A shield segment disease assessment method based on state space equation and physical information neural network

Abstract

The application provides a shield segment disease evaluation method based on a state space equation and a physical information neural network, and comprises the following steps: S1, on the basis of shield segment structure state space analysis theory, introducing disease influencing factors, establishing a shield segment structure state space equation containing diseases, and using the equation to establish a sample database of segment responses containing diseases; S2, based on the control equation, node equation and boundary constraint equation in the state space equation, constructing a shield segment disease identification physical information neural network and training the same; S3, after the training of the physical information neural network is completed, identifying the disease segment and its degree according to limited segment displacement monitoring information. The method has the dual advantages of analytical solution and machine learning algorithm, and since the core is to solve the state space equation derived based on the energy equation, the physical variables have strong interpretability, and the output result also conforms to the physical law.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of computational mechanics and computer science, specifically involving a method for assessing tunnel segment defects based on state-space equations and physical information neural networks. Background Technology

[0002] Existing research methods for shield tunnel defects can be mainly divided into three categories: semi-analytical methods, finite element methods, and machine learning algorithms.

[0003] Among the semi-analytical methods for shield tunnel structures, the state-space method is the most representative. Professor Xu Rongqiao's research group at Zhejiang University systematically developed this method based on Euler curved beam theory, achieving a refined characterization of the inter-layer slip effect between multi-layer linings and the mechanical behavior of segment joints. It can solve for the internal forces and deformations of structures under arbitrary stratum loads and joint distributions. This method features concise expressions; the matrix form of the differential equations avoids complex mesh discretization; it directly relates the load transfer path to the structural response mechanism, providing clear physical concepts; and the analytical solution significantly improves computational speed, making it particularly suitable for parameter sensitivity analysis and optimization design. Currently, this method has been extended to complex structures such as rectangular cross-section tunnels and multi-ring shield tunnels. However, its application has the following two limitations: First, it only supports forward calculations from boundary conditions (such as segment connection methods and soil-structure interaction) to structural response, and cannot invert parameters such as stiffness degradation (such as segment corrosion and bolt loosening) or contact failure (such as soil voiding) based on displacement / strain monitoring data; Second, the values ​​of key parameters in the model (such as soil spring stiffness and interlayer stiffness between segment and grouting layer) depend on empirical assumptions and lack a collaborative calibration mechanism between theoretical analytical solutions and field measured data. Taking soil-structure interaction as an example, when it is simplified to a soil spring model, the spring stiffness needs to be assigned through engineering experience, making it difficult to quantify the time-varying effect of contact stiffness caused by grouting layer deterioration or soil erosion; similarly, the values ​​of the interface stiffness between the segment and the grouting layer also lack joint constraints from constitutive relations and service monitoring data.

[0004] Stress-strain simulation of shield tunnel structures based on the finite element method (FEM) discretizes the tunnel structure and surrounding soil layers into finite element meshes and applies soil constitutive models (such as the Mohr-Coulomb criterion and the modified Cambridge model) to characterize the nonlinear mechanical behavior of the soil, thereby accurately simulating the soil-structure interaction mechanism. This method is typically used for safety assessments of key construction phase nodes (such as tunneling disturbances and transient responses during segment assembly), but is rarely directly applied to operational phase defect analysis. The fundamental reason is that, in terms of load mechanisms, the construction phase model uses the unloading of soil at the excavation face as the core load input, while operational phase defects originate from long-term cumulative damage (such as concrete carbonization, steel corrosion, and time-varying processes like joint stiffness degradation). Furthermore, similar to semi-analytical methods, while the finite element model can output deformation responses, it cannot identify defect parameters (such as segment stiffness reduction rate and grout layer void range) based on monitoring data. Furthermore, compared to semi-analytical methods, the finite element method's refined three-dimensional mesh and nonlinear contact boundary result in high model complexity, making it difficult to abstract into parameterized equations. This, in turn, hinders its use as a physical knowledge embedding tool in intelligent algorithms such as Physics-Informed Neural Networks (PINNs).

