Construction method of prediction model for adjacent building damage induced by subway tunnel construction based on Bayesian network

Abstract

The present invention relates to a method for constructing a prediction model for adjacent building damage induced by subway tunnel construction based on a Bayesian network, and belongs to the field of tunnel engineering risk control. First, engineering cases are collected to form a sample library of adjacent building damage induced by subway tunnel construction, and an indicator system including influencing factors and damage characteristic indicators is established. Next, the hierarchical relationship of the influencing factors is divided by the method of interpreting the structural model, and the initial network structure of the Bayesian network model is determined. Then, the initial network structure is applied to improve the structural learning method of the Bayesian network model, and a basic Bayesian network model is constructed. Furthermore, the randomness of the simulated annealing algorithm search strategy is reduced by the basic Bayesian network model, a hybrid modeling method is formed for structural learning, and an optimized Bayesian network prediction model for adjacent building damage induced by subway tunnel construction is constructed. The sample library of the present invention is reasonably constructed, the mathematical model fits the reality, the prediction performance is efficient, and the application value is high.

Description

Technical Field

[0001] The invention belongs to the field of tunnel engineering risk control and relates to a method for constructing a subway tunnel construction-induced adjacent building damage prediction model based on a Bayesian network. Background Art

[0002] The construction of urban subways provides an effective solution to alleviate urban traffic congestion and other problems. However, the construction of urban subway tunnels often induces damage to adjacent buildings. It is of great value to predict in advance the damage to adjacent buildings that may be induced by subway tunnel construction, provide a technical basis for taking reasonable and effective prevention and control measures, and ensure the safety of adjacent buildings and the smooth progress of urban subway tunnel construction.

[0003] The damage to adjacent buildings induced by subway tunnel construction can be characterized by indicators such as inclination rate, ultimate tensile strain, deflection ratio and crack width, and can be predicted and evaluated by empirical formula method, numerical simulation calculation method and model test method. However, the existing prediction methods have shortcomings such as low accuracy, high computational difficulty and high time cost. With the widespread application of artificial intelligence in all walks of life, machine learning algorithms have generated a large number of applications in the field of tunnel engineering, such as neural networks, support vector machines, logistic regression, random forests, Bayesian Network (BN) models and other machine learning algorithms, which have shown very superior application performance in the fields of tunnel engineering surrounding rock classification, surrounding rock stability analysis, surface settlement prediction and so on. Among them, as one of the most effective uncertainty knowledge expression and reasoning algorithms, BN builds a knowledge system containing deep quantitative logical relationships between nodes by constructing a directed acyclic graph (BN structure) that characterizes the directional connection relationship between network nodes and a conditional probability table (BN parameter) that characterizes the conditional probability relationship between nodes, and applies Bayesian formula, Markov chain rule and conditional independence rule to perform reasoning calculations, which has the advantages of clear physical meaning, strict calculation logic and flexible application. Therefore, the present invention uses the influencing factors and damage characteristic indicators of adjacent building damage induced by subway tunnel construction as the nodes of BN, and constructs a BN model for adjacent building damage prediction based on theoretical analysis and sample data learning to achieve the prediction and diagnosis of adjacent building damage.

[0004] The construction of BN depends on historical sample data. The sample data of subway tunnel construction-induced damage to adjacent buildings has the characteristics of small sample size, many missing values, and many influencing factors, which leads to poor application effect of conventional BN models. Therefore, the present invention optimizes the construction method of conventional BN models to construct a BN model that can realize the prediction of adjacent building damage induced by subway tunnel construction: 1) The hierarchical relationship of the influencing factors of adjacent building damage induced by subway tunnel construction is revealed through the Interpretive Structure Model (ISM) method, which provides basic parameters for data learning of conventional BN structures and improves the efficiency and quality of structure learning; 2) Based on the network structure obtained by conventional BN structure learning, the simulated annealing method is used to further optimize the network structure and construct a BN structure with better quality. The BN model constructed by the above optimization method can effectively predict the risk of adjacent building damage induced by subway tunnel construction; and can diagnose possible disaster-causing factors when adjacent buildings are damaged. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide a method for constructing a subway tunnel construction-induced adjacent building damage prediction model based on Bayesian Network (BN).

[0006] First, data is collected to form a case library of subway construction-induced damage to adjacent buildings, and an indicator system containing influencing factors and damage characteristic indicators is established. Then, the hierarchical relationship of influencing factors is divided by the Interpretive Structure Model (ISM) method to determine the initial network structure of the BN model. Then, based on the initial network structure, the K2 scoring algorithm is used to learn the network structure and determine the basic network structure of the BN model; the data learning method is used to construct the conditional probability table of the BN model. Then, the simulated annealing algorithm is used to further optimize the basic network model to obtain the optimized network structure of the BN model; finally, the data learning method is used to construct the conditional probability table of the BN model to form an optimized BN prediction model for subway tunnel construction-induced damage to adjacent buildings. The constructed optimized BN model is used to realize the prediction of the damage state of adjacent buildings induced by subway tunnel construction and the diagnosis of engineering diseases.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] The method for constructing a prediction model for adjacent building damage induced by subway tunnel construction based on BN includes the following steps:

[0009] (1) Construction of a sample library of damage to adjacent buildings induced by subway tunnel construction. The prediction model involved in the present invention needs to be constructed based on a sample library of subway tunnel construction. Therefore, subway tunnel engineering data are collected to form a case library, and the main influencing factors are determined; the influencing factors are classified into disaster-causing levels, and the damage characteristic indicators are classified into damage levels to form a sample library.

[0010] a. Construction of case library and determination of influencing factors

[0011] Through the research literature and case reports on subway tunnel construction risks, a case library of subway tunnel construction near existing buildings is established. Based on the principle of improving the accuracy and simplicity of the prediction model, combined with the data in the existing case library, the tunnel burial depth (x1), tunnel cover span ratio (x2), tunnel excavation method (x3), bedrock cover thickness (x4), surrounding rock level (x5), relative position between building and tunnel (x6), building length-to-height ratio (x7), building height (x8), building structure form (x9), building foundation form (x10), and other factors are determined. 10 ), building age (x 11 ), maximum building settlement (x 12 ), the overall inclination rate of the building (x 13 ) are 13 factors in total, which are used as the influencing factors of the damage of adjacent buildings induced by subway tunnel construction in the sample library; the maximum crack width of the building (x 14 ) is used as a characteristic indicator for damage evaluation in the sample library.

