Subsea tunnel ion erosion analysis method based on embedded physical information neural network

Abstract

The invention discloses a subsea tunnel ion erosion analysis method based on an embedded physical information neural network. The subsea tunnel ion erosion analysis method comprises the steps of solving and constructing a pore water pressure control equation and obtaining a pore water pressure field; acquiring a seepage velocity field according to the pore water pressure field; inputting the seepage velocity field as a key parameter into a convection-dispersion equation so as to obtain the erosion ion concentration representing the migration process of the erosion ions under the driving of the pore water pressure; acquiring a training set and a test set; performing model training on the constructed physical information neural network model through the training set to obtain a trained physical information neural network model; based on the constructed physical loss function, performing model verification on the trained physical information neural network model to obtain an optimal prediction model; therefore, analysis and prediction of subsea tunnel ion erosion are realized. According to the method, the problem that the accuracy and calculation efficiency of ion erosion prediction of the subsea tunnel are low due to the fact that an existing research method still has many defects in the aspects of calculation precision, efficiency and applicability is solved.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of transportation infrastructure and computer science, and in particular to a method for analyzing ion erosion of submarine tunnels based on a neural network embedded with physical information. Background Technology

[0002] With the rapid development of my country's rail transit, the scale of undersea tunnel construction has been continuously expanding, making them important transportation hubs connecting both sides of the strait. During their long-term service, undersea tunnels must withstand the influence of complex environmental factors such as high water pressure, corrosive ions, and temperature changes. Among these, chloride ions, due to their high concentration, strong penetrability, and high corrosiveness, have become a key factor affecting the durability and service safety of undersea tunnels. Under high water pressure, chloride ions can gradually penetrate into the concrete, leading to steel corrosion, cracking of the concrete cover, and weakening the bond between concrete and steel reinforcement, ultimately reducing the structure's load-bearing capacity. Therefore, studying the chloride ion corrosion mechanism of undersea tunnels under high water pressure is of great significance for ensuring the long-term safe operation of undersea tunnels.

[0003] Currently, research methods for ion erosion mainly include laboratory experiments, theoretical analysis, and finite element numerical simulation. While laboratory experiments can realistically reproduce the erosion process, they are time-consuming and costly, making it difficult to simulate the long-term service environment of subsea tunnels. Theoretical analysis methods can study erosion patterns from a mathematical perspective, but they struggle to handle complex boundary conditions and have limited applicability. Finite element numerical simulation can numerically solve the erosion process, but its computational efficiency is low, and it relies heavily on seepage models, making it difficult to accurately describe the erosion evolution process throughout the entire lifecycle of subsea tunnels. Therefore, existing research methods still have many shortcomings in terms of computational accuracy, efficiency, and applicability, necessitating the introduction of new computational methods to improve the accuracy and computational efficiency of erosion prediction. Summary of the Invention

[0004] This invention provides a method for analyzing ion erosion of submarine tunnels based on a neural network embedded with physical information, in order to overcome the above-mentioned technical problems.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A method for analyzing ion erosion of submarine tunnels based on a neural network embedded with physical information specifically includes the following steps:

[0007] S1: Based on the Hansbo nonlinear seepage model, construct the pore water pressure control equations corresponding to different spatial locations in the submarine tunnel under different tunnel service times, and solve the pore water pressure control equations to obtain the pore water pressure field.

[0008] Based on Hansbo's seepage law, the seepage velocity field is obtained from the pore water pressure field;

[0009] The seepage velocity field is used as a key parameter to input into the pre-set convection-dispersion equation to obtain the concentration of corrosive ions that characterizes the migration process of corrosive ions driven by pore water pressure.

[0010] S2: Obtain the dataset and randomly divide it into a training set and a test set;

[0011] Furthermore, the feature data in the dataset consists of spatiotemporal data corresponding to different spatial locations in the submarine tunnel at different times; the label data of the spatiotemporal data consists of pore water pressure field and erosion ion concentration.

[0012] S3: Construct a physical information neural network model to simultaneously solve for pore water pressure and corrosion ion concentration. Train the physical information neural network model using a training set to obtain the trained physical information neural network model. Based on the constructed physical loss function, validate the trained physical information neural network model to obtain the optimal prediction model.

[0013] S4: Based on the optimal prediction model, realize the analysis and prediction of ion erosion of submarine tunnels based on a neural network embedded with physical information.

[0014] Furthermore, the method for constructing the pore water pressure control equations corresponding to different spaces in the submarine tunnel at different times in S1 specifically includes:

[0015] S11: Based on the Hansbo nonlinear seepage model, the diffusion rate of corrosive ions carried by pore water in a submarine tunnel is constructed:

[0016] And the model expression for the diffusion rate is:

[0017]

[0018] In the formula: u represents the diffusion rate of corrosive ions carried by pore water in the submarine tunnel, and u is the simplified form of u(x); k hc k represents the permeability coefficient corresponding to the curve segment in Hansbo's law. hl represents the permeability coefficient corresponding to the straight segment in Hansbo's law; i1 represents the critical hydraulic gradient used to distinguish between the straight and curved segments in Hansbo's law; m represents the nonlinear parameter; ρ represents the density of pore water; g represents the acceleration due to gravity; p represents the pore water pressure; x represents the radial position within the lining or grouting ring of a submarine tunnel; u c This represents the critical velocity at the transition point from a curved segment to a straight segment in Hansbo's law.

