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

Abstract

The present invention discloses a bridge scour single-phase flow calculation method based on a physical information neural network, comprising the following steps: selecting training samples and prediction samples to obtain corresponding coordinate data; inputting the training sample coordinate data into a first neural network for training, outputting the sediment elevation change, and calculating the corresponding riverbed elevation; inputting the corresponding riverbed elevation into a second neural network for training as partial input, and outputting the corresponding flow field parameters; after the training errors of both networks converge, obtaining two trained neural networks in series; inputting the prediction sample coordinate data into the trained first neural network, forward calculating and outputting the corresponding sediment elevation change, and calculating the corresponding riverbed elevation; and inputting the predicted sample riverbed elevation and a randomly selected point within a certain range above the riverbed elevation into the trained second neural network, and forward calculating and outputting the corresponding flow field parameters. The present invention has wide applicability.

Description

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. Summary of the Invention

[0005] 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.

[0006] 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:

[0007] (1) Select training samples and prediction samples, and obtain the coordinate data of the training samples and prediction samples. The coordinate data includes X coordinate, Y Coordinates and time of sample T ;

[0008] (2) The training samples X coordinate, Y Coordinates and time of sample T It is put into the first neural network as input for training and outputs the change in sediment elevation △ H , and calculate the corresponding riverbed elevation Z ;

[0009] (3) The corresponding riverbed elevation calculated in step (2) Z As part of the input, it is put into the second neural network for training, and the output is the corresponding flow field parameters. The flow field parameters include X Directional speed u 、 Y Directional speed v 、 Z Directional speed w and pressure magnitude P ;

[0010] (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;

[0011] (5) The predicted sample X coordinate, Y Coordinates and time of sample T Input the first trained neural network, and the forward calculation output is the corresponding sediment elevation change △ H , and calculate the corresponding riverbed elevation Z ;

[0012] (6) The riverbed elevation of the predicted sample Z and riverbed elevation Z Randomly sample points within a certain range upwards as the input of the trained second neural network, and forward calculation outputs the corresponding flow field parameters. The flow field parameters include X Directional speed u 、 Y Directional speed v 、 Z Directional speed w and pressure magnitude P .

[0013] Wherein, step (1) specifically includes the following steps:

[0014] (1.1) Random sampling is used to select training samples from 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.

[0015] (1.2) Define the absolute space rectangular coordinate system;

[0016] (1.3) Calculate the training samples and prediction samples X coordinate, Y Coordinates and time of the sample T .

[0017] Preferably, step (2) specifically includes the following steps:

[0018] (2.1) The first neural network is a multi-layer perceptron neural network model, which transforms the training samples into X coordinate, Y Coordinates, sample time T Input the first neural network and forward calculate the initial sediment elevation change △ H ;

[0019] (2.2) According to the output of the initial sediment elevation change △ H Calculate riverbed elevation Z ;

[0020] (2.3) Calculate the error of the first neural network, where the error is defined as a linear combination of the initial condition error of the first neural network and the error of the sediment transport physical equation constraint of the first neural network;

[0021] (2.4) Error backpropagation, updating weights and biases until the training error converges.

[0022] Furthermore, the initial sediment elevation change △ in step (2.1) H The specific steps of forward calculation are:

[0023] Define the activation function Swish function:

[0024] ,

[0025] in x Is the input of the activation function;

[0026] Assume there is k Layer hidden layer, a hidden layer has n neurons, the input vector is P =[ X,Y,T ],in ; The hidden layer l Layer i The output of a neuron for:

[0027] ,

[0028] in is the output of the previous hidden layer, is the hidden layer The weight matrix, is the hidden layer The bias vector of

[0029] Recursively, for l The overall output vector of the layer for:

[0030] ,

[0031] in For the l Layer n The output of a neuron;

[0032] Each forward calculation of the output layer's output △ H Expressed as:

[0033] ,

[0034] in is the weight matrix of the output layer, is the bias vector of the output layer, H k For the k The output matrix of the hidden layer;

[0035] The output of the entire neural network △ H express:

[0036] ,

[0037] in Indicates the k The weight matrix of the hidden layer, It is k Bias vector for the hidden layer.

