A three-dimensional ground stress adaptive synthesis optimization method for three-hole intersection in alpine valley region

Abstract

This invention provides an adaptive optimization method for the synthesis of three-dimensional geostress at the intersection of three boreholes in high-altitude valleys, belonging to the field of geotechnical engineering and engineering geological data inversion technology. Based on multi-pore two-dimensional stress data, this invention constructs a system of linear equations for three-dimensional stress synthesis and performs data quality diagnosis based on the weighted least squares benchmark solution. Depending on the risk and severity of outliers, two optimization paths are adaptively selected: particle swarm optimization combined with Huber robust loss to suppress the influence of outliers, or Levenberg-Marquardt iteration combined with piecewise regularization and physical constraint penalties to ensure numerical stability and geological rationality. This invention achieves adaptive and robust solutions for three-dimensional geostress synthesis under complex terrain conditions, providing a more reliable geostress input for the stability evaluation of underground engineering in high-altitude valleys.

Description

Technical Field

[0001] This invention relates to the interdisciplinary technical field of geotechnical engineering, engineering geology, geostress testing and data fusion inversion. Specifically, it is an adaptive synthesis optimization method for three-dimensional geostress at the intersection of three boreholes in high-altitude valleys and other complex terrain conditions. This method utilizes multi-hole two-dimensional borehole wall stress observation data to synthesize three-dimensional geostress and improves stability and reliability through robust optimization and regularization optimization. Background Technology

[0002] The initial stress field of the rock mass is a fundamental load condition that must be considered in the design and construction of underground engineering projects (such as deep-buried tunnels, underground powerhouses, mine roadways, and energy storage caverns). Especially in high mountain and valley areas, due to the strong topographic relief, deep valley incision, and significant unloading effects, coupled with regional tectonic compression, the stress field often exhibits significant non-uniformity and directional variations in three-dimensional space. Relying solely on two-dimensional or single-hole measurement information is insufficient to fully characterize the spatial distribution of the stress tensor, thus affecting the reliability of surrounding rock stability assessment, rockburst / large deformation prediction, and support parameter design.

[0003] In current engineering practice, two-dimensional borehole wall stress testing (such as borehole wall response parameters related to stress relief of hollow inclusions) has advantages such as convenient construction and relatively controllable cost. However, single-hole two-dimensional information can only provide stress projections in a limited number of directions. To obtain a three-dimensional stress state that can be used for engineering analysis, it is usually necessary to fuse two-dimensional observations from multiple boreholes, such as vertical and horizontal boreholes, to construct an inversion or synthesis model of three-dimensional stress components. A common approach is to convert the observations of each section into a linear system of equations A·x=b and solve it using the (weighted) least squares method.

[0004] However, three-dimensional synthesis methods based on the least squares criterion face two typical difficulties in complex engineering sites: First, outlier observations are unavoidable, such as errors in azimuth calibration of the measurement section, observation disturbances caused by local rock mass heterogeneity, instrument noise, or construction disturbances. Once a small number of outlier residuals exist, the squared loss will significantly amplify their impact, causing the solution results to deviate. Second, the equation system may exhibit ill-conditioned or approximately singular behavior, such as insufficient borehole azimuth combinations, highly correlated observation redundancy, or insufficient effective independent information, leading to… As the condition number increases, the least squares solution becomes extremely sensitive to noise and may even be numerically unstable.

[0005] Furthermore, existing methods often lack adaptive selection mechanisms for data quality: robust estimation should be prioritized when outliers dominate, and regularized stable solutions should be prioritized when ill-conditioned risks are prominent; if a single solver is still used, unacceptable engineering scenarios such as "good fit but unstable" or "stable but large bias" are likely to occur. Therefore, proposing a three-dimensional geostress synthesis optimization method and system that can adaptively switch between outliers and ill-conditioned risks while taking into account both robustness and stability is of significant engineering importance. Summary of the Invention

[0006] The purpose of this invention is to address the problems of outlier sensitivity and ill-conditioned instability in existing three-dimensional geostress synthesis methods in complex terrain engineering such as high mountains and valleys. This invention provides a three-dimensional pore stress synthesis method that can automatically select robust optimization or regularization optimization paths based on data quality, thereby improving the robustness, stability, and engineering usability of the solution results.

