An intelligent prediction method for shield tunnel-induced ground displacement field

Abstract

The present invention proposes an intelligent prediction method for the stratum displacement field induced by a shield tunnel, which relates to the field of tunnel engineering technology; specifically includes the following steps: S1: using a machine learning model to establish an intelligent prediction method for surface displacement; S2: using a line search method to adjust the displacement function of the non-uniform deformation mode in the analytical method, and obtaining the stratum displacement field by calculating the displacement function; S3: evaluating the stratum displacement distribution characteristics, determining the potential instability area of ​​the stratum, and optimizing the shield tunneling parameters. The present invention adopts the above-mentioned intelligent prediction method for the stratum displacement field induced by a shield tunnel to develop the tunnel analytical theory from being able to only evaluate stratum displacement to intelligent prediction and evaluation of stratum displacement, which has the advantages of convenient calculation and accurate prediction.

Description

Technical Field

[0001] The invention relates to the technical field of tunnel engineering, and in particular to an intelligent prediction method for a stratum displacement field induced by a shield tunnel. Background Art

[0002] Shield construction has the advantages of safety, high efficiency, high degree of mechanization, and little interference with urban ground traffic. It is currently the preferred construction method for most urban rail transit. Urban rail transit tunnels are characterized by shallow burial depth, relatively weak rock and soil, and complex geological conditions. During the shield excavation process, the surrounding strata will inevitably be disturbed due to the cutting of the cutterhead, the friction between the shield machine and the surrounding soil, and the gap between the shield tail and the surrounding rock and soil, inducing the redistribution of the stratum stress field and displacement field. If improperly controlled, it will have a great impact on the surrounding environment, such as excessive ground settlement, deformation and cracking of adjacent buildings, and even catastrophic consequences such as ground collapse and house collapse in severe cases. It is urgent to propose an intelligent prediction method for the stratum displacement field induced by shield tunnels, evaluate the influence of tunnel excavation on stratum disturbance, and effectively optimize the shield excavation plan.

[0003] Numerical simulation methods can take into account many factors such as complex geological conditions, the interaction between shield machine, lining and surrounding rock, etc. However, the constitutive model parameters in numerical simulation methods are usually obtained based on limited borehole sampling samples, which obviously cannot reflect the entire stratum conditions. The analytical method can quantitatively and reasonably consider the coupling effects of tunnel geometry parameters, geomechanical parameters, and excavation parameters, and is an applicable method for studying stratum displacement in shield tunnels. Reasonable boundary conditions at the tunnel section are the key factor in obtaining the analytical solution of stratum displacement during tunnel excavation. At present, the displacement boundary conditions in the analytical method are obtained based on the on-site monitoring data after the tunnel excavation is completed, and then substituted into the complex function analytical equation to obtain the stratum displacement value at any position. Therefore, the analytical method is currently mainly used to study the stratum deformation distribution law and displacement transmission mechanism after tunnel excavation, and the function of predicting stratum displacement before tunnel excavation has not been realized.

[0004] Therefore, an intelligent prediction method for the stratum displacement field induced by a shield tunnel is provided to solve the above problems. Summary of the invention

[0005] The present invention provides an intelligent prediction method for the stratum displacement field induced by a shield tunnel, which solves the problems that the current stratum displacement field calculation method fails to comprehensively consider various coupling factors such as geological conditions, the interaction between a shield machine, a lining and surrounding rock soil, the calculation result has poor accuracy, and the displacement of the next excavation step cannot be predicted before tunnel excavation. The present invention combines a machine learning model and a complex function analytical solution method, considers the influence of various factors during shield tunnel excavation, and realizes the prediction function of the stratum displacement field before tunnel excavation.

[0006] To achieve the above object, the present invention provides an intelligent prediction method for the stratum displacement field induced by a shield tunnel, which is based on a network training module and a transfer learning module training detection method, and specifically includes the following steps:

[0007] S1: Use machine learning models to establish intelligent prediction methods for surface displacement;

[0008] S2: Use the line search method to adjust the displacement function of the non-uniform deformation mode in the analytical method, and obtain the formation displacement field by calculating the displacement function;

[0009] S3: Evaluate the distribution characteristics of stratum displacement, determine the potential unstable areas of the stratum, and optimize the shield tunneling parameters.

