A method for geological safety assessment of underground space

Abstract

This invention relates to the field of urban underground space development technology and proposes a method for evaluating the geological safety of underground space, comprising the following steps: S1, establishing a hierarchical underground space geological safety evaluation index system; S2, obtaining basic geological data vector maps for each secondary index to form a hierarchical vector map; S3, forming a comprehensive vector map, dividing the evaluation units, and obtaining hierarchical data for each secondary index within each evaluation unit; S4, obtaining subjective weights using the G1 method, obtaining objective weights using the improved CRITIC method, and finally obtaining the combined weights of each secondary index; S5, constructing a Bayesian network structure; S6, obtaining the prior probability of the root node and the conditional probabilities of other nodes to complete the construction of the Bayesian network model; S7, calculating the underground space geological safety score for each evaluation unit. This invention avoids the limitations of single weighting and solves the challenge of obtaining basic data when using traditional Bayesian network models to evaluate the geological safety of underground space.

Description

Technical Field

[0001] This invention relates to the field of urban underground space development technology, and specifically to a method for evaluating the geological safety of underground space. Background Technology

[0002] Against the backdrop of rapid urbanization, the contradiction between scarce land resources and surging urban functional demands is becoming increasingly prominent. Underground space has become an important means to enhance the comprehensive carrying capacity of cities and alleviate the tension of land resources. However, during the construction of underground spaces, safety accidents such as ground subsidence, sudden water inrush in tunnels, and burial at exits occur frequently, seriously affecting the safety of urban operations. Therefore, conducting scientific and accurate geological safety assessments of underground spaces, identifying the geological inducing factors behind geological problems, and quantitatively evaluating the geological safety of different areas are crucial for ensuring the safe development of urban underground spaces.

[0003] Currently, commonly used evaluation methods include the Analytic Hierarchy Process (AHP), fuzzy comprehensive evaluation, and TOPSIS. These methods have greatly enriched the research content on the suitability assessment of underground space development, but some shortcomings remain. For example, the AHP is highly subjective, with the construction of the judgment matrix relying on expert experience and making it difficult to guarantee consistency in judgments; the fuzzy comprehensive evaluation lacks a unified standard for determining membership functions, easily leading to fuzziness and subjective bias in the evaluation results; and the TOPSIS model ignores the interaction between decision criteria, which may cause the decision results to be biased towards decision problems with significant interaction effects.

[0004] With the rise of artificial intelligence, some scholars have recently applied machine learning to comprehensive evaluation in the geological field. This includes Bayesian networks, a method that can effectively express and fuse multi-source geological information, integrating professional knowledge and experience data. Compared to traditional mathematical models, it possesses more accurate probabilistic reasoning capabilities and higher computational efficiency. However, in the field of underground space geological safety evaluation, it is difficult to obtain accurate node conditional probability values ​​and other fundamental data, which hinders the widespread adoption of Bayesian networks in this area. Furthermore, single weighting methods have significant subjective or objective limitations, necessitating the use of more scientific weighting models. Summary of the Invention

[0005] To address the problems existing in the background technology, this invention proposes a method for geological safety evaluation of underground space, comprising the following steps:

[0006] S1. The geological safety influencing factors of the underground space in the evaluated area are classified as indicators to establish a graded underground space geological safety evaluation index system, wherein the indicators include multiple primary indicators, and each primary indicator includes multiple secondary indicators.

[0007] S2. Obtain the basic geological data vector map of each secondary indicator, classify each secondary indicator, establish the secondary indicator classification standard, and divide each vector map into zones according to the classification standard to form the classification vector map of each secondary indicator.

[0008] S3. Based on ArcGIS software, the vector maps are overlaid to form a comprehensive vector map. The comprehensive vector map is then divided into multiple evaluation units. The attribute table of the comprehensive vector map covers the hierarchical data of each secondary indicator within the scope of all evaluation units. Each row of the attribute table carries the hierarchical data of each secondary indicator within an evaluation unit.

[0009] S4. The subjective weights of the secondary indicators are obtained using the G1 method, and the objective weights of the secondary indicators are obtained using the improved CRITIC method. Finally, the subjective and objective weights are optimized using a genetic algorithm to obtain the combined weights of each secondary indicator, providing a reference for subsequent expert evaluation.

[0010] S5. Based on the evaluation index system, identify the dependency relationship between underground space geological safety and evaluation indicators at all levels, build a Bayesian network structure, and use D-separation to test the conditional independence assumption of the Bayesian network to ensure the rationality of the Bayesian network structure.

[0011] S6. Obtain the prior probability of the root node and the conditional probabilities of other nodes to complete the construction of the Bayesian network model.

[0012] S7. Input the graded data of the secondary indicators of each evaluation unit as the root node data into the Bayesian network model, and then use the Bayesian network model to perform forward reasoning to complete the calculation of the underground space geological safety score of each evaluation unit. Integrate the underground space geological safety scores of each evaluation unit, formulate the underground space geological safety level classification standard according to the score, and perform visualization processing to generate the underground space geological safety zoning map of the evaluation area.

