Tunnel surrounding rock displacement time series curve prediction method based on dynamic bayesian network

Abstract

This invention belongs to the field of tunnel surrounding rock stability analysis, specifically disclosing a method for predicting tunnel surrounding rock displacement time series curves based on dynamic Bayesian networks. The method includes: S1. Discretizing influencing factors and surrounding rock displacement to establish a sample library; S2. Improving the construction method of the interpretive structure model to establish an interpretive structure model; S3. Constructing a static Bayesian network model for predicting tunnel surrounding rock displacement based on the interpretive structure model; S4. Improving the structure construction method and parameter learning method of the dynamic Bayesian network model; S5. Constructing a dynamic Bayesian network model inference method to establish a dynamic Bayesian network model; S6. Predicting the tunnel surrounding rock displacement time series curve. This invention optimizes the construction methods of the interpretive structure model, static Bayesian network model, and dynamic Bayesian network model, enabling the determination of the dynamic development of surrounding rock displacement before tunnel construction. This has significant guiding value for tunnel site selection, advanced support, construction method selection, and engineering defect diagnosis.

Description

Technical Field

[0001] This invention belongs to the field of tunnel surrounding rock stability analysis, and specifically relates to a method for predicting the time series curve of tunnel surrounding rock displacement based on dynamic Bayesian networks. Background Technology

[0002] Surrounding rock deformation is a key indicator to monitor during tunnel construction. Excessive deformation can lead to instability and failure, resulting in serious consequences such as economic losses, construction delays, and even casualties. Currently, the main method for predicting surrounding rock displacement is through on-site monitoring and measurement to track real-time displacement and predict impending displacements based on past movements, thus preparing countermeasures for potential engineering disasters. Currently, methods for predicting the displacement time-series curve of surrounding rock are mainly divided into two types: one is a theoretical analysis method based on the rock properties and deformation characteristics of the surrounding rock; the other is a machine learning analysis method based on displacement data, such as regression analysis, grey system theory, time series analysis, neural networks, and support vector machines.

[0003] Existing methods have made significant contributions to the prediction of time series curves of displacement of surrounding rock in tunnels, but they still have certain limitations: (1) The theoretical analysis method based on empirical theoretical formulas cannot accurately guide the construction of tunnel projects in complex geological environments; (2) Regression analysis and time series prediction methods are linear models, which are different from the nonlinear characteristics of the time series of displacement of surrounding rock; (3) Neural network models require a large number of samples and are prone to overfitting under small sample conditions.

[0004] Most importantly, existing prediction methods, including grey system models and support vector machines which are well-suited for small samples, have high accuracy and very small errors compared to measured displacements. However, these methods predict displacement development several days in advance based on displacements already occurring in tunnels under construction. Because the interval between monitored and predicted displacements is short, they often cannot effectively prevent engineering disasters. If, before tunnel construction, the displacement time-series curve of the surrounding rock could be predicted based on natural environmental factors such as engineering geology and hydrology, as well as the construction methods used, to determine the range of cumulative surrounding rock deformation and predict when the deformation might exceed the surrounding rock deformation control benchmark, it would be of great significance for tunnel site selection, advanced support measures, and construction method selection.

[0005] Bayesian network models can effectively utilize complex influencing factors in geotechnical engineering, such as engineering geology, hydrogeology, topography, and human disturbance, to predict engineering disasters. They are widely used in various fields of geotechnical engineering, such as slope stability prediction, earthquake liquefaction prediction, and tunnel construction risk prediction. However, the Bayesian network models applied in geotechnical engineering are mainly static, failing to reflect the dynamic changes of engineering variables over time. Dynamic Bayesian network models are rarely used in geotechnical engineering, primarily because the complex environment and numerous influencing factors make their construction very difficult. Taking the time series curve of tunnel surrounding rock displacement as an example: according to investigations, at least 20 influencing factors, including engineering geology, hydrogeology, topography, and construction disturbance, affect tunnel surrounding rock displacement. Consequently, the dynamic Bayesian network model constructed using traditional Markov process methods is too simplistic and cannot accurately reflect the relationship between displacement at time points and influencing factors. Furthermore, the method of setting model parameters through transition probability matrices is also too simplistic and cannot quantitatively characterize the relationship between displacement at time points and influencing factors.