[0010] Preferably, in step S1, the machine learning model adopts an extreme machine learning model, including an input layer, a hidden layer and an output layer; the weight matrix w and the threshold matrix b of the input layer are random numbers, and the weight matrix β connecting the hidden layer and the output layer is obtained by calculating the equation group, and the extreme learning machine model is expressed as:

[0011] H=f(Xw+b)

[0012] ||Hβ-Y||=0

[0013] Where X and Y are the input and output matrices of the machine learning model, respectively, and H is the output matrix of the hidden layer. The optimal machine learning model is determined by minimizing ||Hβ-Y||, and the accuracy of the prediction model depends on the input random number weight matrix w and the threshold matrix b.

[0014] Establishing an intelligent prediction method for surface displacement includes the following steps:

[0015] S11: Construct a surface displacement prediction database based on shield tunneling parameters, stratum mechanical conditions and tunnel geometric parameters;

[0016] S12: Using the global sensitivity analysis method, the optimal input parameter combination for surface displacement prediction is obtained;

[0017] S13: Using the particle swarm optimization algorithm, the optimal random number of the extreme learning model is determined and an intelligent prediction method for surface displacement is established.

[0018] Preferably, in step S11, equivalent cohesion, internal friction angle and uniaxial rock compressive strength are used to describe the mechanical properties of the surrounding rock, which specifically includes the following steps:

[0019]

[0020]

[0021]

[0022] Where h is the tunnel depth, h i and t i are the depth and thickness of the surrounding rock mass of the i-th layer, c i , and U i They are the cohesion, internal friction angle and uniaxial rock compressive strength of the i-th layer of surrounding rock soil. A prediction database including stratum mechanics parameters, tunnel geometric parameters, shield excavation parameters and surface displacement was constructed. 80% of the data in the database were randomly extracted for training the machine learning model, and 20% of the data were used to test the established prediction model.

[0023] Preferably, in step S12, if the stratum deformation exceeds the specification limit, a global sensitivity analysis method is used to adjust the existing parameter combination, and the stratum displacement field of the next excavation step is predicted again until the stratum displacement meets the stratum deformation specification requirements;

[0024] The Pearson correlation coefficient PCC method is used to determine the optimal input parameter combination. The PCC formula is as follows:

[0025]

[0026] Where r is the correlation coefficient, x i and i are the two variables of the i-th sample, and x and y are the averages of the two samples respectively;

[0027] The calculated value of PCC is between -1 and 1, and the calculated value reflects the correlation between the two parameters;

[0028] If PCC is greater than 0, the two parameters are positively correlated; if PCC is less than 0, the two parameters are negatively correlated;

[0029] The larger the absolute value of PCC, the higher the correlation between parameters; the smaller the absolute value of PCC, the weaker the correlation between parameters;

[0030] The mean absolute error (MAE), mean root mean square error (RMSE) and determination coefficient (R) were used. 2 Performance indicators evaluate the calculation accuracy of input feature combinations:

[0031]

[0032]

[0033]

[0034] Where r i is the measured value, p iis the predicted value, r is the average of the measured values, and n is the number of samples.

[0035] Preferably, in step S13, a particle swarm optimization algorithm PSO is applied to optimize the weight matrix w and the threshold matrix b, and the optimization steps are:

[0036] S131: Determine the parameters of PSO and evaluate the fitness function of each particle;

[0037] S132: Update the position and velocity of the particle to determine the optimal position;

[0038] S133: Iterate the above steps S131 and S132, and when the error meets the set requirements, determine the optimal w and b;

[0039] The speed and position update expressions of the particle swarm optimization algorithm are as follows:

[0040]

[0041]

[0042] Where w is the weight factor; c1 and c2 are learning factors, ranging from [0,2]; r1 and r2 are random numbers between [0,1]; P i k is the optimal position of the i-th particle in the k-th iteration step; P g k is the optimal position of the population in the kth iteration.

[0043] Preferably, in step S2, the following steps are specifically included:

[0044] S21: The non-uniform deformation mode with unknown parameters is used as the boundary condition of the tunnel section, and the analytical solution of displacement at any position of the stratum is obtained by using the complex function method;

[0045] S22: The line search method is used to calibrate the parameters of the non-uniform deformation mode and to establish an intelligent prediction method for the displacement of the shield tunnel stratum field.

