Tunnel support design method and system based on probabilistic knowledge graph and risk decision

Abstract

The present disclosure provides a tunnel support design method and system based on a probabilistic knowledge graph and risk decision, relating to the technical fields of underground engineering and intelligent decision, comprising: constructing a domain knowledge graph supporting probabilistic reasoning; generating a joint probability distribution of geological parameters through uncertainty quantification rules and parameter correlation processing; inputting the joint probability distribution as evidence into the domain knowledge graph through a deterministic evidence assignment or a virtual evidence mechanism, and automatically selecting a reasoning algorithm according to the network size to generate the top K candidate support schemes; taking the candidate support scheme set as input, establishing a multi-objective optimization model, providing two criteria of an automatic recommendation mode of minimizing the expected total cost and an interactive decision mode based on a risk preference coefficient, and introducing sensitivity evaluation for decision analysis. The present disclosure improves the support decision efficiency of complex tunnel projects with significant uncertainty and the need to quantitatively trade off safety risks and engineering costs.

Description

Technical Field

[0001] This disclosure relates to the fields of underground engineering and intelligent decision-making technology, specifically to a tunnel support design method and system based on probabilistic knowledge graphs and risk decision-making. Background Technology

[0002] The statements in this section are merely background information relating to this disclosure and do not necessarily constitute prior art.

[0003] One of the core challenges in tunnel support design lies in the inherent uncertainty of geological conditions. Unlike above-ground structures, the rock and soil masses traversed by tunnels are complex media formed through long-term geological processes, exhibiting significant spatial variability in their mechanical parameters (such as elastic modulus, cohesion, and internal friction angle) and groundwater conditions. During the exploration phase, limited by cost and technical means, data from discrete points can typically only be obtained through limited borehole sampling and geophysical methods. These data often have large intervals, making it difficult to fully characterize the true changes in geological conditions along the tunnel route. Therefore, the surrounding rock parameters obtained based on exploration information are essentially estimates of the actual geological conditions, containing significant statistical and cognitive uncertainties.

[0004] This uncertainty directly affects the safety and economy of the support scheme. Current tunnel support methods have the following limitations: (1) Knowledge graph-based tunnel support design methods typically treat the input geological and mechanical parameters as fixed values. Neither the empirical rules of "a certain type of surrounding rock corresponds to a certain type of support" stored in the knowledge graph nor the parameter values ​​used in numerical model calculations reflect their possible range of variation. This makes it difficult for existing systems to make comprehensive decisions.

[0005] (2) The safety factor method uses an empirical overall coefficient to cover all uncertainties, but this method cannot distinguish the differences in uncertainty between different parameters, often leading to a "one-size-fits-all" design that is either redundant or insufficient. Reliability design methods (such as the JC method and Monte Carlo simulation) can consider the randomness of parameters and calculate the probability of failure, but they also have several limitations: they require prior assumptions about the probability distribution type and statistical characteristics of the parameters, which are often difficult to obtain accurately during the survey stage; the calculation process is relatively complex and not easy to combine with experience-based knowledge graph reasoning; their output results (such as reliability indicators) are usually not directly related to the economic cost of the project and are not intuitive enough in design decisions. More importantly, most existing reliability analysis methods are independent of engineering knowledge graph and case base systems and fail to utilize a large amount of historical engineering data to assist in probabilistic inference and decision-making.

[0006] (3) Lack of dynamic updating capability. Tunnel construction is a dynamic process. As excavation progresses, new information such as geological sketches of the tunnel face, on-site load tests, and surrounding rock deformation monitoring are constantly generated. This information could be used to update and correct the initial geological parameter estimates, thereby gradually reducing uncertainty and optimizing subsequent support design. However, existing knowledge graph systems are mostly static and cannot achieve online updates of probabilistic models based on construction feedback, thus missing the opportunity to improve design accuracy by utilizing real-time information. Summary of the Invention

[0007] To address the aforementioned issues, this disclosure proposes a tunnel support design method and system based on probabilistic knowledge graphs and risk decision-making. It explicitly handles the uncertainty of geological parameters, deeply integrates knowledge graph empirical reasoning with mechanical mechanism analysis, constructs a risk-cost multi-objective decision-making model, and generates natural language descriptions of the decision explanations.

[0008] According to some embodiments, the present disclosure adopts the following technical solutions: A tunnel support design method based on probabilistic knowledge graphs and risk decision-making includes: Construct a domain knowledge graph that supports probabilistic reasoning based on relevant parameters of tunnel support design; It receives discrete geological exploration data and generates a joint probability distribution of geological parameters through uncertainty quantification rules and correlation processing between parameters; The joint probability distribution is used as evidence. It is input into the domain knowledge graph through deterministic evidence assignment or virtual evidence mechanism. The inference algorithm is automatically selected according to the network size to calculate the posterior probability distribution of all unobserved nodes in the network. The top K candidate support schemes are generated by using a branch-bound pruning strategy. Using a set of candidate support schemes as input, a multi-objective optimization model is established with the direct cost of each scheme as the cost objective and the product of the failure probability and failure consequences as the risk expected loss objective. It provides two criteria: an automatic recommendation mode that minimizes the expected total cost and an interactive decision-making mode based on the risk preference coefficient. Sensitivity assessment is introduced for decision analysis. The final support plan and its decision analysis results will be presented and exported in a comprehensive manner in multiple forms.

[0009] According to some embodiments, the present disclosure adopts the following technical solutions: A tunnel support design system based on probabilistic knowledge graphs and risk decision-making includes: The knowledge graph construction module is used to construct a domain knowledge graph that supports probabilistic reasoning based on relevant parameters of tunnel support design. The probability quantization module is used to receive discrete geological exploration data and generate a joint probability distribution of geological parameters through uncertainty quantification rules and correlation processing between parameters. The scheme generation module is used to take the joint probability distribution as evidence, input it into the domain knowledge graph through deterministic evidence assignment or virtual evidence mechanism, automatically select the inference algorithm according to the network size, calculate the posterior probability distribution of all unobserved nodes in the network, and generate the top K candidate support schemes using the branch-bound pruning strategy. The multi-objective decision-making module takes a set of candidate support schemes as input, uses the direct cost of each scheme as the cost objective, and the product of the failure probability and the failure consequence as the risk expected loss objective to establish a multi-objective optimization model. It provides two criteria: an automatic recommendation mode that minimizes the expected total cost and an interactive decision-making mode based on the risk preference coefficient. Sensitivity assessment is introduced for decision analysis. The scheme presentation module is used to comprehensively present and export the final support scheme and its decision analysis results in multiple formats.

[0010] According to some embodiments, the present disclosure adopts the following technical solutions: A computer program product includes a computer program that, when executed by a processor, implements the tunnel support design method based on probabilistic knowledge graphs and risk decision-making.

[0011] According to some embodiments, the present disclosure adopts the following technical solutions: A non-transitory computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the tunnel support design method based on probabilistic knowledge graphs and risk decision-making.

[0012] According to some embodiments, the present disclosure adopts the following technical solutions: An electronic device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to implement the tunnel support design method based on probabilistic knowledge graph and risk decision-making.

[0013] Compared with the prior art, the beneficial effects of this disclosure are as follows: The tunnel support design method based on probabilistic knowledge graphs and risk decision-making disclosed herein quantifies the uncertainty of discrete geological exploration data and generates a joint probability distribution of geological parameters by combining the correlation between parameters. This transforms the fluctuations of surrounding rock parameters, exploration errors, and cognitive uncertainties that are difficult to express in traditional support design into computable and inferable probabilistic information. It avoids the problem of conservative or unsafe support design caused by simply treating geological parameters as certain values, and improves the adaptability and reliability of the support scheme generation results to complex geological conditions.

[0014] This disclosed tunnel support design method based on probabilistic knowledge graphs and risk decision-making constructs a risk-cost multi-objective decision-making model by using the direct cost of candidate support schemes as the cost objective and the product of failure probability and failure consequences as the risk expected loss objective. This model can ensure the safety of the project while taking into account the economic efficiency of the support, avoiding the one-sidedness of relying solely on a single safety factor or a single cost index for scheme selection. At the same time, through automatic recommendation mode, interactive decision-making mode, and sensitivity assessment, it can provide designers with different risk preferences with quantifiable, comparable, and interpretable basis for scheme selection.