[0006] The complexity of tunnel engineering limits the successful prediction of displacement time-series curves using machine learning algorithms. However, the engineering hazards caused by the deformation of the surrounding rock in tunnels create an urgent need for the early prediction of displacement time-series curves. Summary of the Invention

[0007] The purpose of this invention is to address the shortcomings of existing technologies by proposing a method for predicting tunnel surrounding rock displacement time-series curves based on dynamic Bayesian networks. This method involves: establishing a sample library of tunnel surrounding rock displacement time-series curves and their influencing factors through literature review and data processing; establishing an interpretative structural model through correlation analysis of the influencing factors; optimizing the construction method of the static Bayesian network model using the interpretative structural model to establish a static Bayesian network model containing the quantitative relationship between tunnel surrounding rock displacement and influencing factors; improving the construction method and parameter learning method of the dynamic Bayesian network model by setting the static Bayesian network model and time nodes, successfully establishing a dynamic Bayesian network model containing the quantitative relationship between tunnel surrounding rock displacement time-series curves and influencing factors; and substituting the influencing factor values ​​obtained from field surveys into the dynamic Bayesian network model, allowing the acquisition of the surrounding rock displacement time-series curves before tunnel construction, thus overcoming the limitation of existing methods that cannot predict displacement time-series curves in advance.

[0008] This invention proposes a method for predicting the time series curve of tunnel surrounding rock displacement based on dynamic Bayesian networks.

[0009] Includes the following:

[0010] S1. Determine the influencing factors of tunnel surrounding rock displacement, and discretize the influencing factors and surrounding rock displacement; collect data and establish a sample library containing influencing factors and displacement time series curves;

[0011] S2. Based on the distribution of influencing factors and displacement stability values, conduct variable correlation analysis, improve the construction method of the explanatory structural model, and establish an explanatory structural model for tunnel surrounding rock displacement;

[0012] S3. Based on the interpretive structural model, improve the construction method of the static Bayesian network model structure, and construct a static Bayesian network model for tunnel surrounding rock displacement prediction;

[0013] S4. Based on the static Bayesian network model, improve the structure construction method and parameter learning method of the dynamic Bayesian network model;

[0014] S5. For the improved dynamic Bayesian network model, construct its inference method and establish a dynamic Bayesian network model for predicting the time series curve of tunnel surrounding rock displacement.

[0015] S6. Input the measured values ​​of influencing factors to predict the time series curve of tunnel surrounding rock displacement.

[0016] As a preferred implementation, in S1, the influencing factors include 14 factors such as surrounding rock grade, surrounding rock lithology, surrounding rock structure, initial ground stress state, dip angle of main structural plane, tunnel depth, tunnel excavation span, stratum water content, groundwater control, advanced support method, excavation method, degree of surrounding rock disturbance, support timing and support strength.

[0017] In a preferred embodiment, S2 includes 15 variables, including surrounding rock displacement and influencing factors. Based on the correlation analysis results, a mutual influence matrix of the variables is established to construct the explanatory structural model. If the Pearson correlation coefficient between variables is less than 0.05, they are considered correlated; otherwise, they are not correlated. The construction of the explanatory structural model specifically includes the following steps:

[0018] (1) Based on the results of the correlation analysis, construct the mutual influence matrix of the variables;

[0019] (2) Transform the mutual influence matrix into an adjacency matrix A:

[0020]

[0021] in Representing variables right Influence relationship, =1 means right There is an impact. =0 indicates that there is no effect;

[0022] (3) Perform an exponentiation operation on the adjacency matrix to obtain the reachability matrix M; the reachability matrix is ​​a matrix that represents the reachability of any two variables in the system after traversing a path of arbitrary length. Its specific calculation process is as follows:

[0023] in for The path is long. It is the identity matrix;

