A shield tunnel deformation real-time calculation method and system based on PINN

Abstract

This invention provides a real-time deformation calculation method and system for shield tunnels based on PINN, relating to the field of shield tunnel engineering mechanics calculation and safety monitoring technology. The method includes: constructing a coupled physical model of the shield tunnel lining-foundation-load, and deriving the physical control equations; pre-training the deformation prediction basic model; collecting real-time monitoring data from the site, constructing data information loss, and forming a data-physical fusion loss function; based on the data-physical fusion loss function, using an incremental training mode to iteratively correct the deformation prediction basic model in real time; and calculating the full-section deformation of the shield tunnel in real time based on the corrected deformation prediction basic model. This invention takes into account both physical laws and measured data, adapts to a small amount of monitoring data, ensures real-time performance through incremental training, and has high calculation accuracy. It can guide the construction and operation of shield tunnels and is suitable for structural safety assessment during the construction and operation phases.

Description

Technical Field

[0001] This invention relates to the field of mechanical calculation and safety monitoring technology for shield tunnel engineering, specifically to a method and system for real-time calculation of shield tunnel deformation based on PINN (Physics-Informed Neural Networks). Background Technology

[0002] Shield tunnels are a core structural form in major underground engineering projects such as urban rail transit and cross-river / sea passages. Accurate calculation of their deformation state is crucial for ensuring project safety. Currently, the mechanical calculation of shield tunnels mainly relies on traditional numerical methods, such as the finite difference method (FDM) and the finite element method (FEM). These methods are based on continuum mechanics theory, obtaining calculation results by discretizing the structure and solving equilibrium equations. However, their accuracy is highly dependent on the accuracy of the load model. In actual engineering, factors such as the complexity of the geological strata where the tunnel is located, the randomness of construction disturbances, and the time effect of soil creep make it difficult to accurately characterize loads such as earth pressure and water pressure using existing theoretical formulas. Deviations in load input directly cause significant discrepancies between the calculation results of traditional numerical methods and actual field measurements, failing to provide reliable support for real-time safety decisions.

[0003] To address the shortcomings of traditional methods, some studies have attempted to use purely data-driven neural network models for prediction. However, this type of method has significant drawbacks: First, it relies on a large amount of high-quality field monitoring data, but in the case of shield tunnel field monitoring, sensors are only deployed at key points such as the arch crown, arch bottom, and arch waist, resulting in a relatively limited amount of data. Second, purely data-driven models lack constraints from physical laws, making them prone to problems such as "data overfitting" or "prediction results not conforming to the common sense of mechanics," leading to a high risk of uncontrolled errors.

[0004] In summary, traditional methods cannot simultaneously ensure the rigor of physical laws and the authenticity of measured data, and cannot solve the core problems of inaccurate loads in traditional methods and data dependence in purely data-driven methods. Summary of the Invention

[0005] To address the problems of large calculation deviations caused by inaccurate loads in traditional FDM / FEM methods and the reliance on large amounts of data without physical constraints in purely data-driven neural networks, this invention proposes a real-time calculation method and system for shield tunnel deformation based on PINN. This method takes into account both physical laws and measured data, adapts to a small amount of monitoring data, ensures real-time performance through incremental training, and has high calculation accuracy. It can guide shield tunnel construction and operation and maintenance and is suitable for structural safety assessment during the construction and operation phases.

[0006] According to some embodiments, the present invention adopts the following technical solution:

[0007] A real-time deformation calculation method for shield tunnels based on PINN, comprising:

[0008] Based on the structural, geological, and load parameters of the shield tunnel, a coupled physical model of shield tunnel lining-foundation-load is constructed, and the physical control equations are derived.

[0009] Based on the Physical Information Neural Network (PINN), a deformation prediction basic model adapted to the mechanical characteristics of shield tunnels is built. The physical information loss function is constructed using the residual loss of the physical control equation and the boundary condition constraint loss, and the deformation prediction basic model is pre-trained.

[0010] Collect real-time monitoring data from the site, construct a data information loss function, and integrate it into the physical information loss function to form a data-physical fusion loss function;

[0011] Based on the data-physical fusion loss function, the incremental training mode is used to iteratively correct the deformation prediction basic model in real time. Based on the corrected deformation prediction basic model, the deformation of the entire cross section of the shield tunnel is calculated in real time.