[0015] This disclosed tunnel support design method based on probabilistic knowledge graphs and risk decision-making constructs a domain knowledge graph that supports probabilistic reasoning. This graph unifies information such as geological parameters, support schemes, intermediate performance, and engineering cases. It also uses directed acyclic graphs and Bayesian networks to express causal dependencies and conditional probability relationships between entities. This enables the fusion of engineering experience, standard rules, mechanical mechanisms, and historical case data, improving the systematicness and traceability of the support scheme reasoning process. Furthermore, the knowledge graph can be updated with new cases and construction feedback data, which is beneficial for continuously refining the probabilistic model and improving the accuracy of subsequent section support designs. Attached Figure Description

[0016] The accompanying drawings, which form part of this disclosure, are used to provide a further understanding of this disclosure. The illustrative embodiments of this disclosure and their descriptions are used to explain this disclosure and do not constitute an undue limitation of this disclosure.

[0017] Figure 1 This is a flowchart of a tunnel support design method based on probabilistic knowledge graphs and risk decision-making, according to an embodiment of the present disclosure. Figure 2 This is a domain knowledge graph architecture diagram of an embodiment of the present disclosure; Figure 3 Detailed maps are generated for the quantification and joint distribution of geological parameter uncertainties in embodiments of this disclosure. Detailed Implementation

[0018] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0019] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains.

[0020] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this disclosure. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0021] Example 1 One embodiment of this disclosure provides a tunnel support design method based on probabilistic knowledge graphs and risk decision-making, the method steps of which include: Step 1: Construct a domain knowledge graph that supports probabilistic reasoning based on relevant parameters of tunnel support design; Step 2: Receive discrete geological exploration data and generate a joint probability distribution of geological parameters through uncertainty quantification rules and parameter correlation processing; Step 3: Using the joint probability distribution as evidence, input it into the domain knowledge graph through deterministic evidence assignment or virtual evidence mechanism, and automatically select the inference algorithm according to the network size to calculate the posterior probability distribution of all unobserved nodes in the network, and use the branch and bound pruning strategy to generate the top K candidate support schemes. Step 4: Using the set of candidate support schemes as input, with the direct cost of each scheme as the cost objective and the product of the failure probability and failure consequences as the risk expected loss objective, establish a multi-objective optimization model, providing two criteria: an automatic recommendation mode that minimizes the expected total cost and an interactive decision-making mode based on the risk preference coefficient. Introduce sensitivity assessment for decision analysis. Step 5: Present and export the final support plan and its decision analysis results in multiple formats.

[0022] As one embodiment, the tunnel support design method based on probabilistic knowledge graphs and risk decision-making disclosed herein is an intelligent tunnel support design method capable of explicitly handling geological parameter uncertainties, deeply integrating knowledge graph empirical reasoning with mechanical mechanism analysis, supporting risk-cost multi-objective trade-off decisions, and possessing Bayesian dynamic update capabilities. The specific implementation process of this method includes: Step 1: Construct a domain knowledge graph that supports probabilistic reasoning based on relevant parameters of tunnel support design.

[0023] This step aims to construct a domain knowledge graph capable of explicitly expressing uncertainty and supporting probabilistic reasoning. The graph employs a two-layer architecture: the bottom layer is the structural layer, defining the causal and conditional dependencies between entities in the form of a directed acyclic graph (DAG); the upper layer is the probabilistic layer, using a Bayesian network (BN) to assign a quantified probability distribution to each node (random variable) and each edge (dependency) in the structural layer. This allows the graph to possess both a clear causal logical structure and rigorous uncertainty quantification capabilities. The specific implementation steps are as follows: Step 11: Ontology layer of knowledge graph.

[0024] The system predefines four core entity types, and each type can be further divided into subclasses.

[0025] (1) Geological Parameter Entity The description of the natural geological conditions of the tunnel section is divided into qualitative attributes and quantitative attributes.

[0026] ① Qualitative attributes (discrete random variables) Table 1 Qualitative Geological Attribute Parameters

[0027] Note: Categorical distribution is a probability distribution used to describe discrete random variables. Its core characteristics are: the variable can only take a finite number of discrete category values ​​(i.e., values ​​in the set of values); each category has a corresponding probability of occurrence; and the sum of the probabilities of all categories is 100%.

[0028] ② Quantitative attributes (continuous random variables) Table 2 Quantitative Geological Attribute Parameter Table

[0029] (2) Support Scheme This describes a complete set of support design parameters, composed of multiple sub-components. The parameter values ​​of each sub-component are discrete random variables, and their probability distribution depends on the geological conditions and intermediate performance.

[0030] Table 3 Entity Parameter Table of Support Scheme

[0031] (3) Intermediate Performance Connecting geological conditions and support schemes, reflecting mechanical response, it serves as a bridge for probability transmission. All intermediate performance entities are continuous random variables, and their distributions are obtained by substituting the uncertainty of input parameters into the mechanical model.

[0032] Table 4 Intermediate Performance Entity Attribute Table

[0033] (4) Project Case Entities This records complete information about a specific section of a historical tunnel project for empirical verification and subsequent incremental learning. Attributes include: tunnel name, station range, observed geological parameters (with measurement error distribution), support scheme used, construction monitoring data statistics (mean, variance, maximum and minimum values), and project evaluation (success / mostly successful / failure / accident). Case entities exist as "samples" and do not participate in initial inference, but are used for parameter learning and verification.

[0034] Step 12: Define the relation type and conditional probability table.

[0035] Define the directed edges (relationships) between entities and their quantification methods. All relationships form a directed acyclic graph, which is checked for acyclicity using a topological sorting algorithm. Relationships are divided into three categories: causal dependencies, conditional probabilistic relationships, and similarity-based relationships.

[0036] (1) Causal dependency This represents the direct influence of one entity's attribute on another entity's attribute, with the direction determined by mechanical mechanisms or physical laws. This type of relationship does not directly store probability tables; it only serves as a structural edge in the Bayesian network, indicating the direction of probability dependence.

[0037] Definition method: Defined using OWL object property and marked as "causal".

[0038] Typical set of causal edges (predefined, expandable): Table 5 Typical Causal Nodes

[0039] Directed acyclic property guarantee: When constructing the graph, the system performs a topological sort on all nodes. If a cycle is detected (e.g., A→B→C→A), the system refuses to add edges that would cause the cycle and prompts the user to make corrections.

[0040] (2) Conditional probability relationship Each non-root node (especially the support scheme entity node and intermediate performance entity node) is associated with a conditional probability table (CPT), defined as: (1) Where P(·) represents the conditional probability, which is the probability that a child node will take a specific value given the value of the parent node; the child node is the node variable of the probability distribution to be determined in the Bayesian network, such as a certain attribute in the support scheme entity or intermediate performance entity; the parent node represents all the parent node variables that directly point to the child node in the graph structure, which represents the set of attributes that have a causal or statistical impact on the child node.

[0041] Furthermore, the construction of the conditional probability table (CPT) incorporates the following three methods, specifically: Method 1: Empirical statistics based on design specifications Applicable scenarios: Support parameters that are directly affected by the surrounding rock grade, or parameters for which recommended combinations have been clearly given in the specifications.

[0042] ① Extract the "common combinations" and "frequency of use" of support parameters corresponding to different surrounding rock grades from current standards such as the "Design Code for Highway Tunnels" (JTG 3370.1) and the "Design Code for Railway Tunnels" (TB 10003). The standards usually list the recommended relationships of "surrounding rock grade - shotcrete thickness - anchor spacing - steel arch frame model" in tabular form.

[0043] ② Convert the recommended values ​​in the specifications into frequency distributions. For example, under Class IV surrounding rock conditions, the specifications give "shotcrete thickness: 10 cm (common) or 12 cm (optional)", then the system can assign probabilities of 0.7 and 0.3 respectively.

[0044] ③ If the standard does not specify the frequency information, an equal probability distribution or a setting based on engineering experience can be adopted.

[0045] ④ Store the generated CPT in the graph.

[0046] Its mathematical expression is: Set child nodes For discrete variables, parent node If the variable is discrete (such as the surrounding rock grade), then CPT is defined as: (2) in, These are discrete sub-node variables (such as shotcrete thickness, anchor bolt spacing, etc.). Represents the first of Y i One possible value; X Discrete parent node variables (such as surrounding rock grade); express X The j One possible state; Indicates the frequency of joint operations; in historical data, standards, or engineering statistics, when... hour, The number of times this combination appears (or the recommended frequency); Representing marginal frequency (normalized denominator), in a fixed... Under the conditions, for All possible values y k (in k The summation of the frequencies of all possible probabilities ensures that the sum of all conditional probabilities equals 1.