[0024] (4) Divide the reachability matrix into hierarchical parts to form a skeleton matrix; reachability matrix The Middle The set of variables represented by columns with a row value of 1 is called the reachable set. , No. The set of variables represented by rows with a column value of 1 is called the antecedent set. Variable set Let represent the set of variables that exist simultaneously in both the reachability set and the antecedent set. Determine whether the set of variables is a set of highest-level variables based on whether it satisfies the following formula:

[0025]

[0026] (5) Find the set For the first level variable in the hierarchy, delete... middle The new matrix is ​​obtained by determining the row and column of the corresponding variable. And then Repeat the above steps to obtain For the second level of variables, delete them again. middle The corresponding row and column of the variable can be obtained by analogy. Determine the hierarchy of all variables to form a skeleton matrix;

[0027] (6) Based on the skeleton matrix structure, according to the interaction relationship of variables in the same or adjacent levels, and following the rule that higher-level elements point to lower-level elements and higher-level variables are above and lower-level variables are below, a multi-level directed topology graph is drawn by connecting the lines in sequence, ignoring the relationship between cross-level variables, and finally establishing an explanatory structure model.

[0028] As an optimized implementation method, in S3, the construction method of the K2 algorithm for improving the static Bayesian network model structure is improved based on the interpreted structural model. The specific process is as follows:

[0029] (1) Determine the scoring function, using As a scoring function, the formula is:

[0030]

[0031]

[0032] The variables in the scoring function have the following meanings: D: dataset; G: proposed network model; n: number of variables; P(G): prior probability distribution of network structure G; r i :node The number of possible values; i: node number; j: node The value number of the parent node; :node The set of parent nodes; q i : The number of possible values ​​for N; ijk :node parent node set Take the j-th value, The number of samples when taking the k-th value; N ij :node Parent node set The number of samples corresponding to the j-th state combination;

[0033] (2) Based on the interpretable structural model, determine the values ​​of node number i (1, ,2, 3...13) and q. i The possible values ​​of ;

[0034] (3) Based on the explanatory structural model, determine part of the The possible values ​​of ;

[0035] (4) The search strategy is determined to be a greedy search algorithm; the search puts the parent node variable with the largest score function into the set; when the score function cannot be increased, the search stops, and the optimal model is found;

[0036] (5) Based on the sample data of the training set, a static Bayesian network model structure is established through the above-mentioned optimized K2 algorithm.

[0037] As an optimized implementation method, in S3, the maximum likelihood estimation method is used to learn the parameters of the static Bayesian network model. The specific process is as follows:

[0038] (1) The logarithmic function form for determining the likelihood is:

[0039]

[0040] Where N represents the sample data and n represents the number of nodes. The number of nodes; let the nodes The set of parent nodes is q i parent node set The number of possible values ​​for ri For nodes The number of possible values ​​for N; ijk For nodes parent node set Take the j-th value, The number of samples when taking the k-th value; θ ijk For nodes parent node set Take the j-th value, The parameter value corresponding to the k-th value. ;

[0041] (2) Find the maximum value of the above logarithmic function, that is, find the maximum value by taking the derivative with respect to the parameter θ. This will give us the parameter θ. ijk The value can be:

[0042]

[0043] (3) Based on the sample data of the training set, the conditional probability table of the static Bayesian network model is established by the above method.

[0044] As a preferred implementation, in S3, reasoning analysis is performed based on Bayes' theorem, Markov chain theorem, and conditional independence theorem to establish a static Bayesian network model; the model is then trained and tested to verify its correctness.

[0045] As a preferred implementation, in S4, based on the validated static Bayesian network model, the learning method for the structure and parameters of the dynamic Bayesian network model is improved. The specific process is as follows:

[0046] (1) Examine all displacement time series curves, take the longest time series curve as the standard, use extrapolation to extend the time axis of all other displacement time series curves, and divide the time axis into several time nodes;

[0047] (2) Based on the reverse time sequence, the displacement value of each time node is set as the transition node of the dynamic Bayesian network model, as follows: , ... , ... Based on the settings of the transfer nodes, the sample library is updated, and the displacement value of each time node is used as a variable in the sample library.