[0012] According to some embodiments, the present invention adopts the following technical solution:

[0013] A real-time deformation calculation system for shield tunnels based on PINN, comprising:

[0014] The equation derivation module is configured to: construct a coupled physical model of shield tunnel lining-foundation-load based on the structural parameters, geological parameters and load parameters of the shield tunnel, and derive the physical control equations.

[0015] The pre-training module is configured to: build a deformation prediction basic model adapted to the mechanical characteristics of shield tunnels based on the physical information neural network PINN; construct a physical information loss function using the physical control equation residual loss and boundary condition constraint loss; and pre-train the deformation prediction basic model.

[0016] The loss construction module is configured to: collect real-time monitoring data on site, construct data information loss, integrate it into the physical information loss function, and form a data-physical fusion loss function;

[0017] The real-time correction module is configured to: perform real-time iterative correction of the deformation prediction base model based on the data-physical fusion loss function and adopt an incremental training mode; and calculate the full-section deformation of the shield tunnel in real time based on the corrected deformation prediction base model.

[0018] According to some embodiments, the present invention adopts the following technical solution:

[0019] A computer program product includes a computer program that, when executed by a processor, implements the real-time calculation method for shield tunnels that integrates physical information neural networks.

[0020] According to some embodiments, the present invention adopts the following technical solution:

[0021] A non-transitory computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the aforementioned real-time calculation method for shield tunnels incorporating a physical information neural network.

[0022] According to some embodiments, the present invention adopts the following technical solution:

[0023] An electronic device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to execute the real-time calculation method for shield tunnels that integrates physical information neural networks.

[0024] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0025] This invention uses the physical control equations of shield tunnels as the core constraint, a certain amount of field measured data as the basis for correction, and incremental training to achieve rapid model iteration, balancing computational accuracy and real-time performance. It provides reliable technical support for the safety monitoring of shield tunnels, specifically in the following ways:

[0026] This invention incorporates the physical control equations of shield tunnel mechanics into the model training by constructing a physical information neural network. This not only effectively overcomes the systematic bias caused by the inaccuracy of the load model in traditional numerical methods, but also avoids the problems of "prediction distortion" or "violation of mechanical common sense" that may occur in pure data-driven models due to the lack of physical constraints. Through the data-physical fusion loss function, the unity of theoretical rigor and the authenticity of measured data is achieved, ensuring the reliability and high accuracy of the calculation results.

[0027] To address the practical constraints of limited monitoring points (such as the arch crown, arch base, and arch waist) and insufficient data volume in shield tunnel construction, the method of this invention primarily relies on physical laws during the pre-training phase to form prior knowledge of the structural mechanical response. In the real-time correction phase, only the limited real-time monitoring data needs to be incorporated into the model as a data information loss to drive accurate model correction. This design significantly reduces the reliance on massive amounts of high-quality monitoring data, making the method more universal and operable in practical engineering.

[0028] This invention designs an efficient model update mechanism. After obtaining the basic deformation prediction model through pre-training, subsequent corrections based on new monitoring data employ an incremental training mode, updating only the shallow parameters of the model without retraining the entire network. This mechanism ensures extremely short convergence time for each model correction (no more than 5 minutes), meeting the urgent need for rapid safety assessment and real-time decision-making during shield tunnel construction and operation. Attached Figure Description

[0029] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0030] Figure 1 This is a flowchart of the method in Example 1;

[0031] Figure 2 This is a schematic diagram of the physical model of shield tunnel lining-foundation-load coupling in Example 1;

[0032] Figure 3 This is a schematic diagram of the deformation prediction basic model structure in Example 1;

[0033] Figure 4 This is a comparison chart of the radial displacement calculation results in Example 1;

[0034] Figure 5 This is a comparison chart of the tangential displacement calculation results in Example 1. Detailed Implementation

[0035] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0036] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0037] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0038] Example 1

[0039] One embodiment of the present invention provides a method for real-time calculation of shield tunnel deformation based on PINN, such as... Figure 1 As shown, it includes five basic steps:

[0040] Step S1: Obtain the structural parameters, geological parameters, and load parameters of the shield tunnel.

[0041] Structural parameters include the radius of the lining centerline. R =6.5m, lining thickness t =0.5m, elastic modulus E =35GPa, shear modulus G =14.58GPa, moment of inertia of cross section I =0.0104m 4 Segment stiffness reduction factor η =0.9.

[0042] Geological parameters include the horizontal subgrade coefficient of the surrounding rock. =60000kN / m³, vertical subgrade coefficient =30000kN / m³, Tangential spring stiffness =20000kN / m³.

