Hydraulic tunnel surrounding rock mechanical parameter inversion method based on FGO-CB collaborative optimization algorithm

Abstract

The invention provides a hydraulic tunnel surrounding rock mechanical parameter inversion method based on an FGO-CB collaborative optimization algorithm, and relates to the technical field of hydraulic and hydro-power engineering, the method combines an FGO global optimization algorithm with a CB local agent model, gives full play to the super-strong exploration capability of the FGO algorithm in the aspect of global optimization, and improves the performance of the FGO-CB collaborative optimization algorithm. And meanwhile, by utilizing the excellent prediction regression analysis capability of the CB model on the search space of the hypha population, the calling times of the refined numerical model in the inversion process are remarkably reduced, the convergence condition is quickly achieved, and the inversion precision is further improved.

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 surrounding rock in hydraulic tunnels based on the FGO-CB collaborative optimization algorithm. Background Technology

[0002] With the systematic advancement and continuous investment in the national water network strategy, the construction of hydraulic tunnels in China's water conservancy and hydropower projects has entered a high-intensity, network-based stage. Major water network projects, such as the South-to-North Water Diversion Project (Middle Route), the Yangtze River-to-Huai River Water Diversion Project, and the Guangdong Water Resources Allocation Project around the Beibu Gulf, are being implemented continuously. The national water network has formed a comprehensive system based on natural rivers and lakes, with water diversion and drainage projects as channels, water storage projects as nodes, and intelligent regulation as a means, integrating optimized water resource allocation, basin flood control and disaster reduction, and water ecological protection. Within this system, a large number of hydraulic tunnels have been planned, designed, and constructed to connect water networks at various levels and to link water source areas with water user areas. These hydraulic tunnels have become the core infrastructure ensuring the "skeleton" implementation of the water network's functions.

[0003] The stability of the surrounding rock in hydraulic tunnels is a core issue for ensuring the smooth implementation of water network construction. In recent years, the scale of hydraulic tunnels in water network projects has significantly expanded, and the length of individual tunnels has generally increased, leading to more complex geological environments. Long-distance tunneling requires traversing various geological strata combinations, with frequent alternations of high-stress zones, fracture zones, karst, and water-rich, unfavorable sections. The mechanical properties of the surrounding rock exhibit significant heterogeneity and uncertainty, significantly increasing the difficulty of analyzing its mechanical behavior. Especially under the coupled conditions of long tunnels and complex geology, once the surrounding rock becomes unstable, it can easily trigger risks such as collapses, seepage, and sudden water and mud inrushes, thereby affecting construction safety, schedule, and construction costs. Therefore, in-depth characterization and accurate understanding of the stress mechanism of the surrounding rock have become a key prerequisite for ensuring the safety and stability of tunnel groups; and achieving this goal currently mainly relies on advanced numerical simulation and optimization design methods.

[0004] However, a major challenge in applying numerical simulation technology is the "parameter inaccuracy" of the numerical simulation model. The mechanical parameters of the surrounding rock change dynamically with the geological conditions along the tunnel route. For example, if the geological conditions of a section of the tunnel undergo significant changes, the mechanical parameters of the surrounding rock may change significantly, causing the displacement results of the numerical simulation using earlier mechanical parameters to differ beyond the range from the actual monitored deformation of the surrounding rock. This leads to numerical simulation distortion and an inability to effectively simulate the mechanical behavior of the surrounding rock in the existing tunnel section. To address this issue, an optimized back-analysis method based on sidewall displacement monitoring data has been proven to be an effective strategy. During the construction phase, the displacement of the tunnel sidewalls is monitored in real time, and these displacement changes are closely related to the mechanical parameters. By using on-site monitoring data to quickly conduct displacement back-analysis, the mechanical parameters of the tunnel sidewalls can be accurately determined, thereby improving the prediction accuracy and reliability of the numerical calculation model.

[0005] The continuous improvement of engineering safety standards has placed more stringent demands on the accuracy of optimization back analysis based on numerical simulation models. In practical engineering applications, the error tolerance for simulation results has tightened by orders of magnitude. Traditional optimization inversion algorithms (such as particle swarm optimization and genetic algorithms) are no longer sufficient to meet the computational accuracy requirements of modern engineering. Against this backdrop, a new generation of intelligent optimization algorithms has emerged, with the Bat Optimization Algorithm (BO algorithm) being a typical example. These improved algorithms have significant advantages in global optimization capabilities. However, as the mesh of numerical simulation models becomes increasingly fine, the numerical computation time increases dramatically. Taking a fine-grained hydraulic tunnel project as an example, a single numerical simulation typically takes tens of minutes to several hours. Completing the parameter inversion of such a fine model often requires tens of thousands of model calculations. This level of computational load not only significantly extends the inversion cycle but also creates a prominent contradiction with the real-time feedback requirements of the engineering site, severely restricting the practical application value of advanced algorithms in dynamic optimization design for construction. Summary of the Invention

[0006] To address the technical problems raised in the background section, it is necessary to provide a method for inverting the surrounding rock mechanical parameters of hydraulic tunnels based on the FGO-CB collaborative optimization algorithm, so as to achieve accurate estimation of the surrounding rock mechanical parameters of the current excavation section of the tunnel and improve the efficiency of the algorithm inversion.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A method for inverting the mechanical parameters of surrounding rock in hydraulic tunnels based on the FGO-CB collaborative optimization algorithm includes the following steps:

[0009] S1. Establish a numerical calculation model for the surrounding rock of the hydraulic tunnel: Based on the design drawings of the hydraulic tunnel, a detailed model of the hydraulic tunnel and its surrounding rock is carried out, and an elastoplastic constitutive model conforming to the Hawke-Brown failure criterion is used to establish a numerical calculation model for the surrounding rock of the hydraulic tunnel.

[0010] S2, Determine the optimization variables: Use the rock mechanics parameters of the elastoplastic constitutive model that conforms to the Hawke-Brown failure criterion as the optimization variables;

[0011] S3, Establish the objective function for minimizing displacement error: Use the residual between the displacement calculation value of the numerical calculation model and the measured displacement value in the engineering as the objective function;

[0012] S4. The FGO-CB collaborative optimization algorithm is used to perform global optimization of the objective function in the parameter space, thereby obtaining the optimal rock mechanics parameters;

[0013] S5, the optimal rock mechanics parameters are input into the numerical calculation model of the surrounding rock of the hydraulic tunnel, and the support optimization and surrounding rock deformation management are carried out based on the rock mechanics parameters obtained by inversion from the numerical calculation model of the surrounding rock of the hydraulic tunnel with the optimal rock mechanics parameters.