[0019] S12: Select two cross-sections separated by a distance dx inside the concrete of the undersea tunnel, and obtain the flow difference of pore water through the two cross-sections. The expression for this difference is:

[0020]

[0021] In the formula: ΔQ represents the flow difference; Q Ι Q Π This represents the inflow rate at two cross-sections separated by a distance dx; A represents the cross-sectional area of ​​the grout-filled concrete body; t represents the time parameter.

[0022] S13: Obtain the bulk modulus of elasticity of concrete in the undersea tunnel, its expression is:

[0023]

[0024] Where: K v dp represents the bulk modulus of elasticity; dp represents the osmotic pressure difference.

[0025] S14: Based on the bulk modulus K v The osmotic pressure difference is expressed as the flow rate difference ΔQ.

[0026]

[0027] By simultaneously establishing the expression for the osmotic pressure difference and the model for the diffusion rate, the pore water pressure control equations corresponding to different spaces in the submarine tunnel at different times are constructed. The expression is as follows:

[0028]

[0029] In the formula: a and b represent the rate of change of the permeability coefficient and the initial permeability coefficient.

[0030] Furthermore, the method for obtaining the concentration of corrosive ions characterizing the migration process of corrosive ions driven by pore water pressure in S1 specifically includes:

[0031] S100: Solve and obtain the pore water pressure field p(x,t) based on the pore water pressure control equation;

[0032] S200: Based on Hansbo's seepage law, the hydraulic gradient i is obtained from the gradient of the pore water pressure field p(x,t), and the seepage velocity field v(x,t) is obtained from the hydraulic gradient i.

[0033] And the formula for obtaining the seepage velocity field v(x,t) is:

[0034]

[0035] In the formula: v represents the abbreviation of v(x,t); The gradient of pore water pressure is represented by ρ; k(i) represents the permeability coefficient defined by the Hansbo nonlinear seepage model; ρ represents the density of water; and g represents the acceleration due to gravity.

[0036] S300: The seepage velocity field is input as a key parameter into the convection-dispersion equation to obtain the concentration of corrosive ions C(x,t) that characterizes the migration process of corrosive ions driven by pore water pressure. The corresponding equation is:

[0037]

[0038] In the formula: C represents the concentration of corrosive ions, and C represents the abbreviation of C(x,t); D represents the hydrodynamic dispersion coefficient of the given corrosive ions in the porous medium.

[0039] Furthermore, a physical information neural network model is constructed in S3 to simultaneously solve for pore water pressure and corrosion ion concentration, which includes an input layer, a feature extraction module, and an output layer connected in sequence.

[0040] The input layer is used to transmit feature data with label data to the hidden layer;

[0041] The feature extraction module includes several cascaded hidden layers for extracting features from the feature data, and the expression for feature extraction is as follows:

[0042] h l =σ(W l h l-1 +b l ), l=1,...,6

[0043] Where: h l The output of the l-th hidden layer is represented by σ; the activation function is represented by h. l-1 W represents the output of the (l-1)th hidden layer. l b represents the weights of the feature extraction module; l Indicates the bias of the feature extraction module;

[0044] The output layer is used to obtain predicted label data [p, C] based on the output of the feature extraction module;

[0045] And the formula for obtaining the predicted label data [p, C] is:

[0046] [p,C]=W out h l +b out

[0047] In the formula: W out b represents the weights of the output layer. out This indicates the bias of the output layer.

[0048] Furthermore, the methods for obtaining the optimal prediction model in S3 specifically include:

[0049] S31: Input the training set into the constructed physical information neural network model to train the model and obtain the trained physical information neural network model;

[0050] S32: Based on the constructed physical loss function, the trained physical information neural network model is validated through the validation set, that is, it is determined whether the output of the trained physical information neural network model converges.

[0051] If the output of the trained physical information neural network model converges, then the trained physical information neural network model is confirmed to be the optimal prediction model.

[0052] Otherwise, based on the backpropagation algorithm, the weight parameters of the trained physical information neural network model are adaptively adjusted, and step S31 is repeated until the weight parameters of the trained physical information neural network model with converged output are confirmed to be the optimal weight parameters, and the physical information neural network model is reconstructed to obtain the optimal prediction model.

[0053] Furthermore, the expression for the physical loss function in S32 is as follows:

[0054] L total =λ PDE L pde +λ BC L bc +λ IC L ic +λ data L data

[0055] In the formula: L total L represents the loss function; pde L represents the residuals relating pore water pressure and convection dispersion. bc Indicates boundary condition error; L ic Indicates the initial condition error; L data λ represents the data fitting error; PDE ,λ BC ,λ IC ,λ data Indicates the weighting coefficient;

[0056] The residual L regarding pore water pressure and convection dispersion pde The expression is:

[0057]

[0058] Where: N pde Σ represents the total number of residual points randomly collected within the computational domain; Σ represents the sum of all N. pde Summing is performed on each residual point; f pde1 (x i ,ti ) indicates that in spatiotemporal data (x) i ,t i The residuals of the upper pore water pressure control equation; f pde2 (x i ,t i ) indicates that in spatiotemporal data (x) i ,t i The residuals of the convection-diffusion equations on the upper part;

