Tunnel lining external load inversion method and system based on physical information neural network

Abstract

The present application relates to a tunnel lining external load inversion method and system based on a physical information neural network, obtaining monitoring data of the inner surface of the tunnel lining to be inverted; according to curved beam theory, establishing a control equation of external load and lining neutral axis deformation, and determining boundary conditions; according to the theory of material mechanics, establishing the corresponding relationship between the strain and displacement of the inner surface of the lining and the strain and displacement of the neutral axis position; constructing a physical information neural network, taking the spatial coordinates of the lining as the input of the physical information neural network, and taking the normal displacement, tangential displacement of the neutral axis at different coordinates and the external load of the lining as the output, and converting the neutral axis displacement into the strain and displacement of the inner surface of the lining; through training of the physical information neural network, the input-output relationship satisfies the control equation of the external load and the lining deformation, the boundary conditions and the monitoring data, and the normal displacement, tangential displacement of the neutral axis at the corresponding coordinates and the external load of the lining are obtained, which are the inversion results.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tunnel engineering, in particular to a tunnel lining external load inversion method and system based on a physical information neural network. BACKGROUND

[0002] The statements in this section merely provide background information related to the present application and do not necessarily constitute the prior art.

[0003] During the construction of adjacent projects near tunnels and tracks, the existing tunnel surrounding rock or soil may be disturbed, causing changes in the external load of the tunnel lining, and further causing safety risks to the tunnel structure. Therefore, it is necessary to evaluate the changes in the external load of the tunnel lining to ensure the safety of the tunnel structure.

[0004] Currently, there are three methods for evaluating the external load of the tunnel lining: direct measurement, numerical analysis, and back analysis.

[0005] Direct measurement involves placing soil pressure cells between the lining and the stratum to test the pressure between the stratum and the lining. This method can directly obtain the external load, but the measurement results require high installation technology, and once the sensor fails, it cannot be replaced, making it difficult to apply to long-term monitoring of operating tunnels.

[0006] The accuracy of the numerical method depends on sufficient understanding of the surrounding rock geological conditions and reasonable selection of the rock and soil body constitutive model and parameters, and the accuracy under complex conditions is difficult to guarantee.

[0007] The back analysis method inverses the external load based on the structure monitoring results. Generally, the actual response of the structure is used to determine the external load in combination with the numerical method. This method generally requires repeated calculations in combination with the rock and soil body model, and the results depend on the rock and soil body model and parameters. SUMMARY

[0008] To solve the technical problems in the background art, the present application provides a tunnel lining external load inversion method and system based on a physical information neural network, which uses the actual monitored physical information to construct a function model, and converts the parameters related to the inversion results into input and output quantities of the physical information neural network. The learning process of the physical information neural network obtains a solution that is more consistent with the basic physical laws. The required physical parameters are easy to monitor, and the cost is lower than that of the traditional back analysis method.

[0009] To achieve the above purpose, the present application adopts the following technical solutions:

[0010] The first aspect of the present application provides a tunnel lining external load inversion method based on a physical information neural network, comprising the following steps:

[0011] Obtaining monitoring data of an inner surface of a tunnel lining to be inverted;

[0012] According to the curved beam theory, control equations of external loads and neutral axis deformation of the lining are established, and boundary conditions are determined;

[0013] According to the material mechanics theory, a corresponding relationship between strains and displacements of the inner surface of the lining and strains and displacements of the position of the neutral axis is established;

[0014] A physical information neural network is constructed, in which spatial coordinates of the lining are input, normal displacement and tangential displacement of the neutral axis at different coordinates and external loads of the lining are output, and the neutral axis displacement is converted into strains and displacements of the inner surface of the lining;

[0015] Through training of the physical information neural network, input-output relationship meets the control equations of external loads and lining deformation, boundary conditions and monitoring data, and normal displacement and tangential displacement of the neutral axis at the corresponding coordinates and external loads of the lining are obtained, which are inversion results.

[0016] Further, the monitoring data of the tunnel lining to be inverted include displacement, strain, convergence and the like.

[0017] Further, the control equations of external loads and neutral axis deformation of the lining are as follows:

[0018]

[0019] In the formula, p is the external load, and are tangential and normal displacement of the neutral axis, O is the center of the tunnel and is the polar coordinate origin, R is the radius of the tunnel, is a polar angle, M, N and Q are bending moment, axial force and shear force of the beam respectively.