[0014] Further, in step S2, the objective function is:

[0015] ;

[0016] In the formula, i is the i-th displacement measuring point, X is the combination of optimized variables obtained by the optimization algorithm, that is, the optimal value of the rock mechanics parameters of the model; n is the number of displacement measuring points; This is a numerical model to calculate the displacement value of the i-th displacement measuring point of the surrounding rock in the current tunnel excavation section by inputting operator X; This represents the measured displacement value of the i-th displacement measuring point in the current tunnel excavation section.

[0017] The purpose of global optimization in the parameter space in step S3 is to minimize the objective function f(X), that is, to minimize the average error between the numerical model displacement calculation value and the measured displacement value of the surrounding rock displacement measuring point in the current tunnel excavation section.

[0018] Furthermore, the optimization variables include the elastic modulus E, Poisson's ratio v, and the empirical parameter m of the Hoek-Brown criterion. b s, a and the uniaxial compressive strength σ of rock ci The rock mass rating system RMR and the rock mass integrity coefficient K are used as the basis for the evaluation. v Replace the empirical rock mass parameter m as an optimization variable to be considered. b,s,a; where the rock mass rating system RMR is determined by comprehensively evaluating the rock mass quality indicators based on five factors: uniaxial compressive strength of the rock block, RQD value of the rock core, joint spacing, joint conditions, and the effect of groundwater.

[0019] Furthermore, step S3 includes the following steps:

[0020] Step A1: Set the parameters of the FGO-CB co-optimization algorithm: Determine the seed size N based on the number of rock mass parameters to be inverted, and set the convergence accuracy ε of the algorithm to solve for the exploration rate E. r Exploration and attraction weight Maximum number of optimization attempts t max Number of times the local proxy is entered (t) CB and the number of training samples, m;

[0021] Step A2: Population initialization: Randomly initialize N mycelial populations;

[0022] Step A3: Obtain the nutritional status of all mycelial locations by solving the objective function. With optimal mycelium ;

[0023] Step A4: The mycelial population is controlled by random numbers r1 and r2, where r1 and r2 are random numbers between 0 and 1. If r1 > r2, the mycelial population exhibits mycelial tip growth behavior; otherwise, it exhibits mycelial branching and spore germination behavior.

[0024] Step A5: If the mycelial population exhibits hyphal tip growth behavior, then:

[0025] The mycelia in the mycelial population were compared by nutritional status P i With exploration rate E r To distinguish whether it has entered the growth exploration or growth attraction phase: if the hyphae P i > E r If so, the mycelium will explore its growth and update its growth location according to the following formula;

[0026] ;

[0027] In the formula, This represents the growth position of the i-th hyphae after renewal. represents the current growth position of the i-th hyphae; E represents the growth rate of the hyphae. This indicates the direction of mycelial growth.

[0028] Conversely, P i ≦ The mycelium enters the growth attraction phase, and its growth location is updated according to the following formula:

[0029] ;

[0030] In the formula, A random number between 0 and 1; The mycelium is attracted to the most nutrient-rich hyphae, causing it to change its growth direction. Environmental impact parameters;

[0031] If the mycelial population exhibits hyphal branching and spore germination behavior, then:

[0032] The mycelial individuals in the mycelial population are controlled by a generated random number r8 to perform mycelial branching or spore germination. r8 is a random number between 0 and 1. When r8 > 0.5, the mycelium branches and grows, and the growth position is updated according to the following formula.

[0033] ;

[0034] In the formula, This refers to the location of the renewed hyphae during the hyphal branching stage. E represents the current position of a hypha in the hyphal branching stage. L For branch growth rate, and These represent the growth directions influenced by individual mycelia and mycelia in the most nutrient-rich areas, respectively, with r9 being a random number between 0 and 1.

[0035] Conversely, when r8≦0.5, the mycelium germinates spores and updates its growth position according to the following formula;

[0036] ;

[0037] In the formula, For the new location of the updated spores, This is the current location of the spore; A random value that is either -1 or 1. The direction of growth of new spores; r 10 A random value between 0 and 1; E is the mycelial growth rate; The dimension of the representative problem;

[0038] Step A6: Compare the nutritional status of the current location of the mycelium with that of its growth location, i.e., compare the objective function values ​​corresponding to the current location and the growth location. If > Then the mycelium grows to Conversely, mycelium does not grow. ;

[0039] Step A7: If i is not less than N, then all mycelial individuals in the mycelial population have completed the growth position update; otherwise, i = i + 1, and return to step A5.

[0040] Step A8: If the current number of optimization attempts t is less than the number of times the local proxy is entered t CB If t = t + 1, then return to step A4; otherwise, t CB =t+ t CB ;

[0041] Step A9: Select m closest values ​​in sequence The mycelial growth locations are selected, along with the corresponding nutritional information for each of the m selected mycelial growth locations. As training samples;

[0042] Step A10: Set the training parameters of the CB local proxy model and train the CB local proxy model using training samples to obtain the fitness. exist Distribution of the CB approximate optimization objective function in the local neighborhood ;

[0043] Step A11: Obtain the function optimal value in the distribution corresponding , Let the hyphal position be the optimal value predicted by the CB local surrogate model, if the function optimal value in the distribution Superior Then update = ;

[0044] Step A12: If < ε, or t greater than t max If the result is positive, the optimization ends; otherwise, t = t + 1 and return to step A4.

[0045] Step A13: Output the current globally optimal mycelial position. Current global optimal hyphal position These are the optimal rock mechanics parameters.

[0046] Furthermore, t CB With the maximum number of optimization attempts t max The ratio is between 10 and 40, meaning that local proxies are performed 10 to 40 times during the optimization process.

[0047] Furthermore, the number of training samples m is between 50 and 100.

[0048] By adopting the above technical solution, the present invention has the following beneficial effects:

[0049] This invention combines the FGO global optimization algorithm with the CB local proxy model, fully leveraging the FGO algorithm's superior exploration capabilities in global optimization while utilizing the CB model's excellent predictive regression analysis capabilities for the mycelial community search space. This significantly reduces the number of calls to the refined numerical model during the inversion process, quickly reaching convergence conditions and further improving inversion accuracy. Compared to the FGO algorithm without a proxy model and other traditional inversion methods—Bat Optimization (BO), Ant Colony Optimization (ACO), and Differential Evolution (DE) algorithms—this method can more efficiently and quickly obtain the combination of surrounding rock mechanical parameters from the refined numerical simulation model of hydraulic tunnels. This effectively solves the engineering problem of being unable to apply displacement optimization inversion analysis technology to the dynamic feedback construction of hydraulic tunnels due to excessive calls to the refined model resulting in long computation times. Attached Figure Description

[0050] Figure 1 The flowchart illustrates a preferred embodiment of the present invention for the inversion method of mechanical parameters of surrounding rock in hydraulic tunnels based on the FGO-CB collaborative optimization algorithm.