[0059] The boundary condition error L bc The expression is

[0060]

[0061] Where: N bc This indicates the total number of sampling points on the inner boundary of the lining or the outer boundary of the grouting ring in a submarine tunnel. This indicates the coordinates of a point located at the upper boundary of the inner boundary of the lining or the outer boundary of the grouting ring in a submarine tunnel. This represents the pore water pressure predicted at the boundary points by the physical information neural network model. Indicates at the boundary point The specified pore water pressure value; This represents the ion concentration predicted by the physical information neural network model at the boundary points; Indicates at the boundary point The specified ion concentration value;

[0062] The initial condition error L ic The expression is

[0063]

[0064] In the formula: This represents a spatial point representing the radial position within the lining or grouting ring of the submarine tunnel, acquired at the initial time t=0. and N is a predefined initial distribution function of pore water pressure and ion concentration; ic This indicates the number of spatial points at the radial position within the lining or grouting ring of the submarine tunnel collected at the initial moment.

[0065] The data fitting error L data The expression is

[0066]

[0067] In the formula: This represents the spatiotemporal data coordinates corresponding to the data measured in the pre-set experiment; These represent the experimental values ​​of pore water pressure and ion concentration at the corresponding spatiotemporal data coordinate points, respectively; N data This represents the total number of experimental data points, i.e., the total number of spatiotemporal data coordinate points. This represents the pore water pressure measurement value obtained from the corresponding spatiotemporal data coordinate point; This represents the measured ion concentration value obtained from the corresponding spatiotemporal data coordinate point.

[0068] Furthermore, the method for obtaining the residuals of the pore water pressure control equation and the convection-dispersion equation includes the following steps:

[0069] S01: Physical Information Neural Network Model in Spatiotemporal Data (x) i ,t i The output predicted pore water pressure value p(x) i ,t i ) and predicted erosion ion concentration C(x) i ,t i );

[0070] S02: Use automatic differentiation techniques to obtain the predicted value p(x) i ,t i ) and predicted erosion ion concentration C(x) i ,t i ), in spatiotemporal data (x i ,t i derivative on ) Derivative The corresponding spatiotemporal data (x) i ,t i ) as residual points;

[0071] S03: Derivative Compared with the predicted value p(x) i ,t i Substituting the value of ) into the pore water pressure control equation, we obtain the residual equation pde1 for Hansbo;

[0072] Derivative Compared with the predicted erosion ion concentration value C(x) i ,t i Substituting the value of ) into the convection-diffusion equation, we obtain the residual equation pde2 for convection-diffusion.

[0073] S04: Construct the residual f based on the residual equation pde1 for Hansbo and the residual equation pde2 for convection dispersion, respectively. pde1 (x i ,t i ) and f pde2 (x i ,ti );

[0074]

[0075] Beneficial Effects: This invention provides a method for analyzing ion erosion in submarine tunnels based on an embedded physical information neural network. It constructs and solves pore water pressure control equations corresponding to different spaces within the submarine tunnel at different times to obtain the pore water pressure field. Based on Hansbo's law of seepage, it obtains the seepage velocity field from the pore water pressure field. The seepage velocity field is input as a key parameter into the convection-dispersion equation to obtain the concentration of corrosive ions characterizing the migration process of corrosive ions driven by pore water pressure. By constructing a physical information neural network model to simultaneously solve for pore water pressure and corrosive ion concentration, it efficiently predicts the spatiotemporal distribution of pore water pressure and ion concentration. Simultaneously, it utilizes automatic differentiation technology to introduce the residuals of the pore water pressure control equations into the loss function, ensuring that the solution conforms to the constraints of the control equations during the model training process of the physical information neural network model. Through the optimal prediction model, it achieves prediction of the erosion depth of the submarine tunnel throughout its entire life cycle, improving the prediction accuracy and efficiency of ion erosion in submarine tunnels. Attached Figure Description

[0076] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0077] Figure 1 This is a flowchart of the ion erosion analysis method for submarine tunnels based on embedded physical information neural networks of the present invention;

[0078] Figure 2 This is a schematic diagram of the ion erosion mechanism based on Hansbo nonlinear flow in this embodiment;

[0079] Figure 3 This is a schematic diagram of the physical information neural network model in this embodiment;

[0080] Figure 4 This is a simulation curve of service time versus void water pressure in this embodiment;

[0081] Figure 5 This is a simulation curve of service time versus corrosion ion concentration in this embodiment;

[0082] Figure 6 This is a simulation curve of service time versus lining erosion depth in this embodiment;

[0083] Figure 7This is a comparison chart of the service time versus pore water pressure between the traditional Darcy linear seepage method and the method based on Hansbo nonlinear seepage in this embodiment.

[0084] Figure 8 This is a comparison chart of the difference in lining thickness and pore water pressure between the traditional Darcy linear seepage method and the method based on Hansbo nonlinear seepage in this embodiment.

[0085] Figure 9 This is a comparison chart of the erosion differences in service time versus erosion ion concentration between the traditional Darcy linear flow method and the method based on Hansbo nonlinear flow in this embodiment. Detailed Implementation

[0086] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, those skilled in the art will understand...

[0087] All other embodiments obtained through creative effort are within the scope of protection of this invention.