[0012] b. Construction of sample library

[0013] According to the relevant standards and specifications of tunnel engineering, the disaster-causing level of influencing factors and the damage level of damage characteristic indicators are divided, and the data in the case library are quantitatively represented to form a sample library; the missing values ​​in the sample library are filled by the majority method to form a complete sample library. The sample library is divided into a training set and a test set. The training set is used to build the BN model, and the test set is used to verify the effectiveness of the BN model.

[0014] (2) Construction of the initial network structure. The present invention uses the ISM method to perform a hierarchical analysis of the influencing factors to obtain the hierarchical relationship of the influencing factors; the influencing factors with direct influencing relationships are connected in a directional manner to establish the initial network structure of the BN prediction model for adjacent building damage induced by subway tunnel construction, providing a reference for the structural learning of the prediction model. The process is as follows: Figure 1 shown.

[0015] a. Constructing the adjacency matrix

[0016] The mutual influence relationship between factors is determined based on the knowledge of tunnel engineering and expressed in the form of adjacency matrix. ij) N×N , where N = 14 represents the total number of factor variables,

[0017] b. Constructing the reachability matrix

[0018] According to the Boolean matrix operation rules, let I be the unit matrix, and perform the power operation of A+I. When A+I≠(A+I) 2 ≠(A+I) 3 ≠…≠(A+I) n-1 =(A+I) n When , we get the reachable matrix R = (A + I) n .

[0019] c. Hierarchical structure division

[0020] According to formula (1) and formula (2), we can calculate the influencing factor x i The reachable set R(x i ) and the antecedent set Q(x i ).

[0021] R(x i )={x j |a ij =1},i=1,2…,14 (1)

[0022] Q(x i )={x j |a ij =1},i=1,2…,14 (2)

[0023] When R(x i )∩Q(x i )=R(x i ), x i The influencing factors of the current level that meet the conditions are selected to form a level; the influencing factors of the current level (high level) are removed from the original reachable matrix to form an updated matrix; in the updated matrix, formula (1) and formula (2) are recalculated to obtain the influencing factors of the next level (low level); in this way, the influencing factors are systematically divided into levels, and finally a clear hierarchical structure of influencing factors is obtained. In the entire hierarchical structure, influencing factors with similar effects are at the same level, and factors at the lower level can affect factors at the higher level.

[0024] d. Construction of initial network structure

[0025] According to the interaction relationship between factors represented by the adjacency matrix, directed lines are used to connect the factors with direct interaction relationship in adjacent levels (the starting point factor of the line will have a direct impact on the end point factor of the line) to obtain the initial network structure.

[0026] (3) Construction of basic BN model. The present invention proposes a method for constructing a basic model for predicting damage to adjacent buildings induced by subway tunnel construction. The process is as follows: Figure 2 As shown in the figure. First, the initial network structure is used as the reference of the K2 scoring algorithm to form a hybrid modeling method for structural learning to obtain the BN basic structure; then, the maximum likelihood estimation method is used for parameter learning to form the basic BN model; then, the effectiveness of the basic BN model is verified based on sample data.

[0027] a. Structural learning of basic models

[0028] Based on the initial network structure, the present invention sets the search rules of the BN structure learning K2 scoring algorithm to optimize the search efficiency of the K2 scoring algorithm. Based on the initial network structure obtained by ISM analysis, first, 1) determine the prior order of nodes (influencing factors) (x1, x2, ..., x 14 ): In the hierarchical relationship, the high-level nodes should be ranked before the low-level nodes, and the "maximum crack width of the building" as the target node (damage characteristic index) should be ranked first. The meaning of this order is that the back node can be the parent node of the front node, and the front node cannot be the parent node of the back node; here (x1, x2, ..., x 14 ) is different from the sequence number in the sample library. i Represents the i-th variable in X after reordering. Next, 2) determine the maximum number of parent nodes: comprehensively consider the maximum number of nodes in each layer of the initial network structure and the complexity of the model, and determine the maximum number of parent nodes for each node. Then, 3) set fixed edges in the learning process: the directional edges that already exist in the initial network structure are set as fixed edges, which remain unchanged during the process of searching the network structure by the K2 scoring algorithm. Based on the above three rules established by the initial network structure, the K2 scoring algorithm based on the hill climbing method is applied to perform BN structure search, and the optimal network structure is determined according to the K2 scoring algorithm scoring function shown in formula (3).

[0029]

[0030] Where P(B S ,D) is the score of the model. The higher the score, the better the model performance. S is the BN topology; D is the sample data; P(B S ) is the prior probability of the model, which can be obtained through historical data; n = 14 represents the number of variables; q i Indicates the number of parent node status levels of the variable; r i Indicates the number of state levels of the variable; N ijk is the variable x in the data iThe parent node set π i When the state of is j, the amount of data of the variable state k; N ij is the variable x in the data i The parent node set π i When the state is j, the amount of data of all states of the variable.

[0031] The specific process of learning the basic model structure is as follows Figure 3 As shown, the implementation process is mainly divided into the following steps:

[0032] Step 1: Set the initial network structure according to ISM, set the node sorting, and set the maximum number of parent nodes m;

[0033] Step 2: Take the initial network structure as the starting point of structure learning and calculate the network score according to formula (3); obtain the parent node set of each node according to the initial network structure;

[0034] Step 3: Initialize i=1, i represents the child node x of the parent node to be added i Serial number;

[0035] Step 4: Select x according to the prior order of nodes i The node performs the parent node addition operation;

[0036] Step 5: Determine whether the number of parent nodes of node i is greater than or equal to m; if so, set i=i+1 and jump to Step 10; otherwise, continue to Step 6;

[0037] Step 6: Initialize j = i + 1, j represents the parent node x to be added j The serial number of x j Is it already x i If the parent node is true, set j=j+1 and jump to Step 9 to add the next parent node; otherwise, continue to execute Step 7;

[0038] Step 7: Select x according to the node prior order j Node as x i The parent node of the node;

[0039] Step 8: Calculate the network structure score after adding the parent node according to formula (3). If the score increases, keep the added parent node and update the network score. Otherwise, remove it from the parent node set π. i Delete from ; set j = j + 1;

[0040] Step 9: Determine whether j is greater than the total number of nodes n=14 or whether the number of parent nodes of the current node is greater than or equal to the maximum number of parent nodes m. If so, set i=i+1 and proceed to the next step to execute Step 10; otherwise, return to execute Step 7;

[0041] Step 10: Determine whether i is greater than the total number of nodes n=14. If so, end the search and output the network structure; otherwise, return to execute Step 4.