[0047] Method 2: Forward simulation based on mechanical model Applicable scenarios: Support parameters that are affected by multiple continuous variables and have a clear mechanical mechanism, such as (tunnel wall displacement, presence or absence of steel arch) → shotcrete thickness.

[0048] ① Parent node discretization: Divide each continuous parent node variable into several intervals. Discretization strategies can include equal-width method, equal-frequency method, or non-uniform partitioning based on mechanical sensitivity. For example, tunnel wall displacement. It can be divided into based on experience. mm.

[0049] ② Enumerate the combinations of parent node states Assume the parent node contains There are 10 variables, each variable is divided into 100 variables. There are intervals, then there are a total of Combinations of parent node states.

[0050] ③ Perform Monte Carlo simulations for each combination. Within the parameter space corresponding to a given combination of parent node states (e.g.) mm and steel arch frame = none), randomly sample a set of geological parameters ( The joint distribution of (etc.). Number of samplings. (like Statistical stability should be ensured.

[0051] For each sampling point, call the mechanical model (convergence-constraint method or finite element method) to calculate the structural safety factor FoS under the candidate support parameters (such as the thickness of shotcrete being 5, 8, 10, 12, 15, 20 cm).

[0052] Determine the target safety factor (e.g.) Minimum shotcrete thickness .

[0053] Considering construction variations, the actual spraying thickness is taken as... ,in , The precision required for construction (e.g., 0.5 cm) will then be determined. Round to the nearest value in the discrete set of values.

[0054] ④ Statistical probability: Statistically determine the frequency of each discrete injection thickness value under the state combination of the parent node, and use it as the conditional probability under the corresponding conditions.

[0055] ⑤ Summary: Repeat steps 3–4 for all parent node state combinations to form a complete CPT.

[0056] As one example, the process of calling the mechanical model includes: ① Convergence-Constraint Method Model: Input includes surrounding rock characteristic curves (from...) Calculate the displacement of the tunnel wall before support ) and support characteristic curve (support stiffness calculated from support parameters) The equilibrium displacement is obtained by solving for the intersection of the two curves. and support pressure Then, the safety factor is calculated: (3) in, The safety factor is a dimensionless quantity that represents the safety reserve of the support structure or surrounding rock. The maximum load that the support structure or surrounding rock can withstand (unit: MPa or kN / m) is determined by the material strength and geometric dimensions. To balance the support pressure (unit: MPa or kN / m), the intersection point of the surrounding rock characteristic curve and the support characteristic curve is used to determine the actual surrounding rock pressure borne by the support structure.

[0057] ② Finite element method model: Automatically generates a two-dimensional plane strain model to simulate the excavation and support process and output displacement and internal force results.

[0058] Method 3: Based on empirical statistical formulas Applicable scenarios: When there is an empirical regression formula relationship, such as the empirical relationship between the thickness of shotcrete and the amount of deformation.

[0059] ① Obtain empirical formulas, which generally take the following form: (4) in, This is a child node variable representing the design or measured thickness of the shotcrete. This is a parent node variable representing the radial displacement of the tunnel wall; The linear regression coefficient (slope) represents the average increase in the thickness of the sprayed concrete required for every 1 mm increase in the displacement of the tunnel wall. It is obtained through regression analysis of historical data. This is the linear regression intercept term, in centimeters. Its physical meaning is the theoretically required thickness of the foundation shotcrete when the displacement of the tunnel wall is zero (u=0). This is the random error term, which is key to transforming deterministic formulas into probabilistic models. It represents all the uncertainties that empirical formulas cannot fully explain.

[0060] ②Parent node Discretize into several intervals, and select a representative value (such as the midpoint of the interval) in each interval.

[0061] ③Calculation Conditional distribution: given , Follows a normal distribution .

[0062] ④ Map the continuous distribution to the set of discrete values: Calculate the probability mass of each discrete value (i.e. the probability of falling into the interval corresponding to the discrete value) through the normal cumulative distribution function.

[0063] ⑤ Store the obtained probability distribution as CPT.

[0064] (3) Similarity relationship Similarity associations are used to connect entities with different geological parameters or different engineering case entities, representing their degree of similarity in the attribute space. This relationship supports case-based reasoning (CBR) and does not participate in reasoning as a probabilistic dependency edge in a Bayesian network.

[0065] ① Attribute standardization For each entity, its attribute vector Standardization process: (5) in, These are the standardized attribute values, with a mean of 0 and a standard deviation of 1, used to eliminate the influence of differences in the units of different attributes. For the entity in the first i The original values ​​of each attribute (such as Rc, Kv, etc.); For all entities of the same type in the first i The mean of each attribute; For all entities of the same type in the first i Standard deviation of each attribute.

[0066] ② Weighted Euclidean distance Calculate the weighted Euclidean distance between entity A and entity B: (6) in: This is the weighted Euclidean distance between entity A and entity B. This is the final calculation result, directly measuring the degree of dissimilarity between the two entities; For the first i The weight coefficient of the nth attribute. Its value is the nth attribute weight coefficient. i coefficient of variation of each attribute The reciprocal of, that is .in For the first i The coefficient of variation of an attribute is the ratio of the attribute's standard deviation to its mean, reflecting the relative dispersion of the attribute. This means that; Indicates the first i Standard deviation of each attribute; Indicates the first i The mean of each attribute. Attributes with greater uncertainty (larger coefficient of variation) have higher weights. Conversely, the smaller the value, the weaker its influence in distance calculation; For entity A in the th i Standardized values ​​for each attribute. Standardization has eliminated the influence of dimensions, allowing for fair comparisons between attributes at different scales. For entity B in the 1st i Standardized values ​​for each attribute.

[0067] ③ Similarity conversion The distance is mapped to a similarity value using a Gaussian kernel function: (7) in, For entities With entity The similarity between the two values ​​is in the range (0,1]. The closer the value is to 1, the more similar the two are. When the distance is infinitely large, the similarity approaches 0. ) is an entity With entity The weighted Euclidean distance between them represents the original, untransformed degree of dissimilarity between the two. This is the bandwidth parameter of the Gaussian kernel. This is a key adjustment parameter that controls the rate at which similarity decays with increasing distance. The larger the bandwidth, the slower the decay, and the smoother the change in similarity with distance.

[0068] ④ Storage strategy To control the graph size, each entity retains only its top K neighbor entities with the highest similarity (K=10), and the remaining edges are not included in the graph storage.

[0069] Step 13: Learning and updating the parameters of the conditional probability table.

[0070] The initially constructed CPT may contain some biases, and as engineering practice progresses and case data accumulates, it is necessary to dynamically update and calibrate the CPT. This disclosure employs a Bayesian parameter learning method to iteratively correct the probability distribution in the CPT using newly added observation data.

[0071] (1) Sources of learning data The data used for CPT parameter learning mainly comes from the following three sources: ① Project Case Entities Successful or unsuccessful cases recorded in historical engineering projects include complete geological parameter observations and the actual support schemes used.

[0072] ② Numerical simulation database Artificial sample data, generated through calculations using a mechanical model with a large number of parameter combinations, is used to supplement sparse or missing working conditions in actual engineering projects.

[0073] ③ Construction feedback data Field monitoring data acquired during tunnel construction (such as surrounding rock deformation and support structure stress) are standardized and outlier removed, then transformed into training samples for learning. This data is used to dynamically calibrate the probabilistic knowledge graph during the construction phase, thereby improving the accuracy of subsequent section support design.

[0074] (2) Learning of discrete node CPT For discrete child nodes Given a combination of its parent nodes CPT parameters are defined as follows: The parameter update adopts a Bayesian estimation framework, using the Dirichlet distribution as the conjugate prior.