[0088] This embodiment provides a method for analyzing ion erosion in submarine tunnels based on a neural network embedded with physical information, such as... Figure 1 As shown, the specific steps include:

[0089] S1: Based on the Hansbo nonlinear seepage model, construct the pore water pressure control equations for different spatial locations in the submarine tunnel under different tunnel service times, i.e., the radial positions within the lining or grouting ring of the submarine tunnel.

[0090] Specifically, this includes: establishing a permeation erosion model for submarine tunnels under high water pressure; studying the erosion mechanism of submarine tunnels throughout their entire life cycle based on the Hansbo nonlinear flow model of corrosive ions permeating the tunnel structure; the Hansbo nonlinear flow model consists of a curved segment Law A and a straight segment Law B; under different service times, corrosive ions follow different stages of Hansbo's law within the submarine tunnel structure. In this embodiment, based on the Hansbo nonlinear flow model, the ion erosion process of submarine tunnels is subdivided into three stages, providing reliable guidance for the durability study of submarine tunnels: the initial erosion stage (Stage I), the erosion development stage (Stage II), and the accelerated erosion stage (Stage III), as follows... Figure 2 As shown:

[0091] Stage I: In the early stage of service, the erosion rate of corrosive ions on the grouting ring and lining is relatively slow. The pore water carrying corrosive ions is in a low-speed seepage stage and obeys Law A.

[0092] Stage II: As the submarine tunnel structure ages, the grouting ring is subjected to increased erosion and numerous internal cracks appear. The corrosive ions inside enter a high-speed seepage stage, and the seepage model follows Law B. Under the protection of the grouting ring, the lining still follows Law A.

[0093] Stage III: As erosion intensifies, the protective effect of the grouting ring fails, and the corrosive ions within the lining enter a high-speed seepage stage; at this point, both the grouting ring and the lining obey Law B.

[0094] A three-stage erosion process model for submarine tunnels, such as... Figure 1 As shown, in this model, p i k represents the initial water pressure. g With k l Let r represent the permeability coefficients of the grouting ring and the lining zone of the submarine tunnel, respectively; the inner and outer diameters of the lining zone are r0 and r1, respectively; and the radius of the grouting ring is r. g Then, the relationship between the flow velocity v and the hydraulic gradient i in the Hansbo nonlinear seepage model is:

[0095]

[0096] In the formula: v represents the ion percolation velocity; i represents the hydraulic gradient; k hc ,k hl Let i and i0 represent the permeability coefficients of the curved and straight segments in Hansbo's law, respectively; i0 represents the horizontal intercept of the straight segment in Hansbo's law; i1 represents the critical hydraulic gradient that distinguishes the straight and curved segments in Hansbo's law; m represents the nonlinear parameter; and m and the critical hydraulic gradient i1 are generally measured by existing experimental tests; and the permeability coefficient and hydraulic gradient in Hansbo's law have the following relationship:

[0097]

[0098] In a specific embodiment, the method for constructing the pore water pressure control equations corresponding to different spaces in the submarine tunnel at different times includes the following steps:

[0099] S11: Based on the Hansbo nonlinear seepage model, a model can be constructed to demonstrate the diffusion rate of corrosive ions carried by pore water in a submarine tunnel.

[0100] And the model expression for the diffusion rate is:

[0101]

[0102] In the formula: u represents the diffusion rate of corrosive ions carried by pore water in the submarine tunnel, and u is the simplified form of u(x); k hc k represents the permeability coefficient corresponding to the curve segment in Hansbo's law. hl represents the permeability coefficient corresponding to the straight segment in Hansbo's law; i1 represents the critical hydraulic gradient used to distinguish between the straight and curved segments in Hansbo's law; m represents the nonlinear parameter; ρ represents the density of pore water; g represents the acceleration due to gravity; p represents the pore water pressure; x represents the radial position within the lining or grouting ring of a submarine tunnel; u c This represents the critical seepage velocity at the transition point from the curved segment to the straight segment in Hansbo's law.

[0103] In this embodiment, formula (3) is a relation obtained by solving formulas (1) and (2) simultaneously using the physical condition that "the velocities of the curved segment and the straight segment are equal at the critical point" according to Hansbo's law. Wherein, "the critical seepage velocity u..." c The method for determining this is as follows: Based on the Hansbo nonlinear seepage model, at the critical hydraulic gradient i1, the seepage velocity calculated by Law A is equal to the seepage velocity calculated by Law B, i.e. Solving the system simultaneously yields the following results: Therefore, the critical seepage velocity criterion for the change of seepage state can be clearly defined.

[0104] S12: Select two cross-sections separated by a distance dx inside the concrete of the undersea tunnel, and obtain the flow difference of pore water through the two cross-sections. The expression for this difference is:

[0105]

[0106] In the formula: ΔQ represents the flow difference; Q Ι Q Π dx represents the inflow rate at two cross-sections separated by a distance of dx; A represents the cross-sectional area of ​​the grout-filled concrete body; t represents the time parameter, i.e., the tunnel service time.

