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

Abstract

The invention relates to a tunnel lining external load inversion method and system based on a physical information neural network. The method comprises the following steps: acquiring monitoring data of the inner surface of a to-be-inverted tunnel lining; according to the curved beam theory, a control equation of external load and lining neutral axis deformation is established, and boundary conditions are determined; according to the material mechanics theory, the corresponding relation between the strain and displacement of the inner side surface of the lining and the strain and displacement of the neutral axis position is established; a physical information neural network is constructed, lining space coordinates serve as input of the physical information neural network, neutral axis normal displacement, tangential displacement and lining external load at different coordinates serve as output, and neutral axis displacement is converted into lining inner surface strain and displacement; the physical information neural network is trained, so that the input and output relation meets the control equation, boundary conditions and monitoring data of the external load and lining deformation, and the normal displacement, tangential displacement and lining external load of the neutral axis at the corresponding coordinates are obtained, namely, the inversion result is obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of tunnel engineering, and in particular to a method and system for inversion of external loads of tunnel lining based on physical information neural network. Background Art

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

[0003] During the construction of adjacent projects near tunnels and tracks, the surrounding rock or soil of the existing tunnel will be disturbed, causing changes in the external load of the tunnel lining, which in turn poses a safety risk 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] At present, there are three main methods for evaluating the external load of tunnel lining: direct measurement method, numerical analysis method and inverse analysis method.

[0005] Direct measurement is to test the pressure between the lining and the ground by placing an earth pressure cell between the lining and the ground. This method can directly obtain the external load, but the measurement results have high requirements for installation technology, and the sensor cannot be replaced once it fails, so it is difficult to apply it to long-term monitoring of tunnels during operation.

[0006] The accuracy of numerical methods depends on a full understanding of the surrounding rock geological conditions and the reasonable selection of rock and soil constitutive models and parameters. It is difficult to ensure accuracy under complex conditions.

[0007] The inverse analysis method inverts the external load based on the structural monitoring results. It generally uses the actual response of the structure and combines numerical methods to determine the external load. This method generally requires repeated calculations in combination with the rock and soil model, which is costly and its results depend on the rock and soil model and parameters. Summary of the invention

[0008] In order to solve the technical problems existing in the above-mentioned background technology, the present invention provides a tunnel lining external load inversion method and system based on physical information neural network, which uses the physical information actually monitored to build a function model, and converts the parameters of the inversion results into input and output of the physical information neural network. The learning process of the physical information neural network is used to obtain a solution that is more in line with the basic laws of physics. The required physical parameters are easy to monitor and the cost is lower than that of traditional inverse analysis methods.

[0009] In order to achieve the above object, the present invention adopts the following technical solution:

[0010] A first aspect of the present invention provides a method for inversion of external loads of a tunnel lining based on a physical information neural network, comprising the following steps:

[0011] Obtain monitoring data of the inner surface of the tunnel lining to be inverted;

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

[0013] According to the material mechanics theory, 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;

[0014] Construct a physical information neural network, with the lining space coordinates as the input of the physical information neural network, the neutral axis normal displacement, tangential displacement and lining external load at different coordinates as the output, and the neutral axis displacement is converted into the lining inner surface strain and displacement;

[0015] By training the physical information neural network, the input-output relationship is made to satisfy the control equations, boundary conditions and monitoring data of the external load and lining deformation, and the normal displacement, tangential displacement and external load of the lining at the corresponding coordinates are obtained, which are the inversion results.

[0016] Furthermore, the monitoring data of the tunnel lining to be inverted include displacement, strain, convergence, etc.

[0017] Furthermore, the governing equations of external load and lining neutral axis deformation are shown below:

[0018]

[0019] Where p is the external load, and are the tangential and normal displacements of the neutral axis, O is the center of the tunnel and the origin of the polar coordinates, R is the radius of the tunnel, is the polar angle, M, N, Q are the section bending moment, axial force and shear force of the beam respectively.