[0075] ① Prior distribution specification Regarding the parent node state parameter vector The prior distribution is: (8) in: Let be the vector of probability parameters to be estimated. It is a vector containing the known parameters... Under the condition, child nodes The conditional probability of taking each possible value; The distribution is a Dirichlet distribution. It is a continuous multivariate probability distribution defined on the "probability simplex" (i.e., a non-negative vector whose sum of all components is 1). It is the conjugate prior distribution of the multivariate distribution, which means that when observation data is introduced, its posterior distribution is still a Dirichlet distribution, making Bayesian update computation very simple. child node The number of discrete states (values); The hyperparameter (pseudo-count) of the Dirichlet distribution corresponds to the state of the parent node. x At that time, the sub-nodes of "pre-conceived" or "subjective belief" Take the first i Values ​​( y i The "virtual number" of occurrences. All Sum of values The equivalent sample size, known as the prior, reflects the strength of confidence in this prior belief.

[0076] The determination of prior parameters follows these principles: if no prior knowledge is available, a uniform prior is used: If an initial CPT exists, then the initial probability is converted into a pseudo-count: (9) in, is the pseudo-counting parameter, a hyperparameter in the Dirichlet distribution. Its meaning is: when the parent node's state is... At that time, subjectively presupposed, the child node is considered Values The "virtual occurrence count" directly It determines the shape of the prior distribution. The equivalent sample size for prior knowledge determines the amount of prior knowledge to be assigned (i.e., The "confidence strength" of a priori experience is indicated by its value. A higher value indicates greater confidence in prior experience, and more actual observational data are needed to change this initial belief. This is the initial conditional probability, typically derived from domain experts or historical norms. It represents the expert's belief, before any new data is available, that "in..." The probability estimate of the occurrence of the event "when".

[0077] ② Posterior update Let the observation dataset be... Include Each independent sample. For the parent node state... Observed The frequency is According to Bayes' theorem, the posterior distribution remains a Dirichlet distribution: (10) in, Let be the posterior distribution, representing the conditional probability vector after the dataset D has been observed. The latest understanding, used to... Make probabilistic inferences; Let be the vector of probability parameters to be estimated. It is a vector containing the known parameters... Under the condition, the conditional probability of child node Y taking each possible value; The observation dataset contains N independent and identically distributed samples, used to update new evidence for cognition; The observation frequency, which is the core evidence gleaned from data D, indicates "when..." The number of times that the case Y=yi was actually observed; For the hyperparameters (pseudo-counts) of the Dirichlet distribution; These are the posterior distribution parameters. This is prior knowledge. The direct sum of ) and actual evidence (n) perfectly embodies the Bayesian update idea: posterior cognition = prior cognition + observational evidence.

[0078] ③ Point estimation Point estimates of the CPT parameters are obtained using maximum a posteriori (MAP) estimation: (11) in, This is the maximum posterior point estimate of the conditional probability; Hyperparameters of the Dirichlet distribution (Pseudo-counting); The observation frequency, which is the core evidence gleaned from data D, indicates "when..." The number of times that the case Y=yi was actually observed; These are the posterior distribution parameters; The total effective sample size represents the summation of the posterior pseudo-counts of all K possible values ​​of child node Y under the same parent node state x. Let Y be the total number of possible discrete states for child node Y.

[0079] ④ Bayesian smoothing When data is sparse (i.e.) When the sample size is small, the MAP estimate will automatically shrink towards the prior probability, thus effectively avoiding overfitting. A minimum sample size threshold can be set; when the cumulative sample size is below this threshold, the prior distribution will still be used as the CPT value.

[0080] (3) Learning of continuous node CPT For continuous child nodes, a parameterized conditional probability density function is typically used for modeling, as shown in the following formula: (12) in, For continuous child node variables, the model is to describe or predict continuous results, and their values ​​are continuous real numbers; As a parent node variable, it has an impact The variables can be a single variable or a vector of multiple variables; they can be discrete or continuous. This refers to the specific value of the parent node. When it is a vector, Represents a specific combination of values; It follows a normal distribution (Gaussian distribution); Let be the conditional mean function, representing the expression for a given condition. = Under the conditions, The expected value (average), it is a value about The function that describes Follow Systemic trends of change. Let be the conditional variance function, representing the variance under given conditions. = Under the conditions, The degree of volatility or uncertainty, it is also a matter of... The function means The magnitude of the fluctuation may vary with The accuracy of the prediction changes depending on the different states.

[0081] ① Linear regression model When the conditional mean can be approximated as a linear combination of the parent nodes, let: (13) in, consecutive child nodes The conditional mean function represents the expression after taking the value of a given parent node. The average value; Let m be the specific values ​​of the parent nodes, and let these parent nodes collectively influence the child nodes. These can be continuous or discrete variables; The intercept of the linear regression model is the child node when all parent nodes are 0. The conditional mean provides a baseline for the model; These are the regression coefficients corresponding to each parent node. These are the key parameters of the model. Quantitatively expressed the first Parent nodes child nodes The strength of the "marginal impact". Specifically, while keeping other parent nodes unchanged, For every additional unit, conditional mean average change Units.

[0082] Parameter learning employs Bayesian linear regression: i. Prior distribution: regression coefficients ,variance .

[0083] ii. Posterior distribution: After obtaining the observation data, the posterior distribution can be calculated using analytical expressions or the Gibbs sampling algorithm.

[0084] iii. Update mechanism: The posterior estimate of the regression coefficients is continuously updated using new data, thereby correcting the conditional distribution.

[0085] ② Non-parametric processing methods When the relationships between variables are complex and difficult to express in simple parametric form, a nonparametric method based on discretization can be used: i. Discretize the continuous parent node into several intervals according to a certain strategy.

[0086] ii. Within each interval, assume It follows a normal distribution, and the mean and variance are estimated using the observed samples within this interval.

[0087] iii. Store the fitted conditional probability distribution as a CPT table for use in Bayesian network inference.

[0088] Step 2: Receive discrete geological exploration data and generate a joint probability distribution of geological parameters through uncertainty quantification rules and parameter correlation processing.

[0089] This step aims to automatically transform discrete exploration information provided by users through forms, files, or databases into an evidence form (i.e., a probability distribution) acceptable to Bayesian networks by applying rules such as multi-sample fitting, single-sample combined with empirical coefficient of variation, direct assignment of qualitative parameters, and marginalization inference for missing parameters, based on the richness of the data. After processing the correlations between parameters, a joint probability distribution of geological parameters is generated, providing input for the Bayesian inference in the subsequent step 3. Specific implementation steps include: Step 21: Input interface design.

[0090] The following three input methods are provided to accommodate geological data from different sources and formats.

[0091] (1) Form input Users can enter the values ​​of various geological parameters one by one through a graphical interface. For qualitative parameters (such as surrounding rock grade and groundwater status), the interface provides drop-down menus for selection; for quantitative parameters (such as uniaxial compressive strength Rc of rock), users can enter a single value, multiple sample values, or directly specify the probability distribution type and its parameters.

[0092] (2) File import It supports batch import of exploration data in Excel, CSV, and other formats. Each line in the file represents a complete record of a measuring point or a borehole. The system will automatically parse the fields and map them to the corresponding internal geological parameters.

[0093] (3) Database integration By directly connecting to geological exploration databases (such as borehole databases and geophysical results databases) via standardized APIs, the system automatically reads relevant fields and completes data format conversion, reducing manual data entry.

[0094] Step 22: Uncertainty Quantification Rules.

[0095] Based on the richness of the input data, the following rules are automatically applied to transform the original input into a probability distribution.

[0096] Rule 1: Multiple Sample Fitting If a user provides multiple observation samples for the same parameter (e.g., measurements from multiple boreholes) value ,and The system will automatically perform distribution fitting, and the process is as follows: ① Calculate the sample mean with sample standard deviation .

[0097] ② Perform a normality test (using the Shapiro-Wilk test, significance level 0.05). ).like If the value is >0.05, the normality assumption is accepted, and the data is fitted to a normal distribution. .

[0098] ③ If the normality test fails, try a log-normal distribution: take the logarithm of the sample and perform the normality test again. If it passes, then fit the data to a log-normal distribution with the parameters set to [parameter value missing]. , .

[0099] ④ If neither of the above two distributions passes the test, or the sample size is less than 5, then the fit is a triangular distribution: the minimum value is taken as... The most likely value is the sample median, and the maximum value is... .

[0100] After the fitting is completed, the system outputs the fitting results and goodness-of-fit indices (such as...). (Value, root mean square error), users can confirm or manually adjust the distribution type and parameters.