[0013] Preferably, the step of obtaining the subjective weights of the secondary indicators using the G1 method in S4 includes: determining the order relationship between the secondary indicators, determining the importance between adjacent secondary indicators, and calculating the weight of each secondary indicator.

[0014] Preferably, the step of obtaining the objective weights of the secondary indicators using the improved CRITIC method in S4 includes: constructing the original evaluation matrix, performing matrix standardization, eliminating indicator differences using the coefficient of variation, calculating the correlation coefficient, and obtaining the objective weights of each secondary indicator.

[0015] Preferably, the step in S4 of using a genetic algorithm to optimize subjective and objective weights and obtain the combined weights of secondary indicators includes: taking minimizing the difference between subjective and objective weights as the objective function, repeatedly performing selection, crossover, and mutation operations to optimize the weight combination generation by generation, and finally finding a weight combination with the minimum fitness.

[0016] Preferably, the step of obtaining the prior probability of the root node in step S6 includes: calculating the area of ​​each level partition of the hierarchical vector diagram of each of the secondary indicators; the ratio of the area of ​​a certain level partition to the total area of ​​the evaluation area is the probability of occurrence of the corresponding basic event in the root node after the transformation of the secondary indicator; and calculating the probability of occurrence of all basic events in the root node to obtain the prior probability of the root node.

[0017] Preferably, the method for obtaining the conditional probabilities of other nodes in step S6 includes the following steps:

[0018] S6.1. Take into full account the experts’ professional positions, educational backgrounds, and years of experience to determine the expert weights;

[0019] S6.2. Experts, based on a combination of engineering experience and secondary indicators, use Pythagorean triangular fuzzy numbers to sequentially score the probability of occurrence of basic events contained in all nodes except the root node, thus eliminating the need for conversion from fuzzy language description to Pythagorean triangular fuzzy numbers. The Pythagorean triangular fuzzy numbers are expressed as follows:

[0020]

[0021] Among them, fuzzy numbers α The most likely value is b The least likely value is a and c , w α and u α They represent α The maximum and minimum membership degrees, and satisfying ;

[0022] S6.3 Calculating the Pythagorean triangular fuzzy number under the influence of expert weights

[0023]

[0024] in, α j For the first j The Pythagorean triangular fuzzy number obtained by the experts in scoring the event W j For the first j The weight of each expertg This is the balance coefficient;

[0025] S6.4 Calculation The scoring function, based on the score Sort in descending order to get The scoring function is expressed as:

[0026]

[0027] Among them, fuzzy numbers The most likely value is The least likely value is and , and They represent The maximum and minimum membership degree;

[0028] S6.5. Based on the Pythagorean triangular fuzzy hybrid geometric operator, aggregate the expert scores of a single basic event within a single node, and calculate the aggregated Pythagorean triangular fuzzy number of the event under the influence of expert weights and location weights. β The Pythagorean triangular fuzzy hybrid geometric operator is expressed as:

[0029]

[0030] in, ω j Position weights associated with the Pythagorean triangular fuzzy hybrid geometry operator;

[0031] S6.6. Defuzzify the Pythagorean triangular fuzzy number using the centroid method and convert it into an accurate score. S ,

[0032]

[0033] Among them, fuzzy numbers β The most likely value is The least likely value is and , and These are the aggregated Pythagorean triangular fuzzy numbers. β Membership functions and non-membership functions are denoted as:

[0034]

[0035]

[0036] in, and Representing fuzzy numbers respectivelyβ The maximum and minimum membership degree;

[0037] S6.7 Following steps S6.1-S6.7, calculate the exact probability of other basic events occurring at this node to obtain the conditional probability table for this node; similarly, obtain the conditional probability tables for the remaining nodes.

[0038] Preferably, the Bayesian network is written in Python software.

[0039] Preferably, in step S7, a geological safety level classification standard for underground space is formulated based on the scores, specifically as follows:

[0040] Evaluation results with scores in the range [0, 0.25] are classified as poor security level;

[0041] Evaluation results with scores in the range of (0.25, 0.5) are classified as having poor security.

[0042] Evaluation results with scores in the range of (0.5, 0.75) are classified as having a relatively good level of safety.

[0043] Evaluation results with scores in the range (0.75, 1) are classified as having good safety.

[0044] The beneficial effects of this invention are as follows:

[0045] (1) This invention optimizes the subjective and objective weights of evaluation indicators based on genetic algorithms. It takes the subjective judgment of experts and the quantitative laws of data as optimization targets at the same time. It automatically searches and iterates in a huge weight combination space, which can effectively balance subjective experience and objective data, avoid the one-sidedness of single weighting, and thus obtain scientific and reasonable optimal weights.

[0046] (2) This invention introduces Pythagorean fuzzy set theory into the field of underground space evaluation, establishes a Pythagorean fuzzy Bayesian network, and solves the challenge of obtaining basic data when traditional Bayesian network models are used to assess the geological safety of underground space, further enhancing the generalization value of Bayesian network models. The research of this invention can provide new ideas for the geological safety evaluation of underground space.