[0051] Figure 2 The flowchart illustrates the process of using the FGO-CB collaborative optimization algorithm to perform global parameter space optimization on the objective function in the hydraulic tunnel surrounding rock mechanical parameter inversion method based on the FGO-CB collaborative optimization algorithm, which is a preferred embodiment of the present invention.

[0052] Figure 3 This invention provides a refined model of a hydraulic tunnel established using the FGO-CB collaborative optimization algorithm-based method for inverting the mechanical parameters of the surrounding rock of a hydraulic tunnel according to a preferred embodiment of the present invention.

[0053] Figure 4 The distribution map of the six measured monitoring points selected for Example 2 using the inversion method of hydraulic tunnel surrounding rock mechanical parameters based on the FGO-CB collaborative optimization algorithm of the preferred embodiment of the present invention.

[0054] Figure 5 This is a comparison chart of the calculated displacement values ​​and measured displacement values ​​of each monitoring point obtained by the inversion method of hydraulic tunnel surrounding rock mechanical parameters based on the FGO-CB collaborative optimization algorithm of the present invention.

[0055] Figure 6 This is a comparison chart showing the fitness and computation time of the hydraulic tunnel surrounding rock mechanical parameter inversion method based on the FGO-CB collaborative optimization algorithm of the present invention with the FGO algorithm, BO algorithm, ACO algorithm, and DE algorithm. Detailed Implementation

[0056] Please see Figure 1A preferred embodiment of the present invention provides a method for inverting the mechanical parameters of surrounding rock in hydraulic tunnels based on the FGO-CB collaborative optimization algorithm, comprising the following steps:

[0057] S1. Establish a numerical calculation model for the surrounding rock of the hydraulic tunnel: Based on the design drawings of the hydraulic tunnel, a detailed model of the hydraulic tunnel and its surrounding rock is constructed, and an elastoplastic constitutive model conforming to the Hoek-Brown failure criterion is used to establish a numerical calculation model for the surrounding rock of the hydraulic tunnel.

[0058] Elastoplastic constitutive models based on the Hoek-Brown failure criterion are widely used in underground engineering to effectively simulate rock fracture and instability. The generalized Hoek-Brown failure criterion is expressed as follows:

[0059] (1);

[0060] Where σ1 and σ3 are the maximum and minimum principal stresses at rock mass failure, respectively; σ ci The uniaxial compressive strength of the rock; m b s and a are empirical parameters of the rock mass; when the rock mass conditions are good or the rock mass quality is not carefully distinguished, a is usually taken as 0.5 to simplify calculations and facilitate engineering applications.

[0061] Among them, the empirical rock mass parameter m of Hoek-Brown b s can be correlated with the rock mass integrity coefficient K through the rock mass rating system RMR. v The calculated expression is as follows:

[0062] (2);

[0063] (3);

[0064] In the formula, Let m be the Hoek-Brown constant value for the rock.

[0065] S2, Determine the optimization variables: Use the rock mechanics parameters of the elastoplastic constitutive model that conforms to the Hoek-Brown failure criterion as the optimization variables.

[0066] Specifically, the optimization variables include the elastic modulus E, Poisson's ratio v, and the empirical parameter m of the Hoek-Brown criterion. b s, a and the uniaxial compressive strength σ of rock ci In this embodiment, the rock mass rating system RMR and the rock mass integrity coefficient K are used. v Replace the empirical rock mass parameter m as an optimization variable to be considered. bFor details, please refer to formulas (2)-(3) in step S1. Among them, the rock mass rating system RMR is determined by comprehensively evaluating the rock mass quality indicators based on five factors: uniaxial compressive strength of rock blocks, RQD value of rock cores, joint spacing, joint conditions, and the role of groundwater. These factors can be well obtained from geological survey reports for evaluation and are suitable for most rock masses.

[0067] Rock mechanics parameters for elastoplastic constitutive models conforming to the Hoek-Brown failure criterion typically include the elastic modulus E, Poisson's ratio v, and the empirical parameter m of the Hoek-Brown criterion. b s, a and the uniaxial compressive strength σ of rock ci Due to the significant influence of elastic modulus E and Poisson's ratio v on the deformation field of the surrounding rock, these two mechanical parameters need to be given special consideration under the inversion framework controlled by measured displacement. Furthermore, important mechanical parameters affecting the Hoek-Brown failure criterion in the Hoek-Brown model should also be given priority consideration, including but not limited to the empirical rock mass parameter m. b s, a and the uniaxial compressive strength σ of rock ci However, m b The range of values ​​for s and a is wide, for example, m b The value of is between 0.0000001 and 25, and the value of s is between 0 and 1. The wide range of values ​​and the unclear meaning of the empirical coefficients make it particularly difficult to determine a suitable range of values ​​based on geological survey reports and other data.

[0068] Based on the rock mass rating system RMR and the rock mass integrity coefficient K v Determine m b The range of values ​​for s and a is a feasible method. The Rock Mass Rating System (RMR) is determined by comprehensively evaluating rock mass quality indicators based on five factors: uniaxial compressive strength of rock blocks, RQD value of rock cores, joint spacing, joint conditions, and the effect of groundwater. These factors can be readily obtained from geological survey reports and are suitable for most rock masses. Rock mass integrity coefficient K v Rock mass integrity is one of the important indicators for rock mass classification. Furthermore, the integrity of a rock mass effectively reflects the degree of disturbance it has undergone. The correlation between rock mass integrity and the degree of disturbance is shown in Table 1. Therefore, the Rock Mass Rating System (RMR) and the Rock Mass Integrity Coefficient (K) are used in this study. v Replace the empirical rock mass parameter m as an optimization variable to be considered. b ,s,a is more appropriate.

[0069] Table 1. Correspondence between rock mass integrity and degree of disturbance

[0070]

[0071] S3, Establish the objective function for minimizing displacement error: Use the residual between the displacement calculation value of the numerical calculation model and the measured displacement value in the engineering as the objective function.

[0072] When the constitutive model used in numerical simulation can accurately characterize the actual mechanical response of the surrounding rock in hydraulic tunnels, the deviation between the numerical model calculation results and the actual monitoring data mainly stems from the differences in the values ​​of the surrounding rock mechanical parameters. Studies show that the closer the rock mass parameters input into the numerical model are to the physical and mechanical properties of the actual geological body, the higher the degree of agreement between the displacement prediction results and the field measured values. Based on this, the residual between the numerically simulated displacement field and the engineering measured displacement data is used as the objective function, and the equivalent mechanical parameter combination that characterizes the actual rock mass is iteratively solved through a collaborative optimization algorithm. Therefore, the following objective function is established:

[0073] (4);

[0074] In the formula, i is the i-th displacement measuring point, X is the combination of optimized variables obtained by the optimization algorithm, that is, the optimal value of the rock mechanics parameters of the model; n is the number of displacement measuring points; This is a numerical model to calculate the displacement value of the i-th displacement measuring point of the surrounding rock in the current tunnel excavation section by inputting operator X; This represents the measured displacement value of the i-th displacement measuring point in the current tunnel excavation section.