[0101] Rule 2: Single sample + empirical coefficient of variation If the user provides only one observation value (Or a representative value automatically selected from multiple samples), the system will retrieve the typical range of its coefficient of variation (COV) from the built-in knowledge base based on the surrounding rock grade and engineering experience of the parameter. Reference COV ranges for some parameters are as follows: ① Uniaxial compressive strength of rock Typical COV values ​​for Class IV surrounding rock are 0.20–0.30; ② Elastic modulus Typical COV values ​​are 0.25–0.40; ③ Cohesion Typical COV values ​​are 0.30–0.50; ④ Angle of internal friction Typical COV values ​​are 0.10–0.20.

[0102] The system generates a triangular distribution based on this: the minimum value is taken as... The most likely value is The maximum value is taken Users can adjust the COV value using the slider and observe changes in the distribution shape in real time.

[0103] Rule 3: Qualitative Parameter Processing For qualitative parameters (such as surrounding rock grade and groundwater condition), users can directly select a category. The system treats this category as definitive evidence, setting the probability of the corresponding condition to 1.0. If the user's judgment of the qualitative parameter is uncertain (e.g., "the surrounding rock may be grade IV or grade V"), they can directly input a probability vector through advanced mode, such as {Ⅳ: 0.7, Ⅴ: 0.3}.

[0104] Rule 4: Handling Missing Parameters If the user does not provide a value for a certain parameter (e.g., does not enter the rock mass integrity index), The system will utilize the dependency relationship between this parameter and other known parameters to perform marginal reasoning from the conditional probability table of the knowledge graph, obtaining a prior distribution as a substitute. For example, when the surrounding rock grade is known to be Class IV, the conditional distribution can be directly extracted from the CPT. As The prior distribution of .

[0105] Step 23: Handling the correlation between parameters.

[0106] There is a general correlation between geological parameters (e.g.) and Positive correlation, and (Also showing a positive correlation). To accurately characterize the joint distribution of parameters, the system provides the following two processing methods.

[0107] Method 1: Gaussian Copula Method First, the marginal distributions of each parameter are mapped to a standard normal space using a Probability Integral Transform (PIT). Then, the correlation coefficient matrix is ​​calculated in the normal space (this matrix can be learned from historical cases in the knowledge graph or specified directly by the user). Finally, Gaussian Copula is used to generate joint samples that preserve the correlation structure.

[0108] Method 2: Conditional Probability Decomposition By directly utilizing the causal dependencies already modeled in the knowledge graph, the joint distribution is decomposed into a product of a series of conditional probabilities: (14) in, The joint probability distribution represents all listed parameters (uniaxial compressive strength of rock). Rock mass integrity coefficient Cohesion internal friction angle The probability (or probability density) of all of them taking specific values ​​simultaneously; The marginal probability distribution represents the parameter. Its own probability distribution, without considering other parameters; Let be a conditional probability distribution, representing the conditional probability distribution under known uniaxial compressive strength of rock. Under the given conditions, the rock mass integrity factor The probability distribution, which quantifies right Statistical dependence; Let be a conditional probability distribution, representing the condition that is known at the same time. and Under the given conditions, cohesion The probability distribution, which quantifies right and Joint dependencies; For the continuation of the solution, it means that this decomposition process can continue in this pattern, and each subsequent term is the conditional probability of the current variable given all previously occurring variables.

[0109] The sampling process starts from the root node and generates values ​​for each node sequentially based on conditional probabilities. This method naturally inherits the dependency structure in the graph, eliminating the need to specify an additional correlation coefficient matrix.

[0110] Step 24: Generation and output of the joint probability distribution.

[0111] After processing according to the above rules, the system will generate a joint probability distribution of geological parameters for the target tunnel section, specifically including the following: (1) For discrete parameters, store the probability mass function of each state; (2) For continuous parameters, store the distribution type and parameters, and optionally store the discretized probability table for subsequent Bayesian network inference; (3) For the correlation between parameters, store the correlation coefficient matrix or Copula related parameters.

[0112] The final results are output in JSON or HDF5 format for loading by the Bayesian inference engine in step 3. Simultaneously, the system will display the uncertainty quantification results in visual formats (such as probability density curves, box plots, and correlation matrix heatmaps) for user review and confirmation.

[0113] Step 3: Perform Bayesian inference based on probabilistic knowledge graphs.

[0114] This step uses the joint probability distribution of geological parameters generated in step 2 as evidence. It inputs the evidence into the probabilistic knowledge graph (i.e., Bayesian network) through deterministic evidence assignment or virtual evidence mechanism. Based on the network size, it automatically selects the connection tree exact inference algorithm or the Gibbs sampling approximate inference algorithm to calculate the posterior probability distribution of all unobserved nodes in the network (especially the support scheme entity nodes and intermediate performance entity nodes). Then, it outputs the posterior distribution of intermediate performance such as tunnel wall displacement and safety factor, as well as the posterior probability of each support parameter value. Finally, it uses a branch and bound pruning strategy to generate the top K candidate support schemes.

[0115] Step 31: Evidence input.

[0116] The probability distributions of various geological parameters determined or quantified in step 2 are set as the probability states of the corresponding evidence nodes in the Bayesian network. The specific processing method is as follows: (1) Deterministic evidence: If a parameter takes a definite value (e.g., the surrounding rock grade = grade IV), then the probability of that state is set to 1.0, and the probability of other states is set to 0.

[0117] (2) Probabilistic evidence: If a parameter exhibits a probability distribution (e.g. If the distribution follows a continuous distribution, then a virtual evidence mechanism is used for soft evidence injection. Specifically, a likelihood node is constructed, and its conditional probability table is defined as follows: The observations are fixed, thus updating the prior distribution with posterior information.

[0118] (3) Missing information nodes: For nodes that do not provide any observation information, their prior distribution remains unchanged.

[0119] Step 32: Bayesian inference algorithm.

[0120] The appropriate inference algorithm is automatically selected based on the network size and complexity.

[0121] (1) Exact reasoning (small-scale network, number of nodes ≤ 50) The Junction Tree Algorithm is used, and the specific steps are as follows: ①Moralization: Transform the directed acyclic graph of the Bayesian network into an undirected moral graph by adding undirected edges between parent nodes that share a common child node.

[0122] ② Triangulation: Triangulate the moral graph to obtain a chord graph, which controls the size of subsequent cliques.

[0123] ③ Construct a connection tree: Identify all maximal cliques in the graph and construct a connection tree, where each node (clique) is a set of interconnected variables.

[0124] ④ Belief propagation: A two-phase message passing process is performed on the connection tree: i. Collection phase: Messages are passed from leaf nodes to root nodes level by level; ii. Distribution phase: Messages are sent back from the root node to the leaf nodes.

[0125] ⑤ Calculate the marginal posterior: After belief propagation is completed, the marginal posterior probability distribution of any node can be extracted from the potential function of each cluster.

[0126] This algorithm can accurately solve for the posterior probability, and its time complexity is exponentially related to the tree width of the network. It is suitable for networks of medium to small size.

[0127] (2) Approximate reasoning (large-scale network, number of nodes > 50) The Gibbs sampling method in Markov Chain Monte Carlo (MCMC) is used, and the steps are as follows: ① Initialization: Assign random initial states to all unobserved nodes (which can be sampled from their respective prior distributions).

[0128] ② Iterative sampling: Set the total number of iterations Combustion period In each iteration: i. Iterate through each non-evidence node in turn, and calculate the conditional probability distribution of the node based on the current state of its Markov blanket (including parent node, child node and other parent nodes of the child node); ii. Extract a new state from the conditional distribution and update the node values.

[0129] ③ Sample collection: After the combustion period ends, in order to reduce sample autocorrelation, the sample status is saved every 10 steps.

[0130] ④ Posterior estimation: Statistically count the frequency of different states of each node in the collected samples, and use it as an approximate estimate of the posterior probability.

[0131] Gibbs sampling is suitable for large-scale networks, but the convergence of Markov chains needs to be diagnosed (e.g., using the Gelman-Rubin diagnostic method).

[0132] (3) Implementation of the inference engine The system can encapsulate open-source Bayesian network libraries (such as pgmpy, PyMC, and Stan) or self-developed high-efficiency inference engines, and provide users with a unified application programming interface, including: i.set_evidence(evidence_dict): Sets the evidence; ii.query(variables): Specifies the variables to be queried; iii.get_posterior(): Get the posterior probability result.

[0133] Step 33: Output the reasoning results.

[0134] After the reasoning is completed, the following three types of core information will be output.