[0042] b. Parameter learning of the basic model

[0043] For the basic network structure, based on the sample library, the maximum likelihood estimation method is used to learn the BN parameters. The maximum likelihood estimation method calculates the likelihood of the BN parameters under given sample conditions using the logarithmic function shown in formula (4).

[0044]

[0045] Where N is the sample size; n = 14 is the number of nodes x i The number of i For any node x i The number of combinations of parent node states; r i For any node x i The number of states; θ ijk For node x i The kth state and x i The parameters corresponding to the j-th state combination of the parent node set.

[0046] According to the likelihood, the BN parameter θ is derived to obtain the maximum value of θ This is the BN parameter that needs to be calculated.

[0047] According to the basic network structure and its corresponding parameters, the basic BN model for predicting adjacent building damage induced by subway tunnel construction is obtained.

[0048] c. Verification of the basic model

[0049] The test set samples are used to verify the effectiveness of the basic BN model. With reference to methods such as logistic regression and random forest in engineering, the overall accuracy, precision, recall rate and F1 value of the model are used as evaluation indicators to verify the effectiveness of the basic BN model.

[0050] (4) Construction of optimized BN model. The present invention proposes a construction method for optimizing the BN model based on the simulated annealing algorithm. The network structure of the basic BN model is used as the starting point for the simulated annealing algorithm to search for optimal results, the randomness of the simulated annealing algorithm search strategy is reduced, and a hybrid modeling method is formed to perform structural learning to obtain the BN optimized structure; the maximum likelihood estimation method is used to perform parameter learning to form an optimized BN model; and the effectiveness of the optimized BN model is verified based on sample data.

[0051] a. Structural learning of optimization models

[0052] Combined with the characteristics of BN structure learning, the process of finding the optimal BN structure is analogous to the process of searching for the optimal solution by the simulated annealing algorithm. The specific process is as follows Figure 4 As shown, the implementation process is mainly divided into the following steps:

[0053] Step 1: Set the hyperparameters of the simulated annealing algorithm, including the initial temperature T0 and the termination temperature T f and cooling coefficient α, the hyperparameters are related to the search degree of the algorithm. Reasonable values ​​are the guarantee for the algorithm to obtain high-quality solutions with as few iterations as possible; input sample library data as the basis for calculation of formula (3), the adjacency matrix corresponding to the basic model network structure as the starting point of iterative search, and calculate the score of the basic network structure; initialize the initial value of the iterative network number i = 0;

[0054] Step 2: From (x1, x2, ..., x 14 ) randomly selects two nodes n1 and n2, and determines the state of the edge between the two nodes: if there is no edge between the two nodes, continue to execute the operation of Step 3; otherwise, jump to execute the operation of Step 7;

[0055] Step 3: Add an edge between two nodes n1 and n2, with n2 as the parent node, to form a new network structure, such as Figure 5 As shown; i=i+1, T i =αT i-1 ;

[0056] Step 4: Determine whether the new network structure exists. Figure 6 Illegal structures such as isolated point structures, bidirectional variable structures or inner loop structures shown in the figure are removed; if there is no illegal structure, continue to execute Step 5; otherwise, restore the operations between nodes, restore to the state of Step 2, and jump to execute the operation of Step 11;

[0057] Step 5: Use formula (3) to score and increment the network structure, and use the Metropolis acceptance criterion to determine whether the network structure is accepted: If the network structure is accepted, continue to execute the operation of Step 6; otherwise, restore the operation between nodes and jump to execute the operation of Step 11;

[0058] The mathematical expression of Metropolis criterion is as shown in formula (5), where T i For real-time temperature, the current network structure in the search process is set to S i , the corresponding network score is set to P(S i ), the network structure after iterative update is set to S i+1 , the network score is P(S i+1 ), the system accepts the network structure iteration by S i Change to S i+1 The probability p follows the Metropolis criterion;

[0059]

[0060] Step 6: Update the network structure and network structure score, and jump to Step 11;

[0061] Step 7: Reverse the direction of the edge between two nodes to form a new network structure, such as Figure 5 As shown; i=i+1, T i =αT i-1 ;

[0062] Step 8: Determine whether the new network structure exists. Figure 6 Illegal structures such as isolated point structures, bidirectional variable structures or inner loop structures shown in the figure; if there is no illegal structure, continue to execute the operation of Step 9; otherwise, restore the reverse edge and jump to execute the operation of Step 11;

[0063] Step 9: Use formula (3) to score and calculate the increment of the network structure, and use the Metropolis acceptance criterion to determine whether to accept the network structure: if the network structure is accepted, return to execute the operation of Step 6; otherwise, continue to execute the operation of Step 10;

[0064] Step 10: Delete the edges between nodes to form a new network structure, such as Figure 5 As shown; i=i+1, T i+1＝ αT i ; Return to execute Step 4;

[0065] Step 11: Determine the current temperature T i Is it less than the termination temperature Tf : If it is less than, stop the iteration and output the updated network structure as the optimal network structure; if it is greater than or equal to, return to Step 2 to continue execution.

[0066] b. Optimize model parameter learning

[0067] The maximum likelihood estimation method shown in formula (4) is applied to obtain the parameters of BN and form a complete optimized BN model.

[0068] c. Validation of the optimization model

[0069] The effectiveness of the optimized BN model is verified by using the test set samples. The effectiveness of the optimized BN model is verified by using the commonly used methods in engineering such as logistic regression and random forest as references and the overall accuracy, precision, recall rate and F1 value of the model as evaluation indicators.

[0070] (5) Application method of BN model. The BN model for predicting damage to adjacent buildings induced by subway tunnel construction can be applied to the risk prediction of building damage and the diagnosis and analysis of disaster-causing factors.

[0071] a. Risk prediction of damage to adjacent buildings caused by subway tunnel construction

[0072] For a specific project, after determining the value of the relevant influencing factor X = e, the probability of the damage level of the adjacent buildings induced by the subway tunnel construction can be predicted based on the Bayesian formula, Markov chain rule and conditional independence formula, as shown in formula (6).

