Intelligent prediction method and system for ground loss rate of shield tunneling based on deep learning

Abstract

The application provides a shield tunneling stratum loss rate intelligent prediction method and system based on deep learning, which comprises the following steps: firstly, obtaining stratum multi-source basic data of a small-radius curve segment in a target engineering section, and calculating stratum basic loss rate and stratum overbreak loss rate respectively; adopting a physical-guided two-stage feature screening method, locking a set of essential features based on physical mechanism, and then screening supplementary features through improved D-optimal criterion to obtain an optimal feature subset; based on the optimal feature subset, generating a synthetic training sample set by finite element numerical simulation and Monte Carlo sampling, and training a generalized regression neural network model; finally, using the field measured settlement data of a limited section to fine-tune the model through transfer learning, obtaining a final stratum loss rate prediction model, superimposing the basic loss rate, overbreak loss rate and lateral extrusion loss rate prediction values to determine the total stratum loss rate, and significantly improving the total stratum loss rate prediction accuracy in the small-radius curve segment construction scenario.

Description

Technical Field

[0001] This application relates to the field of tunnel construction technology, specifically to a method and system for intelligent prediction of ground loss rate in shield tunneling based on deep learning. Background Technology

[0002] In shield tunnel construction, the ground loss rate is a core parameter causing surface settlement, and its accurate prediction is crucial for construction risk management. Existing ground loss rate prediction methods mainly fall into two categories: one is empirical methods based on analytical formulas, which establish a mapping relationship between ground loss rate and surface settlement using formulas such as Peck's formula, and provide an empirical range for the ground loss rate based on construction experience. This type of method is simple to calculate, but relies on engineering analogies, has strong subjectivity in parameter selection, and limited prediction accuracy. The other category is data-driven methods based on machine learning, which collect geological parameters, construction parameters, and surface settlement monitoring data from historical projects, and train models such as neural networks and support vector machines to predict the ground loss rate. This type of method can capture the nonlinear coupling relationship of multiple factors, has relatively high prediction accuracy, and has been widely used in predicting ground loss rate in straight-segment shield tunneling.

[0003] However, the existing methods mentioned above are all designed for shield tunneling on straight or general curved sections, and have significant shortcomings in the scenario of shield tunneling on small-radius curved sections. In addition to the same foundation soil loss (caused by the construction gap between the cutterhead and the segments) and over-excavation loss (caused by additional cutting determined by the curve geometry) as in straight sections, shield tunneling on small-radius curved sections also suffers from a unique lateral compression loss. When the shield machine turns on a curve, the machine body adjusts its posture through the articulated mechanism, and the outer side of the shield exerts forced lateral compression on the surrounding soil, causing plastic deformation and lateral movement of the soil, forming an asymmetric additional soil loss component. Existing technologies treat these three types of losses together, failing to separately model and quantify the lateral compression loss rate. This leads to a significant increase in prediction errors in small-radius curved section construction, and cannot provide reliable quantitative basis for optimizing construction parameters and early warning of surface settlement risks. Summary of the Invention

[0004] This application provides a method and system for intelligent prediction of ground loss rate in shield tunneling based on deep learning, which can significantly improve the prediction accuracy of total ground loss rate in construction scenarios with small radius curves.

[0005] A first aspect of this application provides a deep learning-based intelligent prediction method for ground loss rate in tunnel boring machines, the method comprising: Obtain multi-source foundational data of the stratigraphy for the small-radius curve segment within the target engineering section; Based on the aforementioned multi-source foundation data of the strata, the foundation loss rate and the over-excavation loss rate of the strata are calculated respectively. A physical-guided two-stage feature screening method was adopted to determine the key influencing factors of lateral compression loss rate of the formation from the multi-source basic data of the formation, and to obtain the optimal feature subset. Based on the optimal feature subset, a synthetic training sample set is generated using finite element numerical simulation and Monte Carlo sampling, and a generalized regression neural network model is constructed based on the synthetic training sample set. Using on-site measured settlement data from a limited section of the engineering section, the generalized regression neural network model was fine-tuned through transfer learning to obtain the final model for predicting the ground loss rate of small-radius curved shield tunnels. The final model for predicting the stratum loss rate of the small-radius curve shield tunnel is used to predict the cross section to be predicted, and the predicted value of the lateral compression loss rate of the stratum is obtained. Based on the stratum foundation loss rate, the stratum over-excavation loss rate and the predicted value of the lateral compression loss rate of the stratum, the total stratum loss rate is determined.

[0006] In one possible implementation, the physically-guided two-stage feature screening method determines the key influencing factors of formation lateral compression loss rate from the multi-source basic data of the formation, and obtains an optimal feature subset, including: A candidate feature set is constructed from the multi-source basic data of the strata; Based on the physical mechanism of lateral extrusion of shield tunnels with small radius curves, the curve radius, hinge angle and jack thrust difference are locked as the mandatory feature set from the candidate feature set; An improved D-optimal criterion is adopted to select the supplementary features that have the largest information increment after being combined with the required features from the remaining candidate features, thus obtaining the optimal feature subset.

[0007] In one possible implementation, the improved D-optimal criterion is used to select supplementary features from the remaining candidate features that, when combined with the required features, yield the supplementary features with the largest information increment, thus obtaining the optimal feature subset, including: Initialize the feature index set by adding the indices of the required feature set to the feature index set; Iterate through each candidate feature that is not currently selected into the feature index set, calculate the variance inflation factor between the candidate feature and the existing features in the feature index set, and filter out candidate features whose variance inflation factor exceeds a preset collinearity threshold. For candidate features that pass the collinearity filtering, they are temporarily added to the feature index set. The corresponding columns are extracted from the candidate feature matrix to construct a temporary feature submatrix. The difference between the determinant of the temporary feature submatrix and the determinant of the current feature submatrix is ​​calculated as the determinant increment. Select the candidate feature that maximizes the increment of the determinant and permanently add it to the feature index set; Repeat the above filtering, calculation and selection steps until the determinant increment of the newly added features is lower than the preset threshold or the total number of selected features reaches the preset upper limit, and then merge the features corresponding to the feature index set into the optimal feature subset.

[0008] In one possible implementation, the step of generating a synthetic training sample set based on the optimal feature subset using finite element numerical simulation and Monte Carlo sampling, and constructing a generalized regression neural network model based on the synthetic training sample set, includes: Based on the range of geological parameters and construction parameters in the multi-source basic data of the strata, the Monte Carlo method is used to randomly sample within the distribution range of each parameter to generate multiple sets of parameter combinations. A three-dimensional finite element numerical model was established for each set of parameters to simulate the shield tunneling process with a small radius curve and to extract the surface settlement curve. The surface settlement curve is compared with the theoretical settlement curves corresponding to the foundation loss rate and over-excavation loss rate of the stratum. The difference is extracted and substituted into the Peck formula to back-calculate and obtain the label value of the lateral compression loss rate of the stratum. Construct a synthetic training sample set consisting of the values ​​of the optimal feature subset and the label values ​​of the formation lateral compression loss rate; The generalized regression neural network model was trained using the synthetic training sample set, and the optimal smoothing factor was determined using leave-one-out cross-validation.

[0009] In one possible implementation, the step of using on-site measured settlement data from a limited cross-section of the engineering section to fine-tune the generalized regression neural network model through transfer learning to obtain the final model for predicting the ground loss rate of a small-radius curved shield tunnel includes: Monitoring sections were selected on the small-radius curve segments within the engineering section to obtain on-site measured surface settlement data for each section. The total formation loss rate was calculated from the measured surface settlement data using the Peck formula, and the formation foundation loss rate and formation over-excavation loss rate were deducted to obtain the measured value of the formation lateral compression loss rate. The values ​​of the optimal feature subset corresponding to each measured section are obtained and together with the measured value of the lateral compression loss rate of the formation, they constitute a small sample measured dataset. Using the small sample measured dataset as calibration data, the output layer parameters and summation layer parameters of the generalized regression neural network model are used as fine-tunable parameters. A limited number of iterations are performed using a preset learning rate to obtain the final model for predicting the ground loss rate of small-radius curved shield tunnels.

[0010] In one possible implementation, calculating the formation foundation loss rate based on the multi-source formation foundation data includes: Extract the cutterhead diameter and segment outer diameter from the multi-source basic data of the formation; The foundation loss rate is calculated based on the ratio of the difference between the cutterhead diameter and the outer diameter of the tunnel segments to the tunnel cross-sectional area.

[0011] In one possible implementation, calculating the formation over-excavation loss rate based on the multi-source foundation data of the formation includes: The curve radius, tunnel boring machine length, and tunnel diameter are extracted from the multi-source geological data. Calculate the over-excavation area per unit length based on the geometric relationship between the curve radius, the length of the tunnel boring machine, and the tunnel diameter; The over-excavation loss rate of the stratum is calculated based on the ratio of the over-excavated area per unit length to the tunnel cross-sectional area.