[0007] Another objective of this invention is to introduce robust estimation based on Huber piecewise loss to reduce the impact weight of outlier observations on the objective function while preserving the efficiency of solving linear equations. It also introduces Levenberg-Marquardt iteration and piecewise regularization to stabilize ill-conditioned solutions. At the same time, different prior constraints are applied to normal stress and shear stress through the regularization matrix L, and physical rationality penalties can be superimposed to suppress unreasonable principal stress sequences and extreme stress amplitudes.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] An adaptive synthesis and optimization method for three-dimensional geostress at the intersection of three boreholes in a high-altitude valley region includes the following steps:

[0010] Step S1: Acquire and preprocess two-dimensional hole wall stress data: Acquire two-dimensional hole wall stress test data of at least one vertical hole and at least one horizontal hole in the engineering area. The test data includes the stress observation values ​​SA and SB of each test segment and the corresponding azimuth information. The test data is then standardized in terms of units, angle conversion and quality verification to obtain a preprocessed standardized observation dataset.

[0011] Step S2: Construct a three-dimensional hole stress synthesis equation set: Based on the standardized observation dataset obtained in step S1, construct a linear equation set A·x=b on a segment-by-segment basis, where A is the observation coefficient matrix, and each row corresponds to an equation consisting of the observed values ​​SA, SB and azimuth angle α. A The derived coefficients of the observation equation reflect the linear mapping from "stress components to two-dimensional hole wall stress response"; x is the stress vector composed of the six stress components to be determined; b is the observation vector, derived from SA+SB and (SA−SB)cos(2α). A ), (SA−SB)sin(2α)A The observation items are composed row by row; depending on whether the measurement segment has imprint information, the corresponding number of observation equations are written, and a weight matrix W related to the observation quality is constructed.

[0012] Step S3: Benchmark Solution and Data Quality Diagnosis: Using the system of equations A·x=b and the weight matrix W constructed in step S2, the benchmark solution is obtained by weighted least squares. Then calculate the residual vector. Mean Square Error (MSE) and Ill-conditioned Indices of the Equation System And construct an outlier risk index based on the statistical distribution of the residual vector r0;

[0013] Step S4: Adaptive Path Selection: Based on the outlier risk indicators and ill-conditioned indicators obtained in Step S3 Automatically select either a robust optimization path or a regularization optimization path: when the outlier risk index exceeds the first preset threshold, proceed to the particle swarm optimization-Huber robust path in step S5; when the ill-conditioned index exceeds the second preset threshold, proceed to the LM-regularization path in step S6.

[0014] Step S5: Perform Particle Swarm Optimization - Huber Robust Path: Adaptively determine the Huber threshold δ based on the residual scale, and construct a path based on... Let be the objective function of the fitness function, where Segmented loss for Huber Let λ2 be the i-th component of the residual b−Ax corresponding to the current candidate solution x, and λ2 be the L2 regularization coefficient; use particle swarm optimization to search for the robust optimal stress solution x that minimizes the objective function. * ;

[0015] Step S6: Execute the LM-regularization path: based on the ill-conditioned indicators obtained in step S3. Determine the regularization strength in segments. Construct the cost function ,in To obtain the diagonal regularization matrix that assigns different weights to the normal stress and shear stress components, the Levenberg-Marquardt iterative method is used. A physical rationality penalty term is added to the cost function to suppress stress solutions that do not conform to geomechanical principles, thus obtaining the regularized optimal stress solution x. * ;

[0016] Step S7: Output and evaluate the three-dimensional geostress results: Output the six stress components and principal stress information corresponding to the optimal stress solution x* obtained through step S5 or step S6, calculate the final residuals and error indices, and generate a three-dimensional geostress synthesis report for engineering stability evaluation, which can be used for stability evaluation and risk analysis of underground engineering in high mountain valleys.

[0017] Furthermore, the outlier risk indicator in step S3 is: statistically analyzing the residual vector r0 that satisfies... The number of residual components, where std(r0) is the residual standard deviation and k is the preset threshold coefficient.

[0018] Furthermore, the Huber threshold in step S5 according to Determined, where c is a preset proportional coefficient.

[0019] Furthermore, the regularization strength in step S6 Based on the pathological indicators calculated in step S3 Segmentation determination: When >T1 time take 1; T2< Take at T1 time 2; when Take at T2 time 3; where T1 and T2 are preset disease severity thresholds, and T1>T2; 1. 2. 3 represents the corresponding regularization strength value, and 1> 2> 3.

[0020] Furthermore, the regularization matrix L in step S6 is a diagonal matrix. The first three diagonal elements correspond , , The last three diagonal elements correspond , , ,and > .

[0021] Furthermore, the physical rationality penalty in step S6 includes at least: failure to satisfy the principal stress ordering. 1 2 The penalty for 3, the penalty for tensile stress below the tensile stress threshold, and the penalty for the difference between the maximum and minimum principal stresses ( 1- 3) Penalty for exceeding the preset principal stress difference threshold.