[0047] (3) The present invention integrates optimization algorithms and machine learning methods, which improves computational efficiency and accuracy compared with traditional mathematical evaluation models. Attached Figure Description

[0048] Figure 1 A schematic diagram of the process for geological safety assessment of underground space provided by the present invention;

[0049] Figure 2A schematic diagram of the Bayesian network structure for underground space geological safety provided by this invention;

[0050] Figure 3 A schematic diagram illustrating the main criteria for the D-separation test of conditional independence between nodes in a Bayesian network structure, provided by this invention.

[0051] Figure 4 The geological safety zoning map of underground space provided for this invention. Detailed Implementation

[0052] To make the present invention clearer and more understandable, the technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the given embodiments are only one or more of the implementation methods and do not represent all embodiments.

[0053] In this article, terms such as "inner," "outer," "upper," and "lower" are established based on the positional relationships shown in the attached drawings. Depending on the attached drawings, the corresponding positional relationships may also change. Therefore, they should not be interpreted as an absolute limitation on the scope of protection.

[0054] Combined with appendix Figure 1 - Appendix Figure 4 This invention describes a method for assessing the geological safety of underground spaces, comprising the following steps:

[0055] S1. The geological safety influencing factors of the underground space in the evaluated area are classified as indicators to establish a graded underground space geological safety evaluation index system, wherein the indicators include multiple primary indicators, and each primary indicator includes multiple secondary indicators.

[0056] Specifically, the primary indicators include topography, rock and soil characteristics, hydrogeological conditions, and adverse geological processes;

[0057] Topographic and geomorphological conditions: Topographic and geomorphological conditions include two secondary indicators: geomorphological type and topographic slope. Geomorphological type is the macro-background for the geological safety of underground spaces, determining the main rock and soil types and potential geological hazard risks in the region. Mountainous and hilly areas have hard rock masses but complex terrain, and may be threatened by tectonic fault zones and high-stress areas, while plains often face problems such as soft soil, high groundwater levels, and uneven settlement. Topographic slope constitutes a fundamental control over the site selection, structural design, and construction safety of underground engineering. Excavation in steep slope areas easily disturbs the stress balance, inducing disasters and significantly increasing the difficulty of support and construction risks.

[0058] Rock and soil characteristics: Rock and soil characteristics include four secondary indicators: rock and soil type, rock bearing capacity, soil bearing capacity, and soil compression modulus. Rock and soil are the environmental media for underground space development. Differences in rock and soil types directly affect the stability, deformation characteristics, and geological hazard risks of the surrounding rock of underground space, and are the key basis for evaluating and controlling the geological safety of underground engineering. Differences in the bearing capacity of the foundation (rock and soil) have a significant impact on the geological safety of underground space development. Generally speaking, the greater the bearing capacity, the simpler the support measures required for underground excavation and construction. Soil compression modulus characterizes its resistance to compression deformation. The smaller the modulus, the greater the settlement after loading, which easily leads to uneven settlement of the structure, especially in deep soft soil or highly sensitive soil layers, where uneven settlement is more prominent.

[0059] Hydrogeological conditions include two secondary indicators: groundwater level and groundwater corrosivity. The level of groundwater directly alters the mechanical properties of the soil and surrounding rock, as well as the stress state of the support structure. High groundwater levels can easily lead to sudden inrushes, quicksand, foundation heave, and leakage. Groundwater can erode concrete and reinforced concrete structures. Highly corrosive environments (coastal and cross-sea projects) place extremely high demands on the materials and processes used in underground engineering.

[0060] Adverse geological processes include four secondary indicators: ground subsidence, distance from active faults, soil liquefaction, and ground fissures. Adverse geological processes have a significant impact on underground space development. Ground subsidence can easily lead to uneven settlement of underground structures. The tectonic activity in the area surrounding active faults is intense and seriously threatens construction safety. Ground fissures may cause ground deformation and collapse. Soil liquefaction caused by seismic activity or other activities can significantly reduce the self-stability of the surrounding rock, making underground engineering construction much more difficult.

[0061] The final geological safety evaluation index system for underground space is shown in Table 1:

[0062] Table 1. Geological Safety Evaluation Index System for Underground Space

[0063]

[0064] S2. Obtain the basic geological data vector maps of each secondary indicator. Based on the actual geological conditions of the region, expert opinions, and the previous research foundation of the region, classify each secondary indicator, establish the secondary indicator classification standard, and divide each basic geological data vector map into zones according to the classification standard to form the classification vector maps of each secondary indicator.

[0065] Specifically, the basic geological data vector maps of the acquired secondary indicators include topographic slope maps, landform type maps, rock and soil type maps, rock bearing capacity maps, soil bearing capacity maps, soil compression modulus maps, groundwater level maps, groundwater corrosivity maps, ground settlement maps, distance from active fault maps, sand liquefaction maps, and ground fissure distribution maps.

