A method for inversion of mechanical parameters of surrounding rock of hydraulic cavern group based on PO-SVM collaborative optimization algorithm

Abstract

This invention provides a method for inverting the surrounding rock mechanical parameters of hydraulic cavern groups based on the PO-SVM collaborative optimization algorithm, relating to the field of water conservancy and hydropower engineering technology. This method combines the efficient search capability of the Parrot Optimization (PO) algorithm with the Linear Support Vector Machine (SVM), which can fully utilize the advantages of the PO algorithm in its strong global optimization capability and the efficient data learning capability of the SVM surrogate model, significantly reducing the number of global optimizations and the number of fitness evaluations of the objective function, thereby making the inversion of the surrounding rock mechanical parameters of the refined multi-grid model of hydraulic cavern groups more efficient and reliable.

Description

Technical Field

[0001] This invention relates to the field of water conservancy and hydropower engineering technology, and in particular to a method for inverting the mechanical parameters of the surrounding rock of hydraulic cavern groups based on the PO-SVM collaborative optimization algorithm. Background Technology

[0002] With the accelerated construction of the national water network, hydraulic tunnels are showing a trend towards longer distances, more complex clusters, and more integrated systems, leading to the continuous formation of larger and more functionally complex hydraulic cavern complexes. On the energy side, the installed capacity of pumped storage power stations nationwide is projected to reach 62 million kilowatts by 2025, further accelerating the construction of large-scale hydraulic cavern complexes. These trends indicate that hydraulic cavern complexes have become key engineering units for water network conveyance, basin regulation, and the operation of pumped storage power stations.

[0003] Compared to single hydraulic tunnels, hydraulic cavern complexes are larger in scale, more complex in spatial layout, and more multifunctional, making the stability of their surrounding rock more critical. Hydraulic cavern complexes often traverse various geological formations, including high-stress zones and fractured fault zones, resulting in significant heterogeneity and uncertainty in the surrounding rock. Furthermore, the interaction between multiple caverns within the complex leads to significant stress redistribution and coupling effects. Instability in the surrounding rock can easily trigger large-scale collapses, leaks, and water inrushes, directly threatening construction safety, schedule, and cost, and potentially causing systemic failure of the entire project. To ensure the safety and stability of hydraulic cavern complexes, the mechanical behavior analysis of the surrounding rock and support structures relies on advanced numerical simulation and optimization design methods. By conducting refined numerical simulations and analyses of the stability of the surrounding rock under complex geological conditions, a scientific basis is provided for the rational support design and safe operation of the cavern complex throughout its entire life cycle.

[0004] However, one of the main challenges faced by numerical simulation technology in its application is the inaccuracy of model parameters. The mechanical parameters of the sidewalls change dynamically with variations in geological conditions and the progress of construction. For example, when a construction section encounters significant changes in geological conditions or differences in lithology, the displacement and relaxation depth of the cavern sidewalls may exceed expectations. In such cases, continuing to use early mechanical parameters for analysis will lead to significant deviations between the calculated results and the actual situation, making it impossible to effectively control the mechanical behavior of the high sidewalls. To address this issue, an optimized back-analysis method based on sidewall displacement monitoring data has proven to be an effective solution. During construction, the displacement of the cavern sidewalls is continuously monitored, and these displacement changes are directly affected by the mechanical parameters. By utilizing on-site monitoring data for timely displacement back-analysis, the mechanical parameters of the cavern sidewalls can be accurately identified, thereby improving the prediction accuracy and reliability of the numerical calculation model.

[0005] With increasingly stringent engineering safety requirements, the tolerance for errors between numerical simulation results and actual engineering projects is decreasing. Traditional optimization back-analysis algorithms, such as Particle Swarm Optimization (PSO) or Genetic Algorithm (GA), are finding it increasingly difficult to meet the high efficiency and accuracy requirements of current engineering projects. Newer and more intelligent optimization algorithms, such as Zebra Optimization (ZO), have been proposed and are being used. While these algorithms offer superior performance and excellent global optimization capabilities, global optimization requires calling the numerical calculation model of underground caverns thousands or even hundreds of thousands of times. The long computation time of numerical calculations results in low inversion efficiency, making it difficult to adapt to construction and design requirements in practical applications. Summary of the Invention

[0006] To address the technical problems mentioned in the background section, it is necessary to provide a method for inverting the mechanical parameters of the surrounding rock of hydraulic cavern groups based on the PO-SVM collaborative optimization algorithm, which can improve the efficiency of inverting the mechanical parameters of the surrounding rock of hydraulic cavern groups.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for inverting the mechanical parameters of the surrounding rock of hydraulic cavern groups based on the PO-SVM collaborative optimization algorithm includes the following steps: S1. Establish a numerical model of the surrounding rock of the hydraulic cavern group: Determine the constitutive model of the surrounding rock of the hydraulic cavern group based on the geological survey report and the results of indoor and outdoor rock mechanics tests, and establish a FLAC3D numerical calculation model of the surrounding rock of the hydraulic cavern group. S2, Establish the objective function of the inversion optimization problem: Transform the parameter inversion problem into an optimization problem and establish the objective function of the inversion optimization problem; S3, Determine the optimization variables: Based on the geological conditions, select the surrounding rock mechanical parameters of the numerical model that are most significantly affected by geological conditions as the optimization variables of the objective function; S4. The PO-SVM collaborative optimization algorithm is used to search for the global optimal surrounding rock mechanical parameters of the objective function in order to obtain the optimal surrounding rock mechanical parameters. S5. The optimal parameters are then input into the FLAC3D numerical calculation model of the surrounding rock of the hydraulic cavern group. The surrounding rock mechanical parameters obtained by inversion based on the optimal parameters of the FLAC3D numerical calculation model guide the subsequent excavation and reinforcement work of the hydraulic cavern group.