[0046] Preferably, in step S21, the non-uniform deformation function of the tunnel section reflects the uniform deformation, vertical translation and elliptical deformation characteristics of the tunnel section, and the expression is as follows:

[0047]

[0048] In the formula, It reflects the stratum loss in the tunnel section. g is the gap parameter at the top of the tunnel; It reflects the overall vertical displacement of the tunnel section. It reflects the elliptical deformation of the tunnel section, θ′ is the angle between the line connecting any point of the tunnel section and the origin of the coordinate system and the horizontal axis; u′0 reflects the stratum loss of the tunnel section;

[0049] The potential function of the elastic theory of stratum displacement during tunnel excavation is expressed as and ψ(z), the ground surface is a zero stress surface, and the displacement boundary condition of the tunnel section is expressed by a non-uniform deformation function. The two potential functions and In the complex variable domain, Laurent series is used to express it as:

[0050]

[0051]

[0052] In the formula, a0, a k ,b k ,c0,c k ,d k is the Laurent series expansion coefficient; z is the stratum position coordinate, expressed as x+yi, and i is a complex unit; substituting the boundary conditions of the surface and the tunnel section, determining the Laurent series, the analytical expression of the stratum displacement at any position of the shield tunnel is obtained by the following expression:

[0053]

[0054] In the formula, u x and u y are the horizontal displacement and vertical displacement of the formation respectively; G is the shear modulus of the formation; κ=3-4ν, ν is the Poisson's ratio of the formation.

[0055] Preferably, in step S22, the initial value of u′0 is set to 0 mm, and the line search method is used to find the optimal u′0 value with an incremental step of 0.01 mm, so that the maximum surface displacement obtained by the analytical method is equal to the maximum surface displacement of the shield tunnel predicted based on steps S11, S12 and S13. At this time, the u′0 value is the optimal solution. The determined u′0 value is substituted into the tunnel section displacement boundary function, and the analytical method established in step S21 is combined to obtain the horizontal and vertical displacements at any position of the stratum.

[0056] Preferably, in step S3, based on the established shield tunnel stratum displacement field prediction method, the settlement trough curve law of the stratum above the tunnel, the maximum settlement value and the transmission mechanism of stratum loss with depth are studied to determine the potential instability and damage area of ​​the stratum;

[0057] If the ground deformation exceeds the specification limit, a sensitivity analysis of the excavation parameters is carried out to obtain the optimal excavation parameter combination.

[0058] Therefore, the present invention adopts the above-mentioned intelligent prediction method of the shield tunnel-induced stratum displacement field, based on the analytical theory of tunnel excavation stratum displacement, and introduces machine learning technology to optimize and determine the boundary conditions of the analytical method, thereby effectively improving the prediction accuracy. At the same time, it has the advantages of being easy to perform parameter analysis, convenient calculation, and adaptable to actual scenarios.

[0059] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a schematic flow chart of an intelligent prediction method for a shield tunnel-induced stratum displacement field in an embodiment of the present invention;

[0061] Figure 2 is a machine learning model for predicting ground displacement in an embodiment of the present invention;

[0062] Figure 3 It is an analytical mechanical model of the shield tunnel stratum displacement in the embodiment of the present invention. DETAILED DESCRIPTION

[0063] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0064] Unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0065] The present invention provides a training detection method based on a network training module and a transfer learning module, which specifically includes the following steps:

[0066] S1: Using a machine learning model, an intelligent prediction method for surface displacement is established; in step S1, the machine learning model uses an extreme machine learning model, including an input layer, a hidden layer, and an output layer; the weight matrix w and the threshold matrix b of the input layer are random numbers, and the weight matrix β connecting the hidden layer and the output layer is obtained by calculating the equation group. The extreme learning machine model is expressed as:

[0067] H=f(Xw+b)

[0068] ||Hβ-Y||=0

[0069] Where X and Y are the input and output matrices of the machine learning model, respectively, and H is the output matrix of the hidden layer. The optimal machine learning model is determined by minimizing ||Hβ-Y||, and the accuracy of the prediction model depends on the input random number weight matrix w and the threshold matrix b.

[0070] Establishing an intelligent prediction method for surface displacement includes the following steps:

[0071] S11: Based on shield tunneling parameters, stratum mechanical conditions and tunnel geometric parameters, a surface displacement prediction database is constructed; in step S11, equivalent cohesion, internal friction angle and uniaxial rock compressive strength are used to describe the mechanical properties of the surrounding rock, which specifically includes the following steps:

[0072]

[0073]

[0074]

[0075] Where h is the tunnel depth, h i and t i are the depth and thickness of the surrounding rock mass of the i-th layer, c i , and U i They are the cohesion, internal friction angle and uniaxial rock compressive strength of the i-th layer of surrounding rock soil. A prediction database including stratum mechanics parameters, tunnel geometric parameters, shield excavation parameters and surface displacement was constructed. 80% of the data in the database were randomly extracted for training the machine learning model, and 20% of the data were used to test the established prediction model.