[0066] The established secondary indicator grading standards are shown in Table 2 as an example:

[0067] Table 2. Grading Standards for Secondary Indicators

[0068]

[0069] S3. Based on ArcGIS software, the various hierarchical vector maps are overlaid to form a comprehensive vector map. The comprehensive vector map is then divided into multiple evaluation units. The attribute table of the comprehensive vector map covers the hierarchical data of each secondary indicator within all evaluation units. Each row of the attribute table carries the hierarchical data of each secondary indicator within an evaluation unit. Taking terrain slope as an example, the hierarchical data is the data corresponding to the specific slope value of a certain evaluation unit and its category under its hierarchical standard. For example, if the terrain slope of a certain evaluation unit is 2.5°, it corresponds to the "Good (Ⅰ)" category according to its hierarchical standard. The number 1 represents its level. "1" is the hierarchical data of the terrain slope of this unit.

[0070] Specifically, the basic geological data vector graphics of each secondary indicator in the evaluation area are imported into ArcGIS software. A unified geographic coordinate system is established and boundaries are calibrated. Each basic geological data vector graphic is then partitioned according to a grading standard, forming tiered vector graphics for each secondary indicator. These tiered vector graphics are then overlaid using ArcGIS's composite tools to generate a comprehensive vector graphic. Evaluation units, formed through automated calculations based on the spatial attribute boundaries of each indicator, are then delineated. These evaluation units vary in size and shape, but offer higher accuracy and scientific rigor compared to traditional manual grid division methods. The tiered data of the secondary indicators for each evaluation unit can be extracted from the attribute table of the comprehensive vector graphic.

[0071] S4. The subjective weights of the secondary indicators are obtained using the G1 method, and the objective weights of the secondary indicators are obtained using the improved CRITIC method. Finally, the subjective and objective weights are optimized using a genetic algorithm to obtain the combined weights of the secondary indicators, providing a reference for subsequent expert evaluation.

[0072] Specifically, the subjective weights are obtained using the G1 method. Compared to the Analytic Hierarchy Process (AHP), the G1 method demonstrates better applicability when assigning weights to geological safety evaluation indicators for underground space, mainly in the following two aspects: First, it constructs a hierarchical judgment matrix without requiring consistency checks, greatly simplifying the calculation process; second, it can effectively handle the uncertainty issues in expert judgments of multiple geological safety indicators, thereby improving the scientific rigor of weight determination. The steps for calculating subjective weights based on the G1 method are as follows:

[0073] S4a.1 Determine the order relationship between secondary indicators

[0074] Assuming there is a totalk The two secondary indicators are as follows: C 1, C 2, …, C k Experts, based on their engineering experience, ranked the secondary indicators from highest to lowest importance, thus establishing the order relationship between the secondary indicators:

[0075]

[0076] S4a.2 Determine the importance of adjacent secondary indicators

[0077] For any two adjacent secondary indicators and Its relative importance can be expressed as , i = k , k -1, ...,2. The values ​​assigned are [1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9]. The larger, Compared to The more important;

[0078] in, Representative secondary indicators The weight, Representative secondary indicators The weight.

[0079] S4a.3 Calculate the weights of each secondary indicator

[0080] According to the decision-makers The value is first calculated based on the least important secondary indicator (the second most important one). k Subjective weighting of (position):

[0081]

[0082] Then, recursively calculate the first... k Subjective weight of a secondary indicator :

[0083]

[0084] By recursively calculating backwards, the weights arranged in order can be obtained.

[0085] S4a.4 Restoring the original weights of secondary indicators

[0086] The calculated weights are arranged in order. Based on the order relationship determined in the first step, the corresponding original secondary indicators are assigned. C 1, C 2, …, C k This yields the final subjective weight vector. .

[0087] Objective weights are determined using an improved CRITIC method. The CRITIC method considers both the comparative strength and conflict between indicators, effectively reflecting the differences between objective geological information. However, the traditional CRITIC method fails to reflect the variability (dimension and magnitude) between indicators. By introducing a coefficient of variation, the method can more accurately characterize the variability of each indicator and its contribution to geological safety assessment. The steps for calculating objective weights based on the improved CRITIC method are as follows:

[0088] S4.b1 Construction of the original evaluation matrix

[0089] Let the number of evaluation units be... m The number of secondary indicators is k Then the first h The first evaluation unit i Individual Indicator Values x hi Construct the original evaluation matrix X = (x hi ) m×k ;

[0090] S4.b2, Standardize the elements in the original matrix X:

[0091]

[0092] in, It is the first i The average of each secondary indicator; s i It is the first i The mean square deviation of each secondary indicator.

[0093] The standardized matrix obtained after standardization is as follows:

[0094]

[0095] S4.b3 Calculate the coefficient of variation for each indicator.

[0096]

[0097] S4.b4 Calculate the correlation coefficient

[0098] Based on the standardized matrix X Calculate the Pearson correlation coefficients among the evaluation indicators and obtain the correlation coefficient matrix. The formula for calculating the Pearson correlation coefficient is as follows:

[0099]

[0100] in, and X The Middle h The first evaluation unit i The, the l The standardized values ​​of each secondary indicator, and X The Middle i The, the l The mean of the standardized values ​​of each secondary indicator. p il For the first i The second-level indicator and the first l Pearson correlation coefficients among the secondary indicators.