[0075] Therefore, the objective of this invention is to minimize the objective function f(X), that is, to minimize the average error between the numerical model displacement calculation value and the actual displacement value of the surrounding rock displacement measuring point in the current tunnel excavation section.

[0076] S4. The FGO-CB collaborative optimization algorithm is used to perform global optimization of the objective function in the parameter space to obtain the optimal rock mechanics parameters.

[0077] The specific description of the FGO-CB collaborative optimization algorithm is as follows:

[0078] (1) The FGO algorithm is inspired by the growth behavior of fungi in nature. It simulates the growth behavior of hyphal tips, branching and spore germination. It is a robust optimization algorithm with a variety of exploration and development operators. Its specific principle is as follows:

[0079] ① Initialization of mycelial population

[0080] N hyphae are randomly diffused within the search space, where each hyphae consists of a size d, corresponding to the dimension of the optimization problem:

[0081] (5);

[0082] In the formula, It is a vector containing a lower bound of d dimensions in an optimization problem. ⊙ represents performing the Hadamard product of two vectors, and represents the operator performing the Hadamard product of two vectors. It is a vector in an optimization problem that has a d-dimensional upper bound. It is a random number in [0,1]. This represents the position of the i-th hyphae.

[0083] ② Growth at the tip of the hyphae

[0084] Hyphae tip growth can be divided into exploration and attraction phases. Initially, all hyphae explore the search space to find the most nutrient-rich locations. As the exploration progresses, some hyphae will be attracted to other hyphae located in the most nutrient-rich areas, causing them to grow towards those areas. In the FGO algorithm, by comparing nutrient status P... i With exploration rate E r To distinguish the growth stages of mycelium within a population:

[0085] (6);

[0086] In the formula, f i is the nutritional status at the location of the hyphae (i.e., the corresponding objective function value), and f is the nutritional status at the locations of all hyphae in the population. These are the few numbers that prevent zero-splits.

[0087] (7);

[0088] In the formula, To explore and attract weights, t represents the number of optimization iterations. max This represents the maximum number of optimization attempts.

[0089] If the hyphae P i > E r If the hyphae do not exhibit growth characteristics, then P will explore its growth; otherwise, P will not. i ≦E r The mycelium will attract growth.

[0090] The location of regenerated hyphae in the exploratory growth phase depends on their growth rate E and growth direction. ,

[0091] (8);

[0092] In the formula, This represents the growth position of the i-th hyphae after renewal. represents the current growth position of the i-th hyphae; E represents the growth rate of the hyphae. This indicates the direction of mycelial growth.

[0093] Mycelia extend in straight lines to explore the search space and seek the most nutrient-rich region. At this point, mycelial growth is related to the nutrient level of the current region. In the FGO algorithm, the growth rate E is represented by an exponential function related to the current fitness:

[0094] (9);

[0095] In the formula, f i The nutritional status of the location of the i-th hyphae; f k It represents the sum of the nutritional status of all hyphae in the mycelial population.

[0096] However, certain environmental and chemical factors can cause hyphae to shift their growth direction. To characterize this property, the growth direction... Represented as:

[0097] (10);

[0098] In the formula, and These are two different hyphae randomly selected from the current hyphal population.

[0099] Hyphae in the growth attraction phase are attracted by hyphae in nutrient-rich areas, and their growth location is represented as follows:

[0100] (11);

[0101] In the formula, A random number between 0 and 1; Attracted by the most nutrient-rich mycelium, the mycelium changes its growth direction:

[0102] (12);

[0103] In the formula, and A random number between 0 and 1; It is the optimal mycelium. It is a mycelial location randomly selected from the mycelial population;

[0104] In addition, the growth of mycelium also takes into account the influence of environmental changes, environmental influence parameters :

[0105] (13);

[0106] In the formula, and A random number between 0 and 1; It is another mycelial location randomly selected from the mycelial population.

[0107] Hyphae branching and spore germination are crucial for the growth and development of individual mycelial populations. Individual mycelia within the population undergo either branching or spore germination based on a generated random number r8, which is between 0 and 1. When r8 > 0.5, the mycelium branches; conversely, it germinates.

[0108] ③ Hyphae branching

[0109] Hyphae in the branching stage are influenced by the hyphae in the most nutrient-rich area of ​​the population and by the influence of a particular individual hyphae in the population, resulting in hyphal branching. The branching regeneration location... for:

[0110] (14);

[0111] In the formula, E represents the current position of a hypha in the hyphal branching stage. L For branch growth rate, and These represent the growth directions influenced by individual mycelia and mycelia in the most nutrient-rich areas, respectively, with r9 being a random number between 0 and 1.

[0112] In terms of growth rate, hyphal branching exhibits the same growth rate as the mother hyphae, especially under optimal conditions. However, the development rate of lateral branching can vary depending on environmental conditions, such as nutrient availability and hyphal species. To model this behavior, the growth rate E of hyphae produced through lateral branching is used. L The calculation is as follows:

[0113] (15);

[0114] The growth direction of hyphal branching is influenced by both individual hyphae within the population and the hyphae in the most nutrient-rich areas. The growth direction influenced by individual hyphae within the population... Growth direction influenced by mycelium in the most nutrient-rich areas The calculation is as follows:

[0115] (16);

[0116] (17);

[0117] In the formula, It is a mycelium randomly selected from the mycelial population.

[0118] ④ Spore germination

[0119] The location of spore germination and renewal in mycelium during the spore germination stage. for:

[0120] (18);

[0121] In the formula, For the new location of the spore, The current position of the spore; s g A random value that is either -1 or 1. This indicates the growth direction of the new spores. 10 A random value between 0 and 1; E is the mycelial growth rate; The dimension of the problem;

[0122] Based on the average value of the optimal nutrient location and the location of two randomly selected hyphae, new spores are sent to the new location. :

[0123] (19);

[0124] In the formula, and Two randomly selected hyphal locations.

[0125] After the spores germinate at these locations, new hyphae are produced and grow. At this point, the growth direction of these new hyphae... Based on three randomly selected hyphal locations , Location relative to current nutritional status Distance between:

[0126] (20);

[0127] In the formula, , and Three randomly selected hyphal locations.