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

[0021] Furthermore, the lining deformation monitoring point is located on the inner surface of the lining, and the control equation is the deformation relationship between the external load and the neutral axis. Therefore, it is necessary to determine the relationship between the strain and displacement of the inner surface of the lining and the strain and displacement of the neutral axis position, as shown in the following formula:

[0022]

[0023] w s =w

[0024]

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

[0026] Furthermore, the physical information neural network is trained. When the loss value is greater than the set threshold, the hyperparameter tuning is performed by updating the parameters of the neural network. When the set number of iterations or the sum of all losses is minimized, the normal displacement of the neutral axis, the tangential displacement and the external load of the lining at the corresponding coordinates are output.

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

[0028] The physical information module is configured to: obtain monitoring data of the tunnel lining to be inverted; establish the control equations of the external load and the neutral axis deformation of the lining according to the curved beam theory, and determine the boundary conditions; establish 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 according to the material mechanics theory;

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

[0030] The training and output module is configured as follows: by training the physical information neural network, the input-output relationship satisfies the control equations, boundary conditions and monitoring data of the external load and lining deformation, and the normal displacement, tangential displacement and external load of the lining at the corresponding coordinates are obtained, which are the inversion results.

[0031] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the above-mentioned method for inversion of external loads of tunnel linings based on physical information neural network.

[0032] The fourth aspect of the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps in the above-mentioned method for inversion of external loads of tunnel lining based on physical information neural network are implemented.

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

[0034] 1. Use the actual monitored physical parameters to build a function model, and transform the parameters of the inversion results into the input and output of the physical information neural network. Use the learning process of the physical information neural network to obtain a solution that is more in line with the basic laws of physics. The required physical parameters are easy to monitor and have lower costs than traditional inverse analysis methods.

[0035] 2. Compared with direct measurement of external loads, the measurement of lining deformation is easier and more stable. Because direct measurement of external loads has high requirements on installation technology, and once the sensor fails, it cannot be replaced, and it is difficult to apply it to long-term monitoring of tunnels during operation. Therefore, inversion through monitoring deformation is more feasible and more accurate.

[0036] 3. The accuracy of the numerical method depends on a full understanding of the surrounding rock geological conditions and the reasonable selection of the constitutive model and parameters of the rock and soil mass. The accuracy is difficult to guarantee under complex conditions. However, deformation monitoring is usually more direct and accurate, so this method has a better accuracy guarantee.

[0037] 4. In the past, there were also inverse analysis methods used for external load inversion, but the previous methods usually assumed the form of the external load and were inefficient. This method does not assume the form of the external load and is highly efficient. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0039] Figure 1 It is a schematic diagram of the inversion process of the external load of the tunnel lining based on the physical information neural network provided by one or more embodiments of the present invention;

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

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

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

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

[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 invention;

[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 invention;

[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 invention;

[0047] Fig. 9 is a strain comparison diagram of a PINN result and a FEM calculation result provided by one or more embodiments of the present invention;

[0048] Fig.10 is a displacement comparison diagram of a PINN result and a FEM calculation result provided by one or more embodiments of the present invention;

[0049] Fig.11 It is a schematic diagram comparing the PINN inversion external load results and the FEM external load results provided by one or more embodiments of the present invention. DETAILED DESCRIPTION

[0050] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0051] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

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

[0053] Embodiment 1:

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

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

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

[0057] According to the material mechanics theory, 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] Construct a physical information neural network, with the lining space coordinates as the input of the physical information neural network, the neutral axis normal displacement, tangential displacement and lining external load at different coordinates as the output, and the neutral axis displacement is converted into the lining inner surface strain and displacement;

[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 the external load and lining deformation, and the normal displacement, tangential displacement and external load of the lining at the corresponding coordinates are obtained, which are the inversion results.