[0022] An adaptive synthesis optimization system for three-dimensional geostress at the intersection of three boreholes in a high-altitude valley region includes:

[0023] The data acquisition and preprocessing module is used to acquire two-dimensional hole wall stress test data of at least one vertical hole and at least one horizontal hole within the engineering area. The test data includes stress observation values ​​SA and SB of each test segment and corresponding azimuth information. The module also performs unit unification, angle conversion and quality verification on the test data to obtain a preprocessed standardized observation dataset.

[0024] The equation system construction module is used to construct a linear equation system A·x=b based on the standardized observation dataset obtained from the data acquisition and preprocessing module, on a segment-by-segment basis. Here, A is the observation coefficient matrix, and each row corresponds to an equation consisting of the observed values ​​SA, SB, and azimuth angle α. A The derived coefficients of the observation equation reflect the linear mapping from "stress components to two-dimensional hole wall stress response"; x is the stress vector composed of the six stress components to be determined; b is the observation vector, derived from SA+SB and (SA−SB)cos(2α). A ), (SA−SB)sin(2α) A The observation items are composed row by row; depending on whether the measurement segment has imprint information, the corresponding number of observation equations are written, and a weight matrix W related to the observation quality is constructed.

[0025] The benchmark solution and diagnostic module is used to obtain the benchmark solution from the system of equations A·x=b and the weight matrix W constructed by the system of equations construction module using weighted least squares. Then calculate the residual vector. Mean Square Error (MSE) and Ill-conditioned Indices of the Equation System And construct an outlier risk index based on the statistical distribution of the residual vector r0;

[0026] The path selection module is used to solve outlier risk indicators and ill-conditioned indicators obtained from the benchmark solution and diagnosis module. The system automatically selects either the robust optimization module or the regularization optimization module: when the outlier risk index exceeds the first preset threshold, the robust optimization module is executed; when the ill-conditioned index exceeds the second preset threshold, the regularization optimization module is executed.

[0027] The robust optimization module is used to adaptively determine the Huber threshold based on the residual scale. , construct Let be the objective function of the fitness function, where Segmented loss for Huber Let λ2 be the i-th component of the residual b−Ax corresponding to the current candidate solution x, and λ2 be the L2 regularization coefficient; use particle swarm optimization to search for the robust optimal stress solution x that minimizes the objective function. * ;

[0028] The regularization optimization module is used for optimization based on ill-conditioned indicators. Determine the regularization strength in segments. Construct the cost function ,in To obtain the diagonal regularization matrix that assigns different weights to the normal stress and shear stress components, the Levenberg-Marquardt iterative method is used. A physical rationality penalty term is added to the cost function to suppress stress solutions that do not conform to geomechanical principles, thus obtaining the regularized optimal stress solution x. * ;

[0029] The results output and evaluation module is used to output the optimal stress solution x obtained by the robust optimization module or the regularization optimization module. * The corresponding six stress components and principal stress information are used to calculate the final residuals and error indices, and generate a three-dimensional geostress synthesis report for engineering stability evaluation, which can be used for stability evaluation and risk analysis of underground engineering in high mountain valleys.

[0030] Furthermore, the outlier risk indicator is: statistically analyzing the residual vector r0 that satisfies... The number of residual components, where std(r0) is the standard deviation of the residuals, and k is a preset threshold coefficient; Huber threshold according to Determined, where c is a preset proportional coefficient.

[0031] Furthermore, the regularization strength According to pathological indicators Segmentation determination:

[0032] when >T1 time take 1; T2< Take at T1 time 2; when Take at T2 time 3; where T1 and T2 are preset disease severity thresholds, and T1>T2; 1. 2. 3 represents the corresponding regularization strength value, and 1> 2> 3.

[0033] Furthermore, the regular matrix L is a diagonal matrix. The first three diagonal elements correspond , , The last three diagonal elements correspond , , ,and > .

[0034] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0035] (1) Improved robustness: When outlier observations exist, the large residual term is transformed from quadratic growth to linear growth through Huber robust loss, which significantly reduces the impact of outliers on the synthesis results and improves the anti-interference ability of three-dimensional stress component identification;

[0036] (2) Stability improvement: When the system of equations is ill-conditioned, the numerical stability is improved by piecewise regularization and LM iteration, which alleviates the problem of solution divergence or sensitivity to noise caused by excessive condition number;

[0037] (3) Adaptive and traceable: Based on outlier risk and pathological indicators, the system automatically selects the optimal path and records the parameters and path to facilitate project review and quality traceability;

[0038] (4) Strong engineering applicability: It is applicable to areas with significant spatial changes in stress field, such as high mountain valleys and deep buried caverns, and can provide more reliable three-dimensional geostress input for surrounding rock stability evaluation, rockburst risk identification and support optimization. Attached Figure Description

[0039] Figure 1 This is a schematic diagram illustrating the specific implementation process of the three-dimensional adaptive synthesis optimization method for three-dimensional geostress at the intersection of three boreholes in a high-altitude valley area according to the present invention.