[0038] Optionally, the riverbed elevation corresponding to the calculation Z The formula is:

[0039] ,

[0040] where △ H is the elevation change output by the first neural network, Z 0 is the riverbed elevation at the initial moment.

[0041] Preferably, the specific steps of step (2.3) are:

[0042] Initial condition error of the first neural network Expressed as:

[0043] ,

[0044] in 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;

[0045] The physical error constraint of the sediment transport equation of the first neural network is expressed as:

[0046] ,

[0047] In the formula is the number of internal training points of the first neural network, Z is the riverbed elevation, n is the porosity of riverbed sediment, which can be taken as 0.41; is the longitudinal single-width volume sediment transport rate, is the volumetric sediment transport rate per lateral width, and The sum of the sediment transport rate per unit width Decomposed to get the sum of the single width volume sediment transport rate The calculation formula is: , is the sediment transport rate per unit width of the bed load in the plane, is the sediment repose angle, For Related constants;

[0048] Calculate the error of the first neural network :

[0049] ,

[0050] in α is the physical error linear superposition coefficient of the first neural network, β is the linear superposition coefficient of the initial condition error of the first neural network, and the magnitudes of the two are on the order of 10.

[0051] Furthermore, step (3) specifically includes the following steps:

[0052] (3.1) The second neural network uses a neural network model in the form of DEEPONET or a multi-layer perceptron neural network model to transform the riverbed elevation Z and riverbed elevation Z Randomly sample points within the upper 10 median sediment particle sizes as the input of the second neural network, and forward calculate the flow field parameters of the training samples;

[0053] (3.2) Calculate the error of the second neural network. The error is defined as the initial condition error of the second neural network, the boundary condition error of the second neural network, and the error of the second neural network. NS Linear combination of equation constraint errors;

[0054] (3.3) Error backpropagation, updating weights and biases until the training error converges.

[0055] 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:

[0056] The riverbed elevation Z and the median particle size of sediment 10 meters above the riverbed elevation Z are calculated. d 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;

[0057] ,

[0058] choose N Input functions:

[0059] ,

[0060] calculate m Evaluation points in N matrix of values in the input function F :

[0061] ,

[0062] Will F As branch(b k ) network input, Z as trunk(t k ) network input, the flow field parameter matrix Q( u , v , w 、 P ):

[0063] .

[0064] Preferably, when the second neural network adopts a multilayer perceptron neural network model, the step (3.1) specifically includes the following steps:

[0065] The riverbed elevation Z and the median particle size of sediment 10 meters above the riverbed elevation Z are calculated. d 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;

[0066] ,

[0067] Define the activation function Swish function:

[0068] ,

[0069] Where x is the input of the activation function;

[0070] Assume there are k hidden layers, each hidden layer has n neurons, and the input vector is Z, where ,

[0071] The hidden layer l Layer i The output of a neuron for: ,in is the output of the previous hidden layer, is the hidden layer The weight matrix, is the hidden layer The bias vector of

[0072] Recursively, for l The overall output vector of the layer for: , among which l Layer n The output of a neuron;

[0073] Each forward calculation of the output matrix Q of the output layer ( u , v , w 、 P ) is expressed as: ,in is the weight matrix of the output layer, is the bias vector of the output layer, H k For the k The output matrix of the hidden layer; the output Q of the entire neural network ( u , v , w 、 P )express: ,in represents the weight matrix of the kth hidden layer, is the bias vector of the kth hidden layer.