[0135] (1) Posterior distribution of intermediate performance entities Cave wall displacement The posterior probability density function (or discretized histogram) is given, along with statistics such as mean, standard deviation, and quantiles (5%, 50%, 95%).

[0136] Safety factor The posterior distribution is obtained, and the failure probability is calculated accordingly: (15) in, The failure probability, with a value ranging from 0 to 1, quantitatively represents the likelihood that the tunnel support is in an unsafe state. The safety factor is a continuous random variable whose probability distribution (posterior distribution) incorporates the uncertainty of all input parameters (such as geotechnical parameters, loads, etc.). It is no longer a fixed value in traditional design, but a probability distribution that includes possible values. For the event The cumulative probability is less than 1.0. Mathematically, it is equal to the safety factor. The posterior probability density function in the interval The integral area on the curve directly quantifies the proportion of the distribution curve that falls within the danger zone.

[0137] (2) Posterior probability of the support scheme entity The posterior probability of each support parameter (such as shotcrete thickness, anchor spacing, and steel arch frame type) for each possible value. For example:

[0138] This is a specific engineering decision probability output, which shows the posterior probability distribution of the support scheme calculated by the Bayesian network model after inputting current survey data (such as surrounding rock grade, displacement value, etc.) as evidence.

[0139] This means that, based on existing geological evidence, the probability of choosing a 10-centimeter shotcrete thickness is 55%, the probability of choosing a 12-centimeter thickness is 35%, and the probability of choosing a 15-centimeter thickness is only 10%. This set of probabilities is not a traditional mathematical formula, but a direct result of model reasoning. It transforms complex models and data into a clear decision support chart, quantifying the relative suitability of each alternative under specific current conditions, thereby helping engineers make more scientific choices based on an understanding of uncertainty.

[0140] (3) Generation of candidate support schemes The system enumerates all possible values ​​for each support parameter and calculates the posterior joint probability of each complete scheme. To avoid combinatorial explosion (e.g., 5 types of shotcrete thickness × 4 types of anchor spacing × 5 types of steel arch frame), the system employs a branch-and-bound pruning strategy: sorting by posterior probability from high to low, only the top K schemes with the highest probabilities are retained (K is user-defined, default value is 10), forming a set of candidate support schemes. For each candidate scheme, the corresponding intermediate performance condition distribution (such as displacement, safety factor, etc.) is also provided.

[0141] Step 34: Visualization of uncertainty propagation.

[0142] To visually demonstrate the information update process in a Bayesian network, the following visualization tools are provided: (1) Entropy reduction diagram (Sankey diagram or heat map): shows the amount of entropy reduction of each node before and after the introduction of evidence, that is, the distribution of information gain.

[0143] (2) Parallel coordinate graph: shows the posterior probability ranking of candidate support schemes and their distribution characteristics in the multidimensional parameter space.

[0144] (3) Prior-posterior comparison diagram: The prior distribution and the posterior distribution are compared in the form of probability density curves, which intuitively reflects the effect of observation data on reducing cognitive uncertainty.

[0145] Step 4: Construct a risk-cost multi-objective optimization decision-making model.

[0146] This step takes the candidate support scheme set generated in step 3 as input, uses the direct cost of each scheme as the cost objective, and the product of the failure probability and failure consequences as the risk expected loss objective to establish a multi-objective optimization model. The Pareto front is solved by the fast non-dominated sorting algorithm, and two criteria are provided: an automatic recommendation mode that minimizes the expected total cost and an interactive decision-making mode based on the risk preference coefficient. At the same time, sensitivity analysis of key parameters such as failure consequences and unit cost price is used to provide decision-makers with an objective basis for quantitative trade-offs between cost and risk and a robustness assessment.

[0147] Step 41: Define decision variables and objective function.

[0148] ① Decision variables Candidate support options ( Each scheme consists of a set of defined support parameter values ​​(e.g., shotcrete thickness). Anchor spacing (The steel arch frame model is I16, etc.).

[0149] ② Cost Target

[0150] plan The support cost (unit: yuan / meter) is directly calculated from the derived attributes carried by the support scheme entity in step 1.

[0151] The unit price of each sub-component is dynamically retrieved from the quota database and can be updated according to market price changes. Since all support parameters in the scheme are already defined as specific values, It is a definite value.

[0152] ③ Risk Objectives

[0153] The risk objective is defined as expected loss, which is the product of the probability of failure and the consequences of failure. (16) in, For support scheme The expected loss due to risk. This is the final quantitative indicator for the decision, representing the expected risk cost per meter of tunnel that must be borne on average in the long run when adopting this scheme; For the first The candidate support schemes are the objects of decision-making. Different schemes (such as different support thicknesses and support types) will have different failure probabilities and costs, which are used to quantify their risk costs. For the plan The failure probability. This value is directly derived from the Bayesian inference and reliability analysis results of the previous step (Formula 15). It is a probability value between 0 and 1, which quantitatively reflects the technical risk of the scheme; The failure consequence is a constant measured in monetary terms, with the unit being "yuan / meter". It covers all direct and indirect economic losses incurred per meter of tunnel in the event of a safety accident and is usually determined through engineering experience or a special assessment.

[0154] Furthermore, if the plan The corresponding posterior distribution of the safety factor cannot be directly provided. (For example, only provided) If the mean and standard deviation are given, then we can assume that... If it follows a log-normal distribution, the failure probability can be approximated by the following formula: (17) in, The failure probability represents the probability that the safety factor is less than 1.0. Let be the cumulative distribution function of the standard normal distribution, and let its function value be... The standard normal random variable is given a value less than The probability of; The mean of lnFoS is the safety factor. Taking the natural logarithm of this random variable yields a new variable. Then calculate the expected value of the new variable. Let lnFoS be the standard deviation; Reliability index In approximate form, this negative ratio is a dimensionless number, usually denoted as - , The higher the value, the higher the probability of failure. The smaller.

[0155] Step 42: Multi-objective Pareto optimization.

[0156] Map all candidate solutions to a two-dimensional decision space with cost C on the horizontal axis and risk R on the vertical axis.

[0157] (1) Pareto dominance The plan Domination Plan (recorded as) ), if and only if both of the following conditions are met: ① and ; ②At least one of the above two inequalities is strictly true.

[0158] (2) Pareto optimality (non-dominated solution) If no other solution can be used S i ,but S i This is called a Pareto optimal solution. The set of all Pareto optimal solutions is called the Pareto Frontier. (3) Frontier computing algorithms The Fast Non-dominated Sort algorithm is used, and the specific steps are as follows: ① For each scheme Calculate two quantities: i. Domination count : Dominate The number of options; ii. Dominating set :quilt The set of schemes under control.

[0159] ② Filter out all that meet the requirements The proposed scheme categorizes it as the first frontier. .

[0160] ③ For each solution in the list, iterate through its... Each scheme in ,Will Subtract 1. If Reduce to 0, then It is now included in the next frontier.

[0161] ④ Repeat step 3 until all schemes are assigned to a frontier.

[0162] (4) Visualization All candidate schemes are displayed in scatter plot format, with Pareto front schemes connected and highlighted by a red curve. Each data point supports hover interaction, allowing users to view detailed support parameter information for the corresponding scheme.

[0163] Step 43: Decision-making criteria and recommendations.

[0164] Two decision-making modes are provided, allowing users to flexibly choose according to the actual needs of the project.

[0165] Mode 1: Automatic Recommendation Mode (Minimize Expected Total Cost) Calculate the Total Expected Cost (TEC) for each option: (18) in, For the plan The expected total cost is the final economic indicator for decision-making, and its unit is "yuan / meter". It represents the total economic burden that each meter of tunnel will need to bear on average throughout the project's entire life cycle after adopting the plan, and it is the direct basis for comparing and selecting plans. For the first One candidate support plan to be compared; For the plan The direct cost is a relatively certain one-time investment cost that occurs during the construction period, and the unit is "yuan / linear meter". It covers all costs of materials, construction and other aspects of all engineering measures under the plan. :plan The expected loss of risk is the expected value of potential losses that may occur during the operating period at the time of decision-making. For the plan The failure probability is derived from the preceding reliability analysis (Formula 15). As for the consequences of failure, the total economic loss per meter of tunnel in the event of a failure event is a constant that is assessed and determined.