[0040] Figure 2 This diagram compares the Huber loss function with the traditional squared loss function. The horizontal axis represents the standardized residuals, and the vertical axis represents the loss value. When the residuals exceed a threshold... At that time, the squared loss increases sharply in a parabolic manner, while the Huber loss turns to linear growth to reduce the impact of outliers on the weights.

[0041] Figure 3 This is a schematic diagram of the regularization matrix L in the LM algorithm. L is a 6×6 diagonal matrix, corresponding to the 6 stress components to be determined. x、 y、 z is assigned a relatively large weight of 0.8. xy、 yz、 zx is assigned a small weight of 0.3 to introduce physical prior constraints and ensure the stability of the solution.

[0042] Figure 4This is a flowchart of an embodiment of the present invention for an adaptive synthesis and optimization method of three-dimensional geostress at the intersection of three boreholes in a high mountain valley area. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0044] like Figure 1 and Figure 4 As shown, this invention provides a three-dimensional adaptive synthesis and optimization method for geostress at the intersection of three boreholes in a high-altitude valley area, comprising the following steps:

[0045] Step S1: Acquire and preprocess two-dimensional hole wall stress data: Acquire two-dimensional hole wall stress test data of at least one vertical hole and at least one horizontal hole in the engineering area. The test data includes the stress observation values ​​SA and SB of each test segment and the corresponding azimuth information. The test data is then standardized in terms of units, angle conversion and quality verification to obtain a preprocessed standardized observation dataset.

[0046] Step S2: Construct a three-dimensional hole stress synthesis equation set: Based on the standardized observation dataset obtained in step S1, construct a linear equation set A·x=b on a segment-by-segment basis, where A is the observation coefficient matrix, and each row corresponds to an equation consisting of the observed values ​​SA, SB and azimuth angle α. A The derived coefficients of the observation equation reflect the linear mapping from "stress components to two-dimensional hole wall stress response"; x is the stress vector composed of the six stress components to be determined; b is the observation vector, derived from SA+SB and (SA−SB)cos(2α). A ), (SA−SB)sin(2α) A The observation items are composed row by row; depending on whether the measurement segment has imprint information, the corresponding number of observation equations are written, and a weight matrix W related to the observation quality is constructed.

[0047] Step S3: Benchmark Solution and Data Quality Diagnosis: Using the system of equations A·x=b and the weight matrix W constructed in step S2, the benchmark solution is obtained by weighted least squares. Then calculate the residual vector. Mean Square Error (MSE) and Ill-conditioned Indices of the Equation System An outlier risk index is constructed based on the statistical distribution of the residual vector r0; wherein, the outlier risk index is: a statistical distribution of the residual vector r0 that satisfies the following conditions: The number of residual components, where std(r0) is the standard deviation of the residual, and k is a preset threshold coefficient, preferably k=2.

[0048] Step S4: Adaptive Path Selection: Based on the outlier risk indicators and ill-conditioned indicators obtained in Step S3 Automatically select either a robust optimization path or a regularization optimization path: when the outlier risk index exceeds the first preset threshold, proceed to the particle swarm optimization-Huber robust path in step S5; when the ill-conditioned index exceeds the second preset threshold, proceed to the LM-regularization path in step S6.

[0049] Step S5: Perform Particle Swarm Optimization - Huber Robust Path: Adaptively determine the Huber threshold δ based on the residual scale, and construct a path based on... Let be the objective function of the fitness function, where Segmented loss for Huber Let λ2 be the i-th component of the residual b−Ax corresponding to the current candidate solution x, and λ2 be the L2 regularization coefficient; use particle swarm optimization to search for the robust optimal stress solution x that minimizes the objective function. * Among them, Huber threshold according to It is determined that c is a preset proportionality coefficient, preferably c=1.345, and λ2 is preferably 0.001.