[0012] This application provides a deep learning-based intelligent prediction method for ground loss rate in shield tunneling. First, it acquires multi-source foundation data of the ground in the small-radius curve segment of the target project section. Based on this data, it calculates the ground foundation loss rate and the ground over-excavation loss rate. Then, it employs a physical-guided two-stage feature selection method. Based on the physical mechanism of lateral extrusion of the shield in the small-radius curve, it locks in the required feature set. Next, it introduces a pre-filtering method using variance expansion factors and collinearity, along with a determinant-based incremental greedy iteration, through an improved D-optimal criterion to select the supplementary features with the largest information increment from the candidate features, thus obtaining the optimal feature subset. Finally, based on the optimal feature subset... A synthetic training sample set was generated using finite element numerical simulation and Monte Carlo sampling. The difference between the numerically simulated surface settlement curve and the theoretical settlement curves corresponding to the foundation loss rate and over-excavation loss rate was compared and then used to calculate the label value of the lateral compression loss rate of the formation using the Peck formula. This label value was then used to train a generalized regression neural network model. Finally, the model was fine-tuned using transfer learning with field-measured settlement data from a limited section of the engineering section, resulting in the final model for predicting the formation loss rate. The predicted values ​​of the foundation loss rate, over-excavation loss rate, and lateral compression loss rate were then superimposed to determine the total formation loss rate. The results include the following beneficial effects: 1. This application explicitly decomposes the total ground loss rate in shield tunneling on small-radius curved sections into three independent components: base loss rate, over-excavation loss rate, and lateral compression loss rate. It also models and quantifies the lateral compression loss rate separately, overcoming the shortcomings of existing technologies that mix the three types of losses and cannot accurately model the lateral compression mechanism on small-radius curved sections. This makes the prediction results clearer in a physical sense and significantly improves the prediction accuracy of the total ground loss rate in the construction scenario of small-radius curved sections.

[0013] 2. In the feature selection stage, this application adopts a physically guided two-stage method. First, based on the physical mechanism of lateral compression, three mandatory features are forcibly locked: curve radius, hinge angle, and jack thrust difference. Then, by improving the D-optimal criterion, a variance inflation factor collinearity pre-filtering step is introduced. Before calculating the determinant increment, candidate features that are highly collinear with the selected features are eliminated. This effectively eliminates multicollinearity while ensuring the physical interpretability of the feature set. This allows the generalized regression neural network model to obtain input features with minimal information redundancy and the strongest generalization ability, avoiding the problem of lack of physical basis for feature selection and model instability caused by highly collinear features in pure data-driven methods.

[0014] 3. This application addresses the reality of extremely scarce measured labeled data on lateral compression loss rate of small-radius curve segments in engineering. It adopts a two-stage modeling strategy that combines pre-training of synthetic samples generated by finite element numerical simulation with fine-tuning through transfer learning using a small amount of measured data. The model can be adapted to engineering projects by selecting only a few monitoring sections in the target engineering area, without the need for a large accumulation of field labeled data. This effectively solves the problem of decreased prediction reliability caused by insufficient training samples in new projects by existing data-driven methods, giving the method good engineering applicability and cross-engineering transferability.

[0015] A second aspect of this application provides a deep learning-based intelligent prediction system for ground loss rate in tunnel boring machines, the system comprising: The first module is used to acquire multi-source basic geological data of small-radius curve segments in the target engineering section; The second module is used to calculate the foundation loss rate and the over-excavation loss rate of the strata based on the multi-source foundation data of the strata. The third module is used to determine the key influencing factors of the lateral compression loss rate of the formation from the multi-source basic data of the formation using a physical-guided two-stage feature screening method, and to obtain the optimal feature subset. The fourth module is used to generate a synthetic training sample set based on the optimal feature subset using finite element numerical simulation and Monte Carlo sampling, and to construct a generalized regression neural network model based on the synthetic training sample set. The fifth module is used to fine-tune the generalized regression neural network model by using the on-site measured settlement data of the limited cross section of the engineering section, so as to obtain the final model for predicting the ground loss rate of small radius curve shield tunnel. The sixth module is used to predict the cross section to be predicted using the final model for predicting the stratum loss rate of the small-radius curve shield tunnel, to obtain the predicted value of the lateral compression loss rate of the stratum, and to determine the total stratum loss rate based on the stratum foundation loss rate, the stratum over-excavation loss rate and the predicted value of the lateral compression loss rate of the stratum.

[0016] A third aspect of this application provides a terminal including a processor, an input device, an output device, and a memory, wherein the processor, input device, output device, and memory are interconnected, and the memory is used to store a computer program, the computer program including program instructions, and the processor is configured to call the program instructions to execute the step instructions as described in the intelligent prediction method for ground loss rate of shield tunneling based on deep learning in the first aspect of this application.

[0017] A fourth aspect of this application provides a computer-readable storage medium storing a computer program for electronic data interchange, wherein the computer program causes a computer to perform some or all of the steps described in the intelligent prediction method for ground loss rate of shield tunneling based on deep learning in the first aspect of this application.

[0018] A fifth aspect of this application provides a computer program product, comprising a non-transitory computer-readable storage medium storing a computer program operable to cause a computer to perform some or all of the steps described in the deep learning-based intelligent prediction method for ground loss rate in tunnel boring machines in the first aspect of this application. The computer program product may be a software installation package. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This application provides a schematic diagram of the overall process for a deep learning-based intelligent prediction method for ground loss rate in tunnel boring machines. Figure 2 This application provides a schematic diagram of the overall structure of a deep learning-based intelligent prediction system for ground loss rate in tunnel boring machines. Figure 3 This application provides a schematic diagram of the structure of a terminal. Figure label: Module 1-1, Module 2-2, Module 3-3, Module 4-4, Module 5-5, Module 6-6. Detailed Implementation

[0021] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0022] The terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or apparatuses.

[0023] In this application, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this application can be combined with other embodiments.

[0024] A deep learning-based intelligent prediction method for ground loss rate in shield tunneling is applied to a deep learning-based intelligent prediction system for ground loss rate in shield tunneling. Figure 1 A schematic diagram illustrating the overall process of an intelligent prediction method for ground loss rate in tunnel boring machines (TBMs) based on deep learning is shown. Figure 1 As shown, it includes: S1. Obtain multi-source basic geological data of the small-radius curve segment of the target project area.

[0025] Specifically, multi-source geological foundation data for the small-radius curve segment is obtained from the design drawings, geotechnical investigation reports, and equipment specifications of the target engineering section. This multi-source geological foundation data includes three categories: tunnel design parameters, geological investigation parameters, and shield machine construction parameter ranges.

[0026] The tunnel design parameters include: tunnel diameter (m), curve radius (m) Tunnel depth (m), cutter head diameter (m), outer diameter of the tunnel segment (m) Length of tunnel boring machine (m), shield thickness (m) Maximum rotation angle of the hinge device (°).

[0027] Geological survey parameters include: the thickness of each soil layer in the strata the tunnel traverses. (m), Angle of internal friction (°), cohesion (kPa), elastic modulus (MPa), Poisson's ratio (Dimensionless) Lateral pressure coefficient (Dimensionless), Soil weight (kN / m) 3 ),in Number the soil layers.

[0028] The range of tunnel boring machine (TBM) construction parameters includes: total thrust of jacks. (kN), Difference in thrust between the two jacks (kN), tunneling speed (mm / min), cutter head speed (rpm), grouting pressure (MPa), Grouting filling rate (%), hinge angle (°).

[0029] Tunnel design parameters and shield machine parameters are obtained from engineering design drawings and equipment specifications; geological survey parameters are obtained from geotechnical engineering survey reports; and the range of construction parameters is determined from construction records of similar projects or pre-set construction control ranges.

[0030] S2. Based on the multi-source foundation data of the strata, calculate the foundation loss rate and the over-excavation loss rate of the strata respectively.

[0031] Step S2 includes two sub-steps: A1 to A2 and B1 to B3. The step of calculating the formation foundation loss rate based on the multi-source foundation data includes: A1. Extract the cutterhead diameter and segment outer diameter from the multi-source basic data of the formation.

[0032] Among them, the cutterhead diameter is read from the tunnel design parameters. and the outer diameter of the tunnel segments The cutterhead diameter is the cutting diameter of the outermost edge of the tunnel boring machine's cutterhead, which determines the maximum size of the tunnel boring machine's excavation cross-section; the segment outer diameter is the outer diameter of the tunnel lining after the precast concrete segments are assembled.

[0033] A2. Calculate the foundation loss rate based on the ratio of the difference between the cutterhead diameter and the outer diameter of the tunnel segments to the tunnel cross-sectional area.