[0008] Furthermore, the optimization variable includes the elastic modulus. E Poisson's ratio v .

[0009] Furthermore, the objective function of the optimization problem is: In the formula, x A set of surrounding rock mechanical parameters, di ( x ) is the first i Measured displacement at each displacement monitoring point d i ( x ), For the first i Calculated displacement of each displacement monitoring point n This represents the total number of displacement monitoring points.

[0010] Further, step S4 includes the following steps: Step A1: Set the parameters of the PO-SVM co-optimization algorithm: Determine the seed size based on the number of surrounding rock mechanical parameters to be inverted. N Set the convergence accuracy of the algorithm ξ Maximum number of optimization attempts Max Search strategy coefficient α Number of local optimizations T l Number of neighboring parrots n l ; Step A2: Population Initialization: Randomly generate a set of candidate solutions to construct the initial population. x ; Step A3: Assess the fitness of the initial population and locate the parrots with the optimal fitness. x best ; Step A4: Search for strategy coefficients α Control the random foraging, loitering, communication, or fear of strangers behavior of the parrots in the current population; Step A5-1: If an individual parrot engages in foraging behavior, its position is updated according to the following formula. : ; In the formula, Indicates the first i The current location of the parrot; t Indicates the current iteration number; This represents the average position within the current population. x best This is the best position found so far, which is the parrot position corresponding to the optimal fitness. d The dimension of the problem; Max This represents the maximum number of optimization attempts. rand A random number in the interval [0,1]; Levy ( d To describe the parrot's flight, the expression is: ; In the formula, μ, ν Normal distribution N(0,d) The generated random vector, N(0,d) For those with a mean of 0 d 3D normal distribution Gamma function, γ Levy distribution parameters (default) γ =1.5) 。

[0011] Step A5-2: If an individual parrot exhibits a lingering behavior, its position is updated according to the following formula. : ; In the formula, Ones (1, d ) is the dimension d A row vector of all 1s; Step A5-3: If an individual parrot engages in communicative behavior, the parrot's position is updated according to the following formula. : ; In the formula, Max This represents the maximum number of optimization attempts. p A random number in the interval [0,1] is used to select between two communication strategies with a threshold of 0.5.

[0012] Step A5-4: If an individual parrot exhibits fear of strangers, its position should be updated according to the following formula. : ; Step A6: Evaluate the fitness of the population after the location update and find the parrot location corresponding to the optimal fitness. x best ; Step A7: If the current number of optimizations... t Less than the number of local optimizations T l but t = t +1 and return to step A4; otherwise, T l = t+T l ; Step A8: Select the closest ones in sequence x best The number of parrots has reached the number of neighboring parrots. n l The parrot's location and fitness f ( x ) as training samples; Step A9: Set the training parameters of the SVM local proxy model, that is, set the kernel function and penalty factor of the SVM local proxy model, and train the SVM local proxy model using training samples to obtain the fitness. f ( x )exist x best Distribution of SVM approximate optimization objective function in the local neighborhood f svm ( x ); Step A10: Obtain the function f svm ( x The optimal value in the distribution f svm ( x s-best The corresponding parrot location x s-best If the function f svm ( x The optimal value in the distribution f svm ( x s-best (better than) f ( x best If so, then update x best = x s-best ; Step A11: If f ( x best )< ξ ,or T l Greater than Max If the result is positive, the optimization process ends; otherwise, return to step A4. Step A12: Output the parrot position corresponding to the optimal fitness. x best This means obtaining the optimal combination of surrounding rock mechanical parameters.

[0013] Furthermore, in step S4, the number of local optimization attempts is... T l To determine whether to perform SVM local proxy. T l With maximum number of optimization attempts Max The ratio is between 5 and 30, meaning that local proxies are performed 5 to 30 times during the optimization process.

[0014] Furthermore, in step S4, the number of neighboring parrots nl Between 30 and 100.

[0015] By adopting the above technical solution, the present invention has the following beneficial effects: The present invention provides a method for inverting the surrounding rock mechanical parameters of hydraulic cavern groups based on the PO-SVM collaborative optimization algorithm. This method combines the efficient search capability of the Parrot Optimizer (PO) algorithm with the Linear Support Vector Machine (SVM). It can fully utilize the advantages of the PO algorithm in its strong global optimization capability and the efficient data learning capability of the SVM surrogate model, significantly reducing the number of global optimizations and the number of fitness evaluations of the objective function. This makes the inversion of the surrounding rock mechanical parameters of the refined multi-grid model of hydraulic cavern groups more efficient and reliable. Attached Figure Description

[0016] Figure 1 The flowchart illustrates a preferred embodiment of the present invention for a method of inverting the mechanical parameters of the surrounding rock of a hydraulic cavern group based on the PO-SVM collaborative optimization algorithm.

[0017] Figure 2 The flowchart of the method for inverting the surrounding rock mechanical parameters of a hydraulic cavern group based on the PO-SVM collaborative optimization algorithm, which is a preferred embodiment of the present invention, is shown below.

[0018] Figure 3 This is a FLAC3D numerical calculation model diagram of an underground cavern complex in a hydroelectric power station.