[0107] In this embodiment, "dx" in "distance dx" is a mathematical differential symbol, called the infinitesimal element analysis method, representing an infinitesimal distance, rather than a finite, measurable size (such as 1 cm or 1 m). In this embodiment, it is explained as follows: "To derive the pore water pressure control equation, the infinitesimal element analysis method is used. Imagine two infinitely close cross-sections with a distance of dx along the seepage direction (radial) inside the concrete, thus defining an infinitesimal element. Based on the relationship between the difference in water flow rate through the two cross-sections of this infinitesimal element and the change in pore water pressure within the infinitesimal element, and combined with the law of conservation of mass, it is convenient to subsequently establish the control equation."

[0108] S13: Obtain the bulk modulus of elasticity of concrete in the undersea tunnel, its expression is:

[0109]

[0110] Where: K v dp represents the bulk modulus of elasticity; V represents the initial total volume of the concrete element; dV represents the change in volume of the concrete element due to the flow difference ΔQ; dV / V represents the volumetric strain of the concrete element (i.e., the change in volume per unit volume).

[0111] S14: Based on the bulk modulus K v The osmotic pressure difference is expressed as the flow rate difference ΔQ.

[0112]

[0113] By simultaneously establishing the expression for the osmotic pressure difference and the model for the diffusion rate, the pore water pressure control equations corresponding to different spaces in the submarine tunnel at different times are constructed. The expression is as follows:

[0114]

[0115] In the formula: a and b represent the rate of change of the permeability coefficient and the initial permeability coefficient;

[0116] The pore water pressure control equation is solved to obtain the pore water pressure field; the seepage velocity field is obtained based on Hansbo's seepage law and the pore water pressure field; the seepage velocity field is used as a key parameter and input into the preset convection-dispersion equation to obtain the concentration of corrosive ions that characterizes the migration process of corrosive ions driven by pore water pressure.

[0117] Specifically, the following steps are included:

[0118] S100: Solve and obtain the pore water pressure field p(x,t) based on the pore water pressure control equation;

[0119] S200: Based on Hansbo's seepage law, the hydraulic gradient i is obtained from the gradient of the pore water pressure field p(x,t), and the seepage velocity field v(x,t) is obtained from the hydraulic gradient i.

[0120] And the formula for obtaining the seepage velocity field v(x,t) is:

[0121]

[0122] In the formula: v represents the abbreviation of v(x,t); The gradient of pore water pressure is represented by ρ; k(i) represents the permeability coefficient defined by the Hansbo nonlinear seepage model; ρ represents the density of water; and g represents the acceleration due to gravity.

[0123] S300: The seepage velocity field is input as a key parameter into the convection-dispersion equation to obtain the concentration of corrosive ions C(x,t) that characterizes the migration process of corrosive ions driven by pore water pressure. The corresponding equation is:

[0124]

[0125] In the formula: C represents the concentration of corrosive ions, and C represents the abbreviation of C(x,t); D represents the hydrodynamic dispersion coefficient of corrosive ions in porous media, which is a material constant determined by experiments;

[0126] S2: Obtain the dataset and randomly divide it into a training set and a test set;

[0127] Furthermore, the feature data in the dataset consists of spatiotemporal data corresponding to different spatial locations within the undersea tunnel at different times; specifically, x i (Spatial coordinates): Meaning: Represents the radial position within the tunnel lining or grouting ring, usually with the tunnel center as the origin and the positive direction being outward along the radial direction;

[0128] Value range: from the inner surface r0 of the lining to the outer boundary r of the grouting ring g ;

[0129] For example: in a specific calculation, x i It may be in the interval [r0, r g Uniform or random sampling within the area;

[0130] Function: Used to specify the research location where the prediction results are to be obtained in this embodiment (e.g., 0.1m from the inner surface);

[0131] t i (Time coordinate): Meaning: Represents the tunnel's service life;

[0132] Value range: from the initial time t=0 to the design life t=T (e.g., 100 years), and the time points will also be randomly sampled within this range;

[0133] Function: Used to specify the time when the desired result is to be predicted in this embodiment (e.g., the 10th year of service, the 50th year); and then to x i (spatial coordinates) and t i (Time coordinates) constitute spatiotemporal data;

[0134] The label data for the spatiotemporal data in the dataset are: the pore water pressure field and the concentration of corrosive ions corresponding to the spatiotemporal data.

[0135] S3: Construct a physical information neural network model for simultaneously solving pore water pressure and corrosion ion concentration, such as... Figure 3 As shown, it includes an input layer, a feature extraction module, and an output layer connected in sequence;

[0136] The input layer is used to transmit feature data with label data to the hidden layer;

[0137] The feature extraction module includes several cascaded hidden layers for extracting features from the feature data, and the expression for feature extraction is as follows:

[0138] h l =σ(W l h l-1 +b l ),l=1,...,6 (10)

[0139] Where: h l The output of the l-th hidden layer is represented by σ; the activation function is represented by h. l-1 W represents the output of the (l-1)th hidden layer. l b represents the weights of the feature extraction module; l Indicates the bias of the feature extraction module;

[0140] The output layer is used to obtain predicted label data [p, C] based on the output of the feature extraction module;

[0141] And the formula for obtaining the predicted label data [p, C] is:

[0142] [p,C]=W out h l +b out (11)

[0143] In the formula: W out b represents the weights of the output layer. out Indicates the bias of the output layer;

[0144] The physical information neural network model is trained using a training set to obtain the trained physical information neural network model; and the trained physical information neural network model is validated based on the constructed physical loss function to obtain the optimal prediction model.