[0050] Step S6: Execute the LM-regularization path: based on the ill-conditioned indicators obtained in step S3. Determine the regularization strength in segments. Construct the cost function ,in To obtain the diagonal regularization matrix that assigns different weights to the normal stress and shear stress components, the Levenberg-Marquardt iterative method is used. A physical rationality penalty term is added to the cost function to suppress stress solutions that do not conform to geomechanical principles, thus obtaining the regularized optimal stress solution x. * ;

[0051] Among them, regularization strength Based on the pathological indicators calculated in step S3 Segmentation determination: When >T1 time take 1; T2< Take at T1 time 2; when Take at T2 time 3; where T1 and T2 are preset disease severity thresholds, and T1>T2; 1. 2. 3 represents the corresponding regularization strength value, and 1> 2> 3. The regular matrix L is a diagonal matrix. The first three diagonal elements correspond , , The last three diagonal elements correspond , , ,and > The preferred values ​​are T1=1000 and T2=100. 1 = 1.0 2 = 0.5 3 = 0.1. The preferred diagonal matrix L is L = diag(0.8, 0.8, 0.8, 0.3, 0.3, 0.3).

[0052] Among them, the physical rationality penalty item includes at least: failure to satisfy the principal stress ordering. 1 2 The penalty for 3, the penalty for tensile stress below the tensile stress threshold, and the penalty for the difference between the maximum and minimum principal stresses ( 1- 3) Penalty for exceeding the preset principal stress difference threshold. The tensile stress threshold is preferably −20 MPa, and the principal stress difference threshold is preferably 100 MPa.

[0053] Step S7: Output and evaluate the three-dimensional geostress results: Output the six stress components and principal stress information corresponding to the optimal stress solution x* obtained through step S5 or step S6, calculate the final residuals and error indices, and generate a three-dimensional geostress synthesis report for engineering stability evaluation, which can be used for stability evaluation and risk analysis of underground engineering in high mountain valleys.

[0054] like Figure 2 As shown, the Huber loss becomes linearly increasing after the residual exceeds a threshold δ, thus automatically reducing the weight of outlier observations; for example... Figure 3 As shown, the regularization matrix L is a 6×6 diagonal matrix, which assigns greater weight to the normal stress component and smaller weight to the shear stress component.

[0055] Example 1: Application of 3D geostress synthesis in deep underground cavern engineering in high mountain valleys. The project area features steep terrain, deep valleys, rapid changes in burial depth, and significant tectonic compression, resulting in significant spatial variations in the stress tensor. To obtain 3D stress input suitable for analyzing surrounding rock stability and rockburst risk, one vertical borehole and two horizontal boreholes were installed in the project area. Two-dimensional borehole wall stress tests were conducted on multiple sections to obtain the SA, SB, and corresponding azimuth information for each section.

[0056] (1) Perform preprocessing on the porous data according to step S1, including unifying the units and converting the azimuth from degrees to radians, and marking missing or obviously abnormal records;

[0057] (2) Construct a linear observation equation set A·x=b according to step S2 (where A and b have the same meaning as described in step S2), write three equations for the imprinted section and one equation for the non-imprinted section;

[0058] (3) Following step S3, use WLS to obtain the benchmark solution and calculate the residuals, MSE and cond(AᵀWA).

[0059] When there exists a condition in the residual that satisfies When determining the component, if an outlier risk is identified, proceed to step S5: Set =1.345·std(r0), with Huber loss as the main objective function and robust solution searched using particle swarm optimization; this solution can significantly reduce the influence of outliers on the final stress components when outliers exist.

[0060] when When the value is large, it is determined that there is a risk of ill-conditioned conditions, and proceeds to step S6: use piecewise α and diagonal regular matrix L to solve stably, and can superimpose physical penalty terms to suppress unreasonable principal stress sequence or extreme stress difference, thereby obtaining a numerically stable stress solution that is more in line with engineering priors.

[0061] (4) Output the three-dimensional stress components and principal stress information according to step S7, and provide residual index and error index for engineering verification; when the engineering adds new measuring points or updates the hole section data, steps S1-S7 can be repeated and diagnostic indexes and parameters can be recorded to form a traceable three-dimensional stress synthesis and update process.

[0062] (5) Numerical example and effect verification: Taking the three-hole six-section imprint data of this embodiment as an example (see Table 1), a total of 18 observation equations were established under the condition that the X-axis azimuth angle β0=0° in the geodetic coordinate system and equal weight. The three-dimensional stress components were solved by three strategies, namely WLS, PSO+Huber and LM+regularization, according to steps S3-S7, and the error / robustness was evaluated. The results are compared in Table 2.

[0063] Table 1 Summary of Input Observation Data for Example 1

[0064]

[0065] In this example, all six measurement segments are imprint measurement segments, and the weights are equal.