[0074] Furthermore, the step (3.2) specifically includes the following steps:

[0075] Calculate the initial condition error of the second neural network :

[0076] ,

[0077] in is the number of training points at the initial moment of the second neural network, A sample speed output by the second neural network ; The true value of a sample's initial condition;

[0078] Calculate the boundary condition error of the second neural network :

[0079] ,

[0080] in is the number of training points on the boundary of the two neural networks, A sample speed output by the second neural network ; is the true value of a sample boundary condition;

[0081] Calculate the second neural network NSEquation constraint error :

[0082] ,

[0083] in is the number of training points inside the flow field of the second neural network, A sample speed output by the second neural network , is the pressure of a sample output by the second neural network, is the fluid Reynolds number;

[0084] Calculate the error of the second neural network :

[0085] ,

[0086] in is the physical error linear superposition coefficient of the second neural network, is the linear superposition coefficient of the initial condition error of the second neural network, is the linear superposition coefficient of the boundary condition error of the second neural network, and the three are on the order of 10.

[0087] 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

[0088] Figure 1 is a flow chart of the present invention;

[0089] Figure 2 This is the network structure for a single working condition in Example 1 of the present invention;

[0090] Figure 3 This is the network structure for multiple working conditions in Example 2 of the present invention. DETAILED DESCRIPTION

[0091] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0092] Example 1: Figure 1 and Figure 2 As shown, a single working condition refers to a scour working condition under a specific working condition, such as a scour working condition in which parameters such as the pier radius, pier shape, and flow field size are fixed and unchanged. The present 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 working condition, the present invention provides a bridge scour single-phase flow calculation method based on a physical information neural network, including the following steps:

[0093] (1) Select training samples and prediction samples, and obtain the coordinate data of the training samples and prediction samples. The coordinate data includes X coordinate, Y Coordinates and time of sample T , specifically including the following steps:

[0094] (1.1) Random sampling is used to select training samples from 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.

[0095] (1.2) Define the absolute space rectangular coordinate system;

[0096] (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;

[0097] (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;

[0098] The specific steps include:

[0099] (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 through forward calculation.

[0100] The specific steps for forward calculation of the initial sediment elevation change △H in step (2.1) are as follows:

[0101] Define the activation function Swish function:

[0102] ,

[0103] Where x is the input of the activation function;

[0104] Assume there are k hidden layers, each hidden layer has n neurons, and the input vector is P=[X,Y,T], where ; The output of the i-th neuron in the l-th layer of the hidden layer for:

[0105] ,

[0106] in is the output of the previous hidden layer, is the hidden layer The weight matrix, is the hidden layer The bias vector of

[0107] Recursively, for the overall output vector of layer l for:

[0108] ,

[0109] in is the output of the nth neuron in the lth layer;

[0110] The output △H of each forward calculation output layer is expressed as:

[0111] ,

[0112] in is the weight matrix of the output layer, is the bias vector of the output layer, Hk is the output matrix of the kth hidden layer;

[0113] The output △H of the entire neural network is expressed as:

[0114] ,

[0115] in represents the weight matrix of the kth hidden layer, is the bias vector of the kth hidden layer;

[0116] (2.2) Calculate the corresponding riverbed elevation Z based on the output sediment elevation change △H;

[0117] The formula for calculating the corresponding riverbed elevation Z is:

[0118] ,

[0119] Where △H is the elevation change output by the first neural network, and Z0 is the riverbed elevation at the initial moment;

[0120] (2.3) Calculate the error of the first neural network, where the error is defined as a linear combination of the initial condition error of the first neural network and the error of the sediment transport physical equation constraint of the first neural network;

[0121] The specific steps of step (2.3) are:

[0122] Initial condition error of the first neural network Expressed as:

[0123] ,

[0124] in 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;

[0125] The physical error constraint of the sediment transport equation of the first neural network is expressed as:

[0126] ,

[0127] In the formula is the number of internal training points of the first neural network, Z is the riverbed elevation, and n is the riverbed sediment void ratio, which can be taken as 0.41; is the longitudinal single-width volume sediment transport rate, is the volumetric sediment transport rate per lateral width, and The sum of the sediment transport rate per unit width Decomposed to get the sum of the single width volume sediment transport rate The calculation formula is: , is the sediment transport rate per unit width of the bed load in the plane, is the sediment repose angle, For Related constants;

[0128] Calculate the error of the first neural network :

[0129] ,

[0130] 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.