[0005] Machine learning-based methods for detecting defects in shield tunnels establish a nonlinear mapping relationship between defect features and monitoring data to achieve intelligent diagnosis of structural conditions. However, existing methods generally adopt a data-driven paradigm, and their performance is highly dependent on the completeness, accuracy, and timeliness of the sample data. In actual monitoring, data quality defects caused by sensor drift, environmental noise, and annotation errors can easily lead to model overfitting or errors in physical laws, reducing the accuracy of identification. To enhance the engineering rationality of the model output, some studies have attempted to embed the tunnel alignment control equation into the loss function, forcing the output to meet the structural geometric control requirements. However, as a complex system with multi-field coupling, the evolution of defects in shield tunnels involves factors that are difficult to equation out, such as time-varying soil-structure interactions, nonlinear material degradation, and randomness of construction defects. This makes it difficult to fully embed all control mechanisms using only the loss function, thus limiting the generalization ability of physics-driven deep learning models in complex operational scenarios. Summary of the Invention

[0006] The main objective of this invention is to provide a method for assessing tunnel segment defects based on state-space equations and physical information neural networks, addressing the aforementioned problems.

[0007] Therefore, the above-mentioned objective of the present invention is achieved through the following technical solution: A method for assessing tunnel segment defects based on state-space equations and physical information neural networks includes the following steps: S1. Based on the state-space analysis theory of shield tunnel segment structure, introduce the influencing factors of defects, establish the state-space equation of shield tunnel segment structure including defects, and use the equation to establish a sample database of segment response including defects. S2. Based on the control equations, node equations and boundary constraint equations in the state-space equations, construct and train a physical information neural network for identifying tunnel segment defects. S3. After the physical information neural network is trained, the faulty segments and their extent are identified based on the limited segment displacement monitoring information. It can not only identify the faulty segments and their extent, but also determine the parameters in the shield tunnel segment state space analysis theory.

[0008] While adopting the above technical solutions, the present invention may also adopt or combine the following technical solutions: As a preferred technical solution of the present invention: in step S1, the defects include concrete spalling of pipe segments, corrosion defects, water leakage, loose bolts, slippage between pipe segments and grouting layers, and soil voids.

[0009] As a preferred embodiment of the present invention: in step S2, the governing equation is... In the formula, The coefficient matrix of the state equation, A dimensionless state vector. It is a dimensionless external load vector. It is the central angle of the shield tunnel ring.

[0010] As a preferred embodiment of the present invention: In step S2, the nodal equations are as follows: In the formula, It is dimensionless segment deflection. It is a dimensionless axial displacement at the starting end of the tunnel segment. It is a dimensionless relative axial displacement of the tunnel segments. It is the starting angle of the tunnel segment, It is a dimensionless shear force of the tunnel segment section. It is the generalized axial force of the tunnel segments. It is the generalized axial force of the grouting layer. It is the generalized axial force of the grouting layer and the segments. It is the normal outward load, It is a circumferential outward load, It is the radius of the neutral axis curve of the grouting layer and the segments. It is the elastic modulus of the grouting layer and the segments. It is the cross-sectional area of ​​the grouting layer and the segments. It is the moment of inertia of the grouting layer and the segments. It is the interlaminar shear stiffness between the grouting layer and the segments. It is the normal soil reaction stiffness, Circumferential soil reaction stiffness.

[0011] As a preferred embodiment of the present invention: In step S2, the boundary constraint equation is... In the formula, For the deflection at the beginning of the tunnel segment, For the axial displacement of the starting end of the tunnel segment, The superscript indicates the corner at the beginning of the tunnel segment. j Representing the j The subscript of segment number represents the grouting layer (2) / segment (1), and the subscript of segment number represents the starting end (0) / ending end (1), such as represent j The axial force value of the +1 end segment in the initial section; , , They represent the first j Radial, axial, and steering spring stiffness at each joint.