[0019] Figure 4 This is a layout diagram of 10 displacement monitoring points on the cross section of the busbar tunnel of Unit 3 in the underground cavern group of a hydroelectric power station.

[0020] Figure 5 for Figure 4 The graph shows a comparison between the measured and calculated displacement values ​​at each displacement monitoring point.

[0021] Figure 6 A comparison chart of the fitness and computation time of the PO-SVM algorithm, which is a preferred embodiment of the present invention, with the PO algorithm, ZO algorithm, PSO algorithm, and GA algorithm. Detailed Implementation

[0022] Please see Figure 1 A preferred embodiment of the present invention provides a method for inverting the mechanical parameters of the surrounding rock of a hydraulic cavern group based on the PO-SVM collaborative optimization algorithm, comprising the following steps: S1. Establish a numerical model of the surrounding rock of the hydraulic cavern group: Based on the geological survey report and the results of indoor and outdoor rock mechanics tests, determine the constitutive model of the surrounding rock of the hydraulic cavern group, and establish a FLAC3D numerical calculation model of the surrounding rock of the hydraulic cavern group.

[0023] When designing and constructing hydraulic cavern complexes, determining a suitable constitutive model for the surrounding rock is a primary condition for accurate numerical calculation results. Due to the influence of multiple factors such as diagenesis, geological structure, and geostress, different rocks exhibit significantly different stress-strain relationships. To describe the deformation characteristics of rock materials as comprehensively as possible, hundreds of constitutive models have been proposed, such as elastic models, elastoplastic models, and elastoplastic-brittle-plastic models.

[0024] (1) Elastic constitutive model: This model assumes that the rock undergoes only elastic deformation during the stress process, that is, the rock can completely return to its original state after the external force is removed. This model is suitable for describing the behavior of rock when the stress is small and the yield limit has not been reached. However, the elastic model cannot describe the plastic deformation and failure behavior of rock after the elastic limit is exceeded, so its application in practical engineering is limited.

[0025] (2) Elastoplastic constitutive model: Unlike the elastic model, the elastoplastic model can describe the plastic deformation behavior of rocks after exceeding the elastic limit. When the stress on the rock exceeds its yield strength, plastic deformation will occur, and it cannot be completely restored to its initial state after unloading. This model is suitable for describing the deformation and failure behavior of rocks under large stress and can more accurately reflect the mechanical properties of the surrounding rock in actual engineering. However, the elastoplastic model is not ideal in simulating the range and depth of brittle failure of hard rock engineering media under complex geological conditions. This is because the elastoplastic model assumes that the strength parameters or deformation parameters of the rock mass do not change after yielding, and that the material is in a plastic flow state after yielding.

[0026] (3) Elastic-brittle-plastic constitutive model: To simulate the brittle failure of hard rock engineering media under complex geological conditions, two approaches are usually taken: fracture damage mechanics principles and rock mass parameter weakening. The damage tensor value of the model based on fracture damage mechanics principles is relatively difficult to determine, which is not convenient in practical applications. Another approach is to use a model that softens the strength parameters, such as the common strain hardening / softening model and the CWFS model. This type of model assumes that the rock failure process is a process of gradual decrease or loss of rock strength, which better reflects the brittle failure characteristics of rock mass under high stress conditions.

[0027] In practical applications, the basic idea of ​​constitutive models determined based on geological survey reports is to comprehensively consider the strength, type, and geostress conditions of the rock mass at its location as described in the report, and select the most suitable constitutive model.

[0028] It should be noted that the constitutive model determined based on the geological survey report is empirical. A more accurate model is obtained by combining the results of stress-strain curves and specimen failure mode analysis from indoor and outdoor physical tests. These indoor and outdoor physical tests include, but are not limited to, indoor uniaxial compression tests, indoor conventional triaxial compression tests, indoor true triaxial compression tests, Brazilian disc tests, and in-situ shear strength tests.

[0029] S2, Establish the objective function of the inversion optimization problem: Transform the parameter inversion problem into an optimization problem and establish the objective function of the inversion optimization problem.

[0030] When the mechanical behavior of the numerical constitutive model of the surrounding rock is similar to that of the actual surrounding rock, the error between the numerical calculation results and the actual displacement in the field mainly comes from the difference between the mechanical parameters of the numerical model and the actual surrounding rock. The smaller the difference in rock mechanical parameters between the two, the closer the displacement value of the numerical calculation result is to the displacement value measured in the field. Therefore, taking the squared error between the numerically calculated displacement and the measured displacement of the surrounding rock of the cavern group as the optimization objective, an optimization objective function that minimizes this error is constructed. f ( x The numerical model of surrounding rock mechanics parameters, which approximates the actual surrounding rock, is obtained using the following formula: (1); In the formula, x A set of surrounding rock mechanical parameters, d i ( x ) is the first i Measured displacement at each displacement monitoring point d i ( x ), For the first i Calculated displacement of each displacement monitoring point n This represents the total number of displacement monitoring points.

[0031] Therefore, the objective of this invention is to optimize the objective function of the problem. f ( x Minimize ), that is, minimize the squared error between the actual displacement value of the current displacement monitoring point and the displacement value calculated by FLAC3D numerically.

[0032] S3, Determine the optimization variables: Based on the geological conditions, select the surrounding rock mechanics parameters of the numerical model that are most significantly affected by geological conditions as the optimization variables of the objective function.