[0131] (2.4) Error backpropagation, updating weights and biases until the training error converges.

[0132] (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;

[0133] The specific steps include:

[0134] (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.

[0135] The step (3.1) specifically includes the following steps:

[0136] The riverbed elevation Z and the median particle size of sediment 10 meters above the riverbed elevation Z are calculated. d 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;

[0137] ,

[0138] Define the activation function Swish function:

[0139] ,

[0140] Where x is the input of the activation function;

[0141] Assume there are k hidden layers, each hidden layer has n neurons, and the input vector is Z, where ;

[0142] The hidden layer l Layer i The output of a neuron for:

[0143] ,

[0144] in is the output of the previous hidden layer, is the hidden layer The weight matrix, is the hidden layer The bias vector of

[0145] Recursively, for l The overall output vector of the layer for:

[0146] ,

[0147] Among them is the l The output of the nth neuron in the layer;

[0148] Each forward calculation of the output matrix Q( u , v , w 、 P ) is expressed as:

[0149] ,

[0150] in is the weight matrix of the output layer, is the bias vector of the output layer, H k For the k The output matrix of the hidden layer;

[0151] The output Q( u , v , w 、 P )express:

[0152]

[0153] in represents the weight matrix of the kth hidden layer, is the bias vector of the kth hidden layer;

[0154] (3.2) Calculate the error of the second neural network. 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:

[0155] The step (3.2) specifically includes the following steps:

[0156] Calculate the initial condition error of the second neural network :

[0157] ,

[0158] in is the number of training points at the initial moment of the second neural network, A sample speed output by the second neural network ; is the true value of the initial condition of a sample;

[0159] Calculate the boundary condition error of the second neural network :

[0160] , ,

[0161] in is the number of training points on the boundary of the two neural networks, A sample speed output by the second neural network ; is the true value of a sample boundary condition;

[0162] Calculate the NS equation constraint error of the second neural network :

[0163]

[0164] in is the number of training points inside the flow field of the second neural network, A sample speed output by the second neural network , is the pressure of a sample output by the second neural network, is the fluid Reynolds number;

[0165] Calculate the error of the second neural network :

[0166] ,

[0167] in is the physical error linear superposition coefficient of the second neural network, is the linear superposition coefficient of the initial condition error of the second neural network, is the linear superposition coefficient of the boundary condition error of the second neural network, and the three are generally on the order of 10;

[0168] (3.3) Error backpropagation, updating weights and biases until the training error converges;

[0169] (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;

[0170] (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;

[0171] The formula for calculating the final corresponding riverbed elevation Z is:

[0172] ,

[0173] Where △H is the final elevation change output by the first neural network, and Z0 is the riverbed elevation at the initial moment;

[0174] (6) The riverbed elevation Z of the predicted sample and a random point 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.

[0175] The present invention employs 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.

[0176] Example 2: Figure 1 and Figure 3 As shown, multi-condition refers to general working conditions, such as scour conditions where parameters such as pier radius, pier shape, and flow field size are uncertain and can be changed according to different requirements. The present 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, the present invention provides a bridge scour single-phase flow calculation method based on a physical information neural network, including the following steps:

[0177] (1) Select training samples and prediction samples, and obtain the coordinate data of the training samples and prediction samples. The coordinate data includes X coordinate, Y Coordinates and time of sample T , specifically including the following steps:

[0178] (1.1) Random sampling is used to select training samples from 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.