[0012] Compared with existing technologies, the present invention has the following advantages: The method proposed in this invention combines the advantages of analytical solutions and machine learning algorithms. Since its core lies in solving the state-space equations derived from the energy equation, the physical variables have strong interpretability, and the output results conform to physical laws. At the same time, the data-driven algorithm used in this invention can determine the key parameters and segment defects in the analytical equations based on a small amount of monitoring data, which is difficult to achieve with traditional analytical methods or finite element methods. In addition, compared with conventional data-driven methods, this method embeds the analytical solution into the network training process in the form of a loss term, which improves data efficiency and enhances the network's noise resistance and robustness, thus requiring lower sample quantity and quality. Attached Figure Description

[0013] Figure 1 The flowchart shows the shield tunnel segment defect assessment method based on state-space equations and physical information neural networks provided by this invention.

[0014] Figure 2 This is an analysis model and load model for shield tunnel segment rings.

[0015] Figure 3 A schematic diagram of a physical information neural network for identifying defects in shield tunnel segments. Detailed Implementation

[0016] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0017] like Figure 1 As shown, a method for assessing tunnel segment defects based on state-space equations and physical information neural networks specifically includes the following steps: S1. Based on the state-space analysis theory of shield tunnel segment structure, introduce the influencing factors of defects, establish the state-space equation of shield tunnel segment structure including defects, and use the equation to establish a sample database of segment response including defects. An initial sample library is established using state-space equations. Because the network output is constrained by state-space equations during subsequent network training, the sample size in the sample library is much smaller than that of typical machine learning methods.

[0018] The state-space method treats the tunnel segments as curved beams and establishes the total potential energy equation for the elastic foundation beam. This equation incorporates soil springs to account for the interaction between the tunnel boring machine (TBM) and the soil, and considers interlayer slippage between the tunnel segments and the grouting. Figure 2 As shown in the figure, the loads are as follows: p 1 represents the soil load on the upper part of the tunnel. p 2 represents the soil reaction force at the bottom of the tunnel. p 3. p 4 represents the tunnel. Using the principle of minimum potential energy, the total potential energy equation is derived, resulting in the dimensionless governing equations, as follows: In the formula, The coefficient matrix of the state equation, A dimensionless state vector. It is a dimensionless external load vector. It is the central angle of the shield tunnel ring.

[0019] The nodal equations are In the formula, It is dimensionless segment deflection. It is a dimensionless axial displacement at the starting end of the tunnel segment. It is a dimensionless relative axial displacement of the tunnel segments. It is the starting angle of the tunnel segment, It is a dimensionless shear force of the tunnel segment section. It is the generalized axial force of the tunnel segments. It is the generalized axial force of the grouting layer. It is the generalized axial force of the grouting layer and the segments. It is the normal outward load, It is a circumferential outward load, It is the radius of the neutral axis curve of the grouting layer and the segments. It is the elastic modulus of the grouting layer and the segments. It is the cross-sectional area of ​​the grouting layer and the segments. It is the moment of inertia of the grouting layer and the segments. It is the interlaminar shear stiffness between the grouting layer and the segments. It is the normal soil reaction stiffness, Circumferential soil reaction stiffness.

[0020] At the same time, there are several boundary conditions, and the boundary constraint equations are as follows: Boundary condition 1: To avoid rigid body displacement, it is necessary to constrain the displacement of a certain point on the segment ring, such as... In the formula, For the deflection at the beginning of the tunnel segment, For the axial displacement of the starting end of the tunnel segment, This refers to the angle at the beginning of the tunnel segment.

[0021] Boundary condition 2: The internal forces between the tunnel segments are transmitted through the joint springs, with the following assumptions. In the formula, the superscript j Representing the j The subscript of segment number represents the grouting layer (2) / segment (1), and the subscript of segment number represents the starting end (0) / ending end (1), such as represent j +1 end segment (1) axial force value at the starting end (0). , , They represent the first j Radial, axial, and steering spring stiffness at each joint.