[0048] (3) Based on the node order and transition node order determined by the static Bayesian network model, determine the value of the K2 algorithm number i (1, ,2, 3...13...13+n) and q. i The possible values ​​of ;

[0049] (4) Determine the part of the K2 algorithm based on the directional connections determined by the static Bayesian network model. The value of is consistent with the directional connections in the static Bayesian network model;

[0050] (5) Optimize the K2 algorithm based on the network structure and transition node order of the static Bayesian network model; establish the transition node order using the optimized K2 algorithm. , ... , ... By establishing directional connections with influencing factors, a dynamic Bayesian network model structure can be constructed.

[0051] (6) Based on the structure of the completed dynamic Bayesian network model, the training sample set of the sample library is substituted into it, and the parameters of the dynamic Bayesian network model are learned through the maximum likelihood estimation method to form a complete conditional probability table.

[0052] In a preferred implementation, in S5, it is assumed that the displacement at time t is only related to the displacement at time t-1 and the influencing factors, and is independent of the displacement before time t-1 and the displacement after time t. The posterior probability distribution of the surrounding rock displacement level at the current time is derived by applying Bayes' theorem, Markov chain rule formula, and conditional independence formula. The specific process is as follows:

[0053] (1) Given the influencing factors and the displacement at time t-1, find the displacement at time t. The expression is as follows:

[0054]

[0055] in, As influencing factor nodes, , For transfer nodes;

[0056] (2) Apply Bayes' theorem to derive the above formula. Bayes' theorem is as follows:

[0057]

[0058] In the formula, X represents the evidence item, and Y represents the target item; Here, is the posterior probability, which is the probability of Y occurring given some new evidence e of X. The prior probability is the probability of variable Y before considering new evidence e of X, which is learned from historical data. The likelihood of Y is also a conditional probability, calculated based on historical data. The probability of new evidence for X occurring;

[0059] According to Bayes' theorem, we get:

[0060]

[0061] (3) At this time, because A, B, ..., M, N, , The variables are not independent of each other. and Since it cannot be computed, the classic Bayesian formula cannot be applied; therefore, the Markov chain rule formula is introduced as follows:

[0062]

[0063] in, Represents the variables of each node in a Bayesian network;

[0064] Therefore, we can obtain:

[0065]

[0066]

[0067]

[0068] (4) In the above formula, the prior probability Conditional independence can be obtained from the conditional probability table, while other conditional probabilities cannot. Therefore, the conditional independence formula is introduced as follows:

[0069]

[0070] in, For variables The set of parent nodes;

[0071] Therefore, we can obtain:

[0072]

[0073]

[0074] (5) At this point, all conditional probability terms retain only the parent node terms of the nodes, which can be directly obtained from the conditional probability table, thus enabling the calculation of the formula:

[0075]

[0076] (6) Extract the probability of each surrounding rock displacement level from the posterior probability distribution of the surrounding rock displacement level at each time point, using the following formula:

[0077]

[0078] in, These represent the probabilities of the eight value intervals of the displacement; based on the maximum membership principle, the surrounding rock displacement at each time point is obtained.

[0079] (7) Starting from the first time node, the unique values ​​at each time point are obtained sequentially through the above calculation method to obtain the time series curve of tunnel surrounding rock displacement.

[0080] The innovation of this invention compared to existing technologies lies in:

[0081] 1) This invention uses a dynamic Bayesian network method to predict the time series curve of displacement of tunnel surrounding rock; compared with the traditional displacement time series curve prediction method, this invention can predict the dynamic development of the surrounding rock position before the tunnel project is constructed.

[0082] 2) This invention constructs the factor interaction matrix of the explanatory structural model by calculating the correlation of variables, optimizes the construction method of the explanatory structural model, and improves the objectivity and rationality of the construction of the explanatory structural model;

[0083] 3) By interpreting the structural model, this invention determines the node order and some directional connections of the static Bayesian network model structure, optimizes the construction method of the static Bayesian network model, and improves the accuracy and efficiency of the static Bayesian network model structure construction.

