained; (5) Input the X coordinate, Y coordinate and time T of the predicted sample into the first trained neural network, and forward calculate the output as the corresponding sediment elevation change △H, and calculate the corresponding riverbed elevation Z; (6) The riverbed elevation Z of the predicted sample and the randomly selected points within a certain range above the riverbed elevation Z are used as the input of the trained second neural network, and the corresponding flow field parameters are obtained by forward calculation output. The flow field parameters include the X-direction velocity u, the Y-direction velocity v, the Z-direction velocity w and the pressure magnitude P.

2. The bridge scour single-phase flow calculation method based on physical information neural network according to claim 1 is characterized by: The step (1) specifically includes the following steps: (1.1) Using a random sampling method, training samples are selected from the internal points of the flow field during the prediction period. The training samples include initial training points, boundary training points, and internal training points. Prediction samples are randomly selected within a circular area around the bridge pier within a radius of 4 to 6 times the bridge pier. (1.2) Define the absolute space rectangular coordinate system; (1.3) Calculate the X coordinates, Y coordinates, and time T of the training and prediction samples.

3. The bridge scour single-phase flow calculation method based on physical information neural network according to claim 2 is characterized by: The step (2) specifically includes the following steps: (2.1) The first neural network is a multilayer perceptron neural network model. The X coordinate, Y coordinate, and time T of the training sample are input into the first neural network, and the initial sediment elevation change △H is obtained by forward calculation. (2.2) Calculate the riverbed elevation Z based on the output of the initial sediment elevation change △H; (2.3) Calculate the error of the first neural network. The error is defined as the linear combination of the initial condition error of the first neural network and the constraint error of the sediment transport physical equation of the first neural network. (2.4) Error backpropagation, update weights and biases until the training error converges.

4. The bridge scour single-phase flow calculation method based on physical information neural network according to claim 3 is characterized by: The specific steps for forward calculation of the initial sediment elevation change ΔH in step (2.1) are as follows: Define the activation function Swish function: Where x is the input of the activation function; Assume there are k hidden layers, each hidden layer has n neurons, and the input vector is P = [X, Y, T], where P∈R 3 ; The output H of the i-th neuron in the l-th layer of the hidden layer li for: A li =SiLU(W li H l-1 +b li ) Among them H l-1 is the output of the previous hidden layer, W li is the weight matrix of hidden layer l, b li is the bias vector of hidden layer l; Recursively, for the overall output vector H of the lth layer l for: H l =[H l1 ,H l2 ,H l2 ,....,H ln ] Among them H ln is the output of the nth neuron in the lth layer; The output △H of each forward calculation output layer is expressed as: △H=W o ·H k +b0 Where W o is the weight matrix of the output layer, b0 is the bias vector of the output layer, H k is the output matrix of the kth hidden layer; The output △H of the entire neural network is expressed as: △H=W o ·SiLU(W k ·SiLU(…SiLU(W1 ·SiLU(P+b1)+b k-1 )…) Where W k represents the weight matrix of the kth hidden layer, b k-1 is the bias vector of the k-1th hidden layer.

5. The bridge scour single-phase flow calculation method based on physical information neural network according to claim 4 is characterized by: The formula for calculating the corresponding riverbed elevation Z is: Z = ΔH + Z0 Where △H is the elevation change output by the first neural network, and Z0 is the riverbed elevation at the initial moment.

6. The bridge scour single-phase flow calculation method based on physical information neural network according to claim 5 is characterized by: The specific steps of step (2.3) are: Initial condition error loss of the first neural network IC Expressed as: where N IC is the number of training points at the initial moment of the first neural network, △H is the initial sediment elevation change output by the first neural network; The physical error constraint of the sediment transport equation of the first neural network is expressed as: Where N phy is the number of internal training points of the first neural network, Z is the riverbed elevation, n is the riverbed sediment void ratio, which can be taken as 0.41; bx is the longitudinal single-width volume sediment transport rate, q by is the volumetric sediment transport rate per transverse width, q bx and q by The sum of the sediment transport rates per unit width q b Decompose it and get the sum of the single width volume sediment transport rate q b The calculation formula is: q0 is the volumetric sediment transport rate per unit width of the bed load in the plane, is the sediment repose angle, K0 is a constant related to q0; Calculate the error loss of the first neural network total : loss total =αloss phy +βloss IC Where α is the linear superposition coefficient of the physical error of the first neural network, and β is the linear superposition coefficient of the initial condition error of the first neural network. The sizes of the two are generally on the order of 10.