[0043] Load parameters include vertical earth pressure above the structure. =200kPa, vertical earth pressure below the structure =200kPa, horizontal earth pressure at the top of the structure's arch =100kPa, horizontal earth pressure at the bottom of the structural arch =150kPa, Linear load of lining self-weight =12.5kN / m.

[0044] Step S2: Construct a coupled physical model of shield tunnel lining-foundation-load and derive the physical control equations.

[0045] like Figure 2 As shown, the physical model of shield tunnel lining-foundation-load coupling is set as follows: the lining structure is regarded as a homogeneous circular ring, and the shear deformation of the shield tunnel lining segments is considered using the Timoshenko beam theory; the foundation is represented by a variable stiffness Winkler spring model, the normal spring stiffness varies with the circumferential angle and only plays a role when under compression, and the tangential spring acts continuously throughout the circumference; the load includes radial active load and tangential active load, which is composed of vertical load, horizontal load and lining self-weight.

[0046] Regarding the circumferential angle Using the center of the circular cross-section of the shield tunnel as the origin of polar coordinates, a fixed direction within the cross-section is selected as the zero-degree baseline (in this embodiment, the vertical upward direction of the tunnel (arch top) is taken as 0°). Starting from the baseline, the angle between the target point and the line connecting the target point and the center of the tunnel is defined as the circumferential angle at that point. In this embodiment, clockwise rotation is considered positive and counterclockwise rotation is considered negative.

[0047] Using the above-mentioned lining-foundation-load coupled physical model, a micro-element is selected along the arc direction. Based on the force balance and moment balance relationships, the physical governing equations are derived, specifically:

[0048] Radial equilibrium equations:

[0049] Tangential equilibrium equations:

[0050] in, For bending parameters, For shear deformation parameters, This is the shear correction factor. It is the Heaviside function (characterizing that the normal spring is only compressed). For normal spring stiffness, For tangential spring stiffness, R The radius of the lining centerline. EA For axial stiffness, EI For bending stiffness, w For radial displacement, v For tangential displacement, It is the circumferential angle. , , , , , For the differential terms of radial and tangential displacements, For radial active load, This is a tangential active load.

[0051] Radial active loads are positive outwards, and tangential active loads are positive clockwise. Both are synthesized from vertical earth pressure, horizontal earth pressure, and the self-weight of the lining, specifically as follows:

[0052]

[0053]

[0054] in, This refers to the vertical earth pressure above the structure. This refers to the vertical earth pressure below the structure. This refers to the horizontal earth pressure at the top of the structural arch. This refers to the horizontal earth pressure at the bottom of the arch structure. For the line load of the lining's self-weight, θ It is the circumferential angle.

[0055] Step S3: Based on the Physical Information Neural Network (PINN), build a deformation prediction basic model adapted to the mechanical characteristics of shield tunnels. Construct a physical information loss function using two physical information loss terms: physical control equation residual loss and boundary condition constraint loss, and complete the model pre-training.

[0056] like Figure 3 As shown, the input layer of the deformation prediction basic model is the circumferential angle. The values ​​cover the entire circumference from -π to π, where, Represents the location of the tunnel arch. This represents the location of the tunnel arch bottom. A Fourier feature map is added between the input layer and the first hidden layer to improve the network's ability to learn periodic functions. The Fourier feature map has 7 frequency components, therefore the mapping layer has 15 dimensions. The hidden layer uses a 6-layer fully connected structure, with 200 neurons per layer and the activation function being Tanh. The output layer is a radial displacement. w Tangential displacement v The differential terms of radial and tangential displacements are obtained using the automatic differentiation technique of neural networks. , , , , , .

[0057] Constructing the physical information loss function , For the residual loss of the physical control equation, For boundary condition constraint loss, ω 1. ω 2 represents pre-trained fixed weights. Among them, the residual loss of the physical control equations... The calculation method is as follows:

[0058]

[0059] in, The residual loss caused by the radial equilibrium equation of the shield tunnel is calculated as follows:

[0060]

[0061] The residual loss caused by the tangential equilibrium equation of the shield tunnel is calculated as follows:

[0062]

[0063] Boundary condition constraint loss according to The position is set so that the radial displacements on both the left and right sides are the same, and the tangential displacements are equal and opposite. The calculation method is as follows:

[0064]

[0065] in, for Predicted radial displacement at the location, for Predicted radial displacement value, for Predicted tangential displacement value. for Predicted tangential displacement.

[0066] The neural network was set to 15,000 iterations, batch size to 361, and learning rate to 0.0001.