[0145] The specific steps include:

[0146] S31: Input the training set into the constructed physical information neural network model to train the model and obtain the trained physical information neural network model;

[0147] S32: Based on the constructed physical loss function, the trained physical information neural network model is validated through the validation set, that is, it is determined whether the output of the trained physical information neural network model converges.

[0148] If the output of the trained physical information neural network model converges, then the trained physical information neural network model is confirmed to be the optimal prediction model.

[0149] Otherwise, based on the backpropagation algorithm, the weight parameters of the trained physical information neural network model are adaptively adjusted, and step S31 is repeated until the weight parameters of the trained physical information neural network model with converged output are confirmed to be the optimal weight parameters and the physical information neural network model is reconstructed to obtain the optimal prediction model.

[0150] The physical loss function constructed in S32 has the following expression:

[0151] L total =λ PDE L pde +λ BC L bc +λ IC L ic +λ data L data (12)

[0152] In the formula: L total L represents the loss function; pde L represents the residuals relating pore water pressure and convection dispersion. bc Indicates boundary condition error; L ic Indicates the initial condition error; L data λ represents the data fitting error; PDE ,λ BC ,λ IC ,λ data Indicates the weighting coefficient;

[0153]

[0154] Where: N pde Σ represents the total number of residual points randomly collected within the computational domain; Σ represents the sum of all N. pde Summing is performed on each residual point; f pde1 (x i ,t i ) indicates that in spatiotemporal data (x) i ,t i The residuals of the pore water pressure control equations; f pde2 (x i ,t i ) indicates that in spatiotemporal data (x) i ,ti The residuals of the convection-diffusion equations are given above; the formula for calculating the residuals is:

[0155] S01: Physical Information Neural Network Model in Spatiotemporal Data (x) i ,t i The output predicted pore water pressure value p(x) i ,t i ) and predicted erosion ion concentration C(x) i ,t i );

[0156] S02: Use automatic differentiation techniques to obtain the predicted value p(x) i ,t i ) and predicted erosion ion concentration C(x) i ,t i ), in spatiotemporal data (x i ,t i derivative on ) Derivative The corresponding spatiotemporal data (x) i ,t i ) as residual points;

[0157] S03: Derivative Compared with the predicted value p(x) i ,t i Substituting the value of ) into the pore water pressure control equation (7) in this embodiment, we obtain the residual equation pde1 for Hansbo;

[0158] Derivative Compared with the predicted erosion ion concentration value C(x) i ,t i Substituting the value of ) into the convection-diffusion equation (9) in this embodiment, we obtain the residual equation pde2 for convection-diffusion.

[0159] S04: Construct the residual f based on the residual equation pde1 for Hansbo and the residual equation pde2 for convection dispersion, respectively. pde1 (x i ,t i ) and f pde2 (x i ,t i );

[0160]

[0161] In this embodiment, the residual L pde It is physical information used to measure the severity of a neural network's violation of physical laws at countless points within the domain, and the goal of its training is to make this value as close to zero as possible.

[0162]

[0163] Where: N bc This indicates the total number of sampling points on the inner boundary of the lining or the outer boundary of the grouting ring in a submarine tunnel. This indicates the coordinates of a point located at the upper boundary of the inner boundary of the lining or the outer boundary of the grouting ring in a submarine tunnel. This represents the pore water pressure predicted at the boundary points by the physical information neural network model. Indicates at the boundary point The specified pore water pressure value (e.g., p at the outer boundary of the grouting ring) is given above. target =p i p i Indicates a given pore water pressure value; p represents the inner boundary of the lining. target =0); This represents the ion concentration predicted by the physical information neural network model at the boundary points; Indicates at the boundary point The specified ion concentration value (e.g., the ion concentration value C given at the outer boundary of the grouting ring) is above. target =0.6%; the given ion concentration value C at the inner boundary of the lining. target =0.1%);

[0164]

[0165] In the formula: This represents a spatial point representing the radial position within the lining or grouting ring of the submarine tunnel, acquired at the initial time t=0. and N is a predefined initial distribution function of pore water pressure and ion concentration; ic This indicates the number of spatial points at the radial position within the lining or grouting ring of the submarine tunnel collected at the initial moment.

[0166]

[0167] In the formula: This represents the spatiotemporal data coordinates corresponding to the data measured in the pre-set experiment; These represent the experimental values ​​of pore water pressure and ion concentration at the corresponding spatiotemporal data coordinate points, respectively; N data This represents the total number of experimental data points, i.e., the total number of spatiotemporal data coordinate points. This represents the pore water pressure measurement value obtained from the corresponding spatiotemporal data coordinate point; This represents the measured ion concentration value obtained at the corresponding spatiotemporal data coordinate point. In this embodiment, the data fitting error L... dataThis item is used to fuse experimental data with physical information. If no experimental data is available in practical applications, this item represents the data fitting error L. data Weighting coefficient λ data It can be set to 0.

[0168] S4: Based on the optimal prediction model, realize the analysis and prediction of ion erosion of submarine tunnels based on a neural network embedded with physical information.