[0020] Further, through the boundary conditions of the model, normal displacement, tangential displacement and rotational deformation of the top of the lining are determined.

[0021] Further, the lining deformation monitoring points are located on the inner surface of the lining, and the control equations are the deformation relationship between the external loads and the neutral axis, so it is necessary to determine the relationship between strains and displacements of the inner surface of the lining and strains and displacements of the position of the neutral axis, as shown in the following formula:

[0022]

[0023] w s =w

[0024]

[0025] In the formula, and for the neutral axis tangential and normal displacement, R is the tunnel radius, for the polar angle, z is the distance to the neutral axis, u is the normal displacement of the neutral axis, w is the tangential displacement, ε s for the tunnel lining inner surface strain, ε0 is the tunnel lining neutral axis strain, κ0 is the curvature of the neutral axis, w s for the lining inner surface normal displacement, u s for the lining inner surface tangential displacement.

[0026] Further, the physical information neural network is trained, when the loss value is greater than the set threshold value, the hyperparameter optimization is performed on the parameter update of the neural network, the neutral axis normal displacement, the tangential displacement and the lining external load at the corresponding coordinates are output when the iteration setting number or the sum of all losses is the minimum.

[0027] The second aspect of the present application provides a tunnel lining external load inversion system based on a physical information neural network, comprising.

[0028] The physical information module is configured to: acquire monitoring data of a tunnel lining to be inverted; establish a control equation of the external load and the neutral axis deformation of the lining according to the curved beam theory, and determine the boundary conditions; and establish a corresponding relationship between the strain and displacement of the inner surface of the lining and the strain and displacement of the neutral axis position according to the material mechanics theory;

[0029] The neural network module is configured to: take the lining spatial coordinates as the input of the physical information neural network, and take the neutral axis normal displacement, the tangential displacement and the lining external load at different coordinates as the output, and convert the neutral axis displacement into the strain and displacement of the lining inner surface;

[0030] The training and output module is configured to: train the physical information neural network, so that the input-output relationship satisfies the control equation of the external load and the lining deformation, the boundary conditions and the monitoring data, and obtain the neutral axis normal displacement, the tangential displacement and the lining external load at the corresponding coordinates, which are the inversion results.

[0031] The third aspect of the present application provides a computer readable storage medium, which stores a computer program, and the program is executed by a processor to realize the steps in the above tunnel lining external load inversion method based on a physical information neural network.

[0032] The fourth aspect of the present application provides a computer device, which comprises a memory, a processor and a computer program stored on the memory and executable on the processor, and the processor executes the program to realize the steps in the above tunnel lining external load inversion method based on a physical information neural network.

[0033] Compared with the prior art, the above one or more technical solutions have the following beneficial effects:

[0034] 1. The function model is constructed by actually monitoring physical parameters, and the parameters related to the inversion results are converted into input and output of physical information neural network. The learning process of physical information neural network is used to obtain a solution that is more in line with the basic physical law. The required physical parameters are easy to monitor, and the cost is lower than that of traditional back analysis method.

[0035] 2. Compared with direct measurement of external load, the measurement of lining deformation is easier and more stable, because direct measurement of external load has higher installation technology requirements, and the sensor cannot be replaced once it fails, making it difficult to apply to long-term monitoring of tunnels in operation period. Therefore, inversion through monitored deformation is more feasible and has more accuracy guarantee.

[0036] 3. The accuracy of numerical method depends on sufficient understanding of surrounding rock geological conditions and reasonable selection of rock and soil constitutive model and parameters, and the accuracy under complex conditions is difficult to guarantee. Therefore, the method has more accuracy guarantee.

[0037] 4. There are also back analysis methods for external load inversion in the past, but the previous methods usually assume the form of external load and are low in efficiency. The present method does not assume the form of external load and is high in efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0038] The drawings constituting a part of the specification of the present application are used to provide further understanding of the present application, and the illustrative embodiments of the present application and their descriptions are used to explain the present application, and do not constitute improper limitation on the present application.