[0128] (2) The global optimization process of the FGO algorithm is as follows:

[0129] ① Set FGO algorithm parameters: Determine the mycelial population size N based on the number of rock mass parameters to be inverted, and set the exploration and attraction weights. And the maximum number of optimizations t max ;

[0130] ② Randomly initialize N hyphae: Randomly diffuse N hyphae in the search space, each hyphae consisting of a size d, corresponding to the dimension of the optimization problem;

[0131] ③ Calculate the nutrient status (i.e., the corresponding objective function value) at the current location of the mycelium, and select the mycelium with the richest nutrients as the optimal mycelium. ;

[0132] ④ The mycelial population randomly exhibits mycelial tip growth behavior or mycelial branching and spore germination behavior;

[0133] If the mycelial population exhibits hyphal tip growth behavior, then the hyphae within the mycelial population will compare their nutritional status P. i With exploration rate E r This helps distinguish whether a product has entered the growth exploration or growth attraction phase.

[0134] a. If the hyphae enter the growth exploration stage, the growth position of the hyphae will be updated according to formula (8);

[0135] b. If the hyphae enter the growth attraction stage, the growth position of the hyphae will be updated according to formula (11);

[0136] If the mycelial population exhibits mycelial branching and spore germination behavior, then the mycelia in the mycelial population will control mycelial branching or spore germination according to the generated random number r8:

[0137] a. If the hyphae enter the hyphal branching stage, the hyphae will update their growth position according to formula (14);

[0138] b. If the hyphae enter the spore germination stage, the hyphae will update their growth position according to formula (18);

[0139] ⑤ Compare the nutritional status (i.e., the corresponding objective function value) of the current location of the mycelium with that of its growth location. If > Then the mycelium grows to Conversely, mycelium does not grow. ;

[0140] ⑥ Determine whether the number of iterations t has reached the maximum number of optimization iterations t. max If the maximum number of optimization iterations is reached, convergence is considered achieved, iteration stops, and the current globally optimal mycelial position is output. As the optimal solution for the surrounding rock mechanical parameters; if the maximum number of optimization iterations has not been reached, return to step ④ and continue the iterative optimization process.

[0141] (3) Categorical Boosting (CB) model is a machine learning model based on gradient boosting decision trees. Its main construction idea is similar to GBDT, and the principle is as follows:

[0142] First, it is an ensemble of multiple decision trees, but each decision tree is generated iteratively from the previous round's decision trees. It uses a forward distribution algorithm for classification, assuming a strong learner obtained in the previous round. The loss function is Therefore, in this round of calculation, a weak learner needs to be constructed to minimize the loss function of this round. The loss function of this round is:

[0143] (twenty one);

[0144] In each round, the loss is fitted using the gradient of the loss function. The gradient of the loss function for the i-th sample in the t-th round is grad. t,i Represented as:

[0145] (twenty two);

[0146] use Where i = 1, 2, ..., n, the t-th tree can be constructed, and the non-overlapping regions corresponding to the leaves of the tree are... Where J is the number of leaf nodes.

[0147] For each leaf node sample, minimize the expected loss, which is to find the best output value h for the leaf node. tj :

[0148] (twenty three);

[0149] In the formula, h is a base predictor selected from a family of functions H, y is the true label of the sample, and F... t It is the current ensemble model up to round t.

[0150] The above minimization problem is usually solved using Newton's method, employing a (negative) gradient step size, i.e., the gradient descent method, which uses the least squares approximation:

[0151] (twenty four);

[0152] Then the decision tree fitting function for this round :

[0153] (25);

[0154] In the formula, I(⋅) is the indicator function, which is the function that indicates when sample X falls into the nth leaf region X of the nth round of the decision tree. 𝑡𝑗 When, 𝐼(𝑥∈𝑅 𝑡𝑗 If ) = 1, otherwise take 0.

[0155] The final strong learner obtained in this round is:

[0156] (26);

[0157] By repeatedly performing the above process, the prediction function f can be solved.

[0158] Based on the GBDT framework, the CB model improves machine learning algorithms by adding target statistics and ordered boosting.

[0159] ① Target Statistics

[0160] When GBDT processes categorical features, the features themselves, which contain more information, are usually replaced by the average value of the labels corresponding to the categorical features. This leads to a conditional offset problem when the data structures and distributions of the training dataset and the test dataset are different.

[0161] CB improves the Greedy TS method by adding a prior distribution term, reducing the impact of noise and low-frequency categorical data on the data distribution.

[0162] (27);

[0163] In the formula, p is the added prior term, and a1 is usually a weight coefficient greater than 0. It refers to the value of the nth sample on the nth categorical feature. It is the value of the nth sample in the random permutation of y on the nth feature (it is a category value). Randomly arrange the values ​​of the p-th sample in the n-th feature. It is the first The true label of the sample. For features with a small number of categories, it can reduce noisy data.

[0164] The above method enables the CB model to directly process classification feature information without pre-converting sample features into numerical values, thereby reducing noise and loss of classification feature information. Furthermore, the CB model employs a novel oblivious trees approach to calculate leaf node values, avoiding overfitting issues that can occur when directly calculating values ​​from multiple datasets.

[0165] ② Orderly Improvement

[0166] To overcome the problem of prediction bias caused by using the same dataset to train the model in each iteration of GBDT, the CB model proposes a new algorithm called ordered boosting, which optimizes the model for each sample. Train a separate model M i The model itself uses samples x that are not included.i The training set was obtained. Then M was used. i This method obtains gradient estimates for the samples and uses these gradients to train a base learner, resulting in the final model. By employing this method, the bias in gradient estimation can be mitigated, thereby improving the model's generalization ability.

[0167] This invention proposes a global optimization method for the FGO-CB collaborative optimization algorithm, combining FGO-CB with other algorithms. The flowchart is available in [link to flowchart]. Figure 2 :

[0168] Step A1: Set the parameters of the FGO-CB co-optimization algorithm: Determine the seed size N based on the number of rock mass parameters to be inverted, and set the convergence accuracy ε of the algorithm to solve for the exploration rate E. r Exploration and attraction weight Maximum number of optimization attempts t max Number of times the local proxy is entered (t) CB and the number of training samples, m;

[0169] Step A2: Population initialization: Randomly initialize N mycelial populations;

[0170] Step A3: Obtain the nutritional status of all mycelial locations by solving the objective function. With optimal mycelium ;

[0171] Step A4: The mycelial population is controlled by random numbers r1 and r2, where r1 and r2 are random numbers between 0 and 1. If r1 > r2, the mycelial population exhibits mycelial tip growth behavior; otherwise, it exhibits mycelial branching and spore germination behavior.