[0169] This embodiment describes a method for analyzing ion erosion in submarine tunnels based on a Physically Information-embedded Neural Network (PINN). This method addresses the problems of low computational efficiency and poor adaptability to boundary conditions inherent in traditional methods for predicting the long-term durability of submarine tunnels. By establishing a Hansbo nonlinear seepage model, the ion erosion process is divided into two stages: low-velocity seepage (Law A) and high-velocity seepage (Law B). The seepage velocity field is input as a key parameter into a pre-defined convection-dispersion equation to obtain the ion concentration characterizing the migration process of corrosive ions driven by pore water pressure. The PINN-based neural network efficiently solves for the spatiotemporal distribution of pore water pressure and ion concentration using a six-layer hidden layer structure (32 neurons per layer). Automatic differentiation technology ensures that the solution conforms to the constraints of the governing equations. The critical seepage velocity is used to determine the transition point between the grouting ring and the lining erosion stage, achieving prediction of the erosion depth throughout the entire life cycle. Figures 4 to 9 Compared with traditional methods, the method described in this embodiment does not require mesh generation, can handle complex boundary conditions, and the average relative error between the prediction results and analytical solutions and experimental data is less than 1%, which significantly improves the computational accuracy and efficiency, and is suitable for the durability design and maintenance optimization of submarine tunnels.

[0170] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for analyzing ion erosion of a submarine tunnel based on a physical information-embedded neural network, the method comprising: Specifically comprising the following steps: S1: based on Hansbo nonlinear seepage model, the control equation of the pore water pressure corresponding to different spatial positions in the submarine tunnel under different tunnel service time is constructed, and the pore water pressure field is solved to obtain the pore water pressure field; Based on Hansbo seepage law, the seepage velocity field is obtained according to the pore water pressure field; The seepage velocity field is input as a key parameter into the preset convection-dispersion equation to obtain the erosion ion concentration representing the migration process of the erosive ion under the driving of the pore water pressure; S2: obtain the data set, and randomly divide the data set into training set and test set; And the feature data in the data set is: the space-time data corresponding to different spatial positions in the submarine tunnel under different time; The label data of the space-time data is: the pore water pressure field and the erosion ion concentration; S3: a physical information neural network model for simultaneously solving the pore water pressure and the erosion ion concentration is constructed, the physical information neural network model is trained through the training set, and the trained physical information neural network model is obtained; And based on the constructed physical loss function, the trained physical information neural network model is verified to obtain the optimal prediction model; S4: according to the optimal prediction model, the analysis and prediction of ion erosion of submarine tunnel based on embedded physical information neural network are realized.

2. The method of claim 1, wherein the method is characterized by, The method for constructing the pore water pressure control equation corresponding to different spatial positions in the submarine tunnel under different time in S1, specifically comprises: S11: based on Hansbo nonlinear seepage model, the diffusion velocity of the pore water carrying erosive ion in the submarine tunnel is constructed: And the model expression of the diffusion velocity is wherein: u represents the diffusion speed of the pore water carrying the aggressive ions in the subsea tunnel, and u is a short form of u(x); k hc represents the permeability coefficient corresponding to the curved segment in the Hansbo law; k hl represents the permeability coefficient corresponding to the straight segment in the Hansbo law; i1 represents the critical hydraulic gradient for distinguishing the straight segment and the curved segment in the Hansbo law; m represents the non-linear parameter; p represents the density of the pore water; g represents the gravity acceleration; p represents the pore water pressure; x represents the radial position in the subsea tunnel within the lining or the grouting ring; u c represents the critical speed at which the curved segment in the Hansbo law transitions to the straight segment; S12: select two sections inside the concrete in the submarine tunnel with a distance of dx, obtain the flow difference of the pore water through the two sections, and the expression is wherein: AQ represents the flow difference; Q Ι , Π represents the inflow amount of two cross sections apart by dx; A represents the cross-sectional area of the concrete grouting reinforcement body; and t represents the time parameter. S13: obtain the bulk modulus of the concrete in the submarine tunnel, and the expression is wherein: K v represents the bulk modulus of elasticity; dp represents the difference in osmotic pressure. S14: According to the bulk modulus K v With the flow difference AQ, the osmotic pressure difference is expressed as And the expression of the osmotic pressure difference is parallel to the model of the diffusion velocity, so as to construct the pore water pressure control equation corresponding to different spatial positions in the submarine tunnel under different time, and the expression is In the formula: a, b represent the change rate of permeability coefficient and the initial permeability coefficient.

3. The method of claim 2, wherein the method is characterized by, The method for obtaining the erosion ion concentration representing the migration process of the erosive ion under the driving of the pore water pressure in S1, specifically comprises: S100: according to the pore water pressure control equation, the pore water pressure field p(x, t) is solved and obtained; S200: based on Hansbo seepage law, the hydraulic gradient i is obtained according to the gradient of the pore water pressure field p(x, t), and the seepage velocity field v(x, t) is obtained according to the hydraulic gradient i; And the seepage velocity field v(x, t) is obtained by formula In the formula: v represents the abbreviation of v(x, t); ▽p represents the gradient of pore water pressure; k(i) represents the permeability coefficient defined by Hansbo nonlinear seepage model; ρ represents the density of water; g represents the acceleration of gravity; S300: the seepage velocity field is input as a key parameter into the convection-dispersion equation to obtain the erosion ion concentration C(x, t) representing the migration process of the erosive ion under the driving of the pore water pressure, and the corresponding equation is; In the formula, C represents the concentration of the erosive ion, and C represents a short form of C(x, t); D represents the hydrodynamic dispersion coefficient of a given erosive ion in a porous medium.