[0101] S4.b5. Based on matrix P, calculate the independence coefficients of each secondary evaluation index. η i and comprehensive coefficient C i :

[0102]

[0103] C i = ν i η i

[0104] S4.b6, The objective weights of each secondary indicator are expressed as follows:

[0105]

[0106] Genetic algorithms are suitable for problems with small search spaces, and they have significant advantages when optimizing weights in small datasets. This study uses genetic algorithms to optimize subjective and objective weights. The optimization objective is to minimize the difference between subjective weights (calculated using the G1 algorithm) and objective weights (calculated using the improved CRITIC algorithm). This ensures that the optimized weights effectively combine expert experience with the inherent information of the data, and that the optimization process balances the distribution of the two types of weights, thereby improving the scientific rigor and robustness of the weight allocation.

[0107] The steps for optimizing subjective and objective weights based on genetic algorithms are as follows:

[0108] S4.c1, Constructing the objective function

[0109]

[0110] in, Indicates the first i The subjective weights of each secondary indicator, Indicates the first i The objective weights of each secondary indicator, Indicates the first i The weights of each secondary indicator are randomly generated and combined, and satisfy the following conditions: ;

[0111] S4.c2, Setting Algorithm Parameters

[0112] The main parameters that need to be set in a genetic algorithm include: chromosome length, population size, maximum number of iterations, crossover probability, and mutation probability.

[0113] S4.c3. Initialize the population. The chromosome length corresponds to the number of secondary indicators. In this specific implementation, the number of secondary indicators is 12, so the chromosome length is set to 12. Then, randomly generate... q Individuals in a population, q Individual representatives of a population q A combined weight vector that satisfies the constraints; in this specific implementation, the population size is set to 50.

[0114]

[0115] in, q For population size, Indicates the first t The th randomly generated combined weight vector in the th k The combined weights of the indicators satisfy the following conditions: ;

[0116] S4.c4 Calculate the fitness of each combined weight vector.

[0117]

[0118] S4.c4, Selection, Crossover, Mutation

[0119] 1) Select

[0120] Using the roulette wheel selection method, in a randomly generated... q Individuals in each population collectively conduct q The next roulette wheel selection... q The combined weight vector serves as the parent. The probability of a particular combined weight vector being selected. P for:

[0121]

[0122] This process mimics the natural selection process, making high-fitness weight vector combinations more likely to exist and eliminating low-fitness weight vector combinations. After the roulette wheel selection, there are a total of... q One parent population was selected for subsequent operations.

[0123] 2) Cross

[0124] With a set crossover probability (set to 0.8 in this specific embodiment), the selected parent combination weight vectors are genetically recombined, exchanging some of their combination weights to generate "offspring", that is, new combination weight vectors.

[0125] 3) Variation

[0126] By randomly changing a certain weight of some combined weight vectors with a set mutation probability (0.03 in this specific embodiment), the phenomenon of gene mutation is simulated. This prevents the algorithm from getting stuck in local optima and increases its ability to explore new solutions.

[0127] S4.c5 iteration

[0128] An elite retention strategy is employed, directly passing the combined weight vector with the highest fitness in the current generation to the next generation, ensuring that the algorithm does not lose the discovered optimal solutions. New combined weight vectors generated through crossover and mutation are combined to form a new generation of the population. Step S4.c4 (selection, crossover, mutation) is repeated in each iteration, allowing the population to evolve generation by generation and continuously improve its overall fitness.

[0129] S4.c6 Termination Judgment

[0130] When the set number of iterations is reached (150 in this specific implementation) or the fitness does not improve for several consecutive rounds, the evolution stops and the optimal solution is output. Finally, a combined weight vector with the highest fitness (i.e., the optimal combined weight vector) is found.

[0131] The above process yields the weights of each indicator combination, providing a reference for subsequent expert evaluation.

[0132] S5. Based on the evaluation index system, identify the dependencies between underground space geological safety and evaluation indicators at all levels, construct a Bayesian network structure, and use D-separation to test the conditional independence assumption of the Bayesian network to ensure the rationality of the Bayesian network structure. The content includes:

[0133] Identify the dependencies between underground space geological safety and evaluation indicators at various levels:

[0134] The quality of each primary indicator depends on its subordinate secondary indicators, and the level of geological safety of underground space depends on each primary indicator. By transforming the geological safety of underground space and each evaluation indicator into different types of nodes in a Bayesian network according to their dependencies, the final Bayesian network structure for underground space geological safety is as follows: Figure 2 As shown.

[0135] Combined with appendix Figure 2 Note that the value range of each node in the Bayesian network includes:

[0136] (1) For node X1, the value range is set to two categories, namely {"G: good", "B: bad"};

[0137] (2) For nodes X2-X5, the value range is set to two categories, namely {"G: good", "B: bad"};

[0138] (3) For nodes S1-S12, the value range is set to four categories, namely {"Ⅰ: good", "Ⅱ: relatively good", "Ⅲ: relatively poor", "Ⅳ: poor"}.