[0034] Among them, the base loss rate is the ground loss caused by the difference between the cutterhead diameter and the outer diameter of the tunnel segment (shield tail gap). It is a fixed loss component that exists in any shield tunneling construction and is unrelated to whether the tunnel is a curved section.

[0035] The physical meaning is the proportion of the annular gap between the space formed by the cutterhead excavation and the space occupied by the outer wall of the tunnel segment to the space enclosed by the outer wall of the tunnel segment.

[0036] Among them, the formation base loss rate The calculation formula is as follows: (1) In the formula, The formation foundation loss rate (%). The diameter of the cutter head is in meters (m). The outer diameter of the tunnel segment is (m).

[0037] In the formula, and The difference represents the difference between the cutterhead excavation area and the outer wall area of ​​the segment per unit length, and is the annular void area per unit length. It is the cross-sectional area of ​​the tunnel enclosed by the outer walls of the tunnel segments.

[0038] In this example, the common ground loss component for all shield tunneling operations is calculated. This component is independent of the curve radius and construction parameters, and is determined solely by the geometry of the cutterhead and segments. It serves as a fixed component of the subsequent total ground loss rate.

[0039] The step of calculating the over-excavation loss rate of the strata based on the multi-source basic data of the strata includes: B1. Extract the curve radius, tunnel boring machine length, and tunnel diameter from the multi-source basic data of the strata.

[0040] Among them, the curve radius is read from the tunnel design parameters. Shield machine length and tunnel diameter The curve radius is the horizontal curve radius of the tunnel's design axis. It is a core geometric parameter that distinguishes small-radius curved shield tunnels from straight shield tunnels, determining the degree of abruptness of the shield machine's turn. The shield machine length is the length of the shield machine's main body (including the cutterhead, shield shell, screw conveyor, and other main structures) along the excavation direction, directly affecting the over-excavation amount when the shield machine turns on a curved section. The tunnel diameter is the design outer diameter of the tunnel lining, which, together with the cutterhead diameter, determines the calculation basis for the over-excavation area.

[0041] B2. Calculate the over-excavation area per unit length based on the geometric relationship between the curve radius, the shield machine length, and the tunnel diameter.

[0042] In small-radius curves, to complete the turning maneuver, the tunnel boring machine (TBM) forms an angle with the tunnel's design axis, resulting in additional cutting by the cutterhead on the inside of the turn. The over-excavation area is determined by the curve's geometry and the TBM's kinematics, and is deterministic, independent of the operator's skill level.

[0043] Among them, the over-excavation area per unit length The calculation formula is as follows: (2) In the formula, The over-excavation area per unit length is the area of ​​soil that the tunnel boring machine cuts off on the inside of a turn for every 1 meter of excavation. For the length of the tunnel boring machine, The radius of the curve. Let be the tunnel diameter. The physical meaning of equation (2) is: when the tunnel boring machine turns on a curved section, the projections of the two ends of the cutterhead and the tail of the shield on the horizontal plane deviate from the tunnel design axis, forming a curve radius. and fuselage length The determined geometric deviation. Specifically, The maximum offset of the two ends of the tunnel boring machine relative to the tunnel design axis (the radial component of the over-excavation) is calculated by multiplying the maximum offset by the tunnel diameter. Then, the additional cutting area per unit length caused by this offset is obtained.

[0044] B3. Calculate the over-excavation loss rate of the stratum based on the ratio of the over-excavation area per unit length to the tunnel cross-sectional area.

[0045] Among them, the over-excavation area per unit length With tunnel cross-sectional area Performing a division operation yields the proportion of over-excavated area per unit length to the tunnel's designed cross-section, which is the over-excavation loss rate. Tunnel cross-sectional area , by tunnel diameter Calculated.

[0046] Among them, the over-excavation loss rate of the stratum The calculation formula is as follows: (3) In the formula, The over-excavation loss rate (%) is the soil over-excavation loss rate. Over-excavation area per unit length (m) 2 / m), The tunnel cross-sectional area (m²) 2 ), The length of the tunnel boring machine (m) is given. Let be the radius of the curve (m). The diameter of the tunnel is in meters (m).

[0047] In this example, the overcut loss component is determined by the deterministic geometric relationship between the curve radius, the shield machine length, and the tunnel diameter. It is used as a fixed component of the total formation loss rate to separate it from the total loss, so that subsequent data-driven methods can focus on predicting the more uncertain lateral compression loss rate component.

[0048] S3. Using a physical-guided two-stage feature screening method, the key influencing factors of lateral compression loss rate of the formation are determined from the multi-source basic data of the formation, and the optimal feature subset is obtained.

[0049] Step S3 includes the following sub-steps: C1. Construct a candidate feature set from the multi-source basic data of the strata.

[0050] Among them, the lateral compression effect was extracted from the multi-source basic data of the formation obtained from S1. Each candidate feature constitutes a candidate feature set. .

[0051] The candidate features include: curve radius. Shield machine length Tunnel diameter Tunnel depth Difference in jack thrust tunneling speed Cutter head speed Grouting pressure Grouting filling rate Hinge angle and the internal friction angle of each soil layer Cohesion Elastic modulus Lateral pressure coefficient Soil weight The composite ratio of the strata through which the tunnel passes ,in Number the soil layers.

[0052] Because the dimensions and value ranges of different features vary significantly, Z-score standardization is performed on all candidate features to eliminate the influence of dimensions, resulting in a mean of 0 and a standard deviation of 1. The standardized feature values ​​are then used in all subsequent calculations.

[0053] Among them, candidate features The Z-score standardization formula is shown below: (4) In the formula, For the first The standardized values ​​of the candidate features For the first The original values ​​of each candidate feature. For the first The mean of each candidate feature across all samples For the first The standard deviation of each candidate feature across all samples.

[0054] C2. Based on the physical mechanism of lateral extrusion of shield tunnels with small radius curves, the curve radius, hinge angle and jack thrust difference are locked as the mandatory feature set from the candidate feature set.

[0055] Based on the physical mechanism of lateral extrusion of shield tunnels with small radius curves, features that theoretically must affect lateral extrusion are forcibly locked from the candidate feature set as the mandatory feature set. .

[0056] The physical root cause of lateral compression is analyzed as follows: In small-radius curves, the tunnel boring machine (TBM) cannot advance directly in a straight line. It must adjust its posture through a hinged mechanism to create a certain angle between the TBM's axis and the tunnel's design axis, allowing the TBM to fit the curve and complete the turn. This posture adjustment process causes a forced lateral displacement of the soil on the outer side of the TBM (the outer side of the turn), thus generating the driving force for lateral compression. Based on this physical mechanism, the following three features are identified as mandatory: Curve radius The curve radius determines the abruptness of the tunnel boring machine's turn and is a fundamental controlling factor in whether lateral compression occurs and its severity. The smaller the curve radius, the greater the angle the tunnel boring machine needs to adjust its posture, and the more significant the lateral compression effect on the soil.

[0057] Hinge angle The hinge angle directly reflects the amount of deflection of the tunnel boring machine's body relative to the tunnel's design axis, and is the direct source of lateral compression displacement. The larger the hinge angle, the greater the forced lateral displacement of the tunnel boring machine on the soil.

[0058] Jack thrust difference In small-radius curves, the jacks on both sides of the tunnel boring machine (TBM) need to generate different thrusts to achieve turning, with smaller thrust on the inner side and larger thrust on the outer side. The torque generated by this thrust difference is the direct power source for driving the TBM to turn. The thrust difference of the jacks determines the degree of imbalance of the active compressive force of the TBM on the soil, and is the direct source of lateral compressive force.

[0059] Based on curve radius Hinge angle Difference in thrust with jack Construct the required feature set by selecting the required feature values. The mathematical expression is as follows: (5) In the formula, The radius of the curve. For the hinge angle, The difference in thrust between the two jacks. These three features correspond to "compression conditions (curve radius)," "compression displacement (hinge angle)," and "compression force (thrust difference)" in terms of physical mechanism, respectively. This covers the geometric, kinematic, and mechanical conditions of lateral compression. They are irreplaceable in terms of physical mechanism and are therefore forcibly locked as mandatory features, and will not participate in the subsequent screening and elimination process.

[0060] In this example, based on prior knowledge of the physical mechanisms, three core features that theoretically must affect lateral compression are pre-selected as the mandatory feature set. This pre-selection operation injects physical understanding into the feature selection process, ensuring that subsequent data-driven selection does not overlook the most physically important features, while effectively narrowing the subsequent search space and improving the efficiency and reliability of feature selection. These will serve as the initial columns of the benchmark feature submatrix selected for subsequent steps.

[0061] C3. Using the improved D-optimal criterion, the supplementary features that have the largest information increment after being combined with the required features are selected from the remaining candidate features, thus obtaining the optimal feature subset.