[0039] Figure 1 is a physical information neural network-based tunnel lining external load inversion flowchart provided by one or more embodiments of the present application;

[0040] Figure 2 is a lining mechanical model schematic diagram provided by one or more embodiments of the present application;

[0041] Figure 3 is a Euler beam element mechanical analysis schematic diagram provided by one or more embodiments of the present application;

[0042] Figure 4 is a PINN network structure schematic diagram provided by one or more embodiments of the present application;

[0043] Figure 5 is a schematic diagram of adjacent tunnel excavation provided by one or more embodiments of the present application;

[0044] Figure 6 is a schematic diagram of lining deformation and load increment caused by new tunnel excavation provided by one or more embodiments of the present application;

[0045] Figure 7 is a schematic diagram of training a PINN based on displacement monitoring information provided by one or more embodiments of the present application;

[0046] Figure 8 is a schematic diagram of training a PINN based on strain monitoring information provided by one or more embodiments of the present application;

[0047] Figure 9 is a schematic diagram of a comparison of PINN results and FEM calculation results in terms of strain provided by one or more embodiments of the present application;

[0048] Figure 10 is a schematic diagram of a comparison of PINN results and FEM calculation results in terms of displacement provided by one or more embodiments of the present application;

[0049] Figure 11 is a schematic diagram of a comparison of PINN inversion external load results and FEM external load results provided by one or more embodiments of the present application. DETAILED DESCRIPTION

[0050] The present application will be further described below with reference to the accompanying drawings and embodiments.

[0051] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless otherwise indicated, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present application belongs.

[0052] PINN network, i.e. Physics-Informed Neural Networks, is a machine learning model that combines deep learning and physical knowledge.

[0053] Embodiment I:

[0054] As shown in Figure 1 , the tunnel lining external load inversion method based on the physical information neural network comprises the following steps:

[0055] Obtaining monitoring data of the inner surface of the tunnel lining to be inverted;

[0056] According to the curved beam theory, control equations of external load and lining neutral axis deformation are established, and boundary conditions are determined;

[0057] According to the theory of material mechanics, the corresponding relationship between the strain and displacement of the inner surface of the lining and the strain and displacement of the neutral axis position is established;

[0058] A physical information neural network is constructed, with the spatial coordinates of the lining as the input and the neutral axis normal displacement, tangential displacement and external load of the lining at different coordinates as the output. The neutral axis displacement is converted into the strain and displacement of the inner surface of the lining.

[0059] By training the physical information neural network, the input-output relationship is made to satisfy the control equations, boundary conditions and monitoring data of external load and lining deformation, and the neutral axis normal displacement, tangential displacement and lining external load at the corresponding coordinates are obtained, which is the inversion result.

[0060] This embodiment specifically includes the following steps:

[0061] S1, such as Figures 2-3 As shown, for circular tunnel lining, based on the curved beam theory, the governing equations for external load P and lining neutral axis deformation (including strain, displacement, and convergence obtained from displacement) are established.

[0062] The governing equations for external loads and neutral axis deformation are as follows:

[0063]

[0064] In the formula, p is the external load. and These represent the tangential and normal displacements along the neutral axis. O is the tunnel center and the origin of the polar coordinate system, and R is the tunnel radius. This is the polar angle. M, N, and Q represent the bending moment, axial force, and shear force at the beam's cross-section, respectively, with the arrows in the diagram indicating positive directions.

[0065] In a polar coordinate system, coordinates include polar angle and polar radius. For the circular tunnel involved in this embodiment, the polar radius is the outer diameter of the tunnel, which is a fixed value. Therefore, the polar angle is used alone. That can represent coordinates.

[0066] S2. Establish the boundary conditions of the model, fix the normal displacement, tangential displacement and rotational deformation of the top of the lining, and the equation is as shown in equation (2):

[0067]

[0068] S3. In actual engineering, the lining deformation monitoring points are generally located on the inner surface of the lining. The relationship between the strain and displacement of the inner surface of the lining and the strain and displacement of the neutral axis is shown in Equation (3). Using this equation, the neutral axis displacement can be converted into the strain and displacement of the inner surface of the lining.

[0069]

[0070] w s =w

[0071]

[0072] where z is the distance to the neutral axis, ε s is the strain of the inner surface of the tunnel lining, ε0 is the strain of the neutral axis of the tunnel lining, κ0 is the curvature of the neutral axis, w s is the normal displacement of the inner surface of the lining, u s is the tangential displacement of the inner surface of the lining, is the differential of u and , is the first derivative of u with respect to .

[0073] S4, a physical information neural network (PINN network) based on the inversion of external loads of the lining is established, the network structure is shown in Figure 4 , and the specific steps of the inverse analysis and the algorithm design are shown in Table 1.