[0073]

[0074] Where X=(x1,...,x 13 ) is the evidence item (independent variable), which represents the influencing factors of building damage induced by subway tunnel construction, (x1,...,x 13 ) is the order in the sample library before ISM model analysis; Y = x 14 is the target item (dependent variable), which represents the damage characteristic index of the building; P(Y|X=e) is the posterior probability, which is the probability of Y occurring when a new evidence e of X is known; P(Y) is the prior probability, which is the probability of variable Y before considering the new evidence e of X, which can be learned from historical data; P(X=e) is the probability of the occurrence of new evidence of X; P(X=e,Y) represents (x1,...,x 13 ,y) joint probability distribution; π(x i ) is the variable x i is the set of parent nodes of ; π(y) is the set of parent nodes of y; P(x i |π(x i )) and P(y|π(y)) represent xi The conditional probability of and y can be obtained from the conditional probability table of the BN model.

[0075] When the evidence item X=e is incomplete, such as X=e=(x1,...,x m ,...,x 13 ) only x m When the term is known and the values ​​of other variables are unknown, it is still possible to calculate the value of the tunnel surrounding rock deformation Y, as shown in formula (7).

[0076]

[0077] b. Diagnosis of disaster-causing factors of damage to adjacent buildings induced by subway tunnel construction

[0078] For a specific project, when building damage induced by subway tunnel construction has been observed, the building damage state Y and some known influencing factors X are combined. e The value of is used as the evidence item in the BN model. According to the Bayesian formula, Markov chain rule and conditional independence formula, the value level of each other influencing factor is calculated, as shown in formula (8). The calculated value level is compared and analyzed with the value level determined before construction to find out the factors with inconsistent value levels and complete the diagnosis of the disaster-causing factors of engineering diseases.

[0079]

[0080] The beneficial effects of the present invention are:

[0081] (1) The sample library is constructed reasonably and the mathematical model fits the actual project. A sample library is established from two aspects, namely, subway tunnel construction parameters and adjacent building parameters, to construct the BN model. The sample library contains comprehensive factors that reflect the influencing factors of adjacent building damage induced by subway tunnel construction, and the constructed mathematical model fits the actual project as much as possible.

[0082] (2) The model construction process is reasonable and the model prediction performance is efficient. The integration of hill climbing and simulated annealing methods for searching BN structures makes the optimization process of BN structures more efficient and the optimization results more reasonable. The K2 scoring algorithm used to construct the BN structure usually sets the node prior order, the maximum number of parent nodes and the initial network structure based on experience, which is highly subjective. This study applies the ISM analysis of the influencing factors of adjacent building damage induced by subway tunnel construction to improve the effectiveness of the K2 scoring algorithm. At the same time, the search strategy adopted by the K2 scoring algorithm is hill climbing, which is a local search strategy. During the search process, only the neighboring solutions around the current state are considered, and the best solution is selected for further search. It may miss the area where the global optimal solution is located and fall into the trap of local optimality. It cannot guarantee that the search result is the network structure with the highest matching degree with the sample library. Applying simulated annealing to replace hill climbing for searching BN structures can solve the local optimal problem in the search process of the K2 scoring algorithm: the Metropolis criterion is introduced in the simulated annealing search and optimization process. After each search step, the Metropolis criterion is used to determine whether to accept the most recent search result, which can avoid falling into the local optimal problem. However, the simulated annealing method generally uses an empty network structure or a random network structure as the initial structure for subsequent search and optimization, which has the problems of strong randomness, large amount of calculation, and low optimization efficiency. The present invention uses the effective results of the hill climbing K2 scoring algorithm as the initial network structure of the simulated annealing K2 scoring algorithm, which not only improves the search efficiency of the simulated annealing method, but also effectively improves the search effect of the K2 scoring algorithm.

[0083] (3) The model has diverse functions and high application value. The constructed BN model for predicting damage to adjacent buildings induced by subway tunnel construction is essentially a quantitative knowledge system of complex interaction relationships between many nodes, such as between damage influencing factors and damage results, and between influencing factors. Using this model, not only can the probability prediction of the risk level of damage to adjacent buildings induced by subway tunnel construction be achieved, but it can also be used for diagnostic analysis of disaster-causing factors when building damage has already occurred. The model can also be used to conduct sensitivity analysis of factors affecting building damage.

[0084] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0086] Figure 1 Flowchart constructed for the initial network structure;

[0087] Figure 2 Flowchart for building the basic BN model;

[0088] Figure 3 Flowchart of searching network structure for the general K2 scoring algorithm

[0089] Figure 4 Flowchart for searching the optimal network structure for the simulated annealing method;

[0090] Figure 5 An example of a structure update operation;

[0091] Figure 6 Examples of illegal network structures and adjacency matrix construction;

[0092] Figure 7 It is the hierarchical structure diagram of ISM;

[0093] Figure 8 It is the initial network structure diagram of the BN model;

[0094] Fig. 9 The network structure diagram of the basic BN model;

[0095] Fig.10 The basic BN model network structure and its corresponding adjacency matrix;

[0096] Fig.11 To optimize the network structure diagram of the BN model;

[0097] Fig.12 The building disaster level probability map output by the BN model;

[0098] Fig.13 This is the inference result diagram for engineering disease diagnosis. DETAILED DESCRIPTION

[0099] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0100] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on the present invention. In order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0101] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "front", "rear", etc. indicate the orientation or position relationship, they are based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the terms describing the position relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0102] (1) Construction of a sample library of adjacent building damage induced by subway tunnel construction

[0103] A total of 150 cases of subway tunnels near buildings in 73 tunnels were collected. Most of these cases are located in densely built-up areas in cities, such as Guangzhou Metro Chilu Section, Beijing Metro Dongzhimen Section, Shenzhen Metro Minwu Section, Chongqing Light Rail Section 7, etc. Based on the collected engineering case library, 13 influencing factors and 1 damage characteristic index were selected as independent variables and dependent variables to form a sample library; according to the relevant technical standards and specifications of tunnel engineering, the disaster level of influencing factors and the disaster level of damage characteristic indicators were divided respectively, as shown in Tables 1 and 2. Table 1 shows the classification of disaster levels of influencing factors, with Level I being the most disastrous (disaster), and the higher the level, the weaker the corresponding disaster level. Table 2 shows the classification of building damage disaster levels.