[0062] Step C3 includes the following sub-steps: C301. Initialize the feature index set by adding the indexes of the required feature set to the feature index set.

[0063] Among them, let there be a total Sample data from historical engineering sections or numerical simulation conditions, each sample containing a candidate feature set. All features and corresponding measured values ​​of lateral compression loss rate (or reference values ​​obtained from finite element numerical model simulation) are included.

[0064] Initialize feature index set , select the required feature set Add the corresponding index Extract the columns corresponding to the required features from the sample data to form the current feature submatrix. Its expression is as follows: (6) In the formula, Let be the current eigenvalue submatrix, where The total number of samples; , , curve radius Hinge angle Difference in jack thrust In all The value vectors for each sample have dimensions of 1. .

[0065] C302. Traverse each candidate feature that is not currently selected into the feature index set, calculate the variance inflation factor between the candidate feature and the existing features in the feature index set, and filter out candidate features whose variance inflation factor exceeds a preset collinearity threshold.

[0066] Among them, for the feature index set that is not currently selected Each candidate feature ( ), calculate its relative to the current eigenmatrix The variance inflation factor.

[0067] Specifically, the VIF calculation method is as follows: candidate features... As the dependent variable, the current eigenvalue submatrix Using each column as an independent variable, a linear regression model is established. The expression for the linear regression model is shown below: (7) In the formula, Candidate features The vector of values ​​across all samples, with dimension . ; This is the current feature submatrix, with dimension . ,in This represents the number of currently selected features. Let's be the regression coefficient vector, with dimension 1. ; Let be the residual vector, with dimension . .

[0068] Calculate the coefficient of determination of the regression model The calculation formula is as follows: (8) In the formula, The coefficient of determination reflects the candidate features. The proportion of variance that can be explained by the currently selected features; Candidate features In the The values ​​that can be taken on each sample; For the first predicted by the regression model The values ​​of each sample; Candidate features The mean across all samples; The total number of samples.

[0069] Candidate features variance inflation factor The calculation formula is as follows: (9) In the formula, Candidate features variance inflation factor is the coefficient of determination calculated in formula (8).

[0070] The value reflects the candidate feature The degree of collinearity with currently selected features. The larger the value, the better. The stronger the collinearity with the selected features, The higher the proportion of information that can be explained by the selected features, the less new independent information is added.

[0071] like Exceeding the preset collinearity threshold If the candidate feature is found to have severe multicollinearity with existing features, it will be filtered out from the candidate set and will not proceed to the subsequent determinant optimization step.

[0072] Among them, the collinearity threshold This is a dimensionless parameter with a value range of 5 to 10. In this embodiment, it is preferred. The physical meaning of this threshold is: when When, it represents candidate features More than 90% of the variance can be predicted by existing features, meaning that introducing these features can only add less than 10% of independent information. Introducing them will lead to a significant inflation of the variance in the model parameter estimates, reducing the robustness of the model.

[0073] C303. For candidate features that pass the collinearity filtering, temporarily add them to the feature index set, extract the corresponding columns from the candidate feature matrix to construct a temporary feature submatrix, and calculate the difference between the determinant of the temporary feature submatrix and the determinant of the current feature submatrix as the determinant increment.

[0074] Specifically, for candidate features filtered by VIF collinearity, the improved D-optimal criterion is used to calculate the determinant increment after adding them to the current feature submatrix.

[0075] For any candidate feature filtered by VIF Add it as a new column to the current feature submatrix to form a temporary feature submatrix. Its expression is as follows: (10) In the formula, To select candidate features The temporary feature submatrix after temporary addition has a dimension of ; This is the current feature submatrix, with dimension . ; Candidate features The vector of values ​​across all samples, with dimension . ; This represents the number of columns in the current feature submatrix (the number of currently selected features).

[0076] According to matrix theory, the singular value product of the eigenmatrices and the determinant satisfy the following relationship: (11) In the formula, For the characteristic submatrix The A singular value, The column number of the eigenmatrix. Represents the determinant of a matrix. For matrix The transpose of . Therefore, maximizing the singular value product is equivalent to maximizing .

[0077] For each candidate feature Calculate the determinant increment after adding it to the current feature submatrix. The calculation formula is as follows: (12) In the formula, Candidate features Determinant increment, For temporary eigenmatrices, This is the current eigenvalue submatrix. The larger the value, the more the overall information content of the feature submatrix increases after the feature is added, meaning the stronger the complementarity between the feature and existing features.

[0078] C304. Select the candidate feature that maximizes the increment of the determinant and permanently add it to the feature index set.

[0079] Specifically, the determinant increments of all candidate features filtered by VIF collinearity are compared. , choose to Largest candidate feature The selection criteria are as follows: (13) In the formula, This is the index number of the selected candidate feature in the candidate feature set. The determinant increment is calculated using formula (12).

[0080] Selected candidate features Permanently add to feature index set The update method is as follows: (14) And update the current feature submatrix The update method is as follows: (15) C305. Repeat the above filtering, calculation and selection steps until the determinant increment of the newly added features is lower than the preset threshold or the total number of selected features reaches the preset upper limit, and merge the features corresponding to the feature index set into the optimal feature subset.

[0081] In this process, steps C302 to C304 are repeated. In each iteration, VIF collinearity filtering is first performed on the candidate features that are not currently selected. Then, the determinant increment of the filtered features is calculated and the optimal feature is selected for inclusion. This process continues until any of the following stopping conditions are met: Condition 1: All unselected candidate features are due to VIF exceeding the threshold. And it was filtered out.

[0082] Condition 2: Among the candidate features filtered by VIF, the maximum determinant increment is lower than a preset threshold, as shown in the following formula: (16) In the formula, The preset determinant increment threshold, For the current eigenvalue submatrix, This represents the determinant of the matrix. This condition indicates that even after adding the optimal candidate features, the increase in information content of the feature submatrix is ​​below the preset tolerance level, making it meaningless to continue adding features.

[0083] Condition 3: The total number of selected features has reached the preset upper limit. ,for: (17) In the formula, For feature index set The number of elements in the current selection is the total number of features currently selected. This is a preset upper limit for the total number of features to prevent the model from overfitting due to excessively high feature dimensions.

[0084] After the iteration stops, the feature index set The features corresponding to all indices in the set are the selected supplementary feature set. .

[0085] This example proposes an improved screening process for the D-optimal criterion. This is reflected in the following three aspects: First, before the D-optimal determinant optimization, a VIF collinearity filtering step is introduced to pre-eliminate candidate features that are highly collinear with existing features from a statistical diagnostic perspective. This solves the problem that the standard D-optimal criterion only focuses on maximizing the overall information content and cannot directly exclude highly correlated features.

[0086] Second, by alternating between VIF filtering and D-optimal selection in each iteration, a dual screening mechanism of "VIF collinearity diagnosis + D-optimal information maximization" is formed, ensuring that the final selected features meet both the low collinearity requirement and the requirement of maximizing information.

[0087] III. The entire screening process uses physically locked mandatory features. Starting from this point, the screening results are ensured to have clear physical interpretability. Through iterative screening from steps C301 to C305, the final optimal feature subset is guaranteed in terms of physical mechanism integrity, low collinearity among features, and maximization of overall information content.

[0088] S4. Based on the optimal feature subset, a synthetic training sample set is generated using finite element numerical simulation and Monte Carlo sampling, and a generalized regression neural network model is constructed based on the synthetic training sample set.

[0089] Step S4 includes the following sub-steps: D1. Based on the range of geological parameters and construction parameters in the multi-source basic data of the strata, the Monte Carlo method is used to randomly sample within the distribution range of each parameter to generate multiple sets of parameter combinations.

[0090] In particular, since the measured labeled data of "lateral compression loss rate" in real engineering is extremely scarce and difficult to support the direct training of neural network models, this step uses the Monte Carlo random sampling method to generate a large number of parameter combinations to provide input for subsequent finite element numerical simulation.

[0091] Based on the ranges of geological and construction parameters, determine the reasonable distribution ranges for each parameter. The distribution ranges of geological parameters are determined according to the value ranges of each soil layer parameter in the geotechnical engineering investigation report, including the internal friction angle of each soil layer. Cohesion Elastic modulus Lateral pressure coefficient Soil weight The value range; the distribution range of construction parameters is determined based on construction records of similar projects or preset construction control ranges, including the difference in jack thrust. tunneling speed Cutter head speed Grouting pressure Grouting filling rate Hinge angle The range of values ​​for .

[0092] The Monte Carlo method is used to randomly sample the parameters within their distribution intervals. For each parameter, assuming it follows a uniform or normal distribution within its interval, random numbers are generated independently. After each round of sampling of all parameters, a complete set of parameter combinations is generated.