[0139] The overall assumption of conditional independence exists in Bayesian networks. D-separation is a graphical method used to determine whether nodes satisfy the assumption of conditional independence. Compared to non-graphical methods, this method is more intuitive and computationally simple, and is widely used for verifying the conditional independence assumption in Bayesian networks. The main criteria for determining the conditional independence between nodes in a Bayesian network structure using D-separation are as follows: Figure 3 As shown, combined with Figure 3 The specific steps for determining the conditional independence between nodes in a Bayesian network structure using D-separation are explained below:

[0140] (1) For any two nodes in the Bayesian network structure, find all paths connecting the two nodes;

[0141] (2) Decompose the path into multiple triples. Based on the node observability conditions given in the network structure, check the activation state of each triple. The criteria are as follows: Figure 3 As shown;

[0142] (3) If there is a triplet in the path that is not activated, then the path is not activated and the above two node conditions are independent.

[0143] exist Figure 2 In the Bayesian network structure for underground space geological safety, all nodes except the root node are unobservable. This method is applied to check... Figure 2 After the Bayesian network structure for geological safety in underground space is shown, the overall assumption that the conditions between each node are independent holds.

[0144] S6. Obtain the prior probability of the root node and the conditional probabilities of other nodes to complete the construction of the Bayesian network model.

[0145] The steps to obtain the prior probability of the root node are as follows:

[0146] Calculate the area of ​​each level partition in the hierarchical vector diagram of each secondary indicator. The ratio of the area of ​​a certain level partition to the total area of ​​the evaluation area is the probability of occurrence of the corresponding basic event within the root node after the transformation of the secondary indicator. Calculate the probability of occurrence of all basic events within the root node to obtain the prior probability of the root node.

[0147] The steps to obtain the conditional probabilities of other nodes are as follows:

[0148] S6.1. Taking into full account the experts' professional positions, educational backgrounds, and years of experience, the experts are scored. The scoring criteria are shown in Table 3 as an example:

[0149] Table 3 Expert Weighting Criteria

[0150]

[0151] Scores are assigned according to the criteria, and the weights of each expert are determined using the following formula:

[0152]

[0153] in, Representing the i The scores of the experts, The sum of the scores of the representative experts.

[0154] Taking five experts as an example, their information is shown in Table 4:

[0155] Table 4 Expert Information

[0156]

[0157] According to the above formula, the expert weights are [0.19, 0.22, 0.17, 0.25, 0.17].

[0158] S6.a2、 n Based on engineering experience and a weighted combination of secondary indicators, experts used Pythagorean triangular fuzzy numbers to sequentially score the probability of occurrence of basic events within all nodes except the root node. This eliminates the need for conversion from fuzzy language description to Pythagorean triangular fuzzy numbers, which are expressed as follows:

[0159] ,

[0160] Among them, fuzzy numbers α The most likely value isb The least likely value is a and c , w α and u α They represent α The maximum and minimum membership degrees, and satisfying ;

[0161] The basic operational rules of Pythagorean triangular fuzzy numbers are:

[0162] set up For two Pythagorean triangular fuzzy numbers, λ If > 0, then:

[0163]

[0164]

[0165]

[0166]

[0167] Taking a basic event of node X4 (X4=G|S7=Ⅱ,S8=Ⅱ) as an example, the evaluations of this basic event by five experts are shown in Table 5:

[0168] Table 5 Expert Scoring Sheet for Basic Events (X4=G | S7=Ⅱ, S8=Ⅱ)

[0169]

[0170] Among them, (X4=G|S7=Ⅱ,S8=Ⅱ) represents the basic event of hydrogeological conditions when the groundwater level is Class II (good) and the groundwater corrosivity is Class II (good).

[0171] S6.3 Calculating the Pythagorean triangular fuzzy number under the influence of expert weights

[0172]

[0173] in, α j For the first j The Pythagorean triangular fuzzy number obtained by the experts in scoring the event W j For the first j The weight of each expert g This is the balance coefficient.

[0174] The Pythagorean triangular fuzzy number under the influence of expert weights is calculated using the expert weights [0.19, 0.22, 0.17, 0.25, 0.17]. ,Right now:

[0175]

[0176] S6.4 Calculation The scoring function, based on the score Sort in descending order to get The scoring function is expressed as:

[0177]

[0178] Among them, fuzzy numbers The most likely value is The least likely value is and , and They represent The maximum and minimum membership degree;

[0179] calculate The scoring function, sorted in descending order, yields:

[0180]

[0181] S6.5. Based on the Pythagorean triangular fuzzy hybrid geometry (PTFHG) operator, aggregate the expert scores of a single basic event within a single node, and calculate the aggregated Pythagorean triangular fuzzy number of the event under the influence of expert weights and location weights. β The Pythagorean triangular fuzzy hybrid geometric operator is expressed as:

[0182] in, ω j For the first j Position weights associated with the Pythagorean triangular fuzzy hybrid geometric operator.