[0067] Based on the above model, the pre-training of the basic model for deformation prediction was completed.

[0068] Step S4: Collect a small amount of real-time monitoring data from the site, construct the data information loss, and integrate it into the physical information loss function of the deformation prediction basic model to form a data-physical fusion loss function.

[0069] Real-time on-site monitoring data, selecting deformation data (including radial displacement) of the shield tunnel arch crown, arch base, and both sides of the arch waist. Tangential displacement This real-time data is embedded into a physical information neural network to construct a data information loss mechanism. This value is the mean square error between the predicted value from the deformation prediction model and the real-time monitoring value. The calculation method is as follows:

[0070]

[0071] in, This is the predicted value of radial displacement. This is the predicted value of the tangential displacement. This is the measured value of radial displacement. This represents the measured value of the tangential displacement.

[0072] Furthermore, the data-to-thing fusion loss function is constructed as follows: , ω 3 represents the adaptive weight for data information loss. The weight is dynamically adjusted as the measured data is updated, and the higher the credibility of the measured data, the greater the weight.

[0073] Step S5: Based on the data-object fusion loss function, the model is iteratively corrected in real time using incremental training mode. Using the pre-trained deformation prediction base model as a foundation, only the shallow parameters of the model are updated after each acquisition of new on-site monitoring data; there is no need to retrain the entire network. The iteration convergence threshold is set to 10. -6 The convergence time does not exceed 5 minutes, which meets the requirements for real-time calculation.

[0074] After training, different circumferential angles will be used. Input into the trained deformation prediction base model ， The deformation results of the entire shield tunnel section were obtained and transmitted to the site in real time to guide tunnel construction and operation and maintenance.

[0075] As verification, the calculation results obtained by the finite difference method (FDM) for the shield tunnel in the embodiment, the prediction results of the pre-trained deformation prediction basic model, and the prediction results of the data-physical fusion deformation prediction basic model are compared. Figure 4 , Figure 5 A comparison was conducted; the results show that the results obtained using the pre-trained deformation prediction model are in excellent agreement with those obtained using the finite difference method, thus verifying the reliability of the pre-trained deformation prediction model in solving the deformation problem of shield tunnels. However, there is a certain error between the results obtained by the pre-trained deformation prediction model and the measured results. In contrast, the calculation results obtained by the data-physical fusion deformation prediction model are in excellent agreement with the measured results, while ensuring that the overall deformation law basically conforms to the theoretical deformation law of shield tunnels. This verifies the real-time calculation method for shield tunnels based on the fusion of physical information neural networks proposed in this embodiment.

[0076] Example 2

[0077] One embodiment of the present invention provides a real-time deformation calculation system for shield tunnels based on PINN, comprising:

[0078] The equation derivation module is configured to: construct a coupled physical model of shield tunnel lining-foundation-load based on the structural parameters, geological parameters and load parameters of the shield tunnel, and derive the physical control equations.

[0079] The pre-training module is configured to: build a deformation prediction basic model adapted to the mechanical characteristics of shield tunnels based on the physical information neural network PINN; construct a physical information loss function using the physical control equation residual loss and boundary condition constraint loss; and pre-train the deformation prediction basic model.

[0080] The loss construction module is configured to: collect real-time monitoring data on site, construct data information loss, integrate it into the physical information loss function, and form a data-physical fusion loss function;

[0081] The real-time correction module is configured to: perform real-time iterative correction of the deformation prediction base model based on the data-physical fusion loss function and adopt an incremental training mode; and calculate the full-section deformation of the shield tunnel in real time based on the corrected deformation prediction base model.

[0082] Example 3

[0083] One embodiment of the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the real-time calculation method for shield tunnels that integrates physical information neural networks.

[0084] Example 4

[0085] In one embodiment of the present invention, a non-transitory computer-readable storage medium is provided for storing computer instructions. When the computer instructions are executed by a processor, the real-time calculation method for shield tunnels integrating physical information neural networks is implemented.

[0086] Example 5

[0087] One embodiment of the present invention provides an electronic device, including: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to execute the real-time calculation method for shield tunnels that integrates physical information neural networks.