[0179] (1.2) Define the absolute space rectangular coordinate system;

[0180] (1.3) Calculate the training samples and prediction samples X coordinate, Y Coordinates and time of training samples T ;

[0181] (2) The training samples X coordinate, Y Coordinates and time of sample TIt is put into the first neural network as input for training and outputs the change in sediment elevation △ H , and calculate the corresponding riverbed elevation Z ;

[0182] The specific steps include:

[0183] (2.1) The first neural network is a multi-layer perceptron neural network model, which transforms the training samples into X coordinate, Y Coordinates and time of sample T Input the first neural network and forward calculate the initial sediment elevation change △ H ;

[0184] The initial sediment elevation change in step (2.1) is △ H The specific steps of forward calculation are:

[0185] Define the activation function Swish function:

[0186] ,

[0187] in x Is the input of the activation function;

[0188] Assume there is k Layer hidden layer, a hidden layer has n neurons, the input vector is P =[ X,Y,T ],in ; The hidden layer l Layer i The output of a neuron for:

[0189] ,

[0190] in is the output of the previous hidden layer, is the hidden layer The weight matrix, is the hidden layer The bias vector of

[0191] Recursively, for l The overall output vector of the layer for:

[0192] ,

[0193] in For the l Layer n The output of a neuron;

[0194] Each forward calculation of the output layer's output △ H Expressed as:

[0195] ,

[0196] in is the weight matrix of the output layer, is the bias vector of the output layer, H k For the k The output matrix of the hidden layer;

[0197] The output of the entire neural network △ H express: ,

[0198] in Indicates the k The weight matrix of the hidden layer, It is k The bias vector of the hidden layer;

[0199] (2.2) According to the output sediment elevation change △ H Calculate the corresponding riverbed elevation Z ;

[0200] The corresponding riverbed elevation is calculated Z The formula is:

[0201]

[0202] where △ H is the elevation change output by the first neural network, Z 0 is the riverbed elevation at the initial moment;

[0203] (2.3) Calculate the error of the first neural network, where the error is defined as a linear combination of the initial condition error of the first neural network and the error of the sediment transport physical equation constraint of the first neural network;

[0204] The specific steps of step (2.3) are:

[0205] Initial condition error of the first neural network Expressed as:

[0206] ,

[0207] in 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;

[0208] The physical error constraint of the sediment transport equation of the first neural network is expressed as:

[0209] ,

[0210] In the formula is the number of internal training points of the first neural network, Z is the riverbed elevation, n is the porosity of riverbed sediment, which can be taken as 0.41; is the longitudinal single-width volume sediment transport rate, is the volumetric sediment transport rate per lateral width, and The sum of the sediment transport rate per unit width Decomposed to get the sum of the single width volume sediment transport rate The calculation formula is: , is the sediment transport rate per unit width of the bed load in the plane, is the sediment repose angle, For Related constants;

[0211] Calculate the error of the first neural network :

[0212]

[0213] in α is the physical error linear superposition coefficient of the first neural network, β is the linear superposition coefficient of the initial condition error of the first neural network, and the magnitudes of the two are generally on the order of 10;

[0214] (2.4) Error backpropagation, updating weights and biases until the training error converges;

[0215] (3) The corresponding riverbed elevation calculated in step (2) Z The second neural network is trained as input, and the output is the corresponding flow field parameters. The flow field parameters include X Directional speed u 、 Y Directional speed v 、 Z Directional speed w and pressure magnitude P ;

[0216] The specific steps include:

[0217] (3.1) The second neural network uses the DEEPONET neural network model to convert the riverbed elevation Z and riverbed elevation ZRandomly sample points within the upper 10 median sediment particle sizes as the input of the second neural network, and forward calculate to obtain the initial flow field parameters;

[0218] The step (3.1) specifically includes the following steps:

[0219] The riverbed elevation Z and the median particle size of sediment 10 meters above the riverbed elevation Z are calculated. d 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;

[0220] ,

[0221] choose N Input functions:

[0222] ,

[0223] calculate m Evaluation points in N matrix of values in the input function F :

[0224]

[0225] Will F As branch(b k ) network input, Z as trunk(t k ) network input, the flow field parameter matrix Q( u , v , w 、 P ):