[0166] The economic meaning of this formula is: under the same engineering conditions and with repeated construction over a long period, the total expenditure per linear meter equals the sum of direct costs and expected losses. The system automatically recommends... The solution with the minimum value is selected as the "optimal solution". Simultaneously, the following key metrics of this solution are output for user review: direct cost. Failure probability Expected loss Expected total cost Safety factor mean and 5th percentile.

[0167] Mode 2: Interactive Decision-Making Mode Users can set their risk preference level using the slider. Define the comprehensive utility function: (19) in, For the plan The smaller the overall utility value, the better the overall performance of the plan under the decision-maker's current specific risk preferences.

[0168] The risk preference coefficient has the following meanings: ① : Only consider direct costs, completely ignore risks (risk neutrality); ② : Only consider the level of risk, completely ignore the cost (extreme risk aversion); ③ Costs and risks are weighted equally.

[0169] For the plan The expected loss of risk represents the potential cost of future risk. For the plan The direct cost represents the one-time construction investment cost.

[0170] According to the current Values ​​are calculated in real time for each scheme. The system recommends the option that minimizes this value and highlights it on the Pareto front plot. Users can also directly click on any data point on the Pareto front to manually select their preferred option, and the system will then display the complete support parameters and risk-cost decomposition details of that option.

[0171] Step 44: Sensitivity analysis.

[0172] To assess the robustness of the recommended scheme, the system automatically performs the following three sensitivity analyses.

[0173] (1) Failure consequences Sensitivity analysis Consequences of failure Multiply by 0.5 and 2.0 respectively, and recalculate the expected total cost of each option. Then, a new optimal solution is determined. If the optimal solution changes, it indicates that the recommendation result is incorrect. The value is quite sensitive, and the system will prompt the user to review it. The basis for this setting.

[0174] (2) Analysis of Implicit Risks of Target Safety Factor Although this method does not directly use the safety factor as a decision variable, it can be reverse-checked: if the user requires the minimum safety factor... The corresponding implicit failure probability threshold is The system will output the failure probability of the current optimal solution. Whether it exceeds this threshold is for designers' reference.

[0175] (3) Sensitivity analysis of unit cost The unit prices of major sub-components (such as shotcrete and steel arches) will be increased and decreased by 20% respectively, and the direct cost will be recalculated. and expected total cost Observe whether the optimal solution changes.

[0176] Sensitivity analysis results are output in tabular form and as a Tornado Diagram, helping decision-makers to intuitively grasp the degree of impact of each key parameter on the final solution.

[0177] (4) Comprehensive robustness assessment Based on the above three sensitivity analyses, the system comprehensively rates the robustness of the recommended solutions, and the rating criteria are as follows: ① High robustness: In the three sensitivity analyses, the optimal solution did not change, indicating that the recommended conclusion is not sensitive to the values ​​of key parameters and the decision is highly reliable; ② Moderate robustness: If the optimal solution changes in a sensitivity analysis while the other two remain unchanged, the system will prompt the user to pay attention to the sensitive parameter and suggest strengthening the confirmation or control of the parameter in actual engineering. ③Low robustness: If the optimal solution changes in two or more sensitivity analyses, it indicates that the recommended conclusion is relatively sensitive to the parameter values. The system will suggest that the user expand the range of candidate solutions or supplement the exploration data to reduce uncertainty before re-analyzing.

[0178] The comprehensive robustness assessment results will be an important component of the decision support report, visually presenting the relative impact of each sensitive parameter in the form of radar charts or dashboards to help users determine the reliability of the current recommended solution.

[0179] Step 45: Output the decision results After the decision analysis is completed, the system outputs the following complete results: (1) A complete list of support parameters for the final recommended solution (automatic mode) or the user-selected solution (interactive mode); (2) Risk-cost integrated report, covering direct cost, failure probability, expected loss, expected total cost and posterior distribution statistics of safety factor; (3) Pareto front plot (PNG or SVG format) and a comparison table of all candidate solutions; (4) Sensitivity analysis report.

[0180] The above outputs can be used directly for construction drawing design, or submitted as formal attachments to the design documents.

[0181] Step 5: Output decision support results with uncertainty.

[0182] This step presents the final support scheme and decision analysis results determined in step 4 in a comprehensive manner, including structured parameter tables, uncertainty quantification indicators, alternative scheme comparisons, various visualization charts, and natural language explanatory text. It also explicitly labels and interprets probabilistic indicators such as failure probability and confidence interval to avoid misinterpreting uncertain conclusions as deterministic assertions. The steps also support the export of results in multiple formats such as PDF, Excel, and JSON, and system integration.

[0183] Step 51: Output Content The system outputs the following three types of core information.

[0184] (1) Optimal support scheme (deterministic parameters) The specific parameters of each sub-component of the final selected scheme are clearly listed in a structured table format, as shown in Table 6.

[0185] Table 6 Example of Sub-component Parameters for Support Scheme

[0186] The above parameters can be used directly as a basis for construction.

[0187] For the recommended optimal solution, the following key indicators reflecting the level of uncertainty are output: ① Probability of failure Expressed as a percentage (e.g., 2.3%), with an explanatory note: "Estimated probability of a safety incident occurring under the current geological conditions of variability." ② Safety factor confidence interval: for example, "safety factor" The 90% confidence interval is The average value is 1.45.

[0188] ③ Prediction range of tunnel wall displacement: For example, "the prediction range of 90% of the radial displacement of the tunnel wall is..." mm".

[0189] ④ Risk cost breakdown: Display the relationship between direct costs and expected losses as a percentage of total expected costs using a pie chart or bar chart.

[0190] (3) Comparison of alternative solutions Provides detailed comparative information on 2-3 suboptimal solutions on the Pareto front, including: ① Support parameters, direct costs, failure probabilities, and expected total costs for each scheme; ② Use color coding to identify advantages (e.g., green for lower cost, red for lower risk) to quickly identify differences.

[0191] Step 52: Visualize the output format.

[0192] The following graphical methods help users understand uncertainty and decision-making trade-offs: (1) Probability density curve: showing the safety factor under the optimal solution. The posterior probability density curve is used, and the failure region is clearly marked with a shaded area. The area of ​​).

[0193] (2) Risk-cost scatter plot: plot the distribution of all candidate solutions in the cost-risk two-dimensional plane, highlight the optimal solution, and connect the Pareto front points with a red curve.

[0194] (3) Parallel coordinate graph: The differences between the various schemes in terms of support parameter values, cost, failure probability, etc. are presented in the form of multi-dimensional lines, which facilitates comprehensive comparison.

[0195] (4) Sankey diagram of uncertainty propagation: illustrating the propagation of uncertainty from input parameters (e.g. The distribution of the data is inferred through a Bayesian network and then transmitted to the output index (e.g., the distribution of the data). The information flow process.

[0196] Step 53: Decision support interpretation text.

[0197] Automatically generate natural language explanations for decision-making, making it easier for non-professional decision-makers to intuitively grasp the meaning of the conclusions. An example is shown below: "Based on the current survey data, the recommended solution is: a 12 cm thick sprayed concrete layer and 1.0 m spacing between I16 steel arch frames. The direct cost of this solution is 3500 yuan / linear meter, with an estimated failure probability of 2.3%, corresponding to an expected loss of 23000 yuan / linear meter and an expected total cost of 26500 yuan / linear meter. Compared to the more economical solution (cost 3200 yuan / linear meter, failure probability 5.1%), this solution trades an additional 300 yuan / linear meter for a 2.8% reduction in failure risk. Compared to the safer solution (cost 5200 yuan / linear meter, failure probability 0.3%), this solution significantly saves costs within an acceptable risk range." Step 54: Results Export and Interface.

[0198] Supports exporting output results in multiple formats to meet the needs of different use cases: (1) PDF report: A formal report containing all charts and explanatory text; (2) Excel data table: provides raw data for secondary analysis; (3) JSON / XML format: used for data integration with other software systems or databases; (4) Print directly or push to the construction management system via API.