[0066] Table 2 Comparison of Output and Evaluation Metrics of the Three Algorithms

[0067]

[0068] Table 2 shows that the condition number κ(A) of the coefficient matrix in this example is 3.80e+00, indicating a non-strongly ill-conditioned condition. WLS yields an MSE of 13.639413 in a single solution. PSO+Huber, targeting the Huber loss, converges early in iteration 76, reducing the Huber loss from 6.129708 to 5.983252 (a 2.39% reduction). Residual diagnosis suggests prioritizing robust paths when there is one potential outlier; its MSE is 14.114407, demonstrating that the robustness objective and the squared error index are not entirely consistent. LM+regularization converges in iteration 8, with an MSE of 13.655020 and a Huber loss of 6.128543. The maximum horizontal principal stresses σHmax obtained by the three methods are 15.9188, 16.5294, and 15.7921 MPa, respectively, with corresponding azimuth angles of 141.474°, 139.694°, and 140.846°, which can provide three-dimensional geostress input for the stability analysis of the surrounding rock of the cavern.

[0069] This invention also provides a corresponding three-dimensional geostress adaptive synthesis optimization system for three confluences in high mountain valleys, used to execute the above method, including:

[0070] The data acquisition and preprocessing module is used to acquire two-dimensional hole wall stress test data of at least one vertical hole and at least one horizontal hole within the engineering area. The test data includes stress observation values ​​SA and SB of each test segment and corresponding azimuth information. The module also performs unit unification, angle conversion and quality verification on the test data to obtain a preprocessed standardized observation dataset.

[0071] The equation system construction module is used to construct a linear equation system A·x=b based on the standardized observation dataset obtained from the data acquisition and preprocessing module, on a segment-by-segment basis. Here, A is the observation coefficient matrix, and each row corresponds to an equation consisting of the observed values ​​SA, SB, and azimuth angle α. A The derived coefficients of the observation equation reflect the linear mapping from "stress components to two-dimensional hole wall stress response"; x is the stress vector composed of the six stress components to be determined; b is the observation vector, derived from SA+SB and (SA−SB)cos(2α). A ), (SA−SB)sin(2α) AThe observation items are composed row by row; depending on whether the measurement segment has imprint information, the corresponding number of observation equations are written, and a weight matrix W related to the observation quality is constructed.

[0072] The benchmark solution and diagnostic module is used to obtain the benchmark solution from the system of equations A·x=b and the weight matrix W constructed by the system of equations construction module using weighted least squares. Then calculate the residual vector. Mean Square Error (MSE) and Ill-conditioned Indices of the Equation System And construct an outlier risk index based on the statistical distribution of the residual vector r0;

[0073] The path selection module is used to solve outlier risk indicators and ill-conditioned indicators obtained from the benchmark solution and diagnosis module. The system automatically selects either the robust optimization module or the regularization optimization module: when the outlier risk index exceeds the first preset threshold, the robust optimization module is executed; when the ill-conditioned index exceeds the second preset threshold, the regularization optimization module is executed.

[0074] The robust optimization module is used to adaptively determine the Huber threshold based on the residual scale. , construct Let be the objective function of the fitness function, where Segmented loss for Huber Let λ2 be the i-th component of the residual b−Ax corresponding to the current candidate solution x, and λ2 be the L2 regularization coefficient; use particle swarm optimization to search for the robust optimal stress solution x that minimizes the objective function. * ;

[0075] The regularization optimization module is used for optimization based on ill-conditioned indicators. Determine the regularization strength in segments. Construct the cost function ,in To obtain the diagonal regularization matrix that assigns different weights to the normal stress and shear stress components, the Levenberg-Marquardt iterative method is used. A physical rationality penalty term is added to the cost function to suppress stress solutions that do not conform to geomechanical principles, thus obtaining the regularized optimal stress solution x. * ;

[0076] The results output and evaluation module is used to output the optimal stress solution x obtained by the robust optimization module or the regularization optimization module. * The corresponding six stress components and principal stress information are used to calculate the final residuals and error indices, and generate a three-dimensional geostress synthesis report for engineering stability evaluation, which can be used for stability evaluation and risk analysis of underground engineering in high mountain valleys.

[0077] This invention has the following features and effects:

[0078] 1. Enhanced resistance to anomalies: By introducing the Huber robust loss function, the influence of outlier residuals is transformed from quadratic growth to linear growth, which significantly reduces the interference of anomaly observations on the three-dimensional stress synthesis results and enhances the robustness of the method when there is noise or local perturbation in the data.

[0079] 2. Enhance numerical solution stability: For ill-conditioned problems of equation systems, a strategy combining piecewise adaptive regularization and Levenberg-Marquardt optimization is adopted to effectively reduce the instability and noise sensitivity caused by high condition numbers, ensuring that reliable solutions can still be obtained when information redundancy is insufficient or observations are highly correlated.