[0060] This embodiment specifically includes the following steps:

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

[0062] Among them, the control equations of external load and neutral axis deformation are as follows:

[0063]

[0064] Where p is the external load, and are the tangential and normal displacements of the neutral axis. O is the center of the tunnel and the origin of the polar coordinates, R is the radius of the tunnel, is the polar angle. M, N, Q are the cross-sectional bending moment, axial force and shear force of the beam respectively, and the direction indicated by the arrow in the figure is positive.

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

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

[0067]

[0068] S3. In actual projects, 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 position is as shown in formula (3). This formula can be used to convert the neutral axis displacement 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 inner surface strain of the tunnel lining, ε0 is the neutral axis strain 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, For u and The differential of For u The first derivative of .

[0073] S4. Establish a physical information neural network (PINN network) based on lining deformation inversion external load. The network structure diagram is shown in Figure 4 The specific steps and algorithm design of the reverse analysis are shown in Table 1.

[0074] Table 1 PINN algorithm design for lining external load inversion

[0075]

[0076] In actual engineering, the monitored s , w s and u s The difference between the result of the neural network and the monitoring result can be calculated by using formula (3), and the result of the neural network and the monitoring result can be measured to ensure the accuracy of the neural network inversion. That is to say, the monitoring data loss DATAloss is calculated in S4 using formula (3).

[0077] Method Validation:

[0078] Figure 5 This is a schematic diagram of the impact of the excavation of a nearby tunnel on the original tunnel. The tunnel radius is 5m, the lining thickness is 0.5m, the tunnel depth is 16m, and the distance between the centers of the two tunnels is 15m. The finite element method is used to simulate this working condition. The process is: ground stress balance, removal of soil units at the original tunnel, activation of lining units, and activation of soil units at the adjacent tunnel. The hard contact simulation is used between the lining and the tunnel, 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 Poisson's ratio of lining Soil elastic modulus Poisson's ratio of soil Friction coefficient 30GPa 0.15 200MPa 0.2 0.3

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

[0082] PINN measurement point information and analysis results:

[0083] Based on the lining strain and displacement monitoring information, the external load inversion is performed through PINN.

[0084] The locations of lining displacement measurement points are [pi / 3, pi, 5*pi / 3].

[0085] The locations of lining strain measuring points are [0, pi / 5, 3*pi / 5, 5*pi / 5, 7*pi / 5, 9*pi / 5].

[0086] In this 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 given respectively;

[0087] Fig. 9 and Fig.10 The strain comparison diagram and displacement comparison diagram of PINN results and FEM (Finite element method) calculation results are given respectively;

[0088] Fig.11 A comparison between the PINN inversion external load results and the FEM external load results is given.

[0089] Embodiment 2:

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

[0091] The physical information module is configured to: obtain monitoring data of the tunnel lining to be inverted; establish the control equations of the external load and the neutral axis deformation of the lining according to the curved beam theory, and determine the boundary conditions; establish 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 according to the material mechanics theory;

[0092] The neural network module is configured as follows: the spatial coordinates of the lining are used as the input of the physical information neural network, the normal displacement of the neutral axis, the tangential displacement and the external load of the lining at different coordinates are used as the output, and the neutral axis displacement is converted into the strain and displacement of the inner surface of the lining;

[0093] The training and output module is configured as follows: by training the physical information neural network, the input-output relationship satisfies the control equations, boundary conditions and monitoring data of the external load and lining deformation, and the normal displacement, tangential displacement and external load of the lining at the corresponding coordinates are obtained, which are the inversion results.

[0094] Embodiment three:

[0095] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the steps in the tunnel lining external load inversion method based on physical information neural network as described in the above-mentioned embodiment 2 are implemented.

[0096] Embodiment 4:

[0097] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps in the tunnel lining external load inversion method based on physical information neural network as described in the above-mentioned embodiment 2 are implemented.

[0098] The steps involved in the above embodiments 2 to 4 correspond to those in embodiment 1. For the specific implementation, please refer to the relevant description of embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood to include any medium that can store, encode or carry an instruction set for execution by a processor and enable the processor to execute any method in the present invention.