[0076] S12: Using a global sensitivity analysis method, the optimal input parameter combination for surface displacement prediction is obtained; in step S12, if the stratum deformation exceeds the specification limit, the global sensitivity analysis method is used to adjust the existing parameter combination, and the stratum displacement field of the next excavation link is predicted again until the stratum displacement meets the stratum deformation specification requirements;

[0077] The Pearson correlation coefficient PCC method is used to determine the optimal input parameter combination. The PCC formula is as follows:

[0078]

[0079] Where r is the correlation coefficient, x i and iare the two variables of the i-th sample, and x and y are the averages of the two samples respectively;

[0080] The calculated value of PCC is between -1 and 1, and the calculated value reflects the correlation between the two parameters;

[0081] If PCC is greater than 0, the two parameters are positively correlated; if PCC is less than 0, the two parameters are negatively correlated;

[0082] The larger the absolute value of PCC, the higher the correlation between parameters; the smaller the absolute value of PCC, the weaker the correlation between parameters;

[0083] The mean absolute error (MAE), mean root mean square error (RMSE) and determination coefficient (R) were used. 2 Performance indicators evaluate the calculation accuracy of input feature combinations:

[0084]

[0085]

[0086]

[0087] Where r i is the measured value, p i is the predicted value, is the average of the measured values, and n is the number of samples.

[0088] S13: Using the particle swarm optimization algorithm, determine the optimal random number of the extreme learning model and establish an intelligent prediction method for surface displacement. In step S13, the particle swarm optimization algorithm PSO is used to optimize the weight matrix w and the threshold matrix b. The optimization steps are:

[0089] S131: Determine the parameters of PSO and evaluate the fitness function of each particle;

[0090] S132: Update the position and velocity of the particle to determine the optimal position;

[0091] S133: Iterate the above steps S131 and S132, and when the error meets the set requirements, determine the optimal w and b;

[0092] The speed and position update expressions of the particle swarm optimization algorithm are as follows:

[0093]

[0094]

[0095] Where w is the weight factor; c1 and c2 are learning factors, ranging from [0,2]; r1 and r2 are random numbers between [0,1]; Pi k is the optimal position of the i-th particle in the k-th iteration step; P g k is the optimal position of the population in the kth iteration.

[0096] S2: using a line search method to adjust the displacement function of the non-uniform deformation mode in the analytical method, and obtaining the formation displacement field by calculating the displacement function; in step S2, the following steps are specifically included:

[0097] S21: The non-uniform deformation mode with undetermined parameters is used as the boundary condition of the tunnel section, and the displacement analytical solution at any position of the stratum is obtained by using the complex variable function method; in step S21, the non-uniform deformation function of the tunnel section reflects the uniform deformation, vertical translation and elliptical deformation characteristics of the tunnel section, and the expression is as follows:

[0098]

[0099] In the formula, It reflects the stratum loss in the tunnel section. g is the gap parameter at the top of the tunnel; It reflects the overall vertical displacement of the tunnel section. It reflects the elliptical deformation of the tunnel section, θ′ is the angle between the line connecting any point of the tunnel section and the origin of the coordinate system and the horizontal axis; u′0 reflects the stratum loss of the tunnel section;

[0100] The potential function of the elastic theory of stratum displacement during tunnel excavation is expressed as and ψ(z), the ground surface is a zero stress surface, and the displacement boundary condition of the tunnel section is expressed by a non-uniform deformation function. The two potential functions and ψ(z) are expressed in the complex domain using Laurent series:

[0101]

[0102]

[0103] In the formula, a0, a k ,b k ,c0,c k ,d k is the Laurent series expansion coefficient; z is the stratum position coordinate, expressed as x+yi, and i is a complex unit; substituting the boundary conditions of the surface and the tunnel section, determining the Laurent series, the analytical expression of the stratum displacement at any position of the shield tunnel is obtained by the following expression:

[0104]

[0105] In the formula, u x and uy are the horizontal and vertical displacements of the formation respectively; G is the shear modulus of the formation; κ=3-4ν, ν is the Poisson's ratio of the formation.

[0106] S22: Use the line search method to calibrate the parameters of the non-uniform deformation mode and establish an intelligent prediction method for the displacement of the ground field of the shield tunnel. In step S22, the initial value of u′0 is set to 0mm, and the line search method is used to find the optimal u′0 value with an incremental step of 0.01mm, so that the maximum surface displacement obtained by the analytical method is equal to the maximum surface displacement of the shield tunnel predicted based on steps S11, S12 and S13. At this time, the u′0 value is the optimal solution. The determined u′0 value is substituted into the tunnel section displacement boundary function, and the analytical method established in step S21 is combined to obtain the horizontal and vertical displacements at any position of the formation.