[0172] Step A5: If the mycelial population exhibits hyphal tip growth behavior, then:

[0173] The mycelia in the mycelial population were compared by nutritional status P i With exploration rate E r To distinguish whether it has entered the growth exploration or growth attraction phase: if the hyphae P i > E r If the hyphae are positive, the hyphae will explore growth and update their growth location according to formula (8); otherwise, if the hyphae's P... i ≦E r The mycelium enters the growth attraction stage and updates its growth position according to formula (11);

[0174] If the mycelial population exhibits hyphal branching and spore germination behavior, then:

[0175] The mycelial individuals in the mycelial population are controlled by a generated random number r8 to perform mycelial branching or spore germination. r8 is a random number between 0 and 1: when r8 > 0.5, the mycelium branches and grows, and the growth position is updated according to formula (14); conversely, when r8 ≦ 0.5, the mycelium germinates spores and the growth position is updated according to formula (18).

[0176] Step A6: Compare the nutritional status of the current location of the mycelium with that of its growth location, i.e., compare the objective function values ​​corresponding to the current location and the growth location. If > Then the mycelium grows to Conversely, mycelium does not grow. ;

[0177] Step A7: If i is not less than N, then all mycelial individuals in the mycelial population have completed the growth position update; otherwise, i = i + 1, and return to step A5.

[0178] Step A8: If the current number of optimization attempts t is less than the number of times the local proxy is entered t CB If t = t + 1, then return to step A4; otherwise, t CB =t+ t CB ;

[0179] Step A9: Select m closest values ​​in sequence The mycelial growth locations are selected, along with the corresponding nutritional information for each of the m selected mycelial growth locations. As training samples;

[0180] Step A10: Set the training parameters of the CB local agent model (the training parameters of the CB local agent model include the number of iterations I, the learning rate Lr, and the learning depth De), and train the CB local agent model using training samples to obtain the fitness. exist Distribution of the CB approximate optimization objective function in the local neighborhood ;

[0181] Step A11: Obtain the function optimal value in the distribution corresponding , Let the hyphal position be the optimal value predicted by the CB local surrogate model, if the function optimal value in the distribution Superior Then update = ;

[0182] Step A12: If < ε, or t greater than t maxIf the result is positive, the optimization ends; otherwise, t = t + 1 and return to step A4.

[0183] Step A13: Output the current globally optimal mycelial position. Current global optimal hyphal position These are the optimal rock mechanics parameters.

[0184] In this embodiment, the FGO-CB collaborative optimization algorithm enters the local proxy number t. CB To determine whether to perform local proxying of the CB model, t CB With the maximum number of optimization attempts t max The ratio should be between 10 and 40, that is, 10 to 40 local proxies should be performed during the optimization process.

[0185] In this implementation, the number of training samples, m, controls the performance of the CB local proxy model. If m is too small, the number of samples will be insufficient; if m is too large, the quality of the samples will decrease. To ensure the local proxy performance of the CB model, the number of training samples, m, should ideally be between 50 and 100.

[0186] S5, the optimal rock mechanics parameters are input into the numerical calculation model of the surrounding rock of the hydraulic tunnel, and the support optimization and surrounding rock deformation management are carried out based on the rock mechanics parameters obtained by inversion from the numerical calculation model of the surrounding rock of the hydraulic tunnel with the optimal rock mechanics parameters.

[0187] Specifically, the optimal model surrounding rock mechanical parameters are substituted into the refined numerical calculation model of the hydraulic tunnel to conduct numerical simulation of the next phase of tunnel and support excavation, obtain displacement data after excavation, analyze the displacement and deformation of the tunnel surrounding rock according to the specified surrounding rock deformation management, and make appropriate optimizations to the design support so that the displacement after the next phase of tunnel excavation is within a safe and controllable range.

[0188] The following two specific embodiments illustrate the effectiveness of the hydraulic tunnel surrounding rock mechanical parameter inversion method based on the FGO-CB collaborative optimization algorithm of the present invention.

[0189] Example 1

[0190] To understand the performance of the FGO-CB collaborative optimization algorithm, Example 1 compares the proposed FGO-CB algorithm with the FGO algorithm (without a surrogate model), the Bat Optimization Algorithm (BO algorithm), the Ant Colony Optimization Algorithm (ACO algorithm), and the Differential Evolution Algorithm (DE algorithm) based on single-peak and multi-peak benchmark functions. For all algorithms, the maximum number of iterations is 20,000, and the number of specified operators is 40.

[0191] The benchmark function f1(x) based on a single peak is:

[0192] (28);

[0193] In the formula, For optimization 3D decision variable vector, For the first There are 1 decision variable components, with values ​​ranging from 1 to 10. ; f is the dimension of the decision variables. min The value is 0, and f is used in this case. 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, the comparison algorithms all reach f. best The number of iterations is used to evaluate the convergence and exploratory capabilities of the algorithm.

[0194] The benchmark function f2(x) based on multiple peaks is:

[0195] (29);

[0196] In the formula, For optimization 3D decision variable vector, For the first There are 1 decision variable components, with values ​​ranging from [-600, 600]; f is the dimension of the decision variables. min The value is 0, and the smaller f2(x) is, the better. The multi-peak test function has multiple optimal values, but only one global optimum. The rest are local optima. After the algorithm completes the 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.

[0197] Other parameters of the algorithms used in this comparison are shown in Table 2. For a detailed explanation of the optimization process of the FGO-CB collaborative optimization algorithm, please refer to step S3. Figure 2 .

[0198] Table 2 Control parameter values ​​for each algorithm

[0199]

[0200] The algorithms used in this comparison are shown in Table 3, which compare the number of typical function calls.

[0201] Table 3 Comparison of typical function call counts and optimal values ​​for each algorithm

[0202]

[0203] As shown in Table 3, the computational cost of the FGO-CB algorithm is lower than that of the FGO, BO, ACO, and DE algorithms, while its global optimization capability is stronger, indicating that the PO-SVM collaborative optimization algorithm has significant advantages in typical test functions.

[0204] Example 2

[0205] Example 2 is a hydraulic tunnel with dimensions of 4.9m × 4.9m (width × height). The strata are of homogeneous lithology. Based on the initial in-situ stress field obtained from back analysis of the exploration data, the maximum principal stress σ1 is approximately 3~6MPa.

[0206] Figure 1 A flowchart illustrating a method for inverting the mechanical parameters of surrounding rock in cavern groups based on the FGO-CB collaborative optimization algorithm, provided in an embodiment of the present invention, is as follows:

[0207] Step S1: Based on the design drawings of the hydraulic tunnel, perform detailed modeling of the hydraulic tunnel and its surrounding rock, and establish a numerical calculation model of the surrounding rock of the hydraulic tunnel using an elastoplastic constitutive model that conforms to the Hawke-Brown failure criterion.