[0199] Example 2 One embodiment of this disclosure provides a tunnel support design system based on probabilistic knowledge graphs and risk decision-making, including: The knowledge graph construction module is used to construct a domain knowledge graph that supports probabilistic reasoning based on relevant parameters of tunnel support design. The probability quantization module is used to receive discrete geological exploration data and generate a joint probability distribution of geological parameters through uncertainty quantification rules and correlation processing between parameters. The scheme generation module is used to take the joint probability distribution as evidence, input it into the domain knowledge graph through deterministic evidence assignment or virtual evidence mechanism, automatically select the inference algorithm according to the network size, calculate the posterior probability distribution of all unobserved nodes in the network, and generate the top K candidate support schemes using the branch-bound pruning strategy. The multi-objective decision-making module takes a set of candidate support schemes as input, uses the direct cost of each scheme as the cost objective, and the product of the failure probability and the failure consequence as the risk expected loss objective to establish a multi-objective optimization model. It provides two criteria: an automatic recommendation mode that minimizes the expected total cost and an interactive decision-making mode based on the risk preference coefficient. Sensitivity assessment is introduced for decision analysis. The scheme presentation module is used to comprehensively present and export the final support scheme and its decision analysis results in multiple formats.

[0200] Example 3 One embodiment of this disclosure provides a computer program product, including a computer program that, when executed by a processor, implements the tunnel support design method based on probabilistic knowledge graphs and risk decision-making.

[0201] Example 4 One embodiment of this disclosure provides a non-transitory computer-readable storage medium for storing computer instructions. When these computer instructions are executed by a processor, they implement the tunnel support design method based on probabilistic knowledge graphs and risk decisions.

[0202] Example 5 One embodiment of this disclosure provides an electronic device, including a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to implement the tunnel support design method based on probabilistic knowledge graphs and risk decision-making.

[0203] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0204] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0205] While the specific embodiments of this disclosure have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of this disclosure. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this disclosure are still within the scope of protection of this disclosure.

Claims

1. A tunnel support design method based on probabilistic knowledge graphs and risk decision-making, characterized in that, include: Construct a domain knowledge graph that supports probabilistic reasoning based on relevant parameters of tunnel support design; The construction of a domain knowledge graph supporting probabilistic reasoning based on tunnel support design parameters includes: Four core entity parameter types are defined, as are the relationships between entities and their quantification methods. All relationships constitute a directed acyclic graph. We construct a domain knowledge graph that can explicitly express uncertainty and support probabilistic reasoning. The architecture adopts a two-layer model: the bottom layer is the structural layer, which defines the skeleton of causal and conditional dependencies between entities in the form of a directed acyclic graph; the upper layer is the probabilistic layer, which uses a Bayesian network to assign a quantified probability distribution to each node and each edge in the structural layer. It receives discrete geological exploration data and generates a joint probability distribution of geological parameters through uncertainty quantification rules and correlation processing between parameters; The joint probability distribution is used as evidence. It is input into the domain knowledge graph through deterministic evidence assignment or virtual evidence mechanism. The inference algorithm is automatically selected according to the network size to calculate the posterior probability distribution of all unobserved nodes in the network. The top K candidate support schemes are generated by using a branch-bound pruning strategy. The process involves using the joint probability distribution as evidence, inputting it into the domain knowledge graph through deterministic evidence assignment or a virtual evidence mechanism, automatically selecting an inference algorithm based on the network size, calculating the posterior probability distribution of all unobserved nodes in the network, and generating the top K candidate support schemes using a branch-bound pruning strategy, including: The joint probability distribution of the determined or quantified geological parameters is set as the probability state of the corresponding evidence node in the Bayesian network. Based on the network size and complexity, the algorithm automatically selects either the exact inference algorithm of the connection tree or the approximate inference algorithm of the Gibbs sampling to calculate the posterior probability distribution of all unobserved nodes in the network, and then outputs the posterior distribution of the tunnel wall displacement, the intermediate performance of the safety factor, and the posterior probability of the values ​​of each support parameter. All possible values ​​of each support parameter are combined and enumerated, and the posterior joint probability of each complete scheme is calculated. A branch-bound pruning strategy is adopted to retain the top K schemes with the highest probabilities to form a set of candidate support schemes. Using a set of candidate support schemes as input, a multi-objective optimization model is established with the direct cost of each scheme as the cost objective and the product of the failure probability and failure consequences as the risk expected loss objective. It provides two criteria: an automatic recommendation mode that minimizes the expected total cost and an interactive decision-making mode based on the risk preference coefficient. Sensitivity assessment is introduced for decision analysis. The final support plan and its decision analysis results will be presented and exported in a comprehensive manner in multiple forms.

2. The tunnel support design method based on probabilistic knowledge graph and risk decision-making as described in claim 1, characterized in that, The process of receiving discrete geological exploration data and generating a joint probability distribution of geological parameters through uncertainty quantification rules and parameter correlation processing includes: Acquire discrete geological exploration data provided by users through various means such as forms, files, or databases; Based on the richness of the input data, the system automatically applies predefined rules to transform the original input into a probability distribution. The rules set include multi-sample fitting, single-sample combined with empirical coefficient of variation, direct assignment of qualitative parameters, and marginalization reasoning for missing parameters, which transform discrete geological exploration data into evidence forms that can be accepted by Bayesian networks. Finally, the joint probability distribution of geological parameters is generated after processing the correlation between parameters.

3. The tunnel support design method based on probabilistic knowledge graphs and risk decision-making as described in claim 1, characterized in that, The multi-objective optimization model is established by taking a set of candidate support schemes as input, using the direct cost of each scheme as the cost objective, and the product of the failure probability and the failure consequence as the expected risk loss objective, including: Each candidate support scheme consists of a set of defined support parameter values. The support cost of the scheme is directly calculated from the derived attributes carried by the support scheme entity. The risk target is defined as the expected loss, which is the product of the failure probability and the failure consequence. All candidate solutions are mapped to a two-dimensional decision space with cost as the horizontal axis and risk as the vertical axis. The Pareto front is solved using a fast non-dominated sorting algorithm, and all candidate solutions are displayed in the form of a scatter plot.

4. The tunnel support design method based on probabilistic knowledge graphs and risk decision-making as described in claim 1, characterized in that, It provides two criteria: an automatic recommendation mode that minimizes the expected total cost and an interactive decision-making mode based on risk preference coefficients. It also incorporates sensitivity analysis of key parameters such as failure consequences and unit cost, including: The automatic recommendation mode includes: calculating the expected total cost of each solution, and selecting the solution that minimizes the expected total cost as the optimal solution; The interactive decision-making mode includes: setting the risk preference coefficient via a slider, defining the comprehensive utility function, calculating the comprehensive utility value of each option in real time based on the current risk preference coefficient value, and recommending the option that minimizes the value; Simultaneously assess the robustness of the recommended scheme by performing the following three sensitivity analyses: sensitivity analysis of failure consequences, implicit risk analysis of the target safety factor, and sensitivity analysis of cost per unit price. Based on three sensitivity analyses, the robustness of the recommended scheme is comprehensively rated.

5. A tunnel support design system based on probabilistic knowledge graphs and risk decision-making, characterized in that, Specifically, the tunnel support design method based on probabilistic knowledge graphs and risk decision-making as described in any one of claims 1-4 includes: The knowledge graph construction module is used to construct a domain knowledge graph that supports probabilistic reasoning based on relevant parameters of tunnel support design. The probability quantization module is used to receive discrete geological exploration data and generate a joint probability distribution of geological parameters through uncertainty quantification rules and correlation processing between parameters. The scheme generation module is used to take the joint probability distribution as evidence, input it into the domain knowledge graph through deterministic evidence assignment or virtual evidence mechanism, automatically select the inference algorithm according to the network size, calculate the posterior probability distribution of all unobserved nodes in the network, and generate the top K candidate support schemes using the branch-bound pruning strategy. The multi-objective decision-making module takes a set of candidate support schemes as input, uses the direct cost of each scheme as the cost objective, and the product of the failure probability and the failure consequence as the risk expected loss objective to establish a multi-objective optimization model. It provides two criteria: an automatic recommendation mode that minimizes the expected total cost and an interactive decision-making mode based on the risk preference coefficient. Sensitivity assessment is introduced for decision analysis. The scheme presentation module is used to comprehensively present and export the final support scheme and its decision analysis results in multiple formats.

6. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the tunnel support design method based on probabilistic knowledge graph and risk decision-making as described in any one of claims 1-4.

7. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, which, when executed by a processor, implement the tunnel support design method based on probabilistic knowledge graphs and risk decision-making as described in any one of claims 1-4.

8. An electronic device, characterized in that, include: The device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to implement the tunnel support design method based on probabilistic knowledge graph and risk decision-making as described in any one of claims 1-4.

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