[0107] S3: Evaluate the distribution characteristics of stratum displacement, determine the potential instability area of ​​the stratum, and optimize the shield tunneling parameters. In step S3, based on the established shield tunnel stratum displacement field prediction method, study the curve law of the stratum settlement trough above the tunnel, the maximum settlement value and the transmission mechanism of stratum loss with depth, and determine the potential instability and damage area of ​​the stratum;

[0108] If the ground deformation exceeds the specification limit, a sensitivity analysis of the excavation parameters is carried out to obtain the optimal excavation parameter combination.

[0109] Example

[0110] The present invention provides an intelligent prediction method for the stratum displacement field induced by a shield tunnel. Figure 1 As shown, the following steps are included:

[0111] S1: Use machine learning models to establish an intelligent prediction method for surface displacement; Step S1 specifically includes: S1a: Consider the influence of 11 parameters, including tunnel vault depth, cutterhead torque, shield machine thrust, grouting pressure, grouting volume, excavation speed, soil bin pressure, cutterhead speed, stratum cohesion, internal friction angle, and uniaxial compressive strength of rock, to build a database for predicting the maximum surface displacement of shield tunnels. In order to reflect the influence of stratified soil above the tunnel, the equivalent cohesion, internal friction angle, and uniaxial rock compressive strength are used to consider the mechanical properties of the surrounding rock, and an analytical mechanical model of tunnel stratum displacement is constructed, such as Figure 3 shown.

[0112]

[0113]

[0114]

[0115] In the formula, h,h i and t iare respectively the tunnel burial depth, the burial depth and thickness of the i-th layer of surrounding rock mass. i and U i They are respectively the cohesion, internal friction angle and uniaxial rock compressive strength of the i-th layer of surrounding rock soil. In this embodiment, the geological parameters during tunnel excavation are obtained by drilling and experimenting on the obtained geotechnical materials. Compared with the surface monitoring points, the spatial interval distance of the borehole sampling is larger. Therefore, when calculating the surrounding rock mechanical parameters at the surface monitoring points, the interpolation method is used to comprehensively consider the stratum conditions of the sampling points on both sides of the surface monitoring points and the geomechanical parameters and geometric parameters of each layer to calculate the geomechanical parameters. If the stratum distribution on both sides of the monitoring point is consistent (that is, the number and type of strata are consistent), then the equivalent calculation is performed according to the thickness and parameters of the stratum and then linear interpolation is performed. If the stratum distribution on both sides is inconsistent (for example, the stratum types on both sides are inconsistent, or the distribution order is inconsistent), the equivalent parameters of the stratum on both sides are first calculated, and then the thickness of the stratum that is not on one side is set to 0, and the equivalent parameters of the stratum are calculated again and interpolated for the second time.

[0116] S1b: A reasonable combination of input parameters is the basis for predicting the maximum surface settlement of a shield tunnel. Fewer input parameters cannot reasonably consider the coupling effects of many factors in the shield tunnel; more input parameters affect the calculation efficiency on the one hand, and parameters with weaker correlation affect the calculation results on the other hand. The present invention considers using the Pearson correlation coefficient method to calculate the correlation between the above 11 types of parameters and surface displacement. Parameters with a correlation coefficient less than 0.2 will not be used as input parameters for machine learning prediction. The formula for the Pearson correlation coefficient is as follows,

[0117]

[0118] In the formula, r is the correlation coefficient, x i and i are two variables of the i-th sample, and x and y are the average values ​​of the two samples. In this embodiment, the Pearson correlation coefficient is used to evaluate the linear correlation between each input parameter and the output value. If PCC is greater than 0, the two parameters are positively correlated; if PCC is less than 0, the two parameters are negatively correlated. The larger the absolute value of PCC, the higher the degree of correlation between the two; on the contrary, the smaller the absolute value of PCC, the weaker the degree of correlation between the two. After obtaining the prediction results, the calculated correlation coefficient can assist in reflecting the influence of each input parameter on the output value, and assist in completing the evaluation of the correlation between parameters, as well as the subsequent adjustment of shield excavation parameters for over-limit positions. The PCC value is calculated by programming in Matlab.