[0084] 4) Based on the structure and time node settings of the static Bayesian network model, this invention determines the partial directional connections of the dynamic Bayesian network model structure and optimizes the construction method of the dynamic Bayesian network model structure by applying data learning methods. Compared with the traditional construction method of dynamic Bayesian network model, this invention can establish the directional relationship between the displacement of each time node and the influencing factors, thereby improving the rationality, accuracy and efficiency of model construction.

[0085] 5) Compared with the traditional method of constructing dynamic Bayesian network models, the present invention is based on an optimized dynamic Bayesian network model structure, which can use traditional data learning methods to construct a complete conditional probability table, avoiding the arbitrariness caused by the subjective setting of transition probabilities. Attached Figure Description

[0086] The accompanying drawings, which form part of this specification, are used to further understand the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0087] Figure 1 This is a flowchart of the tunnel surrounding rock displacement time series curve prediction method based on dynamic Bayesian network of the present invention;

[0088] Figure 2 This is a hierarchical structure diagram of the influencing factors in an embodiment of the tunnel surrounding rock displacement time series curve prediction method based on dynamic Bayesian network of the present invention.

[0089] Figure 3 This is a schematic diagram of the structure and parameters of the static Bayesian network in an embodiment of the method for predicting the time series curve of tunnel surrounding rock displacement based on dynamic Bayesian network of the present invention;

[0090] Figure 4 This is a schematic diagram of the structure and parameters of the dynamic Bayesian network in an embodiment of the method for predicting time-series displacement curves of tunnel surrounding rock based on dynamic Bayesian networks according to the present invention.

[0091] Figure 5 The probability distribution diagram of the surrounding rock displacement level node at each time node in the embodiment of the tunnel surrounding rock displacement time series curve prediction method based on dynamic Bayesian network of this invention;

[0092] Figure 6 This invention presents a comparison between the predicted rock displacement level and the actual engineering situation in an embodiment of the tunnel surrounding rock displacement time series curve prediction method based on dynamic Bayesian networks. Detailed Implementation

[0093] The present invention will be further explained in detail below with reference to the accompanying drawings and embodiments.

[0094] It should be noted that the following detailed descriptions are exemplary and used to further illustrate the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood in the art to which this invention pertains. The terminology used is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments of the invention.

[0095] Reference Figure 1 The present invention provides a method for predicting the time series curve of tunnel surrounding rock displacement based on dynamic Bayesian networks, which specifically includes the following steps:

[0096] S1. Determine the influencing factors of tunnel surrounding rock displacement, and discretize the influencing factors and surrounding rock displacement; collect data through literature review, and establish a sample library containing influencing factors and stable displacements;

[0097] S2. Based on the distribution of influencing factors and displacement stability values, conduct variable correlation analysis, improve the construction method of the explanatory structural model, and establish an explanatory structural model for tunnel surrounding rock displacement;

[0098] S3. Based on the interpretive structural model, improve the construction method of the static Bayesian network model structure, and construct a static Bayesian network model for tunnel surrounding rock displacement prediction;

[0099] S4. Based on the static Bayesian network model, improve the structure construction method and parameter learning method of the dynamic Bayesian network model;

[0100] S5. For the improved dynamic Bayesian network model, construct its inference method and establish a dynamic Bayesian network model for predicting the time series curve of tunnel surrounding rock displacement.

[0101] S6. Input the measured values ​​of influencing factors to predict the time series curve of tunnel surrounding rock displacement.

[0102] In this embodiment, in S1, the influencing factors include 14 factors: surrounding rock grade, surrounding rock lithology, surrounding rock structure, initial ground stress state, dip angle of main structural planes, tunnel depth, tunnel excavation span, formation water content, groundwater control, advanced support method, excavation method, degree of surrounding rock disturbance, support timing, and support strength. The discretization results of the influencing factors are shown in Table 1 below.