[0183] The specific values ​​for the position weights can be found in Table 6:

[0184] Table 6 Location-Related Weight Lookup Table

[0185]

[0186] According to Table 6, when n When = 5, the weighted position weight vector of the PTFHG operator is determined according to the normal distribution method. ω =(0.112,0.236,0.304,0.236,0.112)T This operator is used to aggregate expert opinions, thereby obtaining the aggregated Pythagorean triangular fuzzy number. β =<(7.13, 7.61, 8.09), 0.75, 0.22>.

[0187] S6.6. Defuzzify the Pythagorean triangular fuzzy number using the centroid method and convert it into an accurate score. S ,

[0188]

[0189] Among them, fuzzy numbers β The most likely value is The least likely value is and , and These are the aggregated Pythagorean triangular fuzzy numbers. β Membership functions and non-membership functions are denoted as:

[0190]

[0191]

[0192] in, and Representing fuzzy numbers respectively β The maximum and minimum membership degrees.

[0193] The aggregated Pythagorean triangular fuzzy number β The value =<(7.13, 7.61, 8.09), 0.75, 0.22> is defuzzified to obtain its precise score. S The value is 9.8332. Similarly, the Pythagorean triangular fuzzy number of the event relative to the event (X4=B|S7=Ⅱ,S8=Ⅱ) is obtained. β =<(2.14, 2.51, 2.87), 0.79, 0.20>, defuzzify it to obtain its precise score. S The value is 3.828. Normalizing both yields a precise probability of 71.98% for the elementary event (X4=G| S7=Ⅱ, S8=Ⅱ) and a precise probability of 28.02% for the elementary event (X4=B| S7=Ⅱ, S8=Ⅱ).

[0194] S6.7 Calculate the exact probabilities of other basic events occurring at this node according to steps S6.2-S6.6 to obtain the conditional probability table of this node; similarly, the conditional probability tables of the remaining nodes can be obtained.

[0195] More specifically, in S6, the Bayesian network is written using Python software:

[0196] A1. Create a Bayesian network structure using the BayesianNetwork class in the Pgmpy library: Based on the dependencies between underground space geological safety and evaluation indicators at all levels identified in S5 and verified by the D separation test, define the dependencies between nodes and establish a Bayesian network structure.

[0197] A2. Use the TabularCPD class in the Pgmpy library to define the probability distribution for each node and obtain the node model;

[0198] A3. Input the conditional prior probabilities of each root node and the conditional probabilities of other nodes calculated in S6 into the constructed node model.

[0199] A4. Combine the node model with the Bayesian network structure to establish a complete Bayesian network model.

[0200] S7. Input the hierarchical data of the secondary indicators of each evaluation unit as the root node data into the Bayesian network model, and then rely on the Bayesian network model to perform forward inference, that is, call the VariableElimination class in Python software to perform forward inference, complete the calculation of the underground space geological safety score of each evaluation unit, integrate the underground space geological safety scores of each evaluation unit, formulate the underground space geological safety level classification standard based on the scores, and perform visualization processing. Taking the Shibei District of Qingdao City as the evaluation area as an example, generate the underground space geological safety zoning map of the evaluation area as follows. Figure 4 As shown.

[0201] Based on the scores, a standard for classifying the geological safety levels of underground spaces is formulated, as follows:

[0202] Evaluation results with scores in the range [0, 0.25] are classified as poor security level;

[0203] Evaluation results with scores in the range of (0.25, 0.5) are classified as having poor security.

[0204] Evaluation results with scores in the range of (0.5, 0.75) are classified as having a relatively good level of safety.

[0205] Evaluation results with scores in the range (0.75, 1) are classified as having good safety.

[0206] The specific process of visualization includes: importing the geological safety score data of each evaluation unit into ArcGIS software and linking it to the attribute table of the comprehensive vector map to form the "Geological Safety Score" field. According to the geological safety level classification standard, updating the symbol system display of this field in the layer attributes will generate a geological safety zoning visualization map of the evaluation area in ArcGIS software.

[0207] Although embodiments of the invention have been shown and described, those skilled in the art will be able to make various changes, modifications, substitutions and alterations to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for evaluating the geological safety of underground space, characterized in that, Includes the following steps: S1. The geological safety influencing factors of the underground space in the evaluated area are classified as indicators to establish a graded underground space geological safety evaluation index system, wherein the index system includes multiple primary indicators, and each primary indicator includes multiple secondary indicators. S2. Obtain the basic geological data vector map of each secondary indicator, classify each secondary indicator, establish the secondary indicator classification standard, and divide each vector map into zones according to the classification standard to form the classification vector map of each secondary indicator. S3. Based on ArcGIS software, the hierarchical vector maps are overlaid to form a comprehensive vector map. The comprehensive vector map is then divided into multiple evaluation units. The attribute table of the comprehensive vector map covers the hierarchical data of each secondary indicator within all evaluation units. Each row of the attribute table carries the hierarchical data of each secondary indicator within an evaluation unit. S4. The subjective weights of the secondary indicators are obtained using the G1 method, and the objective weights of the secondary indicators are obtained using the improved CRITIC method. Finally, the subjective and objective weights are optimized using a genetic algorithm to obtain the combined weights of each secondary indicator, providing a reference for subsequent expert evaluation. S5. Based on the evaluation index system, identify the dependency relationship between underground space geological safety and evaluation indicators at all levels, build a Bayesian network structure, and use D-separation to test the conditional independence assumption of the Bayesian network to ensure the rationality of the Bayesian network structure. S6. Obtain the prior probability of the root node and the conditional probabilities of other nodes to complete the construction of the Bayesian network model. S7. Input the graded data of the secondary indicators of each evaluation unit as the root node data into the Bayesian network model, and then rely on the Bayesian network model to perform forward reasoning to complete the calculation of the underground space geological safety score of each evaluation unit. Integrate the underground space geological safety scores of each evaluation unit, formulate the underground space geological safety level classification standard according to the score, and perform visualization processing to generate the underground space geological safety zoning map of the evaluation area.