[0022] The internal forces and displacements of the grouting layer are continuous. In the state-space method, matrix theory is applied to solve the above equations. This involves solving for matrix exponents, which requires first calculating the eigenvectors and corresponding eigenvalues ​​of the matrix. This typically relies on numerical methods, making it difficult to obtain solutions in variable form. In this patent, a machine learning model will be used instead of matrix theory to solve the above equations.

[0023] To study the impact of defects on shield tunnel structures, it is first necessary to investigate the representation of different defects in the state-space equations. The following research methods will be adopted for common defects in shield tunnel segment structures: 1) Concrete spalling and corrosion of tunnel segments These types of defects reduce the effective cross-section of the tunnel segments, thereby decreasing the structural stiffness. A segment stiffness reduction method was used for simulation.

[0024] 2) Water leakage Water leakage typically originates from the failure of the waterproofing layer of the tunnel lining segments, defects in the grouting holes, or internal micro-cracks. Long-term leakage can induce corrosion of internal steel bars or joint bolts, ultimately weakening the rigidity of the tunnel lining segments and joints.

[0025] The model is characterized by: simulation of overall stiffness reduction of the tunnel segments (reflecting the stiffness loss of the tunnel segments themselves). In the formula, This indicates the reduction rate of steel reinforcement stiffness. This indicates the cross-sectional diameter of the complete reinforcing bar. This indicates the cross-sectional diameter of the corroded steel bar. This indicates the bending stiffness of a complete steel reinforcement bar. This indicates the bending stiffness of corroded steel bars.

[0026] 3) Loose bolts Vibration, alternating loads, overload, improper installation techniques, and material quality issues can all cause bolt loosening, resulting in joint stiffness degradation. This was simulated by directly reducing the equivalent stiffness parameters of the segment joint.

[0027] 4) Slippage between segments and grouting layer The grouting layer on the outside of shield tunnel segments is formed during shield construction by filling the voids between the segments and the soil through a synchronous grouting process. With increasing service life, due to soil erosion and deterioration of the grouting material, the bond strength between the grouting layer and the segment interface gradually weakens, leading to interface slippage and even localized spalling or complete loss of the grouting layer. This type of damage occurs on the soil-facing side of the structure and is characterized by its high degree of concealment and difficulty in identification through conventional testing. In state-space structural analysis, its mechanical effects can be quantified using the parameter of "segment-grouting layer interface slippage stiffness."

[0028] 5) Soil voids Soil voiding is a hidden defect on the soil-facing surface, specifically manifested as a weakening or loss of the constraint effect on the tunnel lining segments (surrounding rock resistance). It can be simulated by removing (or equivalently significantly reducing) the external soil spring stiffness and prestress at the corresponding location, while ignoring the contribution of the external grouting layer.

[0029] S2. Based on the control equations, node equations and boundary constraint equations in the state-space equations, construct and train a physical information neural network for identifying tunnel segment defects. To achieve efficient defect localization, the state-space equations need to be reconstructed, assuming that defects may occur in every part of the tunnel segment. Therefore, a discretization strategy is first adopted, no longer using the entire tunnel segment as the basic unit, but uniformly discretizing the tunnel segment ring into several segmented units along the circumference. At the same time, a node constraint mechanism is introduced: when adjacent segmented units belong to the same tunnel segment, their internal forces and displacements must satisfy the continuity condition; conversely, if they belong to different tunnel segments, the node constraint equations (such as the force balance and deformation compatibility relationship at the joints) must be strictly satisfied.

[0030] The loss function of the physical information equation is extracted from the control equation, node equation, and boundary constraint equation in the state-space equation.

[0031] Using the monitored response information (e.g., displacement response, but strain and stress response could also be used) and the corresponding segment spatial information as input, and the segment structural information, segment stiffness, and soil spring stiffness as output, a physical information network is trained using a sample database of shield tunnel segment responses with defects. Figure 3 As shown.

[0032] During network training, automatic differentiation techniques are applied to perform differential calculations in the state-space equations. Through iterative training, the output values ​​are made to simultaneously satisfy the governing equations, node equations, and boundary constraint equations.