[0093] Repeat the above random sampling process to generate The mathematical expressions for different combinations of parameters are shown below: (18) In the formula, For the generated set of parameter combinations, ( ) is the first The group parameter combination vector contains the specific values ​​of all geological and construction parameters obtained from the group sampling; This represents the number of sampling groups, ranging from 2000 to 10000. In this example, the preferred value is... This ensures that the sample size is sufficient to cover the diversity of the parameter space, while also taking into account the computational cost of subsequent finite element simulations.

[0094] D2. Establish a three-dimensional finite element numerical model for each set of parameters, simulate the shield tunneling process with a small radius curve, and extract the surface settlement curve.

[0095] For each set of parameter combinations generated by D1 A corresponding three-dimensional finite element numerical model was established to simulate the tunneling process of a small-radius curve shield.

[0096] The three-dimensional finite element numerical model was constructed using ABAQUS. The model range was determined based on the tunnel depth and geological conditions. Normal displacement constraints were applied to the bottom and sides of the model, while the top was a free surface boundary.

[0097] In the model, the soil adopts the Mohr-Coulomb constitutive model, and the mechanical parameters are derived from the geological parameters in each set of parameters ( , , , , The tunneling process of the tunnel boring machine (TBM) is simulated as follows: soil elements in the excavation zone are used to simulate cutterhead excavation; equivalent support pressure is applied at the excavation face to simulate soil chamber pressure; grouting pressure is applied at the tail of the shield, and grouting layer elements are activated to simulate synchronous grouting; the curved turning posture of the TBM is simulated by the hinge angle. Difference in thrust with jack This is achieved by applying asymmetric loads and displacement boundary conditions; the tunneling speed and cutterhead rotation speed are input into the model as time-dependent loading rate parameters.

[0098] Furthermore, after each finite element simulation of a set of parameters is completed, the vertical displacement values ​​of each measuring point are extracted from the transverse profile of the model's surface along the direction perpendicular to the tunnel excavation, forming the surface settlement curve corresponding to that set of parameters. The surface settlement curves corresponding to all parameter combinations constitute a set. The mathematical expression is as follows: (19) In the formula, This is the set of all surface settlement curves. ( ) is the first The surface settlement curve vector corresponding to the combination of parameters includes the vertical displacement value of each measuring point along the transverse profile; This represents the total number of parameter combinations.

[0099] D3. Compare the surface settlement curve with the theoretical settlement curves corresponding to the foundation loss rate and over-excavation loss rate of the stratum, extract the difference, and substitute it into the Peck formula to calculate the label value of the lateral compression loss rate of the stratum.

[0100] For each set of parameters in D2 Corresponding surface subsidence curve It is necessary to separate the settlement contribution caused solely by lateral compression.

[0101] First, based on the tunnel geometry parameters (tunnel diameter) in this set of parameters... Tunnel depth Cutter head diameter , segment outer diameter curve radius Shield machine length Using formulas (1) and (3), the foundation loss rate corresponding to this set of parameters is calculated respectively. and formation over-excavation loss rate .

[0102] Then, and Substituting into the classic Peck formula, we calculate the "theoretical symmetrical settlement curve" caused only by foundation loss and over-excavation loss. The expression for Peck's formula is shown below: (20) In the formula, For the first The combination of parameters is located at the lateral distance from the tunnel centerline. Theoretical settlement value at the location; Based on the loss rate, Over-excavation loss rate; The width of the settling tank. This is the settling trough width coefficient. For tunnel burial depth; This is the horizontal lateral distance from the centerline of the tunnel.

[0103] The actual surface subsidence curve obtained from finite element simulation symmetrical settlement curve with theoretical Subtract point by point and extract the difference. This difference represents the settlement contribution solely caused by lateral compression, and its mathematical expression is shown below: (twenty one) In the formula, For the first The surface subsidence vector caused solely by lateral compression in the parameter combination. This is the vector of the actual surface subsidence curve obtained from the finite element simulation. is the vector of the theoretically symmetrical settlement curve caused only by foundation loss and over-excavation loss.

[0104] Finally, the differential settlement curve The maximum settlement value (located near the tunnel centerline) is substituted into the Peck formula for back-calculation, yielding the label value of the lateral compression loss rate corresponding to this parameter combination. The back-calculation formula is shown below: (twenty two) In the formula, For the first The label value of the lateral extrusion loss rate corresponding to the combination of parameters; Vector of differential settlement curve Maximum settlement value; The width of the settling tank; The radius is the tunnel radius.

[0105] D4. Construct a synthetic training sample set consisting of the values ​​of the optimal feature subset and the label values ​​of the formation lateral compression loss rate.

[0106] For each set of parameter combinations From parameter combinations Extract the optimal feature subset The specific values ​​of each feature constitute the feature vector. At the same time, label the lateral compression loss rate corresponding to this set of parameters. This serves as the output label for the sample.

[0107] eigenvectors With the corresponding tag value Pairing them together creates a synthetic training sample. Traverse all After combining the parameters, a complete synthetic training sample set is obtained. The mathematical expression is as follows: (twenty three) In the formula, To synthesize a training sample set, ( ) is the first The optimal feature subset value vector for each sample, with dimension equal to the optimal feature subset. The number of features in; For the first The label value of the lateral compression loss rate corresponding to each sample; The total number of samples.

[0108] D5. Train the generalized regression neural network model using the synthetic training sample set, and determine the optimal smoothing factor using leave-one-out cross-validation.

[0109] Among them, a synthetic training sample set is used. Train a Generalized Regression Neural Network (GRNN) as a predictive model for lateral squeezing loss rate.

[0110] GRNN is a feedforward neural network based on nonlinear regression. It centers on training samples, calculates the similarity between new inputs and each training sample using a Gaussian kernel function, and then uses this similarity as weight to perform a weighted average of the output labels of the training samples to obtain the prediction result. GRNN requires no iterative training; once the network structure is determined, it can be directly computed, resulting in fast training speed and suitability for regression prediction problems with small to medium-sized samples.

[0111] The GRNN network structure includes an input layer, a pattern layer, a summation layer, and an output layer, with the following configuration for each layer: Input layer: The number of neurons in the input layer equals the optimal feature subset. The number of features in (denoted as) Each neuron corresponds to one input feature. The input layer is only responsible for passing the input feature vector to the pattern layer and does not perform any calculations.

[0112] Pattern layer: The number of neurons in the pattern layer equals the number of training samples. Each training sample corresponds to a pattern layer neuron. The output of each pattern layer neuron Represents the new input vector With the Feature vectors of training samples The similarity between them is calculated using the Gaussian kernel function, and the formula is as follows: (twenty four) In the formula, For the first The output of each pattern layer neuron Let be the optimal feature subset value vector of the sample to be predicted. For the first The feature vectors of each training sample As a smoothing factor, For the sample to be predicted and the first The squared Euclidean distance between each training sample.

[0113] Summation Layer: The summation layer contains two types of summation neurons. The first type of summation neuron performs an arithmetic summation of the outputs of all neurons in the pattern layer, and its calculation formula is as follows: (25) In the formula, The arithmetic sum of the outputs of all neurons in the pattern layer. For the first The output of each pattern layer neuron This represents the total number of training samples.

[0114] The second type of summing neuron performs a weighted summation of the outputs of each neuron in the pattern layer. The weights are the output label values ​​of the corresponding training samples, and the calculation formula is shown below: (26) In the formula, This is a weighted sum of the outputs of each neuron in the pattern layer. For the first The lateral compression loss rate label value of each training sample. For the first The output of each pattern layer neuron.

[0115] Output layer: The output layer has 1 neuron and performs a weighted summation of the summation layer. Divide by arithmetic and The predicted value of the lateral compression loss rate is obtained. The calculation formula is as follows: (27) In the formula, This is the predicted value of the lateral compression loss rate output by GRNN. For the first The label values ​​of each training sample. Smoothing factor during GRNN training The value of directly affects the predictive performance of the model: When the value is too large, the outputs of neurons in each pattern layer tend to be consistent, resulting in underfitting of the model. When the input is too small, the prediction results rely only on a few training samples that are closest to the input, leading to model overfitting. To determine the optimal smoothing factor, this step uses Leave-One-Out Cross-Validation (LOOCV) to optimize hyperparameters.

[0116] The specific implementation method of leave-one-out cross-validation is as follows: From One sample is selected sequentially from each training sample as a validation sample, and the rest... Using a subset of samples as training data, candidate smoothing factors are selected. Calculate the prediction error for the validation samples. After iterating through all samples, calculate this... The average prediction error under the given value is selected to minimize the average prediction error. Value as the optimal smoothing factor Its mathematical expression is as follows: (28) In the formula, The optimal smoothing factor is... For smoothing factor Below, with the first The first sample is the validation sample, and the remaining samples are the training subset. After training the GRNN, the first sample is used as the validation sample. The predicted value for each sample, For the first The true label value of each sample This represents the total number of training samples.