[0208] Specifically, the calculation area for the refined model of the hydraulic tunnel is a rectangular region of 30m × 38.4m × 38.4m (length × width × height). To ensure calculation accuracy, the mesh of the tunnel excavation body and its surrounding area is refined, with a total of 667,520 elements, classifying it as a refined model. The model is as follows: Figure 3 As shown. The numerical model adopts the elastoplastic constitutive model based on the Hawke-Brown failure criterion.

[0209] Step S2: Use the rock mechanics parameters of the elastoplastic constitutive model that conforms to the Hawke-Brown failure criterion as optimization variables.

[0210] Example 2 uses an elastoplastic constitutive model based on the Hawke-Brown failure criterion. The mechanical parameters of the sidewall rock mass to be inversely analyzed are determined as deformation modulus E, Poisson's ratio v, rock mass evaluation parameter RMR, and rock mass integrity coefficient K. v The search range for these parameters was determined based on changes in the excavation location and the deformation and failure characteristics of the rock mass, as shown in Table 4.

[0211] Table 4. Search range of parameters for the model to be inverted in the embodiment and other parameter values.

[0212]

[0213] Step S3: Establish the objective function for minimizing displacement error: Use the residual between the displacement calculation value of the numerical calculation model and the measured displacement value in the engineering as the objective function.

[0214] Based on the detailed explanation in step 3 and formula (4), an optimization objective function command flow is added to the numerical calculation script. Specifically, in Example 2, six measured monitoring points are selected, and the locations of the monitoring points are as follows: Figure 4 As shown in Table 5, the actual displacements at the monitoring points are as follows. Using the residuals between the numerically calculated displacements of the tunnel surrounding rock and the actual measured displacements at these six monitoring points as the optimization objective, a minimized optimization objective function is constructed.

[0215] Table 5 Measured displacement values ​​at each monitoring point

[0216]

[0217] Step S4: Use the FGO-CB collaborative optimization algorithm to perform global parameter space optimization on the objective function to obtain the optimal rock mechanics parameters.

[0218] Specifically, in Example 2, the seed size N = 7 is determined based on the number of rock mass parameters to be inverted, the convergence accuracy of the algorithm is set to ε = 0.2, the maximum number of optimization attempts Max = 100, and the exploration and attraction weights are set accordingly. Number of local proxies t CB =10, iteration count I=48, learning rate Lr=1.00, learning depth De=2.00; then, global optimization is performed according to the specific steps of the FGO-CB collaborative optimization algorithm in step S4.

[0219] Specifically, Example 2 describes a method for assessing the nutritional status of mycelial populations: A joint inversion was performed using the free software Python and the commercial numerical computation software FLAC3D. In the Python environment, the mycelial location coordinates (a set of surrounding rock mechanical parameters) from the FGO-CB co-optimization algorithm were saved to the data file Python_out.txt. A custom script was used to launch the FLAC3D numerical computation software for numerical simulation calculations. A user subroutine built into FLAC3D was then called to read the set of surrounding rock mechanical parameters from the Python_out.txt data file. These parameters were substituted into the established FLAC3D numerical model to obtain the calculated displacement, and thus the objective function value. The objective function value was then saved to the FLAC_out.txt data file. The Python program read the objective function value from the FLAC_out.txt data file, thereby obtaining the nutritional status of the mycelial location.

[0220] In comparison, the FGO algorithm, BO algorithm, ACO algorithm, and DE algorithm were used in the global optimal parameter search in Example 2. The population size of the algorithms was N=14, the optimization objective function was the same, and the other algorithm parameters are shown in Table 6.

[0221] Table 6 Control parameter values ​​for each algorithm in Example 2

[0222]

[0223] The search for the globally optimal surrounding rock mechanical parameters based on the FGO-CB collaborative optimization algorithm in this embodiment has been completed. The results of the optimal numerical model parameters are shown in Table 7. A comparison of the measured and calculated displacement values ​​at each monitoring point using the optimal numerical model parameters is shown in Table 8. 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 9 and [Table 9 is missing from the original text]. Figure 6 .

[0224] Table 7 Inversion Calculation Results

[0225]

[0226] Table 8 Comparison of measured and calculated displacement values ​​at each monitoring point

[0227]

[0228] Table 9 Comparison of calculation results with each algorithm

[0229]

[0230] As can be seen from Table 9, the FGO-CB 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 FGO algorithm without using the surrogate model, as well as the BO algorithm, ACO algorithm and DE algorithm, further demonstrating the superiority of the FGO-CB collaborative optimization algorithm.

[0231] Step S5: Input the optimal rock mechanics parameters into the numerical calculation model of the surrounding rock of the hydraulic tunnel, and carry out support optimization and surrounding rock deformation management based on the rock mechanics parameters obtained by inversion from the numerical calculation model of the surrounding rock of the hydraulic tunnel with the optimal rock mechanics parameters.

[0232] Specifically, the optimal model surrounding rock mechanical parameters are substituted into the refined numerical model of the hydraulic tunnel to conduct numerical simulation of the next phase of tunnel and support excavation. The displacement data after excavation is obtained. Based on the specified surrounding rock deformation management, the displacement and deformation status of the tunnel surrounding rock is analyzed, and the design support is appropriately optimized so that the displacement after the next phase of tunnel excavation is within a safe and controllable range.

[0233] This invention combines the FGO global optimization algorithm with the CB local proxy model, fully leveraging the FGO algorithm's superior exploration capabilities in global optimization while utilizing the CB model's excellent predictive regression analysis capabilities for the mycelial community search space. This significantly reduces the number of calls to the refined numerical model during the inversion process, quickly reaching convergence conditions and further improving inversion accuracy. Compared to the FGO algorithm without a proxy model and other traditional inversion methods—Bat Optimization (BO), Ant Colony Optimization (ACO), and Differential Evolution (DE) algorithms—this method can more efficiently and quickly obtain the combination of surrounding rock mechanical parameters from the refined numerical simulation model of hydraulic tunnels. This effectively solves the engineering problem of being unable to apply displacement optimization inversion analysis technology to the dynamic feedback construction of hydraulic tunnels due to excessive calls to the refined model resulting in long computation times.

[0234] 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 tunnels based on the FGO-CB collaborative optimization algorithm, characterized in that, Includes the following steps: S1. Establish a numerical calculation model for the surrounding rock of the hydraulic tunnel: Based on the design drawings of the hydraulic tunnel, a detailed model of the hydraulic tunnel and its surrounding rock is carried out, and an elastoplastic constitutive model conforming to the Hawke-Brown failure criterion is used to establish a numerical calculation model for the surrounding rock of the hydraulic tunnel. S2, Determine the optimization variables: Use the rock mechanics parameters of the elastoplastic constitutive model that conforms to the Hawke-Brown failure criterion as the optimization variables; S3, Establish the objective function for minimizing displacement error: Use the residual between the displacement calculation value of the numerical calculation model and the measured displacement value in the engineering as the objective function; S4. The FGO-CB collaborative optimization algorithm is used to perform global optimization of the objective function in the parameter space, thereby obtaining the optimal rock mechanics parameters; S5, the optimal rock mechanics parameters are input into the numerical calculation model of the surrounding rock of the hydraulic tunnel, and the support optimization and surrounding rock deformation management are carried out based on the rock mechanics parameters obtained by inversion from the numerical calculation model of the surrounding rock of the hydraulic tunnel with the optimal rock mechanics parameters.