[0226]

[0227] (3.2) Calculate the error of the second neural network. The error is defined as the initial condition error of the second neural network, the boundary condition error of the second neural network, and the error of the second neural network. NS Linear combination of equation constraint errors:

[0228] The step (3.2) specifically includes the following steps:

[0229] Calculate the initial condition error of the second neural network :

[0230] ,

[0231] in is the number of training points at the initial moment of the second neural network, A sample speed output by the second neural network ; is the true value of the initial condition of a sample;

[0232] Calculate the boundary condition error of the second neural network :

[0233] ,

[0234] in is the number of training points on the boundary of the two neural networks, A sample speed output by the second neural network ; is the true value of a sample boundary condition;

[0235] Calculate the second neural network NS Equation constraint error :

[0236] ,

[0237] in is the number of training points inside the flow field of the second neural network, A sample speed output by the second neural network , is the pressure of a sample output by the second neural network, is the fluid Reynolds number;

[0238] Calculate the error of the second neural network :

[0239] ,

[0240] in is the physical error linear superposition coefficient of the second neural network, is the linear superposition coefficient of the initial condition error of the second neural network, is the linear superposition coefficient of the boundary condition error of the second neural network, and the three are generally on the order of 10;

[0241] (3.3) Error backpropagation, updating weights and biases until the training error converges;

[0242] (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;

[0243] (5) The predicted sample X coordinate, Y Coordinates and time of sample TInput the first trained neural network, and the forward calculation output is the corresponding sediment elevation change △ H ; According to the output sediment elevation change △ H Calculate the final corresponding riverbed elevation Z ;

[0244] Calculate the final corresponding riverbed elevation Z The formula is:

[0245] ,

[0246] where △ H is the final elevation change output by the first neural network, Z 0 is the riverbed elevation at the initial moment;

[0247] (6) The riverbed elevation of the predicted sample Z and riverbed elevation Z Randomly sample points within a certain range upwards as the input of the trained second neural network, and forward calculation outputs the corresponding flow field parameters. The flow field parameters include X Directional speed u 、 Y Directional speed v 、 Z Directional speed w and pressure magnitude P .

[0248] 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 prediction samples. The coordinate data includes X coordinate, Y Coordinates and time of sample T ; (2) The training samples X coordinate, Y Coordinates and time of sample T It is put into the first neural network as input for training and outputs the change in sediment elevation △ H , and calculate the corresponding riverbed elevation Z ; (3) The corresponding riverbed elevation calculated in step (2) Z As part of the input, it is put into the second neural network for training, and the output is the corresponding flow field parameters. The flow field parameters include X Directional speed u 、 Y Directional speed v 、 Z Directional speed w and 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) The predicted sample X coordinate, Y Coordinates and time of sample T Input the first trained neural network, and the forward calculation output is the corresponding sediment elevation change △ H , and calculate the corresponding riverbed elevation Z ; (6) The riverbed elevation of the predicted sample Z and riverbed elevation Z Randomly sample points within a certain range upwards as the input of the trained second neural network, and forward calculation outputs the corresponding flow field parameters. The flow field parameters include X Directional speed u 、 Y Directional speed v 、 Z Directional speed w and 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) Random sampling is used to select training samples from 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 training samples and prediction samples X coordinate, Y Coordinates and time of the sample T .