[0033] Specifically, the optimization variables include the elastic modulus. E Poisson's ratio vAnd the rock mechanics parameters that significantly affect displacement changes in the constitutive model. For example, the main parameters of the elastic constitutive model include elastic modulus E, Poisson's ratio v, etc.; the elastoplastic model usually uses the Mohr-Coulomb criterion to describe the yielding and failure of rocks, and its parameters include elastic modulus E, Poisson's ratio v, tensile strength σt, cohesion c, and internal friction angle ϕ, etc.; the elastoplastic-brittle-plastic model usually uses the stress softening model, and its parameters include elastic modulus E, Poisson's ratio v, tensile strength σt, internal friction angle ϕ, peak cohesion c, residual cohesion cl, and degradation curve, etc.

[0034] In this embodiment, the selection of the surrounding rock mechanical parameters most significantly affected by geological conditions as optimization variables in the numerical model is based on the following strategy: changes in geological conditions such as rock lithology, the degree of development of structural planes, and the magnitude and direction of geostress can significantly affect some rock mechanical parameters. When passing through a fracture zone from a relatively intact rock stratum, parameters such as the rock's elastic modulus E and cohesion c are significantly affected. These parameter changes directly relate to the deformation characteristics and stability of the surrounding rock, thus affecting the accuracy and reliability of the numerical simulation. Because changes in geological conditions lead to changes in rock mechanical parameters, the original rock mechanical parameters may no longer be applicable to the numerical calculation of the current cavern surrounding rock. Therefore, using these parameters significantly affected by geological conditions as optimization variables can effectively match the rock mechanical parameters in the numerical model with the actual rock mechanical parameters. By optimizing these parameters, the numerical model can more accurately reflect the actual mechanical behavior of the surrounding rock, thereby improving the accuracy and reliability of the numerical simulation.

[0035] In this embodiment, since displacement is used as the objective function, the elastic modulus E and Poisson's ratio v have a significant impact on the deformation characteristics of the rock, and other rock mechanics parameters in the constitutive model that significantly affect displacement changes should be considered as optimization variables.

[0036] S4. The PO-SVM collaborative optimization algorithm is used to search for the global optimal surrounding rock mechanical parameters of the objective function in order to obtain the optimal surrounding rock mechanical parameters.

[0037] Please see also Figure 2 The specific details of the PO-SVM collaborative optimization algorithm are as follows: (1) The PO algorithm is a novel metaheuristic optimization algorithm inspired by the behavior of trained Pyrrhura Molinae parrots. It finds the optimal solution by simulating four key behaviors of parrots: foraging, staying, communicating, and fear of strangers. This algorithm achieves a good balance between exploration and development, without explicitly distinguishing between the exploration and development phases, effectively avoiding getting trapped in local optima, and demonstrating strong global search capabilities. Its specific principle is as follows: ① Population initialization Population initialization involves constructing an initial population by randomly generating a set of candidate solutions. Each candidate solution represents a potential optimal solution and is called a "parrot." The initial positions of these parrots in the search space are randomly determined to ensure population diversity. Specifically, the position of each parrot... x i It can be generated using the following formula: (2); In the formula, ub This is the upper bound of the search space; lb This serves as the lower bound of the search space. rand A random number in the interval [0,1]; x i For the first i The parrot's initial location.

[0038] ② Parrots foraging In their natural environment, parrots typically forage in food-rich areas, improving foraging efficiency by observing food locations and utilizing group cooperation. The foraging behavior in the PO algorithm mimics this natural foraging process, updating the parrot's position using the following formula. : (3); In the formula, Indicates the first i The current location of the parrot; t Indicates the current iteration number; This represents the average position within the current population. x best This is the best location found so far. Max To maximize the number of optimization attempts ；d The dimension of the problem; Levy ( d To describe the parrot's flight, the expression is: (4); In the formula, μ, ν Normal distribution N(0,d) The generated random vector, N(0,d) For those with a mean of 0 d 3D normal distribution Gamma function γ Levy distribution parameters (default) γ =1.5) 。

[0039] ③ Parrots stay Parrots will randomly perch on a part of their owner's body, observing their surroundings and interacting with other parrots. This behavior demonstrates their sociality and adaptability to their environment. The perching behavior in the PO algorithm mimics this random perching and observation process, represented by randomly selecting a location in the search space and performing a local search. Its formula is: (5); In the formula, Ones (1, d ) is the dimension d A row vector of all 1s.

[0040] ④ Parrot communication Parrots communicate with each other through calls and body language. This communication not only helps them maintain contact within the group but also conveys important information about food sources, dangers, and others. The communication behavior in the PO algorithm mimics this inter-group communication process, promoting cooperation and information sharing among individuals by disseminating information throughout the population. Its expression is: (6); In the formula, Max This represents the maximum number of optimization attempts. p A random number in the interval [0,1] is used to select between two communication strategies with a threshold of 0.5.