[0103] Table 1

[0104]

[0105] The displacement of surrounding rock is classified into eight levels, as shown in Table 2 below:

[0106] Table 2

[0107]

[0108] Based on data collected from literature, a sample library containing 120 samples was established. 80% of the samples in the sample library were divided into the training set and 20% of the samples in the sample library were divided into the test set.

[0109] In this embodiment, S2 includes 15 variables, including surrounding rock displacement and influencing factors. Based on the correlation analysis results, a mutual influence matrix of the variables is established to construct the explanatory structural model. Variables are considered correlated if the Pearson correlation coefficient is less than 0.05; otherwise, they are not correlated. The construction of the explanatory structural model specifically includes the following steps:

[0110] (1) Based on the correlation analysis results, the mutual influence matrix of the variables is constructed as follows:

[0111]

[0112] in, For the surrounding rock grade, For the lithology of the surrounding rock, For surrounding rock structure, For the initial geostress state, For the inclination angle of the main structural surfaces, For tunnel burial depth, For tunnel excavation span, For the water content of the strata, For groundwater control, For advanced support construction methods, For excavation methods, For the degree of disturbance of the surrounding rock, For support timing, For support strength, The displacement level represents the surrounding rock; A indicates that the horizontal variable affects the vertical variable, B indicates that the vertical variable affects the horizontal variable, and O indicates that the two variables do not affect each other.

[0113] (2) Transform the mutual influence matrix into an adjacency matrix A:

[0114]

[0115] in Representing variables right Influence relationship, =1 means right There is an impact. =0 indicates that there is no effect;

[0116] The obtained adjacency matrix is ​​as follows:

[0117]

[0118] (3) Perform an exponentiation operation on the adjacency matrix to obtain the reachability matrix M; the reachability matrix is ​​a matrix that represents the reachability of any two variables in the system after traversing a path of arbitrary length. The specific calculation process is as follows:

[0119] in for The path is long. It is the identity matrix;

[0120] The reachability matrix is ​​obtained as follows:

[0121]

[0122] (4) Divide the reachability matrix into hierarchical parts to form a skeleton matrix; reachability matrix The Middle The set of variables represented by columns with a row value of 1 is called the reachable set. , No. The set of variables represented by rows with a column value of 1 is called the antecedent set. Variable set This represents the set of variables that exist simultaneously in both the reachability set and the antecedent set. Whether a set of variables is a highest-level set is determined by whether it satisfies the following formula:

[0123]

[0124] (5) Find the set For the first level variable in the hierarchy, delete... middle The new matrix is ​​obtained by determining the row and column of the corresponding variable. Then... Repeat the above steps to obtain For the second level of variables, delete them again. middle The corresponding row and column of the variable can be obtained by analogy. The hierarchy of all variables is determined to form a skeleton matrix, as shown in Table 3 below:

[0125] Table 3

[0126]

[0127] (6) Based on the skeleton matrix structure, according to the interaction relationship between variables at the same or adjacent levels, and following the rule of higher-level elements pointing to lower-level elements and higher-level variables above and lower-level variables below, a multi-level directed topological graph is drawn by connecting the lines sequentially, ignoring the relationship between variables across levels. Finally, an explanatory structural model is established, as shown in the appendix. Figure 2 As shown.

[0128] In this embodiment, in S3, the method for constructing the K2 algorithm, which improves the static Bayesian network model structure based on the interpreted structural model, is as follows:

[0129] (1) Determine the scoring function, using As a scoring function, the formula is:

[0130]

[0131]

[0132] The variables in the scoring function have the following meanings: D: Dataset, the 96 training samples collected in this embodiment; G: The proposed network model; n: Number of variables, 15; P(G): Prior probability distribution of the network structure G; r i :node The number of possible values ​​is shown in Table 2; i: node number; j: node The value number of the parent node; :node The set of parent nodes; q i : The number of possible values ​​for N; ijk :node parent node set Take the j-th value, The number of samples when taking the k-th value; N ij :node Parent node set The number of samples corresponding to the j-th state combination;