[0119] S1c: Use the extreme learning machine model. The extreme learning machine model is an improved single hidden layer feedforward neural network method, including an input layer, a hidden layer, and an output layer. Figure 2 As shown. The weight matrix w of the input layer and the threshold matrix b are random numbers, and the weight matrix connecting the hidden layer and the output layer is obtained by calculating the equation group. The extreme learning machine model can be expressed as,

[0120] H=f(Xw+b)

[0121] ||Hβ-Y||=0

[0122] Where X and Y are the input and output matrices of the machine learning model, respectively, and H is the output matrix of the hidden layer. The optimal machine learning model minimizes ||Hβ-Y||, and the accuracy of the prediction model depends greatly on the input random number weight matrix w and the threshold matrix b. Particle swarm optimization (PSO) is an evolutionary optimization calculation method inspired by the foraging behavior of birds. The core idea is to determine the optimal solution through information sharing and collaboration between particles. The PSO algorithm has been widely used in geotechnical engineering due to its strong convergence and robustness. In the present invention, the PSO algorithm is used to optimize the weight matrix w and the threshold matrix b. The optimization steps are: first determine the parameters of the PSO, evaluate the fitness function of each particle, and then update the position and velocity of the particle, and determine the optimal position. The above process is continuously iterated. When the error meets the set requirements, the optimal w and b are determined. Among them, w and b are updated in the following way.

[0123]

[0124]

[0125] Where w is the weight factor; c1 and c2 are learning factors, and their value range is [0,2]; r1 and r2 are random numbers between [0,1]. The introduction of random numbers can enable particles to have the ability to jump out of the local optimal solution; P i k is the optimal position of the i-th particle in the k-th iteration step; P g k is the optimal position of the population in the kth iteration. The extreme learning machine program and the embedded particle swarm optimization algorithm program are implemented through Matlab programming. Among them, after each round of particle swarm optimization, the corresponding w and b are obtained and saved as temporary parameters. After that, the data of the training set and the test set will be read, and the extreme learning machine model will predict the surface displacement based on the w and b obtained in this round of optimization. After obtaining the results, the mean absolute error (MAE), the mean root mean square error (RMSE) and the determination coefficient (R 2) to evaluate the quality of the results. Afterwards, the evaluation results will be compared with the previous results. If the quality of the results obtained after this round of optimization is better, the optimal w and b will be updated as the temporary parameters obtained in this round; if the quality of the results obtained after this round of optimization is not as good as the previous results, the optimal w and b will not be updated. After completing the specified round of optimization, the optimal w and b will be used as the final parameter combination, and the test set will be predicted to obtain the final prediction result, that is, the maximum surface displacement value. The final prediction result obtained at this time has a higher accuracy and is used for subsequent formation displacement field calculations.

[0126] Based on the database for predicting the surface displacement of shield tunnels constructed by S1a, the optimal combination of input parameters was determined using the global sensitivity analysis method of S1b. The optimal combination of input parameters was then substituted into the extreme learning machine model with PSO optimization established by S1c to predict the maximum surface displacement of shield tunnels.

[0127] S2: using a line search method to adjust the displacement function of the non-uniform deformation mode in the analytical method, and obtaining the formation displacement field by calculating the displacement function; specifically, the following steps are included:

[0128] S2a: Reasonable tunnel section boundary conditions are the key factors in obtaining the analytical solution of stratum displacement. The present invention adopts a non-uniform deformation mode, which reflects the uniform deformation, vertical translation and elliptical deformation characteristics of the tunnel section respectively. The expressions are as follows:

[0129]

[0130] Where u′0 reflects the stratum loss in the tunnel section, and the value of u′0 is unknown before tunnel excavation.

[0131] The ground surface is regarded as a zero stress surface, and the non-uniform deformation mode is regarded as the boundary of the tunnel section. The complex potential function is substituted into the complex variable function analytical theory. and ψ(z):

[0132]

[0133]

[0134] In the formula, a0, a k ,b k ,c0,c k ,d k is the Laurent series expansion coefficient; z is the stratum position coordinate, expressed as x+yi, and i is the complex unit. After the Laurent series is determined, the formula The analytical expression of the ground displacement at any position in the shield tunnel is obtained.

[0135]

[0136] In the formula, u x and u y are the horizontal displacement and vertical displacement of the formation respectively; G is the shear modulus of the formation; κ=3-4ν, ν is the Poisson's ratio of the formation.

[0137] S2b: Set the initial value of u′0 to 0mm, and use the line search method to find the optimal u′0 value with an incremental step of 0.01mm, so that the maximum surface displacement obtained by the analytical method is equal to the maximum surface displacement of the shield tunnel predicted based on S1a, S1b and S1c. At this time, the u′0 value is considered to be the optimal solution. Substitute the determined u′0 value into the tunnel section displacement boundary function, and combine it with the established analytical method to obtain the horizontal and vertical displacements at any position in the stratum.