[0080] 3. Achieve path adaptation and traceability: Based on data quality diagnostic indicators, the method automatically selects robust optimization or regularization optimization paths and records the parameters and path information used, making the method adaptive and facilitating engineering review and quality traceability, thereby improving the transparency and credibility of the method.

[0081] 4. Introducing physical constraints to improve engineering rationality: By adding penalty terms for principal stress sequence, tensile stress limit and principal stress difference threshold in the cost function, the space of the constraint solution conforms to the common sense of geomechanics, avoids unreasonable stress states in engineering, and improves the engineering usability of the synthesized results.

[0082] 5. Adapting to the needs of complex terrain engineering: For areas with large topographic relief and significant stress field changes, such as high mountains and valleys, this method can effectively integrate multi-hole two-dimensional observation information to provide stable and reliable three-dimensional full stress tensor, providing key data support for the stability analysis and risk management of surrounding rock in deep-buried caverns, tunnels and other engineering projects.

[0083] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for adaptive synthesis and optimization of three-dimensional geostress at the intersection of three boreholes in a high-altitude valley region, characterized in that, Includes the following steps: Step S1: Acquire and preprocess two-dimensional hole wall stress data: Acquire two-dimensional hole wall stress test data of at least one vertical hole and at least one horizontal hole in the engineering area. The test data includes the stress observation values ​​SA and SB of each test segment and the corresponding azimuth information. The test data is then standardized in terms of units, angle conversion and quality verification to obtain a preprocessed standardized observation dataset. Step S2: Construct a three-dimensional hole stress synthesis equation set: Based on the standardized observation dataset obtained in step S1, construct a linear equation set A·x=b on a segment-by-segment basis, where A is the observation coefficient matrix, and each row corresponds to an equation consisting of the observed values ​​SA, SB and azimuth angle α. A The derived coefficients of the observation equation reflect the linear mapping from "stress components to two-dimensional hole wall stress response"; x is the stress vector composed of the six stress components to be determined; b is the observation vector, derived from SA+SB and (SA−SB)cos(2α). A ), (SA−SB)sin(2α) A The observation items are composed row by row; depending on whether the measurement segment has imprint information, the corresponding number of observation equations are written, and a weight matrix W related to the observation quality is constructed. Step S3: Benchmark Solution and Data Quality Diagnosis: Using the system of equations A·x=b and the weight matrix W constructed in step S2, the benchmark solution is obtained by weighted least squares. Then calculate the residual vector. Mean Square Error (MSE) and Ill-conditioned Indices of the Equation System And construct an outlier risk index based on the statistical distribution of the residual vector r0; Step S4: Adaptive Path Selection: Based on the outlier risk indicators and ill-conditioned indicators obtained in Step S3 Automatically select either a robust optimization path or a regularization optimization path: when the outlier risk index exceeds the first preset threshold, proceed to the particle swarm optimization-Huber robust path in step S5; when the ill-conditioned index exceeds the second preset threshold, proceed to the LM-regularization path in step S6. Step S5: Perform Particle Swarm Optimization - Huber Robust Path: Adaptively determine the Huber threshold δ based on the residual scale, and construct a path based on... Let be the objective function of the fitness function, where Segmented loss for Huber Let λ2 be the i-th component of the residual b−Ax corresponding to the current candidate solution x, and λ2 be the L2 regularization coefficient; use particle swarm optimization to search for the robust optimal stress solution x that minimizes the objective function. * ; Step S6: Execute the LM-regularization path: based on the ill-conditioned indicators obtained in step S3. Determine the regularization strength in segments. Construct the cost function ,in To obtain the diagonal regularization matrix that assigns different weights to the normal stress and shear stress components, the Levenberg-Marquardt iterative method is used. A physical rationality penalty term is added to the cost function to suppress stress solutions that do not conform to geomechanical principles, thus obtaining the regularized optimal stress solution x. * ; Step S7: Output and evaluate the three-dimensional geostress results: Output the six stress components and principal stress information corresponding to the optimal stress solution x* obtained through step S5 or step S6, calculate the final residuals and error indices, and generate a three-dimensional geostress synthesis report for engineering stability evaluation, which can be used for stability evaluation and risk analysis of underground engineering in high mountain valleys.

2. The method according to claim 1, characterized in that, The outlier risk indicator in step S3 is: statistically analyzing the residual vector r0 that satisfies... The number of residual components, where std(r0) is the residual standard deviation and k is the preset threshold coefficient.

3. The method according to claim 1, characterized in that, Huber threshold in step S5 according to Determined, where c is a preset proportional coefficient.