[0104] Table 1

[0105]

[0106]

[0107] Table 2

[0108]

[0109] According to the above classification method, the samples in the sample library are classified into disaster (disaster) levels one by one, and the missing values ​​are filled by the mode filling method to form an updated sample library, as shown in Table 3 (the table shows examples of the first 10 groups of samples). All samples in the sample library are randomly divided into 5 parts, one of which is selected as the test set, and the other 4 are selected as training sets.

[0110] Table 3

[0111] Serial number <![CDATA[x1]]> <![CDATA[x2]]> <![CDATA[x3]]> <![CDATA[x4]]> <![CDATA[x5]]> <![CDATA[x6]]> <![CDATA[x7]]> <![CDATA[x8]]> <![CDATA[x9]]> <![CDATA[x 10 ]]> <![CDATA[x 11 ]]> <![CDATA[x 12 ]]> <![CDATA[x 13 ]]> <![CDATA[x 14 ]]> 1 II I I II III III II I III I III I I I 2 II III I II III III II I III I III III I II 3 II III I II III III II I III I III III I II 4 II II I I II III I I II III III I I I 5 III II I II III III II II II III III I I I 6 I II I II I I II I II III II I II III 7 II II II III III III III I II II III I II III 8 II II II II III III II I II III III I I II 9 II II II II III III II I II III III I I III 10 II III I II III II II I III III I III II III

[0112] (2) Construction of initial network structure

[0113] The Interpretive Structure Model (ISM) method was used to analyze the hierarchical structure of factors affecting damage to neighboring buildings and obtain the initial network structure of the Bayesian Network (BN) model.

[0114] a. Constructing the adjacency matrix

[0115] Based on the knowledge of tunnel engineering, the influence relationship between variables is judged, and the adjacency matrix A is constructed using the rules of the adjacency matrix. ij ) N×N , N = 14, As shown in the following formula (9).

[0116]

[0117] b. Constructing the reachability matrix

[0118] According to the Boolean matrix operation rules, let I be the unit matrix, and perform the power operation of A+I. When A+I≠(A+I) 2 ≠(A+I) 3 ≠…≠(A+I) n-1 =(A+I) n When , we get the reachable matrix R = (A + I) n , as shown in formula (10).

[0119]

[0120] c. Divide the hierarchy

[0121] The reachable set and antecedent set of each variable are obtained by formula (1) and formula (2) respectively. i )∩Q(x i )=R(x i ), x iThe influencing factors of the current level that meet the conditions; the factors of the current level are removed from the original reachable matrix to form an updated matrix; in the updated matrix, the reachable set and the antecedent set are calculated, and the factors in the next level are screened by the same method until all factors are divided into corresponding levels, as shown in Table 4.

[0122] Table 4

[0123]

[0124]

[0125]

[0126] The hierarchical structure divided by the above ISM analysis is L1 = {x 14}, L2={x3,x 10}, L3={x7,x9,x 11}, L4={x5,x6}, L5={x1,x2,x4}, L6={x8,x 12 ,x 13}, the hierarchical structure diagram is as follows Figure 7 shown.

[0127] d. Construction of initial network structure

[0128] Based on the hierarchical structure relationship, according to the interaction relationship between variables represented by the adjacency matrix, directed lines are used to connect the factors with direct interaction relationships in adjacent levels, and the initial network structure of the BN model is obtained as follows: Figure 8 shown.

[0129] (3) Construction of basic BN model

[0130] a. Structural learning of the basic model

[0131] Reference Figure 3 The process shown in the figure uses the BN toolkit pgmpy in the computer programming language python for program design to realize the structural learning of the basic BN model based on the hill climbing K2 scoring algorithm. Considering the need to reorder each node according to the initial network structure, in order to avoid conflicts with the node symbols during the calculation of the ISM model, the 14 variable nodes are named according to the rules shown in Table 5 in the K2 scoring algorithm code. According to the initial network structure, the prior order of the 14 nodes is determined to be X = (x1 = N, x2 = C, x3 = J, x4 = G, x5 = K, x6 = I, x7 = E, x8 = F, x9 = A, x 10 =B,x 11 =D,x 12 =H,x 13 =M,x14 =L), the fixed edge settings are shown in Table 6; considering the complexity of the model, the maximum number of parent nodes is set to 4. Table 6 is a partial definition of the K2 scoring algorithm.

[0132] Table 5

[0133]

[0134]

[0135] Table 6

[0136]

[0137] The results of basic BN model structure learning are as follows Fig. 9 As shown in the figure, the directional connection between nodes represents that the starting node of the arrow can directly affect the terminal node. According to formula (3), the network structure score is -1568.31 (the larger the score value, the better the network structure).

[0138] b. Parameter learning of the basic model

[0139] Parameter learning is performed based on the structure learning results and sample library: According to the maximum likelihood estimation method shown in formula (4), the BN parameter θ is derived to obtain the maximum value of θ As shown in formula (11), the BN toolkit pgmpy in python is used for program design to obtain the conditional probability table of each node. Among them, the conditional probability of the target node N (maximum crack width of the building) is shown in Table 7; since the overall conditional probability table is too large, the conditional probability tables of other nodes are no longer shown.

[0140]

[0141] At this point, the construction of the basic BN model is completed.

[0142] Table 7

[0143]

[0144] Table 7

[0145]

[0146] Table 7

[0147]

[0148] c. Basic model verification

[0149] According to the test set, the prediction performance of the basic BN model is evaluated compared with the logistic regression and random forest models commonly used in engineering, as shown in Table 8. The evaluation indicators are the overall accuracy (Acc), precision (Pre), recall (Rec) and F1 value calculated based on the confusion matrix. As shown in Table 8, the basic BN model has a certain degree of prediction reliability, and its prediction performance is better than that of the logistic regression model and the random forest model as a whole.

[0150] Table 8

[0151] Model Acc Pre Rec <![CDATA[F1]]> Bayesian network basic model 0.87 0.86 0.87 0.86 Logistic regression model 0.70 0.89 0.70 0.78 Random Forest Model 0.83 0.85 0.83 0.84

[0152] (4) Optimizing the construction of the BN model

[0153] a. Structural learning of optimization models

[0154] 1) Initial condition setting

[0155] Based on the network structure of the basic BN model, the simulated annealing search method is used to carry out BN structure optimization learning based on the K2 scoring function. In order to facilitate the use of Python language programming to implement this process, the [0,1] matrix method that is the same as the adjacency matrix is ​​used to represent the BN structure. The adjacency matrix corresponding to the illegal structure is as follows Figure 6 As shown, the adjacency matrix corresponding to the basic BN model network structure is as follows Fig.10 shown.