4. The method of claim 3, wherein the method is characterized by, The physical information neural network model for simultaneously solving the pore water pressure and the erosive ion concentration is constructed in S3, and the model includes an input layer, a feature extraction module and an output layer connected in sequence; The input layer is used for transmitting the feature data with the labeled data to the hidden layer; The feature extraction module includes a plurality of cascaded hidden layers for feature extraction of the feature data, and the expression of the feature extraction is h l = σ(W l h l-1 + b l ), l = 1,..., 6 wherein: h l represents the output of the lth hidden layer; σ represents an activation function; h l-1 represents the output of the (l-1)th hidden layer; W l represents the weight of the feature extraction module; b l represents the bias of the feature extraction module; The output layer is used for obtaining the predicted labeled data [p, C] according to the output of the feature extraction module; The formula for obtaining the predicted labeled data [p, C] is [p, C] = W out h l +b out In the formula, W out represents the weight of the output layer; b out represents the bias of the output layer.

5. The method of claim 3, wherein the method is characterized by, The method for obtaining the optimal prediction model in S3 specifically includes: S31: inputting the training set into the constructed physical information neural network model for model training to obtain a trained physical information neural network model; S32: verifying the trained physical information neural network model based on the constructed physical loss function through the verification set, that is, judging whether the output of the trained physical information neural network model converges or not; If the output of the trained physical information neural network model converges, it is confirmed that the trained physical information neural network model at this time is the optimal prediction model; Otherwise, the weight parameters of the trained physical information neural network model are adaptively adjusted based on the back propagation algorithm, and step S31 is repeatedly executed until the weight parameters of the trained physical information neural network model whose output converges are the optimal weight parameters and the physical information neural network model is reconstructed to obtain the optimal prediction model.

6. The method of claim 5, wherein the method is characterized by, The expression of the physical loss function in S32 is L total = λ PDE L pde + λ BC L bc + λ IC L ic + λ data L data where: L total represents a loss function; L pde represents a residual with respect to pore water pressure and convective dispersion; L bc represents a boundary condition error; L ic represents an initial condition error; L data represents a data fitting error; λ PDE , λ BC , λ IC , λ data represents a weight coefficient; The expression for the residual L of the pore water pressure with respect to the convective dispersion is: pde L = - (1 - 2D) (1 - 2D) where: N pde represents the total number of residual points randomly collected within the computational domain;∑ represents the summation over all N pde residual points; f pde1 (x i ,t i ) represents the residual of the pore water pressure control equation on the spatiotemporal data (x i ,t i ); f pde2 (x i ,t i ) represents the residual of the advection-dispersion equation on the spatiotemporal data (x i ,t i ); The boundary condition error L bc The expression for wherein: N bc represents the total number of acquisition points on the inner boundary of the lining or the outer boundary of the grouting ring in the subsea tunnel; represents the point coordinates of the boundary points located on the inner boundary of the lining or the outer boundary of the grouting ring in the subsea tunnel; represents the pore water pressure predicted by the physical information neural network model at the boundary points; represents the pore water pressure value specified at the boundary points ; represents the ion concentration predicted by the physical information neural network model at the boundary points; represents the ion concentration value specified at the boundary points ; The initial condition error L ic is expressed by wherein: represents a spatial point of the radial position inside the lining or the grouting ring in the submarine tunnel collected at the initial time t = 0; and is a predefined initial distribution function of the pore water pressure and the ion concentration; N ic represents the number of points of the spatial point of the radial position inside the lining or the grouting ring in the submarine tunnel collected at the initial time. The data fitting error L data The expression for In the formula: represents a space-time data coordinate point corresponding to the measured data of the preset experiment; respectively represent the given pore water pressure experimental value and the ion concentration experimental value at the corresponding space-time data coordinate point; N data represents the total number of experimental data points, i.e., space-time data coordinate points; represents the measured pore water pressure measurement value corresponding to the space-time data coordinate point; represents the measured ion concentration measurement value corresponding to the space-time data coordinate point.

7. The method of claim 6, wherein the method is characterized by, The method for obtaining the residual of the pore water pressure control equation and the residual of the convection-dispersion equation includes the following steps: S01: The physical information neural network model outputs a predicted pore water pressure value p(x i ,t i ) and a predicted erosion ion concentration value C(x i ,t i ) for the spatiotemporal data (x i ,t i ); S02: Obtain the derivative of the predicted value p(x i ,t i ) and the predicted erosion ion concentration value C(x i ,t i ) on the spatiotemporal data (x i ,t i ) using an automatic differentiation technique Take the spatiotemporal data (x i ,t i ) corresponding to the derivative as a residual point; S03: Derivatives with the predicted value p(x i ,t i ) into the pore water pressure control equation, and thus obtain the Hansbo residual equation pde1; Taking the derivative with respect to the predicted erosion ion concentration value C(x i ,t i ) and substituting this value into the convection-diffusion equation, a residual equation pde2 with respect to convection-diffusion is obtained; S04: Construct the residuals f according to the residual equation pde1 for Hansbo and pde2 for convection-dispersion, respectively pde1 (x i ,t i ) and f pde2 (x i ,t i );

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