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 multi-layer perceptron neural network model, which transforms the training samples into X coordinate, Y Coordinates, sample time T Input the first neural network and forward calculate the initial sediment elevation change △ H ; (2.2) According to the output of the initial sediment elevation change △ H Calculate riverbed elevation Z ; (2.3) Calculate the error of the first neural network, where the error is defined as a linear combination of the initial condition error of the first neural network and the error of the sediment transport physical equation constraint of the first neural network; (2.4) Error backpropagation, updating 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 initial sediment elevation change in step (2.1) is △ H The specific steps of forward calculation are: Define the activation function Swish function: ， in x Is the input of the activation function; Assume there is k Layer hidden layer, a hidden layer has n neurons, the input vector is P =[ X,Y,T ],in ; The hidden layer l Layer i The output of a neuron for: ， in is the output of the previous hidden layer, is the hidden layer The weight matrix, is the hidden layer The bias vector of Recursively, for l The overall output vector of the layer for: ， in For the l Layer n The output of a neuron; Each forward calculation of the output layer's output △ H Expressed as: ， in is the weight matrix of the output layer, is the bias vector of the output layer, H k For the k The output matrix of the hidden layer; The output of the entire neural network △ H express: ， in Indicates the k The weight matrix of the hidden layer, It is k Bias vector for the 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 riverbed elevation corresponding to the calculation Z The formula is: ， where △ H is the elevation change output by the first neural network, Z 0 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 of the first neural network Expressed as: ， in 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: ， In the formula is the number of internal training points of the first neural network, Z is the riverbed elevation, n is the porosity of riverbed sediment, which can be taken as 0.41; is the longitudinal single-width volume sediment transport rate, is the volumetric sediment transport rate per lateral width, and The sum of the sediment transport rate per unit width Decomposed to get the sum of the single width volume sediment transport rate The calculation formula is: , is the sediment transport rate per unit width of the bed load in the plane, is the sediment repose angle, For Related constants; Calculate the error of the first neural network : ， in α is the physical error linear superposition coefficient of the first neural network, β is the linear superposition coefficient of the initial condition error of the first neural network, and the magnitudes of the two are 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 neural network model in the form of DEEPONET or a multi-layer perceptron neural network model to transform the riverbed elevation Z and riverbed elevation Z Randomly sample points within the upper 10 median sediment particle sizes as the input of the second neural network, and forward calculate the flow field parameters of the training samples; (3.2) Calculate the error of the second neural network. The error is defined as the initial condition error of the second neural network, the boundary condition error of the second neural network, and the error of the second neural network. NS Linear combination of equation constraint errors; (3.3) Error backpropagation, updating 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 particle size of sediment 10 meters above the riverbed elevation Z are calculated. d 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; ， choose N Input functions: ， calculate m Evaluation points in N matrix of values in the input function F : ， Will F As branch(b k ) network input, Z as trunk(t k ) network input, the flow field parameter matrix Q( u , v , w 、 P ): 。 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 adopts a multilayer perceptron neural network model, the step (3.1) specifically includes the following steps: The riverbed elevation Z and the median particle size of sediment 10 meters above the riverbed elevation Z are calculated. d 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; ， 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 , The hidden layer l Layer i The output of a neuron for: ,in is the output of the previous hidden layer, is the hidden layer The weight matrix, is the hidden layer The bias vector of Recursively, for l The overall output vector of the layer for: , among which l Layer n The output of a neuron; Each forward calculation of the output matrix Q of the output layer ( u , v , w 、 P ) is expressed as: ,in is the weight matrix of the output layer, is the bias vector of the output layer, H k For the k The output matrix of the hidden layer; the output Q of the entire neural network ( u , v , w 、 P )express: ,in represents the weight matrix of the kth hidden layer, is the bias vector of the kth 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 of the second neural network : ， in is the number of training points at the initial moment of the second neural network, A sample speed output by the second neural network ; The true value of a sample's initial condition; Calculate the boundary condition error of the second neural network : ， in is the number of training points on the boundary of the two neural networks, A sample speed output by the second neural network ; is the true value of a sample boundary condition; Calculate the second neural network NS Equation constraint error : ， in is the number of training points inside the flow field of the second neural network, A sample speed output by the second neural network , is the pressure of a sample output by the second neural network, is the fluid Reynolds number; Calculate the error of the second neural network : ， in is the physical error linear superposition coefficient of the second neural network, is the linear superposition coefficient of the initial condition error of the second neural network, is the linear superposition coefficient of the boundary condition error of the second neural network, and the three are on the order of 10.

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