[0138] S3: Evaluate the distribution characteristics of stratum displacement, determine the potential unstable areas of the stratum, and optimize the shield tunneling parameters. Specifically include:

[0139] S3: Based on the established method for predicting the displacement field of shield tunnels, the curve law of the stratum settlement groove above the tunnel, the maximum settlement value and the transmission mechanism of stratum loss with depth are studied to determine the potential instability and damage area of ​​the stratum. If the stratum deformation exceeds the specification limit, the excavation parameter sensitivity analysis is carried out to obtain the optimal excavation parameter combination to meet the stratum deformation specification requirements. The parameter sensitivity analysis refers to the PCC of each input parameter to the output value, that is, the maximum surface displacement. Based on the PCC value between the input 11 parameters and the output maximum surface displacement, the correlation between each parameter and the maximum surface displacement can be obtained, and the tunnel excavation parameters at the position where the maximum surface displacement exceeds the limit can be predicted accordingly. For a certain position where the maximum surface displacement exceeds the limit, the tunnel excavation parameters that can be adjusted are first selected from the 11 input parameters, and then these parameters are arranged in order from large to small based on the PCC value. If the PCC between the parameter and the maximum surface displacement is positive, the parameter value is reduced accordingly; if the PCC between the parameter and the maximum surface displacement is negative, the parameter value is increased accordingly. After adjusting each parameter, a corresponding maximum surface displacement prediction calculation is performed. If the maximum surface displacement meets the limit after adjustment, the excavation parameters are modified according to the adjustment results. If the maximum surface displacement result still exceeds the limit after adjusting a parameter, the next parameter is adjusted in the order of the previous sorting until the maximum surface displacement result meets the limit.

[0140] Therefore, the present invention adopts the above-mentioned intelligent prediction method of the shield tunnel-induced stratum displacement field, based on the analytical theory of tunnel excavation stratum displacement, and introduces machine learning technology to optimize and determine the boundary conditions of the analytical method, thereby effectively improving the prediction accuracy. At the same time, it has the advantages of being easy to perform parameter analysis, convenient calculation, and adaptable to multiple scenarios.

[0141] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. An intelligent prediction method for the stratum displacement field induced by a shield tunnel, characterized in that: The specific steps include: S1: Use machine learning models to establish intelligent prediction methods for surface displacement; S2: Use the line search method to adjust the displacement function of the non-uniform deformation mode in the analytical method, and obtain the formation displacement field by calculating the displacement function; In step S2, the following steps are specifically included: S21: The non-uniform deformation mode with unknown parameters is used as the boundary condition of the tunnel section, and the analytical solution of displacement at any position of the stratum is obtained by using the complex function method; In step S21, the non-uniform deformation function of the tunnel section reflects the uniform deformation, vertical translation and elliptical deformation characteristics of the tunnel section, and the expression is as follows: In the formula, It reflects the stratum loss in the tunnel section. g is the gap parameter at the top of the tunnel; It reflects the overall vertical displacement of the tunnel section. It reflects the elliptical deformation of the tunnel section, θ′ is the angle between the line connecting any point of the tunnel section and the origin of the coordinate system and the horizontal axis; u0′ reflects the stratum loss of the tunnel section; The potential function of the elastic theory of stratum displacement during tunnel excavation is expressed as and ψ(z), the ground surface is a zero stress surface, and the displacement boundary condition of the tunnel section is expressed by a non-uniform deformation function. The two potential functions and ψ(z) are expressed in the complex domain using Laurent series: In the formula, a0, a k ,b k ,c0,c k ,d k is the Laurent series expansion coefficient; z is the stratum position coordinate, expressed as x+yi, and i is a complex unit; substituting the boundary conditions of the surface and the tunnel section, determining the Laurent series, the analytical expression of the stratum displacement at any position of the shield tunnel is obtained by the following expression: In the formula, u x and u y are the horizontal displacement and vertical displacement of the formation respectively; G is the shear modulus of the formation; κ = 3-4ν, ν is the Poisson's ratio of the formation; S22: Use the line search method to calibrate the parameters of the non-uniform deformation mode and establish an intelligent prediction method for the displacement of the shield tunnel stratum field; In step S22, the initial value of u′0 is set to 0 mm, and the line search method is used to find the optimal u′0 value with an incremental step of 0.01 mm, so that the maximum surface displacement obtained by the analytical method is equal to the maximum surface displacement of the shield tunnel predicted based on steps S11, S12 and S13. At this time, the u′0 value is the optimal solution. The determined u′0 value is substituted into the tunnel section displacement boundary function, and the analytical method established in step S21 is combined to obtain the horizontal and vertical displacements at any position of the stratum; S3: Evaluate the distribution characteristics of stratum displacement, determine the potential unstable areas of the stratum, and optimize the shield tunneling parameters.