[0156] Based on the principle of maximizing the search capability and efficiency of the simulated annealing search algorithm, through experimental tests, the cooling coefficient α is determined to be 0.99, the initial temperature T0 is determined to be 1475.69, and the termination temperature T is determined to be 10 -10 .

[0157] 2) Based on Figure 4 The algorithm flow is shown in the figure. The BN toolkit pgmpy in Python is used for program design to carry out network structure search. The search results of the optimized BN model network structure after 10 search experiments are shown in Table 9. Considering the randomness of the search results of the simulated annealing method, the network structure output by the experiment 5 with the highest score is taken as the network structure of the optimized BN model, as shown in Fig.11 The corresponding network structure score of Experiment 5 is -1516.98, which is better than the network score of the basic BN model -1568.31, proving that a network structure with a higher degree of fit to the sample data is obtained after further search.

[0158] Table 9

[0159]

[0160]

[0161] b. Optimize model parameter learning

[0162] Based on the optimized BN structure and sample library output from Experiment 5, the conditional probability table is calculated according to formula (4). The BN toolkit pgmpy in Python is used for program design to obtain the conditional probability table of each node and form a complete optimized BN model; the conditional probability of the target node N (maximum crack width of the building) is shown in Table 10; since the overall conditional probability table is too large, the conditional probability tables of other nodes are no longer shown.

[0163] At this point, the construction of the optimized BN model is completed.

[0164] Table 10

[0165] D D(Ⅲ) D(Ⅱ) D(Ⅰ) N(Ⅲ) 0.93 0.67 0.00 N(Ⅱ) 0.05 0.24 0.00 N(Ⅰ) 0.02 0.09 1.00

[0166] c. Validation of the optimization model

[0167] The effectiveness of the optimized BN model is verified by using the test set samples. The effectiveness of the optimized BN model is verified by using the basic BN model, logistic regression and random forest methods as references and the overall accuracy (Acc), precision (Pre), recall (Rec) and F1 value of the model as evaluation indicators. The results are shown in Table 11. As can be seen from Table 11, the various indicators of the optimized BN model are higher than those of the logistic regression model and the random forest model, and are significantly improved compared to the basic BN model.

[0168] Table 11

[0169]

[0170]

[0171] (5) Application methods of BN model

[0172] The application of the BN model includes risk prediction of damage to adjacent buildings induced by subway construction and diagnosis of disaster-causing factors.

[0173] a. Risk prediction of damage to adjacent buildings caused by subway tunnel construction

[0174] For the tunnel section between the starting point and Fuhua Road Station of Chongqing Rail Transit Line 18, the damage risk of the four buildings in this section is predicted. According to the actual tunnel construction and adjacent building parameters, the values ​​of the influencing factors are determined as shown in Table 12.

[0175] Table 12

[0176]

[0177] In the table, * indicates that the specific value of the indicator cannot be obtained in the relevant engineering data. The BN model can calculate samples with default values, which is its biggest advantage compared with other machine learning algorithms.

[0178] Input the variable values ​​of the four samples in Table 12 into the optimized BN model and calculate using formula (7). The output result is as follows: Fig.12 As shown in the figure, the target node N (maximum crack width of the building) of the four buildings is at disaster level III, that is, the load-bearing walls of the target buildings have no cracks or only a few capillary cracks; the frame beams and columns have no cracks; the capillary cracks in the filling walls or decorative layers are less than 1mm wide. The model output results are consistent with the construction site survey data.

[0179] b. Diagnosis of disaster-causing factors of damage to adjacent buildings induced by subway tunnel construction

[0180] Assuming that the building No. 1 of Yongjiang Cuihu has suffered damage of disaster level I, the disaster level of the maximum crack width of the target node building is set to level I. At the same time, other known parameters of the building (foundation form, structural form, height, age and length-to-height ratio) are input into the prediction model as diagnostic evidence. The values ​​of other influencing factors are calculated according to formula (8), as follows: Fig.13 The calculated maximum probability status level of each node and the preset values ​​provided by the engineering data are shown in Table 13. Through diagnostic analysis, it can be seen that the three nodes of tunnel surrounding rock level, tunnel construction excavation method, and relative position between building and tunnel are inconsistent with the preset values, indicating that the cause of the damage to Building 1 of Yongjiang Cuihu may be: the tunnel surrounding rock level in the geological survey report is wrong, the tunnel construction excavation method is different from the design, and the position of the tunnel deviates during the construction process. Next, an investigation and further analysis can be carried out on the above factors.

[0181] Table 13

[0182] node Calculate value Default value A Tunnel Buried Depth Ⅱ Ⅱ C Building settlement Ⅰ * E Tunnel Cover-Span Ratio Ⅱ Ⅱ H tunnel surrounding rock level Ⅰ Ⅱ J Overall building inclination Ⅱ * K Tunnel Construction Excavation Method Ⅲ Ⅱ L Bedrock overburden thickness Ⅲ Ⅲ M Relative position of building and tunnel Ⅰ Ⅱ