2. The method for geological safety assessment of underground space according to claim 1, characterized in that: The steps in S4 for obtaining the subjective weights of secondary indicators using the G1 method include: determining the order relationship between secondary indicators, determining the importance of adjacent secondary indicators, and calculating the weight of each secondary indicator.

3. The method for evaluating the geological safety of underground space according to claim 1, characterized in that: The steps in S4 for obtaining the objective weights of the secondary indicators using the improved CRITIC method include: constructing the original evaluation matrix, performing matrix standardization, eliminating indicator differences using the coefficient of variation, calculating the correlation coefficient, and obtaining the objective weights of each secondary indicator.

4. The method for geological safety assessment of underground space according to claim 1, characterized in that: The step in S4, which uses a genetic algorithm to optimize subjective and objective weights and obtain the combined weights of secondary indicators, includes: taking minimizing the difference between subjective and objective weights as the objective function, repeatedly performing selection, crossover, and mutation operations to optimize the weight combination generation by generation, and finally finding a weight combination with the minimum fitness.

5. The method for geological safety assessment of underground space according to claim 1, characterized in that: The step of obtaining the prior probability of the root node in step S6 includes: calculating the area of ​​each level partition of the hierarchical vector diagram of each secondary indicator; the ratio of the area of ​​a certain level partition to the total area of ​​the evaluation area is the probability of occurrence of the corresponding basic event in the root node after the transformation of the secondary indicator; and calculating the probability of occurrence of all basic events in the root node to obtain the prior probability of the root node.

6. The method for geological safety assessment of underground space according to claim 1, characterized in that: The method for obtaining the conditional probabilities of other nodes in step S6 includes the following steps: S6.

1. Take into full account the experts’ professional positions, educational backgrounds, and years of experience to determine the expert weights; S6.

2. Experts, based on a combination of engineering experience and secondary indicators, use Pythagorean triangular fuzzy numbers to sequentially score the probability of occurrence of basic events contained in all nodes except the root node, thus eliminating the need for conversion from fuzzy language description to Pythagorean triangular fuzzy numbers. The Pythagorean triangular fuzzy numbers are expressed as follows: Among them, fuzzy numbers α The most likely value is b The least likely value is a and c , w α and u α They represent α The maximum and minimum membership degrees, and satisfying ; S6.3 Calculating the Pythagorean triangular fuzzy number under the influence of expert weights in, α j For the first j The Pythagorean triangular fuzzy number obtained by the experts in scoring the event W j For the first j The weight of each expert g This is the balance coefficient; S6.4 Calculation The scoring function, based on the score Sort in descending order to get The scoring function is expressed as: Among them, fuzzy numbers The most likely value is The least likely value is and , and They represent The maximum and minimum membership degree; S6.

5. Based on the Pythagorean triangular fuzzy hybrid geometric operator, aggregate the expert scores of a single basic event within a single node, and calculate the aggregated Pythagorean triangular fuzzy number of the event under the influence of expert weights and location weights. β The Pythagorean triangular fuzzy hybrid geometric operator is expressed as: in, ω j Position weights associated with the Pythagorean triangular fuzzy hybrid geometry operator; S6.

6. Use the centroid method to defuzzify the Pythagorean triangular fuzzy number and convert it into an accurate probability. S , Among them, fuzzy numbers β The most likely value is The least likely value is and , and These are the aggregated Pythagorean triangular fuzzy numbers. β Membership functions and non-membership functions are denoted as: in, and Representing fuzzy numbers respectively β The maximum and minimum membership degree; S6.7 Following steps S6.1-S6.7, calculate the exact probability of other basic events occurring at this node to obtain the conditional probability table for this node; similarly, obtain the conditional probability tables for the remaining nodes.

7. The method for geological safety assessment of underground space according to claim 1, characterized in that: The Bayesian network is written in Python.

8. The method for geological safety assessment of underground space according to claim 7, characterized in that: Based on the scores, S7 establishes a standard for classifying the geological safety levels of underground spaces, specifically as follows: Evaluation results with scores in the range [0, 0.25] are classified as poor security level; Evaluation results with scores in the range of (0.25, 0.5) are classified as having poor security. Evaluation results with scores in the range of (0.5, 0.75) are classified as having a relatively good level of safety. Evaluation results with scores in the range (0.75, 1) are classified as having good safety.

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