[0074] Table 1 PINN algorithm design for inversion of external loads of the lining

[0075]

[0076] In actual engineering, the monitored quantities are ε s , w s and u s , etc., rather than u, w, and the direct output of the neural network is u, w. The difference between the results of the neural network and the monitoring results can be calculated by formula (3), the results of the neural network are measured, and the accuracy of the neural network inversion is ensured, that is, the monitoring data loss DATAloss is calculated in S4 by using formula (3).

[0077] Method verification:

[0078] Figure 5 is a schematic diagram of the influence of the excavation of a nearby tunnel on the original tunnel. The radius of the tunnel is 5 m, the thickness of the lining is 0.5 m, the buried depth of the tunnel is 16 m, and the centers of the two tunnels are 15 m apart. The finite element method is used to simulate this working condition, and the process is: ground stress balance, removal of soil elements at the original tunnel, activation of lining elements, and activation of soil elements at the nearby tunnel. The hard contact between the lining and the tunnel is simulated, and the friction coefficient is 0.3. The specific parameters of the numerical model are shown in Table 2.

[0079] Table 2 Numerical model parameters

[0080] Lining elastic modulus Lining Poisson's ratio Soil elastic modulus Soil Poisson's ratio Friction coefficient 30 GPa 0.15 200 MPa 0.2 0.3

[0081] The finite element numerical simulation results are shown in Figure 6 .

[0082] PINN measurement point information and analysis results:

[0083] The external load is inversed based on the lining strain and displacement monitoring information respectively through PINN.

[0084] The lining displacement monitoring point positions are [pi / 3, pi, 5*pi / 3].

[0085] The lining strain monitoring point positions are [0, pi / 5, 3*pi / 5, 5*pi / 5, 7*pi / 5, 9*pi / 5].

[0086] In the embodiment, Figure 7 and Figure 8 The process of training PINN based on displacement monitoring information and the process of training PINN based on strain monitoring information are respectively given;

[0087] Figure 9 and Figure 10 Strain comparison diagrams and displacement comparison diagrams of PINN results and FEM (Finite element method) calculation results are respectively given;

[0088] Figure 11 A comparison diagram of PINN inversed external load results and FEM external load results is given.

[0089] Embodiment two:

[0090] The tunnel lining external load inversion system based on physical information neural network comprises:

[0091] The physical information module is configured to: acquire monitoring data of a tunnel lining to be inversed; establish control equations of external load and lining neutral axis deformation according to curved beam theory, and determine boundary conditions; and establish a corresponding relationship between strain and displacement of an inner surface of the lining and strain and displacement of the neutral axis position according to material mechanics theory;

[0092] The neural network module is configured to: take lining spatial coordinates as inputs of the physical information neural network, and take normal displacement, tangential displacement of the neutral axis and external load of the lining at different coordinates as outputs, and convert the normal displacement and the tangential displacement of the neutral axis into strain and displacement of the inner surface of the lining;

[0093] The training and output module is configured to: train the physical information neural network so that the input-output relationship satisfies the control equations of the external load and the lining deformation, the boundary conditions and the monitoring data, and obtain the normal displacement, the tangential displacement of the neutral axis and the external load of the lining at the corresponding coordinates, which are the inversion results.

[0094] Embodiment three:

[0095] The embodiment provides a computer readable storage medium, which stores a computer program, and the program is executed by a processor to realize steps in the tunnel lining external load inversion method based on a physical information neural network.

[0096] Embodiment four:

[0097] The embodiment provides a computer device, which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, and the processor realizes steps in the tunnel lining external load inversion method based on a physical information neural network when executing the program.

[0098] Correspondence between each step in the above embodiments two to four and embodiment one is achieved, and the specific embodiment can refer to the related description part of embodiment one. The term 'computer readable storage medium' should be understood as including a single medium or multiple media of one or more instruction sets; and should also be understood as including any medium capable of storing, encoding or carrying instruction sets for execution by a processor and causing the processor to execute any method in the present application.