[0117] In this example, steps D1 to D5 utilize finite element numerical simulation to generate a massive amount of synthetic training samples. This addresses the extreme scarcity of measured label data for lateral compression loss rate in real-world engineering projects. Based on this, a generalized regression neural network (GRNN) is trained as a fast nonlinear surrogate model to achieve millisecond-level prediction of the lateral compression loss rate. Specifically, Monte Carlo sampling (D1) ensures that the synthetic samples cover the diversity of the parameter space; finite element numerical simulation (D2) provides physically consistent settlement responses for the synthetic samples; comparison of theoretical settlement curves with Peck's formula inverse calculation (D3) establishes a quantitative mapping from observable settlement differences to lateral compression loss rate labels; and the GRNN model (D5) achieves a fast mapping from input features to predicted output using a non-iterative forward computation method, saving significant computation time compared to traditional finite element simulation.

[0118] S5. Using the on-site measured settlement data of a limited section of the engineering section, the generalized regression neural network model is fine-tuned through transfer learning to obtain the final model for predicting the ground loss rate of small-radius curved shield tunnels.

[0119] Step S5 includes the following sub-steps: E1. Select monitoring sections on the small-radius curve segments of the engineering section and obtain the on-site measured surface settlement data of each section.

[0120] Among them, select the small radius curve segment in the target engineering section. (Select 2 to 5 monitoring sections) Establish surface settlement monitoring points at each monitoring section. The monitoring points should be arranged along a transverse profile perpendicular to the tunnel excavation direction. The spacing between monitoring points should be determined based on the tunnel depth and geological conditions. The coverage area should extend to 3 to 5 times the tunnel diameter on both sides of the tunnel centerline. Regular observations should be conducted using a precision level or total station to obtain vertical surface displacement data for each monitoring section at different construction stages.

[0121] For each monitoring section, the final stable settlement value of that section after the tunnel boring machine passes through is extracted from the measured data, forming the field measured surface settlement curve for that section. The measured settlement curves of all monitoring sections constitute the measured dataset: (29) In the formula, This is a set of measured settlement curves. ( ) is the first Vector of measured surface subsidence curve of each monitoring section; To monitor the total number of cross sections.

[0122] E2. The total formation loss rate is calculated from the measured surface settlement data using the Peck formula, and the formation foundation loss rate and formation over-excavation loss rate are deducted to obtain the measured value of the formation lateral compression loss rate.

[0123] For each monitoring section The measured surface subsidence curve Substituting into Peck's formula for back calculation, the total formation loss rate of this section is obtained. .

[0124] The inverse calculation process of Peck's formula is as follows: using the nonlinear least squares method, the measured surface settlement curve is transformed... The fit to the standard form of the Peck formula is shown below: (30) In the formula, For the first Each monitoring section is located at a lateral distance from the tunnel centerline. Measured settlement value at the location; The total formation loss rate to be calculated. The radius of the tunnel; For the first The width of the settlement trough at each monitoring section, ,in, This is the settling trough width coefficient. For tunnel burial depth; This is the horizontal lateral distance from the centerline of the tunnel.

[0125] By iteratively solving the problem using the nonlinear least squares method, the sum of squared errors between the predicted and measured values ​​in equation (30) is minimized, thus obtaining the optimal fitting parameters. and .

[0126] Based on this, according to the tunnel geometry parameters (cutterhead diameter) of the monitoring section , segment outer diameter curve radius Shield machine length Tunnel diameter The foundation loss rate of the cross section is calculated using formulas (1) and (3). and formation over-excavation loss rate .

[0127] Then, the base loss rate and over-excavation loss rate are subtracted from the total formation loss rate to obtain the measured value of the lateral compression loss rate of the formation at this monitoring section. The calculation formula is as follows: (31) In the formula, For the first Measured values ​​of lateral compression loss rate of formation at each monitoring section. This is the measured value of the total formation loss rate obtained through back-calculation. The foundation loss rate is calculated based on the geometric parameters of this cross section. This is the over-excavation loss rate of the stratum calculated based on the geometric parameters of this cross section.

[0128] E3. Obtain the values ​​of the optimal feature subset corresponding to each measured section, and combine them with the measured values ​​of the lateral compression loss rate of the formation to form a small sample measured dataset.

[0129] For each monitoring section The optimal feature subset is extracted from the geological survey parameters and construction records of this section. The specific values ​​of each feature constitute the feature vector. Simultaneously, the measured value of the formation lateral compression loss rate obtained through step E2 for this cross section was used. This serves as the output label for the sample.

[0130] eigenvectors With the corresponding tag value Pairing them together creates a small sample of measured data. Traverse all After monitoring each section, a small sample of measured data was obtained. Its mathematical expression is as follows: (32) In the formula, For a small sample of actual test data, ( ) is the first The optimal feature subset value vector of each monitoring section. For the first The measured lateral compression loss rate (%) of each monitoring section was obtained by back-calculation in step E2. To monitor the total number of cross sections.

[0131] E4. Using the small sample measured dataset as calibration data, the output layer parameters and summation layer parameters of the generalized regression neural network model are used as fine-tunable parameters. The model is trained in a limited number of iterations using a preset learning rate to obtain the final model for predicting the ground loss rate of small-radius curve shield tunnels.

[0132] Among them, a small sample of actual test dataset To calibrate the data, the initial GRNN model trained in step D5 is fine-tuned using transfer learning.

[0133] Specifically, the core idea of ​​transfer learning fine-tuning is: the initial GRNN model has already been synthesized on the training sample set. The model learned the basic mapping relationship between lateral compression loss rate and optimal feature subset, but there is a certain systematic bias between synthetic data and real working conditions. Fine-tuning the model with a small number of real samples can eliminate this systematic bias, allowing the model to quickly adapt to the actual geological conditions and construction level of the target project.

[0134] Specifically, the output layer parameters and summation layer parameters of the initial GRNN model are used as fine-tunable parameters, while the pattern layer parameters remain unchanged. In GRNN, the pattern layer parameters determine the distance metric in the input space, reflecting the general knowledge of the relative relationships between features learned from synthetic data, and possessing good universality. The output layer and summation layer parameters determine how to combine the similarity weights output by the pattern layer with the label values ​​to generate the final prediction. This combination relationship is greatly affected by data bias. Therefore, fine-tuning only the parameters of these two levels is sufficient to eliminate the systematic bias between synthetic data and real data, while avoiding the destruction of stable feature representations learned from massive synthetic samples due to fine-tuning the pattern layer parameters.

[0135] During the fine-tuning process, a small sample of actual test data was used. For the training data, the mean squared error is used as the loss function, and its mathematical expression is as follows: (33) In the formula, The loss function during the fine-tuning phase. This is a set of finely adjustable summation layer weight parameters. For parameters The next GRNN for the first The predicted value for each measured sample. For the first Measured values ​​of lateral compression loss rate for each actual sample. This represents the total number of measured samples.

[0136] Minimize the loss function using gradient descent. Preset learning rate For smaller positive values ​​(e.g.) The iterative update formula is shown below: (34) In the formula, For the first The set of fine-tunable parameters at each iteration For the updated parameter set, To preset the learning rate, loss function For parameters exist The gradient at that point.

[0137] During the fine-tuning process, a preset limited number of rounds are used. Perform iterative training, but the number of iterations should not be too large to prevent overfitting on small samples. Monitor the change in the loss function after each iteration, and stop training when the loss function converges or reaches the preset maximum number of iterations.

[0138] After fine-tuning, the final model for predicting the ground loss rate of small-radius curved shield tunnels was obtained. It retains the physical consistency feature representation capability learned from massive synthetic data, and eliminates the systematic deviation between synthetic data and real working conditions by using a small amount of real data, thus accurately adapting to the actual geological conditions and construction level of the target project.

[0139] In this example, a pre-trained GRNN model is fine-tuned using transfer learning with a small amount of real engineering data. This allows the model to quickly adapt to the actual construction conditions of the target project, eliminating systematic biases between the simplified assumptions of finite element numerical simulation and real working conditions. Only a small number of monitoring sections within the target project area are needed for model adaptation, eliminating the need to accumulate large amounts of field-labeled data. This effectively solves the problem of decreased prediction reliability in new projects due to insufficient training samples in existing data-driven methods, giving the method good engineering applicability and cross-project transferability. Furthermore, by fine-tuning only the output and summation layer parameters of the GRNN while keeping the model layer parameters unchanged, the general feature representations learned from massive synthetic data are not destroyed. Simultaneously, effective systematic bias calibration is achieved with only a small number of real samples, avoiding the risk of overfitting due to small sample sizes.