2. The method for inverting the mechanical parameters of surrounding rock in hydraulic tunnels based on the FGO-CB collaborative optimization algorithm as described in claim 1, characterized in that, In step S2, the objective function is: ； In the formula, i For the first i Displacement measurement points, X The optimized combination of variables obtained through the optimization algorithm is the optimal value of the rock mechanics parameters of the model. n This represents the number of displacement measurement points; To input operators X The current tunnel excavation section surrounding rock is being carried out. i Numerical model displacement calculation values ​​for each displacement measuring point; The surrounding rock of the current tunnel excavation section i Measured displacement values ​​at each displacement measuring point; The purpose of global optimization of the parameter space in step S3 is to make the objective function f ( X The minimum value means that the average error between the numerical model displacement calculation value and the actual displacement value of the surrounding rock displacement measuring point in the current tunnel excavation section reaches the minimum value.

3. The method for inverting the mechanical parameters of surrounding rock in hydraulic tunnels based on the FGO-CB collaborative optimization algorithm as described in claim 1, characterized in that, The optimization variables include the elastic modulus. E Poisson's ratio v Empirical parameters of the Hoek-Brown criterion m b , s , a and the uniaxial compressive strength of rock σ ci Rock mass scoring system RMR With rock mass integrity coefficient K v Replace the empirical parameters of the rock mass as optimization variables to be considered. m b , s , a Among them, the rock mass scoring system RMR It is based on the uniaxial compressive strength of the rock block and the rock core. RQD The rock mass quality index is determined by a comprehensive evaluation of five factors: value, joint spacing, joint conditions, and the role of groundwater.

4. The method for inverting the mechanical parameters of surrounding rock in hydraulic tunnels based on the FGO-CB collaborative optimization algorithm as described in claim 1, characterized in that, Step S3 includes the following steps: Step A1: Set the parameters of the FGO-CB collaborative optimization algorithm: Determine the scale based on the number of rock mass parameters to be inverted. N Set the convergence accuracy of the algorithm ε Used to solve for the exploration rate E r Exploration and attraction weight Maximum number of optimizations t max Number of times entering a local proxy t CB and the number of training samples m ; Step A2: Population Initialization: Random Initialization N Individual mycelial colonies; Step A3: Obtain the nutritional status of all mycelial locations by solving the objective function. With optimal mycelium ; Step A4: From random numbers r 1 and r 2. Control mycelial population, r 1 and r 2 is a random number between 0 and 1: If r 1> r 2. Mycelial populations exhibit mycelial tip growth behavior, and conversely, they exhibit mycelial branching and spore germination behavior. Step A5: If the mycelial population exhibits mycelial tip growth behavior, then: The mycelia in the mycelial population are compared by nutritional status P i with exploration rate E r To distinguish whether one has entered the growth exploration or growth attraction phase: If the hyphae P i > E r If so, the mycelium will explore its growth and update its growth location according to the following formula; ； In the formula, For the first i The growth location of each mycelium after renewal; For the first i The current growth position of each hyphae; E is the growth rate of the hyphae; This indicates the direction of mycelial growth. on the contrary, P i ≦ E r The mycelium enters the growth attraction phase, and its growth location is updated according to the following formula: ； In the formula, A random number between 0 and 1 ； The mycelium is attracted to the most nutrient-rich hyphae, causing it to change its growth direction. Environmental impact parameters; If the mycelial population exhibits hyphal branching and spore germination behavior, then: The mycelial individuals in the mycelial population are determined by the generated random numbers. r 8. Control mycelial branching or spore germination. r 8 is a random number between 0 and 1: r When 8 > 0.5, the hyphae branch and grow, and the growth position is updated according to the following formula; ； In the formula, This refers to the location of the renewed hyphae during the hyphal branching stage. This indicates the current position of a hyphae in the hyphal branching stage. E L For branch growth rate, and These represent the growth directions influenced by individual mycelia within the population and by mycelia in the most nutrient-rich areas, respectively. r 9 is a random number between 0 and 1; on the contrary, r 8≦0.5, the mycelium germinates spores, and the growth position is updated according to the following formula; ； In the formula, For the new location of the updated spores, This is the current location of the spore; A random value that is either -1 or 1. The direction of growth of new spores; r 10 A random value between 0 and 1; E The growth rate of mycelium; The dimension of the representative problem; Step A6: Compare the nutritional status of the current location of the mycelium with that of its growth location, i.e., compare the objective function values ​​corresponding to the current location and the growth location. If Then the mycelium grows to Conversely, mycelium does not grow. ; Step A7: If i Not less than N， Then all hyphae within the mycelial population complete the renewal of their growth positions; conversely, i = i +1, and return to step A5; Step A8: If the current number of optimizations... t Less than the number of times to enter the local proxy t CB ,but t = t +1 and return to step A4; otherwise, t CB = t+ t CB ; Step A9: Select in sequence m The closest The location of mycelial growth will be selected. m Location of mycelial growth and corresponding nutritional status As training samples; Step A10: Set the training parameters of the CB local proxy model and train the CB local proxy model using training samples to obtain the fitness. exist Distribution of the CB approximate optimization objective function in the local neighborhood ; Step A11: Obtain the function optimal value in the distribution corresponding , , where is the hyphal position corresponding to the optimal value predicted by the CB local surrogate model, if the function optimal value in the distribution Superior Then update = ; Step A12: If < ε, or t Greater than t max If the search is successful, the optimization process ends; otherwise... t = t +1 and return to step A4; Step A13: Output the current globally optimal mycelial position. Current global optimal hyphal position These are the optimal rock mechanics parameters.

5. The method for inverting the mechanical parameters of surrounding rock in hydraulic tunnels based on the FGO-CB collaborative optimization algorithm as described in claim 4, characterized in that, t CB With maximum number of optimization attempts t max The ratio is between 10 and 40, meaning that local proxies are performed 10 to 40 times during the optimization process.

6. The method for inverting the mechanical parameters of surrounding rock in hydraulic tunnels based on the FGO-CB collaborative optimization algorithm as described in claim 4, characterized in that, Number of training samples m Between 50 and 100.

Images