2. The intelligent prediction method of the shield tunnel induced stratum displacement field according to claim 1 is characterized by: In step S1, the machine learning model adopts an extreme machine learning model, including an input layer, a hidden layer and an output layer; the weight matrix w and the threshold matrix b of the input layer are random numbers, and the weight matrix β connecting the hidden layer and the output layer is obtained by calculating the equation group. The extreme learning machine model is expressed as: H=f(Xw+b) ||Hβ-Y||=0 Where X and Y are the input and output matrices of the machine learning model, respectively, and H is the output matrix of the hidden layer. The optimal machine learning model is determined by minimizing ||Hβ-Y||, and the accuracy of the prediction model depends on the input random number weight matrix w and the threshold matrix b. Establishing an intelligent prediction method for surface displacement includes the following steps: S11: Construct a surface displacement prediction database based on shield tunneling parameters, stratum mechanical conditions and tunnel geometric parameters; S12: Using the global sensitivity analysis method, the optimal input parameter combination for surface displacement prediction is obtained; S13: Using the particle swarm optimization algorithm, the optimal random number of the extreme learning model is determined and an intelligent prediction method for surface displacement is established.

3. The intelligent prediction method of the shield tunnel induced stratum displacement field according to claim 2 is characterized by: In step S11, equivalent cohesion, internal friction angle and uniaxial rock compressive strength are used to describe the mechanical properties of the surrounding rock, which specifically includes the following steps: Where h is the tunnel depth, h i and t i are the depth and thickness of the surrounding rock mass of the i-th layer, c i , and U i They are the cohesion, internal friction angle and uniaxial rock compressive strength of the i-th layer of surrounding rock soil. A prediction database including stratum mechanics parameters, tunnel geometric parameters, shield excavation parameters and surface displacement was constructed. 80% of the data in the database were randomly extracted for training the machine learning model, and 20% of the data were used to test the established prediction model.

4. The intelligent prediction method of the shield tunnel induced stratum displacement field according to claim 2 is characterized by: In step S12, if the stratum deformation exceeds the specification limit, a global sensitivity analysis method is used to adjust the existing parameter combination and predict the stratum displacement field of the next excavation step again until the stratum displacement meets the stratum deformation specification requirements; The Pearson correlation coefficient PCC method is used to determine the optimal input parameter combination. The PCC formula is as follows: Where r is the correlation coefficient, x i and i are the two variables of the i-th sample, and are the averages of the two samples respectively; The calculated value of PCC is between -1 and 1, and the calculated value reflects the correlation between the two parameters; If PCC is greater than 0, the two parameters show a positive correlation; If PCC is less than 0, the two parameters show a negative correlation; The larger the absolute value of PCC, the higher the correlation between parameters; the smaller the absolute value of PCC, the weaker the correlation between parameters; The mean absolute error (MAE), mean root mean square error (RMSE) and determination coefficient (R) were used. 2 Performance indicators evaluate the calculation accuracy of input feature combinations: Where r i is the measured value, p i is the predicted value, is the average of the measured values, and n is the number of samples.

5. The intelligent prediction method of the shield tunnel induced stratum displacement field according to claim 4 is characterized by: In step S13, the particle swarm optimization algorithm PSO is used to optimize the weight matrix w and the threshold matrix b. The optimization steps are: S131: Determine the parameters of PSO and evaluate the fitness function of each particle; S132: Update the position and velocity of the particle to determine the optimal position; S133: Iterate the above steps S131 and S132, and when the error meets the set requirements, determine the optimal w and b; The speed and position update expressions of the particle swarm optimization algorithm are as follows: Where w is the weight factor; c1 and c2 are learning factors, ranging from [0,2]; r1 and r2 are random numbers between [0,1]; P i k is the optimal position of the i-th particle in the k-th iteration step; P g k is the optimal position of the population in the kth iteration.

6. The intelligent prediction method of the shield tunnel induced stratum displacement field according to claim 1 is characterized by: In step S3, based on the established shield tunnel stratum displacement field prediction method, the settlement trough curve law of the stratum above the tunnel, the maximum settlement value and the transmission mechanism of stratum loss with depth are studied to determine the potential instability and damage area of ​​the stratum; If the ground deformation exceeds the specification limit, a sensitivity analysis of the excavation parameters is carried out to obtain the optimal excavation parameter combination.

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