[0140] S6. The final model for predicting the stratum loss rate of the small-radius curve shield tunnel is used to predict the cross section to be predicted, and the predicted value of the lateral extrusion loss rate of the stratum is obtained. Based on the stratum foundation loss rate, the stratum over-excavation loss rate and the predicted value of the lateral extrusion loss rate of the stratum, the total stratum loss rate is determined.

[0141] For the section to be predicted, the optimal feature subset is extracted from the geological exploration parameters and the preset construction parameters. The values ​​of each feature in the vector form the feature vector. .

[0142] eigenvectors The final model for predicting the ground loss rate of small-radius curve shield tunnels, fine-tuned through transfer learning, is input into S5. Perform a forward propagation calculation and output the predicted value of the formation lateral compression loss rate for this cross section. .

[0143] When using this final model for prediction, no iterative calculations or finite element simulations are required. A single GRNN forward propagation can complete the mapping from input features to the predicted output within milliseconds. The calculation process is as follows: (35) In the formula, The predicted value of the lateral compression loss rate of the formation at the section to be predicted is... This is the final prediction model of the GRNN after fine-tuning through transfer learning. The vector represents the optimal feature subset of the cross section to be predicted.

[0144] Subsequently, the foundation loss rate calculated in step S2 is obtained. and formation over-excavation loss rate Combine the two with the predicted lateral compression loss rate. The values ​​are superimposed to obtain the predicted total formation loss rate for the section to be predicted. The calculation formula is as follows: (36) In the formula, The predicted total formation loss rate for the section to be predicted is given. For the formation foundation loss rate, The over-excavation loss rate of the stratum. This is the predicted value of the lateral compression loss rate of the formation.

[0145] Total formation loss rate prediction Further applications will be made in predicting land subsidence. Substituting into the Peck formula, it can be used to calculate the maximum surface settlement value and lateral settlement curve of the section to be predicted, providing a quantitative basis for optimizing construction parameters and early warning of surface settlement risks.

[0146] This example provides a deep learning-based intelligent prediction method for the ground loss rate in tunnel boring machine (TBM) tunneling. First, multi-source foundation data of the ground in the small-radius curve segment of the target project section is acquired. Based on this data, the ground foundation loss rate and the ground over-excavation loss rate are calculated. Then, a physical-guided two-stage feature selection method is employed. Based on the physical mechanism of lateral extrusion of the TBM in the small-radius curve, the essential feature set is locked. Next, an improved D-optimal criterion is used to introduce pre-filtering with variance expansion factor collinearity and incremental greedy iteration with determinant, selecting the supplementary features with the largest information increment from the candidate features to obtain the optimal feature subset. Finally, based on the optimal features... A subset of samples was generated using finite element numerical simulation and Monte Carlo sampling to create a synthetic training sample set. The difference between the numerically simulated surface settlement curve and the theoretical settlement curves corresponding to the foundation loss rate and over-excavation loss rate was compared and then used to calculate the label value of the lateral compression loss rate of the formation using the Peck formula. This label value was then used to train a generalized regression neural network model. Finally, the generalized regression neural network model was fine-tuned using field-measured settlement data from a limited section of the engineering section through transfer learning, resulting in the final model for predicting the formation loss rate. The predicted values ​​of the foundation loss rate, over-excavation loss rate, and lateral compression loss rate were then superimposed to determine the total formation loss rate, yielding the following beneficial effects: 1. This application explicitly decomposes the total ground loss rate in shield tunneling on small-radius curved sections into three independent components: base loss rate, over-excavation loss rate, and lateral compression loss rate. It also models and quantifies the lateral compression loss rate separately, overcoming the shortcomings of existing technologies that mix the three types of losses and cannot accurately model the lateral compression mechanism on small-radius curved sections. This makes the prediction results clearer in a physical sense and significantly improves the prediction accuracy of the total ground loss rate in the construction scenario of small-radius curved sections.

[0147] 2. In the feature selection stage, this application adopts a physically guided two-stage method. First, based on the physical mechanism of lateral compression, three mandatory features are forcibly locked: curve radius, hinge angle, and jack thrust difference. Then, by improving the D-optimal criterion, a variance inflation factor collinearity pre-filtering step is introduced. Before calculating the determinant increment, candidate features that are highly collinear with the selected features are eliminated. This effectively eliminates multicollinearity while ensuring the physical interpretability of the feature set. This allows the generalized regression neural network model to obtain input features with minimal information redundancy and the strongest generalization ability, avoiding the problem of lack of physical basis for feature selection and model instability caused by highly collinear features in pure data-driven methods.

[0148] 3. This application addresses the reality of extremely scarce measured labeled data on lateral compression loss rate of small-radius curve segments in engineering. It adopts a two-stage modeling strategy that combines pre-training of synthetic samples generated by finite element numerical simulation with fine-tuning through transfer learning using a small amount of measured data. The model can be adapted to engineering projects by selecting only a few monitoring sections in the target engineering area, without the need for a large accumulation of field labeled data. This effectively solves the problem of decreased prediction reliability caused by insufficient training samples in new projects by existing data-driven methods, giving the method good engineering applicability and cross-engineering transferability.

[0149] For those consistent with the above, please refer to Figure 2 , Figure 2 This application provides a schematic diagram of the structure of a deep learning-based intelligent prediction system for ground loss rate in tunnel boring machines. (See attached diagram.) Figure 2 As shown, the system includes: Module 1 is used to acquire multi-source basic geological data of small-radius curve segments in the target engineering section.

[0150] The second module 2 is used to calculate the foundation loss rate and the over-excavation loss rate of the stratum based on the multi-source foundation data of the stratum.

[0151] The third module 3 is used to determine the key influencing factors of the lateral compression loss rate of the formation from the multi-source basic data of the formation using a physical-guided two-stage feature screening method, and to obtain the optimal feature subset.

[0152] The fourth module 4 is used to generate a synthetic training sample set based on the optimal feature subset using finite element numerical simulation and Monte Carlo sampling, and to construct a generalized regression neural network model based on the synthetic training sample set.

[0153] Module 5 is used to fine-tune the generalized regression neural network model by using on-site measured settlement data from limited cross-sections of the engineering section, and to obtain the final model for predicting the ground loss rate of small-radius curved shield tunnels.

[0154] Module 6 is used to predict the cross section to be predicted using the final model for predicting the stratum loss rate of the small-radius curved shield tunnel, to obtain the predicted value of the lateral compression loss rate of the stratum, and to determine the total stratum loss rate based on the stratum foundation loss rate, the stratum over-excavation loss rate and the predicted value of the lateral compression loss rate of the stratum.

[0155] For examples consistent with the above embodiments, please refer to... Figure 3 , Figure 3A schematic diagram of a terminal structure provided in an embodiment of this application is shown in the figure. It includes a processor, an input device, an output device, and a memory. The processor, input device, output device, and memory are interconnected. The memory is used to store a computer program, which includes program instructions. The processor is configured to call the program instructions. The program includes instructions for performing the following steps. Obtain multi-source foundational data of the stratigraphy for the small-radius curve segment within the target engineering section; Based on the aforementioned multi-source foundation data of the strata, the foundation loss rate and the over-excavation loss rate of the strata are calculated respectively. A physical-guided two-stage feature screening method was adopted to determine the key influencing factors of lateral compression loss rate of the formation from the multi-source basic data of the formation, and to obtain the optimal feature subset. Based on the optimal feature subset, a synthetic training sample set is generated using finite element numerical simulation and Monte Carlo sampling, and a generalized regression neural network model is constructed based on the synthetic training sample set. Using on-site measured settlement data from a limited section of the engineering section, the generalized regression neural network model was fine-tuned through transfer learning to obtain the final model for predicting the ground loss rate of small-radius curved shield tunnels. The final model for predicting the stratum loss rate of the small-radius curve shield tunnel is used to predict the cross section to be predicted, and the predicted value of the lateral compression loss rate of the stratum is obtained. Based on the stratum foundation loss rate, the stratum over-excavation loss rate and the predicted value of the lateral compression loss rate of the stratum, the total stratum loss rate is determined.

[0156] The above mainly describes the solutions of the embodiments of this application from the perspective of the method execution process. It is understood that, in order to achieve the above functions, the terminal includes the corresponding hardware structure and / or software modules for executing each function. Those skilled in the art should readily recognize that, in conjunction with the units and algorithm steps of the various examples described in the embodiments provided herein, this application can be implemented in hardware or a combination of hardware and computer software. Whether a function is executed in hardware or by computer software driving hardware depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0157] This application embodiment can divide the terminal into functional units according to the above method example. For example, each function can be divided into a separate functional unit, or two or more functions can be integrated into one processing unit. The integrated unit can be implemented in hardware or as a software functional unit. It should be noted that the unit division in this application embodiment is illustrative and only represents one logical functional division. In actual implementation, there may be other division methods.