[0041] ⑤ Fear of strangers Parrots exhibit a clear fear and avoidance behavior towards strangers. When encountering unfamiliar individuals, they quickly fly away and seek a safe environment. The PO algorithm mimics this fear and avoidance process towards strangers by moving away from the neighborhood of the current solution in the search space, as expressed in: (7); 2) The global optimization process of the PO algorithm is as follows: ① Set PO algorithm parameters: Determine the scale based on the number of rock mass parameters to be inverted. N Maximum number of optimization attempts M ax Search strategy coefficient α Initial parameters such as individual position boundaries; ② Population initialization: The initial population is constructed by randomly generating a set of candidate solutions. x ; ③ Assess the fitness of the population and locate the parrots with the optimal fitness. x best ; ④ By searching for strategy coefficients αControlling the random foraging, loitering, communication, or fear of strangers behavior of individual parrots within the population: ⑤ If an individual parrot engages in foraging behavior, its position is updated according to formula (3). ; ⑤ If an individual parrot stops, its position is updated according to formula (5). ; ⑤ If an individual parrot engages in communicative behavior, its position is updated according to formula (6). ; ⑤ If an individual parrot exhibits fear of strangers, its position is updated according to formula (7). ; ⑥ If the current number of optimizations t Greater than the maximum number of optimization attempts Max If , then global optimization is completed; otherwise, t = t +1 and return to step ④; ⑦ Evaluate the fitness of the population that has completed global optimization, and find the parrot position corresponding to the optimal fitness. x best And output it.

[0042] (3) The SVM (Support Vector Machines) mentioned above is a new machine learning method developed based on statistical theory, and it has no limit on dimensionality. The linearly separable SVM uses samples for training. It consists of two categories.

[0043] Assume that a classification hyperplane exists: (8); In the formula, It is a weight vector. b It is a bias term.

[0044] This ensures that the data samples are accurately divided into two categories: (9); In the formula, x i For the first i One data sample point; y i Label the sample category.

[0045] Define data sample points here. x i Spacing to the classification hyperplane for: (10); In equation (8) and b Normalize the spacing, and define the normalized spacing as the geometric spacing. : (11); In the formula, For the weight vector, for The Euclidean norm.

[0046] Define a having l Distance of each dataset to the classification hyperplane for: (12); Error classification number of data samples N Spacing between the data sample set and the classification hyperplane The relationship is as follows: (13); In the formula, , is defined as the longest value among the vectors in the sample set.

[0047] If the distance from the sample point to the classification hyperplane Then the distance between the sample points of the two types of data is Therefore, the optimal classification hyperplane makes Maximize and minimize ,Right now: (14); The above problem can be solved by finding the saddle point of the Lagrange function, that is: (15); In the formula, It is the Lagrangian function, used to combine the objective function and constraints into a "saddle point problem"; These are Lagrange multipliers (dual variables) used to introduce constraints. ; , i =1,2,…, l .

[0048] Solving the above equation using Lagrange's method, equation (14) is transformed into its dual problem, namely: (15); In the formula, Let the objective function be the dual problem. x i , xj The first i, j The input feature vector of each training sample; y i， y j The first i , j The class labels of each training sample; , The first i, j The Lagrange multipliers corresponding to each sample.

[0049] Suppose the optimal solution is The optimal solution can be found. : (16); In the formula, It is a bias term b The optimal solution; It is a weight vector The optimal solution; x r and x s It is any pair of support vectors from the two categories.

[0050] The final result is: (17); g ( x ) is the SVM discriminant function, and its sign determines the classification result.

[0051] If a few outlier samples prevent the finding of an optimal classification hyperplane, the common approach is to introduce slack variables and make corrections, i.e.: (18); In the formula, C It is a punishment factor. It is a slack variable that represents the degree to which the sample violates the interval constraint.

[0052] This can then be transformed into a dual problem, and the constraints will be converted to: (19); (4) This invention combines the Parrot Optimizer (PO) algorithm with the Linear Support Vector Machine (SVM) to form the PO-SVM collaborative optimization algorithm. The global optimization process of the PO-SVM collaborative optimization algorithm is as follows: Step A1: Set the parameters of the PO-SVM collaborative optimization algorithm: Determine the scale based on the number of rock mass parameters to be inverted. NSet the convergence accuracy of the algorithm ξ Maximum number of optimization attempts Max Search strategy coefficient α Number of local optimizations T l Number of neighboring parrots n l ; Step A2: Population Initialization: Randomly generate a set of candidate solutions to construct the initial population. x ; Step A3: Assess the fitness of the initial population and locate the parrots with the optimal fitness. x best ; Step A4: Search for strategy coefficients α Control the random foraging, loitering, communication, or fear of strangers behavior of the parrots in the current population; Step A5-1: If an individual parrot engages in foraging behavior, the parrot updates its position according to formula (3). ; Step A5-2: If an individual parrot exhibits a lingering behavior, its position is updated according to formula (5). ; Step A5-3: If an individual parrot engages in communicative behavior, the parrot updates its position according to formula (6). ; Step A5-4: If an individual parrot exhibits fear of strangers, the parrot's position is updated according to formula (7). ; Step A6: Evaluate the fitness of the population after the location update and find the parrot location corresponding to the optimal fitness. x best ; Step A7: If the current number of optimizations... t Less than the number of local optimizations T l but t = t +1 and return to step A4; otherwise, T l = t+T l ; Step A8: Select the closest ones in sequence x best The number of parrots has reached the number of neighboring parrots. n l The parrot's location and fitness f ( x As training samples, fitness f ( x) represents the objective function value; Step A9: Set the training parameters of the SVM local proxy model, that is, set the kernel function and penalty factor of the SVM local proxy model, and train the SVM local proxy model using training samples to obtain the fitness. f ( x )exist x best Distribution of SVM approximate optimization objective function in the local neighborhood f svm ( x ); Step A10: Obtain the function f svm ( x The optimal value in the distribution f svm ( x s-best ) corresponding x s-best If the function f svm ( x The optimal value in the distribution f svm ( x s-best (better than) f ( x best If so, then update x best = x s-best ; Step A11: If f ( x best )<ξ, or T l Greater than Max If the result is positive, the optimization process ends; otherwise, return to step A4. Step A12: Output the parrot position corresponding to the optimal fitness. x best ; In this embodiment, the PO-SVM collaborative optimization algorithm reduces the number of local optimization attempts. T l To determine whether to perform SVM local proxy. T l With maximum number of optimization attempts Max The ratio should be between 5 and 30, that is, 5 to 30 local proxies should be performed during the optimization process.