4. The method according to claim 1, characterized in that, Regularization intensity in step S6 Based on the pathological indicators calculated in step S3 Segmentation determination: When >T1 time take 1; T2< Take at T1 time 2; when Take at T2 time 3; where T1 and T2 are preset disease severity thresholds, and T1>T2; 1.

2. 3 represents the corresponding regularization strength value, and 1> 2>

3.

5. The method according to claim 1, characterized in that, The regularization matrix L in step S6 is a diagonal matrix. The first three diagonal elements correspond , , The last three diagonal elements correspond , , ,and > .

6. The method according to claim 1, characterized in that, The physical rationality penalty in step S6 includes at least: failure to satisfy the principal stress ordering. 1 2 The penalty for 3, the penalty for tensile stress below the tensile stress threshold, and the penalty for the difference between the maximum and minimum principal stresses ( 1- 3) Penalty for exceeding the preset principal stress difference threshold.

7. A three-dimensional adaptive synthesis optimization system for geostress at the intersection of three boreholes in a high-altitude valley region, characterized in that, include: The data acquisition and preprocessing module is used to acquire two-dimensional hole wall stress test data of at least one vertical hole and at least one horizontal hole within the engineering area. The test data includes stress observation values ​​SA and SB of each test segment and corresponding azimuth information. The module also performs unit unification, angle conversion and quality verification on the test data to obtain a preprocessed standardized observation dataset. The equation system construction module is used to construct a linear equation system A·x=b based on the standardized observation dataset obtained from the data acquisition and preprocessing module, on a segment-by-segment basis. Here, A is the observation coefficient matrix, and each row corresponds to an equation consisting of the observed values ​​SA, SB, and azimuth angle α. A The derived coefficients of the observation equation reflect the linear mapping from "stress components to two-dimensional hole wall stress response"; x is the stress vector composed of the six stress components to be determined; b is the observation vector, derived from SA+SB and (SA−SB)cos(2α). A ), (SA−SB)sin(2α) A The observation items are composed row by row; depending on whether the measurement segment has imprint information, the corresponding number of observation equations are written, and a weight matrix W related to the observation quality is constructed. The benchmark solution and diagnostic module is used to obtain the benchmark solution from the system of equations A·x=b and the weight matrix W constructed by the system of equations construction module using weighted least squares. Then calculate the residual vector. Mean Square Error (MSE) and Ill-conditioned Indices of the Equation System And construct an outlier risk index based on the statistical distribution of the residual vector r0; The path selection module is used to solve outlier risk indicators and ill-conditioned indicators obtained from the benchmark solution and diagnosis module. The system automatically selects either the robust optimization module or the regularization optimization module: when the outlier risk index exceeds the first preset threshold, the robust optimization module is executed; when the ill-conditioned index exceeds the second preset threshold, the regularization optimization module is executed. The robust optimization module is used to adaptively determine the Huber threshold based on the residual scale. , construct Let be the objective function of the fitness function, where Segmented loss for Huber Let λ2 be the i-th component of the residual b−Ax corresponding to the current candidate solution x, and λ2 be the L2 regularization coefficient; use particle swarm optimization to search for the robust optimal stress solution x that minimizes the objective function. * ; The regularization optimization module is used for optimization based on ill-conditioned indicators. Determine the regularization strength in segments. Construct the cost function ,in To obtain the diagonal regularization matrix that assigns different weights to the normal stress and shear stress components, the Levenberg-Marquardt iterative method is used. A physical rationality penalty term is added to the cost function to suppress stress solutions that do not conform to geomechanical principles, thus obtaining the regularized optimal stress solution x. * ; The results output and evaluation module is used to output the optimal stress solution x obtained by the robust optimization module or the regularization optimization module. * The corresponding six stress components and principal stress information are used to calculate the final residuals and error indices, and generate a three-dimensional geostress synthesis report for engineering stability evaluation, which can be used for stability evaluation and risk analysis of underground engineering in high mountain valleys.

8. The system according to claim 7, characterized in that, The outlier risk indicator is: statistically analyzing the residual vector r0 that satisfies... The number of residual components, where std(r0) is the standard deviation of the residuals, and k is a preset threshold coefficient; Huber threshold according to Determined, where c is a preset proportional coefficient.

9. The system according to claim 7, characterized in that, Regularization strength According to pathological indicators Segmentation determination: when >T1 time take 1; T2< Take at T1 time 2; when Take at T2 time 3; where T1 and T2 are preset disease severity thresholds, and T1>T2; 1.

2. 3 represents the corresponding regularization strength value, and 1> 2>

3.

10. The system according to claim 7, characterized in that, The regular matrix L is a diagonal matrix The first three diagonal elements correspond , , The last three diagonal elements correspond , , ,and > .

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