[0033] When the amount of data for a single sample is large, convolution operations can be added to the network to improve the efficiency of the network model in extracting features.

[0034] S3. After the physical information neural network is trained, the faulty segments and their severity are identified based on the limited segment displacement monitoring information, and the values ​​of empirical parameters in the state space equation are guided. At the same time, the layout of measuring points is optimized based on the identification accuracy to provide guidance for the monitoring scheme.

[0035] After the above physical information network is trained, it is possible to identify defective pipe segments and their severity based on limited segment displacement monitoring information.

[0036] Based on recognition accuracy and network robustness, parametric experiments were conducted on monitoring items (such as displacement and strain) and the location and number of monitoring points to obtain the optimal monitoring point layout, which helps to improve recognition accuracy.

[0037] Meanwhile, this network can be used to determine empirical parameters in the state-space equation based on monitoring projects, such as soil spring stiffness, slip stiffness of the interface between the tunnel segment and the grouting layer, and connection stiffness between tunnel segments, thus helping to improve the research method for shield tunnel structures based on the state-space method.

[0038] The technical solution of the present invention has been described in conjunction with the specific experimental procedures shown in the accompanying drawings. However, the scope of protection of the present invention is not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions resulting from such changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A method for assessing tunnel segment defects based on state-space equations and physical information neural networks, characterized in that, Includes the following steps: S1. Based on the state-space analysis theory of shield tunnel segment structure, introduce the influencing factors of defects, establish the state-space equation of shield tunnel segment structure including defects, and use the equation to establish a sample database of segment response including defects. S2. Based on the control equations, node equations and boundary constraint equations in the state-space equations, construct and train a physical information neural network for identifying tunnel segment defects. S3. After the physical information neural network is trained, the faulty segments and their extent are identified based on the limited segment displacement monitoring information. It can not only identify the faulty segments and their extent, but also determine the parameters in the shield tunnel segment state space analysis theory.

2. The method according to claim 1, characterized in that: In step S1, the defects include concrete spalling of the pipe segments, corrosion, water leakage, loose bolts, slippage between the pipe segments and the grouting layer, and soil voids.

3. The method according to claim 1, characterized in that: In step S2, the governing equation is: In the formula, The coefficient matrix of the state equation, A dimensionless state vector. It is a dimensionless external load vector. It is the central angle of the shield tunnel ring.

4. The method according to claim 1, characterized in that: In step S2, the nodal equations are: In the formula, It is dimensionless segment deflection. It is a dimensionless axial displacement at the starting end of the tunnel segment. It is a dimensionless relative axial displacement of the tunnel segments. It is the starting angle of the tunnel segment, It is a dimensionless shear force of the tunnel segment section. It is the generalized axial force of the tunnel segments. It is the generalized axial force of the grouting layer. It is the generalized axial force of the grouting layer and the segments. It is the normal outward load, It is a circumferential outward load, It is the radius of the neutral axis curve of the grouting layer and the segments. It is the elastic modulus of the grouting layer and the segments. It is the cross-sectional area of ​​the grouting layer and the segments. It is the moment of inertia of the grouting layer and the segments. It is the interlaminar shear stiffness between the grouting layer and the segments. It is the normal soil reaction stiffness, Circumferential soil reaction stiffness.

5. The method according to claim 1, characterized in that: In step S2, the boundary constraint equations are: In the formula, For the deflection at the beginning of the tunnel segment, For the axial displacement of the starting end of the tunnel segment, The superscript indicates the corner at the beginning of the tunnel segment. j Representing the j The subscript of segment number represents the grouting layer (2) / segment (1), and the subscript of segment number represents the starting end (0) / ending end (1), such as represent j The axial force value of the +1 end segment in the initial section; , , These represent the radial, axial, and steering spring stiffness at the j-th joint, respectively.

6. The method according to claim 1, characterized in that: In step S2, during network training, automatic differentiation technology is applied to complete the differential calculation in the state space equation. Through iterative training, the output value is made to simultaneously satisfy the control equation, node equation, and boundary constraint equation.

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