[0053] In this embodiment, the performance of the local agent is affected by the quality and quantity of training samples, while the number of neighboring parrots... n lIt controls the quantity and quality of training samples. n l Too small a sample size will result in insufficient sample size. n l An excessively large number of neighboring parrots can lead to a decrease in the quality of the neighboring parrots. To ensure the local proxy performance of SVM, the number of neighboring parrots should be limited. n l The ideal value is between 30 and 100.

[0054] S5. The optimal parameters are then input into the FLAC3D numerical calculation model of the surrounding rock of the hydraulic cavern group. The surrounding rock mechanical parameters obtained by inversion based on the optimal parameters of the FLAC3D numerical calculation model guide the subsequent excavation and reinforcement work of the hydraulic cavern group.

[0055] The following specific embodiments illustrate the method for inverting the surrounding rock mechanical parameters of hydraulic cavern groups based on the PO-SVM collaborative optimization algorithm of the present invention.

[0056] Example 1 To understand the performance of the PO-SVM collaborative optimization algorithm, Example 1 compares the proposed PO-SVM algorithm with the Zebra Algorithm (ZO), Particle Swarm Optimization (PSO), and Genetic Algorithm (GA) based on single-peak and multi-peak benchmark functions. For all algorithms, the maximum number of iterations is 30,000, and the number of specified operators is 30.

[0057] The benchmark function based on a single peak is: (20); The operator search range is [-100, 100]. f min The value is 0, this time f best Let's set it to 1E-4. The single-peaked test function has only one optimum. After the algorithm completes the maximum number of iterations, all comparison algorithms reach... f best The number of iterations is used to evaluate the convergence and exploratory capabilities of the algorithm.

[0058] The benchmark function based on multiple peaks is: (twenty one); The operator search range is [-32, 32]. f 2( x The smaller the better. f min The value is 0. The multi-peaked test function has multiple optimal values, but only one global optimum; the rest are local optima. After the algorithm completes its maximum number of iterations, the optimal values ​​reached by the algorithm are compared. ，To evaluate the algorithm's ability to move from exploring local optima to reaching the global optimum.

[0059] Other parameters of the algorithms compared in this study are shown in Table 1. The specific steps of the optimization implementation process of the PO-SVM collaborative optimization algorithm are detailed in [link to table]. Figure 2 .

[0060]

[0061] The algorithms used in this comparison are shown in Table 2, which compare the number of typical function calls.

[0062]

[0063] As shown in Table 2, the computational cost of the PO-SVM algorithm is lower than that of the PO, ZO, PSO, and GA algorithms, while its global optimization capability is stronger, indicating that the PO-SVM collaborative optimization algorithm has significant advantages in typical test functions.

[0064] Example 2 Example 2 is an underground powerhouse cavern complex in a certain project, consisting of main and auxiliary powerhouses, a main transformer room, and a tailrace surge chamber. The dimensions of the main and auxiliary powerhouse caverns are 178m × 24.5m × 55.8m (length × width × height), the main transformer room cavern dimensions are 182.5m × 20m × 23m (length × width × height), the tailrace gate cavern dimensions are 182.5m × 20m × 23m (length × width × height), and the busbar cavern dimensions are 40m × 9.8m × 9.2m (length × width × height). The strata are homogeneous lithology, and the rocks exhibit obvious "elastic-brittle-plastic" rock mechanical properties. Based on the initial geostress field obtained from back-analysis of the exploration data, the maximum principal stress... σ 1 is approximately 11~14 MPa.

[0065] Figure 2 A flowchart illustrating a method for inverting the surrounding rock mechanical parameters of a hydraulic cavern group based on the PO-SVM collaborative optimization algorithm, provided in this embodiment of the invention, is as follows: Step S1: Establish a numerical model of the surrounding rock of the hydraulic tunnel complex. This embodiment constructs a FLAC3D numerical calculation model of the surrounding rock of the hydraulic tunnel complex based on the geological survey report and design data. The calculation area of ​​the tunnel complex calculation model is a rectangular area of ​​300m × 250m × 150m (length × width × height). To ensure calculation accuracy, the mesh of the powerhouse excavation body and its surrounding area is refined, with a total of 553,628 elements, belonging to a multi-mesh model. The model is as follows... Figure 3 As shown, the rocks in the plant area exhibit obvious "elastic-brittle-plastic" rock mechanical properties, therefore, the elastic-brittle-plastic constitutive model based on the stress softening model is adopted.

[0066] Step S2: Establish the objective function for the inversion optimization problem. Taking the squared error between the numerically calculated displacement and the field measured displacement of the surrounding rock of the cavern group as the optimization objective, construct the optimization objective function that minimizes the error. According to the specific instructions in step S3 and formula (1), add the optimization objective function command flow to the FLAC3D numerical calculation script.

[0067] Specifically, in Example 2, 10 actual monitoring points were selected, and the locations of the monitoring points are as follows: Figure 4 As shown in Table 3, the actual displacements at the monitoring points are as follows. Using the squared error between the numerically calculated displacement and the actual measured displacement at these 10 monitoring points as the optimization objective, a minimized objective function is constructed.