[0158] This application also provides a computer storage medium storing a computer program for electronic data interchange, which causes a computer to perform some or all of the steps of any of the deep learning-based intelligent prediction methods for ground loss rate in tunnel boring machines as described in the above method embodiments.

[0159] This application also provides a computer program product, which includes a non-transitory computer-readable storage medium storing a computer program that causes a computer to perform some or all of the steps of any of the deep learning-based intelligent prediction methods for ground loss rate in tunnel boring machines as described in the above method embodiments.

[0160] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0161] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0162] In the several embodiments provided in this application, it should be understood that the disclosed apparatus can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical or other forms.

[0163] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0164] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software program module.

[0165] If the integrated unit is implemented as a software program module and sold or used as an independent product, it can be stored in a computer-readable storage device (CMD). Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a memory and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned memory includes various media capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0166] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage device, which may include: a flash drive, a read-only memory, a random access memory, a magnetic disk, or an optical disk, etc.

[0167] The embodiments of this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for intelligent prediction of ground loss rate in shield tunneling based on deep learning, characterized in that, include: Obtain multi-source foundational data of the stratigraphy for the small-radius curve segment within the target engineering section; Based on the aforementioned multi-source foundation data of the strata, the foundation loss rate and the over-excavation loss rate of the strata are calculated respectively. A physical-guided two-stage feature screening method was adopted to determine the key influencing factors of lateral compression loss rate of the formation from the multi-source basic data of the formation, and to obtain the optimal feature subset. Based on the optimal feature subset, a synthetic training sample set is generated using finite element numerical simulation and Monte Carlo sampling, and a generalized regression neural network model is constructed based on the synthetic training sample set. Using on-site measured settlement data from a limited section of the engineering section, the generalized regression neural network model was fine-tuned through transfer learning to obtain the final model for predicting the ground loss rate of small-radius curved shield tunnels. The final model for predicting the stratum loss rate of the small-radius curve shield tunnel is used to predict the cross section to be predicted, and the predicted value of the lateral extrusion loss rate of the stratum is obtained. Based on the stratum foundation loss rate, the stratum over-excavation loss rate and the predicted value of the lateral extrusion loss rate of the stratum, the total stratum loss rate is determined.

2. The intelligent prediction method for ground loss rate in shield tunneling based on deep learning according to claim 1, characterized in that, The physically-guided two-stage feature screening method identifies key influencing factors of formation lateral compression loss rate from the multi-source basic data of the formation, and obtains an optimal feature subset, including: A candidate feature set is constructed from the multi-source basic data of the strata; Based on the physical mechanism of lateral extrusion of shield tunnels with small radius curves, the curve radius, hinge angle and jack thrust difference are locked as the mandatory feature set from the candidate feature set; An improved D-optimal criterion is adopted to select the supplementary features that have the largest information increment after being combined with the required features from the remaining candidate features, thus obtaining the optimal feature subset.

3. The intelligent prediction method for ground loss rate in shield tunneling based on deep learning according to claim 2, characterized in that, The improved D-optimal criterion is used to select supplementary features from the remaining candidate features that, when combined with the required features, yield the supplementary features with the largest information increment, thus obtaining the optimal feature subset. include: Initialize the feature index set by adding the indices of the required feature set to the feature index set; Iterate through each candidate feature that is not currently selected into the feature index set, calculate the variance inflation factor between the candidate feature and the existing features in the feature index set, and filter out candidate features whose variance inflation factor exceeds a preset collinearity threshold. For candidate features that pass the collinearity filtering, they are temporarily added to the feature index set. The corresponding columns are extracted from the candidate feature matrix to construct a temporary feature submatrix. The difference between the determinant of the temporary feature submatrix and the determinant of the current feature submatrix is ​​calculated as the determinant increment. Select the candidate feature that maximizes the increment of the determinant and permanently add it to the feature index set; Repeat the above filtering, calculation and selection steps until the determinant increment of the newly added features is lower than the preset threshold or the total number of selected features reaches the preset upper limit, and then merge the features corresponding to the feature index set into the optimal feature subset.

4. The intelligent prediction method for ground loss rate in shield tunneling based on deep learning according to claim 1, characterized in that, The process of generating a synthetic training sample set based on the optimal feature subset using finite element numerical simulation and Monte Carlo sampling, and constructing a generalized regression neural network model based on the synthetic training sample set, includes: Based on the range of geological parameters and construction parameters in the multi-source basic data of the strata, the Monte Carlo method is used to randomly sample within the distribution range of each parameter to generate multiple sets of parameter combinations. A three-dimensional finite element numerical model was established for each set of parameters to simulate the shield tunneling process with a small radius curve and to extract the surface settlement curve. The surface settlement curve is compared with the theoretical settlement curves corresponding to the foundation loss rate and over-excavation loss rate of the stratum. The difference is extracted and substituted into the Peck formula to back-calculate and obtain the label value of the lateral compression loss rate of the stratum. Construct a synthetic training sample set consisting of the values ​​of the optimal feature subset and the label values ​​of the formation lateral compression loss rate; The generalized regression neural network model was trained using the synthetic training sample set, and the optimal smoothing factor was determined using leave-one-out cross-validation.

5. The intelligent prediction method for ground loss rate in shield tunneling based on deep learning according to claim 1, characterized in that, The method utilizes on-site measured settlement data from a limited cross-section of the engineering section to fine-tune the generalized regression neural network model through transfer learning, resulting in the final model for predicting the ground loss rate of small-radius curved shield tunnels. This model includes: Monitoring sections were selected on the small-radius curve segments within the engineering section to obtain on-site measured surface settlement data for each section. The total formation loss rate was calculated from the measured surface settlement data using the Peck formula, and the formation foundation loss rate and formation over-excavation loss rate were deducted to obtain the measured value of the formation lateral compression loss rate. The values ​​of the optimal feature subset corresponding to each measured section are obtained and together with the measured value of the lateral compression loss rate of the formation, they constitute a small sample measured dataset. Using the small sample measured dataset as calibration data, the output layer parameters and summation layer parameters of the generalized regression neural network model are used as fine-tunable parameters. A limited number of iterations are performed using a preset learning rate to obtain the final model for predicting the ground loss rate of small-radius curved shield tunnels.

6. The intelligent prediction method for ground loss rate in shield tunneling based on deep learning according to claim 1, characterized in that, The step of calculating the formation foundation loss rate based on the multi-source foundation data includes: Extract the cutterhead diameter and segment outer diameter from the multi-source basic data of the formation; The foundation loss rate is calculated based on the ratio of the difference between the cutterhead diameter and the outer diameter of the tunnel segments to the tunnel cross-sectional area.

7. The intelligent prediction method for ground loss rate in shield tunneling based on deep learning according to claim 1, characterized in that, The step of calculating the over-excavation loss rate of the formation based on the multi-source basic data of the formation includes: The curve radius, tunnel boring machine length, and tunnel diameter are extracted from the multi-source geological data. Calculate the over-excavation area per unit length based on the geometric relationship between the curve radius, the length of the tunnel boring machine, and the tunnel diameter; The over-excavation loss rate of the stratum is calculated based on the ratio of the over-excavated area per unit length to the tunnel cross-sectional area.

8. A deep learning-based intelligent prediction system for ground loss rate in shield tunneling, characterized in that, include: The first module is used to acquire multi-source basic geological data of small-radius curve segments in the target engineering section; The second module is used to calculate the foundation loss rate and the over-excavation loss rate of the strata based on the multi-source foundation data of the strata. The third module is used to determine the key influencing factors of the lateral compression loss rate of the formation from the multi-source basic data of the formation using a physical-guided two-stage feature screening method, and to obtain the optimal feature subset. The fourth module is used to generate a synthetic training sample set based on the optimal feature subset using finite element numerical simulation and Monte Carlo sampling, and to construct a generalized regression neural network model based on the synthetic training sample set. The fifth module is used to fine-tune the generalized regression neural network model by using the on-site measured settlement data of the limited cross-section of the engineering section, so as to obtain the final model for predicting the ground loss rate of the small radius curve shield tunnel. The sixth module is used to predict the cross section to be predicted using the final model for predicting the stratum loss rate of the small-radius curved shield tunnel, to obtain the predicted value of the lateral compression loss rate of the stratum, and to determine the total stratum loss rate based on the stratum foundation loss rate, the stratum over-excavation loss rate and the predicted value of the lateral compression loss rate of the stratum.

9. A terminal, characterized in that, The device includes a processor, an input device, an output device, and a memory, which are interconnected. The memory stores a computer program, which includes program instructions. The processor is configured to invoke the program instructions to execute the intelligent prediction method for ground loss rate in shield tunneling based on deep learning as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, the computer program including program instructions, which, when executed by a processor, cause the processor to perform the intelligent prediction method for ground loss rate in shield tunneling based on deep learning as described in any one of claims 1 to 7.

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