[0099] The above merely describes the preferred embodiments of the present application and is not used to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A method for tunnel lining external load inversion based on physical information neural network, characterized in that, The method comprises the following steps: obtaining monitoring data of an inner surface of a tunnel lining to be inverted; establishing a control equation of external load and deformation of a neutral axis of the lining according to curved beam theory, and determining boundary conditions; establishing a corresponding relationship between strain and displacement of the inner surface of the lining and strain and displacement of the neutral axis position according to material mechanics theory; constructing a physical information neural network, taking spatial coordinates of the lining as input of the physical information neural network, and taking normal displacement, tangential displacement of the neutral axis at different coordinates and external load of the lining as output, and converting the normal displacement and the tangential displacement of the neutral axis into strain and displacement of the inner surface of the lining; training the physical information neural network so that the input-output relationship satisfies the control equation of the external load and the deformation of the lining, the boundary conditions and the monitoring data, and obtaining the normal displacement, the tangential displacement of the neutral axis at the corresponding coordinates and the external load of the lining, which are the inversion results; the control equation of the external load and the deformation of the neutral axis of the lining is shown in the following formula: ； where p is the external load, u(φ) and w(φ) are the tangential and normal displacements at the neutral axis, O is the center of the tunnel and the origin of the polar coordinate, R is the radius of the tunnel, φ is the polar angle, M , N , Q are the bending moment, axial force and shear force of the cross section of the beam, respectively.

2. The physical information neural network-based tunnel lining external load inversion method of claim 1, wherein, The monitoring data of the tunnel lining to be inverted at least includes tunnel displacement and strain. 3.The tunnel lining external load inversion method based on physical information neural network according to claim 1, wherein, The model boundary conditions are shown in the following formula: ； wherein u is the normal displacement of the neutral axis, w is the tangential displacement. 4.The tunnel lining external load inversion method based on physical information neural network according to claim 1, wherein, The deformation monitoring points of the lining are located on the inner surface of the lining.

5. The physical information neural network-based tunnel lining external load inversion method of claim 4, wherein, The relationship between strain and displacement of the inner surface of the lining and strain and displacement of the neutral axis position is shown in the following formula: ； wherein u(φ) and w(φ) is the tangential and normal displacement of the neutral axis, R is the radius of the tunnel, φ is the polar angle, z is the distance to the neutral axis, u is the normal displacement of the neutral axis, w is the tangential displacement, is the strain of the inner surface of the tunnel lining, is the strain of the neutral axis of the tunnel lining, is the curvature of the neutral axis, is the normal displacement of the inner surface of the lining, is the tangential displacement of the inner surface of the lining. 6.The tunnel lining external load inversion method based on physical information neural network according to claim 1, wherein, The physical information neural network is trained, when the loss value is greater than the set threshold, the hyperparameter optimization is performed on the parameter update of the neural network, and when the iteration set number or the sum of all losses is the minimum, the normal displacement, the tangential displacement of the neutral axis at the corresponding coordinates and the external load of the lining are output.

7. A tunnel lining external load inversion system based on physical information neural network, characterized in that, It comprises: The physical information module is configured to obtain monitoring data of a tunnel lining to be inverted, and establish a control equation of external load and deformation of a neutral axis of the lining according to curved beam theory, and determine boundary conditions; The physical information module is further configured to obtain a relationship between external load of the lining and deformation of the inner surface of the lining by using a corresponding relationship between strain and displacement of the inner surface of the lining and strain and displacement of the neutral axis position, and combining the control equation; The neural network module is configured to take spatial coordinates of the lining as input of the physical information neural network, and take normal displacement, tangential displacement of the neutral axis at different coordinates and external load of the lining as output according to the relationship between the external load of the lining and the deformation of the inner surface of the lining; The relationship between the external load of the lining and the deformation of the neutral axis is shown in the following formula: ； wherein p is the external load, u(φ) and w(φ) are the tangential and normal displacements at the neutral axis, O is the center of the tunnel and is the polar coordinate origin, R is the radius of the tunnel, φ is the polar angle, M , N , Q are the bending moment, axial force and shear force of the cross section of the beam, respectively; The training and output module is configured to train the physical information neural network, and obtain the normal displacement, the tangential displacement of the neutral axis at the corresponding coordinates and the external load of the lining by using the trained physical information neural network, which are the inversion results.

8. A computer-readable storage medium, characterized in that, The computer program is stored on the storage medium, and the program is executed by the processor to realize the steps in the tunnel lining external load inversion method based on the physical information neural network according to any one of claims 1-6.

9. A computer device, comprising: The computer program is stored on the storage medium, and the program is executed by the processor to realize the steps in the tunnel lining external load inversion method based on the physical information neural network according to any one of claims 1-6.

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