[0099] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. The inversion method of external load of tunnel lining based on physical information neural network is characterized by: The following steps are involved: Obtain monitoring data of the inner surface of the tunnel lining to be inverted; According to the curved beam theory, the control equations of external load and lining neutral axis deformation are established, and the boundary conditions are determined; According to the material mechanics theory, 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; Construct a physical information neural network, with the lining space coordinates as the input of the physical information neural network, the neutral axis normal displacement, tangential displacement and lining external load at different coordinates as the output, and the neutral axis displacement is converted into the lining inner surface strain and displacement; By training the physical information neural network, the input-output relationship is made to satisfy the control equations, boundary conditions and monitoring data of the external load and lining deformation, and the normal displacement, tangential displacement and external load of the lining at the corresponding coordinates are obtained, which are the inversion results.

2. The method for inversion of external loads on tunnel lining based on physical information neural network according to claim 1, characterized in that: The monitoring data of the tunnel lining to be inverted includes at least tunnel displacement and strain.

3. The tunnel lining external load inversion method based on physical information neural network according to claim 1 is characterized in that: The governing equations for external loads and lining neutral axis deformation are shown below: Where p is the external load, and are the tangential and normal displacements of the neutral axis, O is the center of the tunnel and the origin of the polar coordinates, R is the radius of the tunnel, is the polar angle, M, N, Q are the section bending moment, axial force and shear force of the beam respectively.

4. The tunnel lining external load inversion method based on physical information neural network according to claim 1 is characterized in that: The model boundary conditions are shown below: Where u is the normal displacement of the neutral axis and w is the tangential displacement.

5. The tunnel lining external load inversion method based on physical information neural network according to claim 1 is characterized in that: The lining deformation monitoring point is located on the inner surface of the lining.

6. The method for inversion of external loads of tunnel lining based on physical information neural network according to claim 5, characterized in that: 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 the following formula: In s =in In the formula, and are the tangential and normal displacements of the neutral axis, R is the tunnel radius, is the polar angle, z is the distance to the neutral axis, u is the normal displacement to the neutral axis, w is the tangential displacement, ε s is the inner surface strain of the tunnel lining, ε0 is the neutral axis strain 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.

7. The method for inversion of external loads on tunnel lining based on physical information neural network according to claim 1, characterized in that: The physical information neural network is trained. When the loss value is greater than the set threshold, the hyperparameter tuning is performed by updating the parameters of the neural network. When the set number of iterations or the sum of all losses is minimized, the normal displacement of the neutral axis, the tangential displacement and the external load of the lining at the corresponding coordinates are output.

8. The tunnel lining external load inversion system based on physical information neural network is characterized by: include: The physical information module is configured to: obtain monitoring data of the tunnel lining to be inverted, establish the control equations of the external load and the neutral axis deformation of the lining according to the curved beam theory, and determine the boundary conditions; The physical information module is further configured to: utilize 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, combined with the control equation, to obtain the relationship between the external load of the lining and the deformation of the inner surface of the lining; The neural network module is configured as follows: according to the relationship between the external load of the lining and the deformation of the inner surface of the lining, the spatial coordinates of the lining are used as the input of the physical information neural network, and the normal displacement of the neutral axis, the tangential displacement and the external load of the lining at different coordinates are used as the output; The training and output module is configured as follows: by training the physical information neural network, using the trained physical information neural network, the normal displacement of the neutral axis, the tangential displacement and the external load of the lining at the corresponding coordinates are obtained, which is the inversion result.

9. A computer-readable storage medium, characterized in that: A computer program is stored thereon, and when the program is executed by a processor, the steps in the tunnel lining external load inversion method based on physical information neural network as described in any one of claims 1 to 7 are implemented.

10. A computer device, characterized in that: The method comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps in the tunnel lining external load inversion method based on physical information neural network as described in any one of claims 1 to 7 are implemented.

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