[0068]

[0069] Step S3: Determine the optimization variables. Example 2, based on the changes in the excavation location and the deformation and failure characteristics of the rock mass, sequentially selects the rock mechanics parameters with the most significant changes, i.e., the surrounding rock mechanics parameters of the numerical model most significantly affected by geological conditions, as the optimization variables. An elastic-brittle-plastic constitutive model using a stress softening model is employed, with the deformation modulus being the rock mass mechanics parameter of the sidewall to be inversely analyzed. E Poisson's ratio v Peak cohesion c Residual cohesion c’ and the angle of friction φ The parameter search range is shown in Table 4.

[0070]

[0071] Step S4: Use the PO-SVM collaborative optimization algorithm to search for the global optimal rock mechanics parameters of the surrounding rock.

[0072] Specifically, Example 2 determines the scale based on the number of rock mass parameters to be inverted. N = 12, sets the convergence precision of the algorithm. ξ =5‰, maximum number of optimization attempts Max = 50, search strategy coefficient α =1:1:1:1, Number of local optimization attempts T l = 10. Number of territorial parrots n l = 40, kernel function is SVR and penalty factor C= 100; Next, global optimization is performed according to the specific steps of the PO-SVM collaborative optimization algorithm in step S4.

[0073] Specifically, Example 2 describes the method for fitness assessment of individual parrots in a population: The free software Python and the commercial numerical computation software FLAC3D are used for joint inversion. In the Python environment, the individual's position coordinates (a set of surrounding rock mechanical parameters) from the PO-SVM co-optimization algorithm are saved to data interface file A. A custom script is used to call commands to start the FLAC3D numerical computation software and enter working mode. The built-in user subroutine of FLAC3D is then called to read the set of surrounding rock mechanical parameters from data interface file A, which are substituted into the established FLAC3D numerical model to obtain the calculated displacement, and thus the objective function value. The objective function value is then saved to data file B, and the Python program reads the objective function value from file B to obtain the fitness value of the individual.

[0074] In comparison, the ZO algorithm, PSO algorithm, and GA algorithm were used in the global optimal parameter search in Example 2. (Algorithm population size) N =12, the objective function is the same, and the other algorithm parameters are shown in Table 5.

[0075]

[0076] Specifically, the search for the globally optimal surrounding rock mechanical parameters based on the PO-SVM collaborative optimization algorithm was completed, and the results of the optimal numerical model parameters are shown in Table 6. A comparison of the measured and calculated displacement values ​​at each monitoring point using the optimal numerical model parameters is shown in Table 7. Figure 5 The measured displacement values ​​of the surrounding rock corresponding to the measuring points obtained using the method of this invention are close to the calculated displacements (the maximum squared error is only 1.6 × 10⁻⁶). -3 The fitness is 3.45 × 10⁻⁶. -3 The fitness and computation time comparison with the other four algorithms are shown in Table 8 and [Table 8 is missing from the original text]. Figure 6 .

[0077]

[0078] As can be seen from Table 8, the PO-SVM collaborative optimization algorithm is more efficient and faster in obtaining the values ​​of the mechanical parameters of the surrounding rock of the cavern group than the PO algorithm without using a surrogate model, as well as the ZO algorithm, PSO algorithm, and GA algorithm, further demonstrating the superiority of the PO-SVM collaborative optimization algorithm.

[0079] Step S5: Input the optimal parameters into the FLAC3D numerical calculation model of the surrounding rock of the hydraulic cavern group. The surrounding rock mechanical parameters obtained by inverting the FLAC3D numerical calculation model based on the optimal parameters guide the subsequent excavation and reinforcement work of the hydraulic cavern group.

[0080] Specifically, the optimal model surrounding rock mechanical parameters are substituted into the FLAC3D numerical model of the underground powerhouse to conduct numerical simulation of the next phase of excavation of the burr hole and support. The stress and displacement data after excavation are obtained, the reinforcement effect of the designed support on the surrounding rock is analyzed, and the support scheme is further improved to achieve better results.

[0081] This invention combines the PO global optimization algorithm with the SVM surrogate model, fully leveraging the PO algorithm's strong global optimization capability. Simultaneously, by utilizing SVM to learn the search space of the parrot population, the number of numerical reanalysis operations during the inversion process can be significantly reduced, allowing for faster convergence and further improving inversion accuracy. Compared to the PO algorithm without a surrogate model and other traditional inversion methods—Zebra Oscillator (ZO), Particle Swarm Optimization (PSO), and Genetic Algorithm (GA)—this method can more efficiently and quickly obtain reasonable values ​​for surrounding rock mechanical parameters in the simulation calculation of hydraulic cavern groups. This effectively solves the problem that displacement-based inversion techniques, due to their long computation time, cannot be applied to the inversion of surrounding rock mechanical parameters in multi-grid models of hydraulic cavern groups with higher computational accuracy.

[0082] The above description is a detailed description of the preferred embodiments of the present invention. However, the embodiments are not intended to limit the scope of the patent application of the present invention. All equivalent changes or modifications made under the technical spirit of the present invention should fall within the patent scope covered by the present invention.