[0183] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A method for constructing a prediction model for adjacent building damage induced by subway tunnel construction based on Bayesian networks, characterized by: The method comprises the following steps: S1: Construct a sample library of adjacent building damage induced by subway tunnel construction; Collect subway tunnel engineering data to form a case library and determine the influencing factors; classify the influencing factors into disaster-causing levels, classify the damage characteristic indicators into damage levels, and form a sample library; S2: construct the initial network structure; The Interpretative Structural Model (ISM) method is used to analyze the hierarchical structure of the influencing factors and obtain the hierarchical structural relationship of the influencing factors. The influencing factors with direct influencing relationships are connected in a directional manner to establish the initial network structure of the Bayesian network (BN) prediction model for adjacent building damage, providing a reference for the structural learning of the prediction model. S3: Build the basic BN model; The initial network structure is used as a reference for the K2 scoring algorithm, and a hybrid modeling method is formed to perform structural learning to obtain the BN basic structure; the maximum likelihood estimation method is used to perform parameter learning to form a basic BN model; the effectiveness of the basic BN model is verified based on sample data; S4: Construct an optimized BN model based on simulated annealing algorithm; The network structure of the basic BN model is used as the starting point for the simulated annealing algorithm to optimize the search, reduce the randomness of the simulated annealing algorithm search strategy, form a hybrid modeling method for structural learning to obtain the BN optimized structure; use the maximum likelihood estimation method to learn parameters to form an optimized BN model; verify the effectiveness of the optimized BN model based on sample data; The S1 specifically includes the following steps: S11: Establish case base and determine influencing factors; Through the research literature and case reports on subway tunnel construction risks, a case library of subway tunnel construction near existing buildings is established; combined with the data in the existing case library, the tunnel burial depth x1, tunnel cover span ratio x2, tunnel excavation method x3, bedrock cover thickness x4, surrounding rock level x5, relative position of building and tunnel x6, building length-to-height ratio x7, building height x8, building structure form x9, building foundation form x1 are determined. 10 , Building age x 11 、Maximum building settlement x 12 、The overall building inclination rate x 13 A total of 13 factors were used as the influencing factors of adjacent building damage induced by subway tunnel construction in the sample library; the maximum crack width of the building x 14 As a characteristic indicator for damage evaluation in the sample library; S12: Build sample library; According to the relevant standards and specifications of tunnel engineering, the disaster-causing level of influencing factors and the damage level of damage characteristic indicators are divided, and the data in the case library are quantitatively represented to form a sample library; the missing values ​​in the sample library are filled by the majority method to form a complete sample library; the sample library is divided into a training set and a test set. The training set is used to build the BN model, and the test set is used to verify the effectiveness of the BN model; The S2 specifically includes the following steps: S21: construct adjacency matrix; The mutual influence relationship between factors is determined based on the knowledge in the field of tunnel engineering and expressed in the form of an adjacency matrix; the adjacency matrix A = (a ij ) N×N , where N = 14 represents the total number of factor variables, S22: Construct the reachability matrix; According to the Boolean matrix operation rules, let I be the unit matrix, and perform the power operation of A+I. When A+I≠(A+I) 2 ≠(A+I) 3 ≠…≠(A+I) n-1 =(A+I) n When , we get the reachable matrix R = (A + I) n ; S23: Hierarchical structure division; According to formula (1) and formula (2), we can calculate the influencing factor x i The reachable set R(x i ) and the antecedent set Q(x i ): R(x i )={x j |a ij =1},i=1,2…,14 (1) Q(x i )={x j |a ij =1},i=1,2…,14 (2) When R(x i )∩Q(x i )=R(x i ), x i The influencing factors of the current level that meet the conditions are selected; the influencing factors that meet the conditions are screened out to form a level; the influencing factors of the current level are removed from the original reachable matrix to form an updated matrix; in the updated matrix, formula (1) and formula (2) are recalculated to obtain the influencing factors of the next level; the influencing factors are systematically divided into levels to obtain a clear hierarchical structure of influencing factors; in the entire hierarchical structure, influencing factors with similar effects are at the same level, and factors at the lower level affect factors at the higher level; S24: construct the initial network structure; According to the interaction relationship between factors represented by the adjacency matrix, directed lines are used to connect the factors with direct interaction relationship in adjacent levels to obtain the initial network structure; The S3 specifically includes the following steps: S31: Structural learning of the basic model; Based on the initial network structure, the search rules of the K2 scoring algorithm are set to learn the BN structure to optimize the search efficiency of the K2 scoring algorithm. Based on the initial network structure obtained by ISM analysis, first, the prior order of nodes (x1, x2, ..., x 14 ): In the hierarchical relationship, the high-level nodes should be ranked before the low-level nodes, and the "maximum crack width of the building" as the target node should be ranked first; (x1, x2, ..., x 14 ) is different from the sequence number in the sample library. i represents the i-th variable in X after reordering; then, determine the maximum number of parent nodes: comprehensively consider the maximum number of nodes in each layer of the initial network structure and the complexity of the model, and determine the maximum number of parent nodes for each node; then, set the fixed edges in the learning process: the directional edges that already exist in the initial network structure are set as fixed edges, which remain unchanged during the process of searching the network structure by the K2 scoring algorithm; based on the above rules established by the initial network structure, the K2 scoring algorithm based on the hill climbing method is applied to perform BN structure search, and the optimal network structure is determined according to the K2 scoring algorithm scoring function shown in formula (3): Where P(B S ,D) is the score of the model. The higher the score, the better the model performance. S is the BN topology; D is the sample data; P(B S ) is the prior probability of the model, obtained through historical data; n = 14 represents the number of variables; q i Indicates the number of parent node status levels of the variable; r i Indicates the number of state levels of the variable; N ijk is the variable x in the data i The parent node set π i When the state of is j, the amount of data of the variable state k; N ij is the variable x in the data i The parent node set π i When the state is j, the amount of data of all states of the variable; The specific process of basic model structure learning is: S311: Setting the initial network structure, setting the node order, and setting the maximum number of parent nodes m according to the ISM; S312: Using the initial network structure as the starting point of structure learning, the network score is calculated according to formula (3); the parent node set of each node is obtained according to the initial network structure; S313: Initialize i=1, i represents the child node x of the parent node to be added i Serial number; S314: Select x according to the node prior order i The node performs the parent node addition operation; S315: Determine whether the number of parent nodes of node i is greater than or equal to m; if so, set i=i+1 and jump to execute the operation of S3110; otherwise, continue to execute the operation of S316; S316: Initialize j=i+1, where j represents the parent node x to be added j The serial number of x j Is it already x i If the parent node is established, set j=j+1 and jump to S319 to add the next parent node; otherwise, continue to execute the operation of S317; S317: Select x according to the node prior order j Node as x i The parent node of the node; S318: Calculate the network structure score after adding the parent node according to formula (3). If the score increases, keep the added parent node and update the network score. Otherwise, remove it from the parent node set π. i Delete from ; set j = j + 1; S319: Determine whether j is greater than the total number of nodes n=14 or whether the number of parent nodes of the current node is greater than or equal to the maximum number of parent nodes m. If so, set i=i+1 and proceed to the next step to execute the operation of S3110; otherwise, return to execute the operation of S317; S3110: Determine whether i is greater than the total number of nodes n=14, if yes, end the search and output the network structure; otherwise, return to execute the operation of S314; S32: Parameter learning of the basic model; For the basic network structure, based on the sample library, the maximum likelihood estimation method is used to learn the BN parameters; the maximum likelihood estimation method calculates the likelihood of the BN parameters under given sample conditions using the logarithmic function shown in formula (4); Where N is the sample size; n = 14 is the number of nodes x i The number of i For any node x i The number of combinations of parent node states; r i For any node x i The number of states; θ ijk For node x i The kth state and x i The parameters corresponding to the j-th state combination of the parent node set; According to the likelihood, the BN parameter θ is derived to obtain the maximum value of θ That is the BN parameter that needs to be calculated; According to the basic network structure and its corresponding parameters, the basic BN model for predicting adjacent building damage induced by subway tunnel construction is obtained; S33: Validation of the basic model; The effectiveness of the basic BN model is verified by using the test set samples; the effectiveness of the basic BN model is verified by using logistic regression and random forest as references and the overall accuracy, precision, recall rate and F1 value of the model as evaluation indicators; The S4 specifically comprises the following steps: S41: Structural learning of optimization models; Combined with the characteristics of BN structure learning, the process of finding the optimal BN structure is analogous to the process of searching for the optimal solution by the simulated annealing algorithm. The specific process is as follows: S411: Set the hyperparameters of the simulated annealing algorithm, including setting the initial temperature T0, the termination temperature T f and cooling coefficient α; input sample library data as the basis for calculation of formula (3), the adjacency matrix corresponding to the basic model network structure as the starting point of iterative search, and calculate the score of the basic network structure; initialize the initial value of the iterative network number i = 0; S412: From (x1, x2, ..., x 14 ) randomly selects two nodes n1 and n2, and determines the state of the edge between the nodes: if there is no edge between the two nodes, continue to execute the operation of S413; otherwise, jump to execute the operation of S417; S413: Add an edge between two nodes n1 and n2, with n2 being the parent node, to form a new network structure; i = i + 1, T i =αT i-1 ; S414: Determine whether the new network structure has an illegal structure such as an isolated point structure, a bidirectional variable structure or an inner loop structure; if there is no illegal structure, continue to execute S415; otherwise, restore the operation between nodes to the state of S412, and jump to execute the operation of S4111; S415: Use formula (3) to score and increment the network structure, and use the Metropolis acceptance criterion to determine whether the network structure is accepted: If the network structure is accepted, continue to execute the operation of S416; otherwise, restore the operation between nodes and jump to execute the operation of S4111; The mathematical expression of Metropolis criterion is as shown in formula (5), where T i For real-time temperature, the current network structure in the search process is set to S i , the corresponding network score is set to P(S i ), the network structure after iterative update is set to S i+1 , the network score is P(S i+1 ), the system accepts the network structure iteration by S i Change to S i+1 The probability p follows the Metropolis criterion; S416: Update the network structure and network structure score, and jump to execute the operation of S4111; S417: Reverse the direction of the edge between two nodes to form a new network structure; i = i + 1, T i =αT i-1 ; S418: Determine whether the new network structure has an illegal structure such as an isolated point structure, a bidirectional variable structure or an inner loop structure; if there is no illegal structure, continue to execute the operation of S419; if not, restore the reverse edge and jump to execute the operation of S4111; S419: Use formula (3) to score and increment the network structure, and use the Metropolis acceptance criterion to determine whether to accept the network structure: If the network structure is accepted, return to execute the operation of S416; otherwise, continue to execute the operation of S4110; S4110: Delete the edges between nodes to form a new network structure; i = i + 1, T i+1 =αT i ; Return to execute the operation of S414; S4111: Determine the current temperature T i Is it less than the termination temperature T f : If it is less than, the iteration is stopped and the updated network structure is output as the optimal network structure; if it is greater than or equal to, the execution is returned to S412 to continue; S42: Optimize model parameter learning; Apply the maximum likelihood estimation method shown in formula (4) to obtain the parameters of BN and form a complete optimized BN model; S43: Validation of the optimization model; The test set samples were used to verify the effectiveness of the optimized BN model. Logistic regression and random forest were used as references, and the overall accuracy, precision, recall rate and F1 value of the model were used as evaluation indicators to verify the effectiveness of the optimized BN model.