[0088] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0089] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0090] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for real-time calculation of shield tunnel deformation based on PINN, characterized in that, include: Based on the structural, geological, and load parameters of the shield tunnel, a coupled physical model of shield tunnel lining-foundation-load is constructed, and the physical control equations are derived. The coupled physical model of shield tunnel lining-foundation-load is set as follows: Based on structural parameters, the lining structure is regarded as a homogeneous circular ring, and the Timoshenko beam theory is used to consider shear deformation and perform equivalent treatment on the tunnel lining segments; based on geological parameters, the foundation is represented by a variable stiffness Winkler spring model, with the normal spring stiffness varying with the circumferential angle and only functioning under compression, while the tangential spring acts continuously throughout the circumference; based on load parameters, the load includes radial active load and tangential active load, which is synthesized from vertical load, horizontal load, and the self-weight of the lining. Based on the Physical Information Neural Network (PINN), a deformation prediction basic model adapted to the mechanical characteristics of shield tunnels is built. A physical information loss function is constructed using the residual loss of the physical control equation and the boundary condition constraint loss to pre-train the deformation prediction basic model. Real-time monitoring data is collected on site, and a data information loss is constructed and integrated into the physical information loss function to form a data-physical fusion loss function. Based on the data-physical fusion loss function, an incremental training mode is used to iteratively correct the deformation prediction basic model in real time. Only the shallow parameters of the model are updated after each acquisition of new on-site monitoring data. Based on the corrected deformation prediction basic model, the full-section deformation of the shield tunnel is calculated in real time. The physical control equations include radial equilibrium equations and tangential equilibrium equations. The radial equilibrium equation is expressed as: The tangential equilibrium equation is expressed by the following formula: in, It is the circumferential angle. For bending parameters, For shear deformation parameters, This is the shear correction factor. For the Heaviside function, For normal spring stiffness, For tangential spring stiffness, R The radius of the lining centerline. EA For axial stiffness, EI For bending stiffness, w For radial displacement, v For tangential displacement, For radial active loads, For tangential active loads; The deformation prediction basic model, with circumferential angle The input is radial displacement w, and the output is tangential displacement v; the physical information loss function is expressed by the formula: in, For the residual loss of the physical control equation, For boundary condition constraint loss, ω 1. ω 2 represents the weight; the residual loss of the physical control equation The calculation method is as follows: in, This represents the residual loss caused by the radial equilibrium equation of the shield tunnel. The differential term represents the residual loss caused by the tangential equilibrium equation of the shield tunnel. , , , , , Obtained using the automatic differentiation technique of neural networks; The data-physical fusion loss function is expressed by the following formula: in, To mitigate data loss, a neural network model is used to predict the mean square error between the predicted data and the real-time monitoring data. ω 3 represents the adaptive weights for data information loss.

2. A real-time deformation calculation system for shield tunnels based on PINN, implemented using the real-time deformation calculation method for shield tunnels as described in claim 1, characterized in that, include: The equation derivation module is configured to: construct a coupled physical model of shield tunnel lining-foundation-load based on the structural parameters, geological parameters and load parameters of the shield tunnel, and derive the physical control equations. The coupled physical model of shield tunnel lining-foundation-load is set as follows: based on the structural parameters, the lining structure is regarded as a homogeneous circular ring, and the Timoshenko beam theory is used to consider shear deformation and perform equivalent treatment on the tunnel lining segments. Based on geological parameters, the foundation is represented by a variable stiffness Winkler spring model. The stiffness of the normal spring varies with the circumferential angle and only plays a role when under compression, while the tangential spring acts continuously throughout the entire circumference. Based on the load parameters, the load includes radial active load and tangential active load, which is composed of vertical load, horizontal load and lining self-weight; The pre-training module is configured to: build a deformation prediction basic model adapted to the mechanical characteristics of shield tunnels based on the physical information neural network PINN; construct a physical information loss function using the physical control equation residual loss and boundary condition constraint loss; and pre-train the deformation prediction basic model. The loss construction module is configured to: collect real-time monitoring data on site, construct data information loss, integrate it into the physical information loss function, and form a data-physical fusion loss function; The real-time correction module is configured to: perform real-time iterative correction of the deformation prediction base model based on the data-object fusion loss function and adopt an incremental training mode; only the shallow parameters of the model are updated after each acquisition of new on-site monitoring data. Based on the revised deformation prediction model, the deformation of the entire cross section of the shield tunnel is calculated in real time.

3. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the real-time calculation method for shield tunnel deformation based on PINN as described in claim 1.

4. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, which, when executed by a processor, implement the real-time calculation method for shield tunnel deformation based on PINN as described in claim 1.

5. An electronic device, characterized in that, include: The device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to implement the real-time calculation method for shield tunnel deformation based on PINN as described in claim 1.

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