Claims

1. A method for inverting the mechanical parameters of surrounding rock in hydraulic cavern groups based on the PO-SVM collaborative optimization algorithm, characterized in that, Includes the following steps: S1. Establish a numerical model of the surrounding rock of the hydraulic cavern group: Based on the geological survey report and the results of indoor and outdoor rock mechanics tests, determine the constitutive model of the surrounding rock of the hydraulic cavern group and establish a FLAC3D numerical calculation model of the surrounding rock of the hydraulic cavern group. S2, Establish the objective function of the inversion optimization problem: Transform the parameter inversion problem into an optimization problem and establish the objective function of the inversion optimization problem; S3, Determine the optimization variables: Based on the geological conditions, select the surrounding rock mechanical parameters of the numerical model that are most significantly affected by geological conditions as the optimization variables of the objective function; S4. The PO-SVM collaborative optimization algorithm is used to search for the global optimal surrounding rock mechanical parameters of the objective function in order to obtain the optimal surrounding rock mechanical parameters. S5. The optimal parameters are then input into the FLAC3D numerical calculation model of the surrounding rock of the hydraulic cavern group. The surrounding rock mechanical parameters obtained by inversion based on the optimal parameters of the FLAC3D numerical calculation model guide the subsequent excavation and reinforcement work of the hydraulic cavern group.

2. The method for inverting the surrounding rock mechanical parameters of hydraulic cavern groups based on the PO-SVM collaborative optimization algorithm as described in claim 1, characterized in that, The optimization variables include the elastic modulus. E Poisson's ratio v .

3. The method for inverting the surrounding rock mechanical parameters of hydraulic cavern groups based on the PO-SVM collaborative optimization algorithm as described in claim 1, characterized in that, The objective function of the optimization problem is In the formula, x A set of surrounding rock mechanical parameters, d i ( x ) is the first i Measured displacement at each displacement monitoring point d i ( x ), For the first i Calculated displacement of each displacement monitoring point n This represents the total number of displacement monitoring points.

4. The method for inverting the surrounding rock mechanical parameters of hydraulic cavern groups based on the PO-SVM collaborative optimization algorithm as described in claim 2, characterized in that, Step S4 includes the following steps: Step A1: Set the parameters of the PO-SVM co-optimization algorithm: Determine the seed size based on the number of surrounding rock mechanical parameters to be inverted. N Set the convergence accuracy of the algorithm ξ Maximum number of optimization attempts Max Search strategy coefficient α Number of local optimizations T l Number of neighboring parrots n l ; Step A2: Population Initialization: Randomly generate a set of candidate solutions to construct the initial population. x ; Step A3: Assess the fitness of the initial population and locate the parrots with the optimal fitness. x best ; Step A4: Search for strategy coefficients α Control the random foraging, loitering, communication, or fear of strangers behavior of the parrots in the current population; Step A5-1: If an individual parrot engages in foraging behavior, its position is updated according to the following formula. : ； In the formula, Indicates the first i The current location of the parrot; t Indicates the current iteration number; This represents the average position within the current population. x best This is the best position found so far, which is the parrot position corresponding to the optimal fitness. d The dimension of the problem; Max This represents the maximum number of optimization attempts. rand A random number in the interval [0,1]; Levy ( d To describe the parrot's flight, the expression is: ； In the formula, μ, ν Normal distribution N(0,d) The generated random vector, N(0,d) For those with a mean of 0 d 3D normal distribution Gamma function, γ Levy distribution parameters (default) γ =1.5); Step A5-2: If an individual parrot exhibits a lingering behavior, its position is updated according to the following formula. : ； In the formula, Ones (1, d ) is the dimension d A row vector of all 1s; Step A5-3: If an individual parrot engages in communicative behavior, the parrot's position is updated according to the following formula. : ； In the formula, Max This represents the maximum number of optimization attempts. p A random number in the interval [0,1] is used to select between two communication strategies with a threshold of 0.5; Step A5-4: If an individual parrot exhibits fear of strangers, its position should be updated according to the following formula. : ； Step A6: Evaluate the fitness of the population after the location update and find the parrot location corresponding to the optimal fitness. x best ; Step A7: If the current number of optimizations... t Less than the number of local optimizations T l but t = t +1 and return to step A4; otherwise, T l = t+ T l ; Step A8: Select the closest ones in sequence x best The number of parrots has reached the number of neighboring parrots. n l The parrot's location and fitness f ( x ) as training samples; Step A9: Set the training parameters of the SVM local proxy model, that is, set the kernel function and penalty factor of the SVM local proxy model, and train the SVM local proxy model using training samples to obtain the fitness. f ( x )exist x best Distribution of SVM approximate optimization objective function in the local neighborhood f svm ( x ); Step A10: Obtain the function f svm ( x The optimal value in the distribution f svm ( x s-best The corresponding parrot location x s-best If the function f svm ( x The optimal value in the distribution f svm ( x s-best (better than) f ( x best If so, then update. x best = x s-best ; Step A11: If f ( x best )< ξ ,or T l Greater than Max If the result is positive, the optimization process ends; otherwise, return to step A4. Step A12: Output the parrot position corresponding to the optimal fitness. x best This means obtaining the optimal combination of surrounding rock mechanical parameters.

5. The method for inverting the surrounding rock mechanical parameters of hydraulic cavern groups based on the PO-SVM collaborative optimization algorithm as described in claim 4, characterized in that, In step S4, the number of local optimization attempts is... T l To determine whether to perform SVM local proxy, T l With maximum number of optimization attempts Max The ratio is between 5 and 30, meaning that local proxies are performed 5 to 30 times during the optimization process.

6. The method for inverting the surrounding rock mechanical parameters of hydraulic cavern groups based on the PO-SVM collaborative optimization algorithm as described in claim 4, characterized in that, In step S4, the number of neighboring parrots n l Between 30 and 100.

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