2. The method for constructing a prediction model for adjacent building damage induced by subway tunnel construction based on Bayesian network according to claim 1 is characterized by: The S4 also includes S5: The BN model for predicting damage to adjacent buildings induced by subway tunnel construction is applied to the risk prediction of building damage and the diagnosis and analysis of disaster-causing factors; S51: Risk prediction of damage to adjacent buildings induced by subway tunnel construction; For a specific project, after determining the relevant influencing factor value X = e, the probability of the damage level of the adjacent building induced by the subway tunnel construction is predicted according to the Bayesian formula, Markov chain rule and conditional independence formula, as shown in formula (6): Where X=(x1,...,x 13 ) is an evidence item, indicating the influencing factors of building damage induced by subway tunnel construction, (x1,...,x 13 ) is the order in the sample library before ISM model analysis; Y = x 14 is the target item, which represents the damage characteristic index of the building; P(Y|X=e) is the posterior probability, which is the probability of Y occurring when a new evidence e of X is known; P(Y) is the prior probability, which is the probability of variable Y before considering the new evidence e of X, which is learned based on historical data; P(X=e) is the probability of the occurrence of new evidence of X; P(X=e,Y) represents (x1,...,x 13 , y) joint probability distribution; π(x i ) is the variable x i is the set of parent nodes of ; π(y) is the set of parent nodes of y; P(x i |π(x i )) and P(y|π(y)) represent x i The conditional probabilities of and y are obtained from the conditional probability table of the BN model; When the evidence item X=e is incomplete, such as X=e=(x1,...,x m , ..., x 13 ) only x m When the term is known and the values ​​of other variables are unknown, the value of the tunnel surrounding rock deformation Y is calculated, as shown in formula (7): S52: Diagnosis of disaster factors of damage to adjacent buildings induced by subway tunnel construction; For a specific project, when building damage induced by subway tunnel construction has been observed, the building damage state Y and some known influencing factors X are combined. e The value of is used as the evidence item in the BN model. According to the Bayesian formula, Markov chain rule and conditional independence formula, the value level of each other influencing factor is calculated, as shown in formula (8). The calculated value level is compared and analyzed with the value level determined before construction to find out the factors with inconsistent value levels and complete the diagnosis of the disaster-causing factors of engineering diseases:

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