7. The bridge scour single-phase flow calculation method based on physical information neural network according to claim 6 is characterized by: The step (3) specifically includes the following steps: (3.1) The second neural network uses a DEEPONET-type neural network model or a multilayer perceptron-type neural network model. The riverbed elevation Z and 10 randomly selected points within the median sediment particle size range above the riverbed elevation Z are used as inputs of the second neural network. The flow field parameters of the training samples are obtained through forward calculation. (3.2) Calculate the error of the second neural network, where the error is defined as a linear combination of the initial condition error of the second neural network, the boundary condition error of the second neural network, and the NS equation constraint error of the second neural network; (3.3) Error backpropagation, update weights and biases until the training error converges.

8. The bridge scour single-phase flow calculation method based on physical information neural network according to claim 7 is characterized by: When the second neural network uses a neural network model in the form of DEEPONET, the step (3.1) specifically includes the following steps: The riverbed elevation Z and the median sediment particle size d 10 meters above the riverbed elevation Z are calculated. 50 Randomly sampling points within the large and small ranges are used as the input of the second neural network to calculate the flow field parameters in a forward direction to adapt to the changing flow field boundary; Z∈[Z,Z+10d 50 ] Select N input functions: Calculate the value matrix F of m evaluation points in N input functions: Use F as branch (b k ) network input, Z as trunk(t k ) network input, the flow field parameter matrix Q (u, v, w, P) is calculated:

9. The bridge scour single-phase flow calculation method based on physical information neural network according to claim 7 is characterized by: When the second neural network uses a multilayer perceptron neural network model, the step (3.1) specifically includes the following steps: The riverbed elevation Z and the median sediment particle size d 10 meters above the riverbed elevation Z are calculated. 50 Randomly sampling points within the large and small ranges are used as the input of the second neural network to calculate the flow field parameters in a forward direction to adapt to the changing flow field boundary; Z∈[Z,Z+10d 50 ] Define the activation function Swish function: Where x is the input of the activation function; Assume there are k hidden layers, each hidden layer has n neurons, and the input vector is Z, where Z∈[Z,Z+10d 50 ]; The output H of the i-th neuron in the l-th layer of the hidden layer li for: A li =SiLU(W li H l-1 +b li ) Among them H l-1 is the output of the previous hidden layer, W li is the weight matrix of hidden layer l, b li is the bias vector of hidden layer l; Recursively, for the overall output vector H of the lth layer l for: H l =[H l1 ,H l2 ,H l3 ,....,H ln ] Among them H ln is the output of the nth neuron in the lth layer; The output matrix Q(u, v, w, P) of the output layer is expressed as: Q=W o ·H k +b0 Where W o is the weight matrix of the output layer, b0 is the bias vector of the output layer, H k is the output matrix of the kth hidden layer; The output Q(u, v, w, P) of the entire neural network is expressed as: Q=W o ·SiLU(W k ·SiLU(…SiLU(W1 ·SiLU(P+b1)+b k-1 )…) Where W k represents the weight matrix of the kth hidden layer, b k-1 is the bias vector of the k-1th hidden layer.

10. The bridge scour single-phase flow calculation method based on physical information neural network according to claim 8 or 9, characterized in that: The step (3.2) specifically includes the following steps: Calculate the initial condition error loss of the second neural network IC′ : where N IC′ is the number of training points at the initial moment of the second neural network, u n A sample speed u output by the second neural network n ={u n , v n ,ω n } T ; The true value of a sample's initial condition; Calculate the boundary condition error loss of the second neural network BC′ : where N BC′ is the number of training points on the boundary of the two neural networks, u n A sample speed u output by the second neural network n ={u n , v n ,ω n } T ; is the true value of a sample boundary condition; Calculate the NS equation constraint error loss of the second neural network phy′ : where N phy′ is the number of training points inside the flow field of the second neural network, u i A sample speed u output by the second neural network i ={u i , v i ,ω i } T , p i is the pressure of a sample output by the second neural network, R e is the fluid Reynolds number; Calculate the error loss of the second neural network total′ : loss total′ =α′loss phy′ +β′loss IC′ +γ′loss BC′ Among them, α′ is the linear superposition coefficient of the physical error of the second neural network, β′ is the linear superposition coefficient of the initial condition error of the second neural network, and γ′ is the linear superposition coefficient of the boundary condition error of the second neural network. The sizes of the three are generally on the order of 10.

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