[0133] (2) According to the interpreted structural model, the order of the nodes is determined as: [2, 3, 1, 4, 6, 11, 7, 10, 8, 12, 13, 5, 9, 14, 15], q i The value of is 6;

[0134] (3) Based on the explanatory structural model, determine part of the The possible values ​​of , such as Figure 2 As shown;

[0135] (4) The search strategy is determined to be a greedy search algorithm; the search puts the parent node variable with the largest score function into the set; when the score function cannot be increased, the search stops, and the optimal model is found;

[0136] (5) Based on the 96 training set samples collected in this embodiment, a static Bayesian network model structure is established using the optimized K2 algorithm described above, as shown in the attached figure. Figure 3 As shown.

[0137] In this embodiment, in step (3), the maximum likelihood estimation method is used to learn the parameters of the static Bayesian network model. The specific process is as follows:

[0138] (1) The logarithmic function form for determining the likelihood is:

[0139]

[0140] Where N represents the sample data, 96; n represents the number of nodes. The number of nodes is 15; let the nodes... The set of parent nodes is q i parent node set The number of possible values ​​for r i For nodes The number of possible values ​​for N; ijk For nodes parent node set Take the j-th value, The number of samples when taking the k-th value; θ ijk For nodes parent node set Take the j-th value, The parameter value corresponding to the k-th value. ;

[0141] (2) Find the maximum value of the above logarithmic function, that is, find the maximum value by taking the derivative with respect to the parameter θ. This will give us the parameter θ. ijk The value can be:

[0142]

[0143] (3) Using the 96 sets of training samples collected in this embodiment, a conditional probability table for the static Bayesian network model is established using the above method; given that the conditional probability table is too large, this embodiment only displays the marginal probabilities of each node, such as Figure 3 As shown.

[0144] In this embodiment, in S3, inference analysis is performed based on Bayes' theorem, Markov chain theorem, and conditional independence theorem to establish a static Bayesian network model. The model is trained and tested to verify its correctness. Table 4 below shows the average prediction results of the three models in the five-fold crossover experiment. It can be seen that, compared with traditional machine learning algorithms, the optimized static Bayesian network model of this invention has better overall accuracy, precision, recall, and... It has an absolute advantage in all four evaluation indicators, including value.

[0145] Table 4

[0146]

[0147] In this embodiment, in step (4), based on the validated static Bayesian network model, the structure construction method and parameter learning method of the dynamic Bayesian network model are improved. The specific process is as follows:

[0148] (1) Examine all displacement time series curves, supplement all original displacement change data to 70 days. If it is less than 70 days, use extrapolation to extend it to 70 days. Then divide it into 15 time nodes with 5 days (the displacement state on the 5th day as the standard).

[0149] (2) According to the reverse time order, the displacement value of each time node is set as the transition node of the dynamic Bayesian network model, as follows: , ... , ... Based on the settings of the transfer nodes, the sample library is updated, and the displacement value of each time node is used as a variable in the sample library.

[0150] (3) Based on the node order and transition node order determined by the static Bayesian network model, the node order of the K2 algorithm is determined as [2, 3, 1, 4, 6, 11, 7, 10, 8, 12, 13, 5, 9, 14, 15, ... , ... , ... ], q i The value of is 6;

[0151] (4) Determine the part of the K2 algorithm based on the directional connections determined by the static Bayesian network model. The value of is consistent with the directional connections in the static Bayesian network model, as shown in the attached figure. Figure 3 As shown;

[0152] (5) Based on the network structure and the order of transition nodes in the static Bayesian network model, the K2 algorithm was optimized; the transition nodes were established using the optimized K2 algorithm. , ... , ... By establishing directional connections with influencing factors, the dynamic Bayesian network model structure can be constructed, as shown in the appendix. Figure 4 As shown;

[0153] (6) Based on the structure of the completed dynamic Bayesian network model, the training sample set is substituted into it, and the parameters of the dynamic Bayesian network model are learned through the maximum likelihood estimation method to form a complete conditional probability table; given that the conditional probability table is too large, this embodiment only shows the marginal probabilities of each node, such as Figure 4 As shown.

[0154] In this embodiment, in step (5), it is assumed that the displacement at time t is only related to the displacement and influencing factors at time t-1, and is not related to the displacement before time t-1 or the displacement after time t; by comprehensively applying Bayes' theorem, Markov chain rule formula and conditional independence formula, the posterior probability distribution of the surrounding rock displacement level at the current time is deduced, and the specific process is as follows:

[0155] (1) Given the influencing factors and the displacement at time t-1, find the displacement at time t. The expression is as follows:

[0156]

[0157] in, As influencing factor nodes, , For time displacement nodes;

[0158] (2) Apply Bayes' theorem to derive the above formula. The formula is as follows:

[0159]

[0160] In the formula, X represents the evidence item, and Y represents the target item; Here, is the posterior probability, which is the probability of Y occurring given some new evidence e of X. The prior probability is the probability of variable Y before considering new evidence e of X, which is learned from historical data. The likelihood of Y is also a conditional probability, calculated based on historical data. The probability of new evidence for X occurring;

[0161] According to Bayes' theorem, we get:

[0162]

[0163] (3) At this time, because A, B, ..., M, N, , The variables are not independent of each other. and Since it cannot be computed, the classic Bayesian formula cannot be applied; therefore, the Markov chain rule formula is introduced as follows:

[0164]

[0165] in, Represents the variables of each node in a Bayesian network;

[0166] Therefore, we can obtain:

[0167]

[0168]

[0169]

[0170] (4) In the above formula, the prior probability Conditional independence can be obtained from the conditional probability table, while other conditional probabilities cannot. Therefore, the conditional independence formula is introduced as follows:

[0171]

[0172] in, For variables The set of parent nodes;

[0173] Therefore, we can obtain:

[0174]

[0175]

[0176] (5) At this point, all conditional probability terms retain only the parent node terms of the nodes, which can be directly obtained from the conditional probability table, thus enabling the calculation of the formula:

[0177]

[0178] (6) Extract the probability of each surrounding rock displacement level from the posterior probability distribution of the surrounding rock displacement level at each time point, using the following formula:

[0179]

[0180] in, The probability of the displacement is given by the eight value intervals; the surrounding rock displacement at each time point is obtained according to the principle of maximum membership.

[0181] (7) Starting from the first time point, the displacement values ​​at each time point are obtained sequentially using the above calculation method, as shown in the appendix. Figure 5 As shown, the displacement time-series curve of the surrounding rock of the tunnel is thus obtained.

[0182] In this embodiment, in S6, the values ​​of influencing factors obtained from actual engineering surveys are substituted into the dynamic Bayesian network model to obtain the displacement time series curve as shown in the attached figure. Figure 6 As shown; from the appendix Figure 6 As can be seen, the displacement time series curve predicted by the dynamic Bayesian network model fits the measured displacement time series curve very well, and can fit the abrupt changes in displacement.

[0183] Most importantly, traditional displacement time series curve prediction methods, such as support vector machines, require early data obtained from tunnel engineering monitoring sections to predict later data development; while dynamic Bayesian network models can successfully predict the changes in displacement time series curves before tunnel construction begins.

[0184] The above description is merely an illustrative embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

[0185] 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 method for predicting time-series displacement curves of tunnel surrounding rock based on dynamic Bayesian networks, characterized by: Includes the following: S1. Determine the influencing factors of tunnel surrounding rock displacement, and discretize the influencing factors and surrounding rock displacement; collect data and establish a sample library containing influencing factors and displacement time series curves; S2. Based on the distribution of influencing factors and displacement stability values, conduct variable correlation analysis, improve the construction method of the explanatory structural model, and establish an explanatory structural model for tunnel surrounding rock displacement; S3. Based on the interpretive structural model, improve the construction method of the static Bayesian network model structure, and construct a static Bayesian network model for tunnel surrounding rock displacement prediction; S4. Based on the static Bayesian network model, improve the structure construction method and parameter learning method of the dynamic Bayesian network model; S5. For the improved dynamic Bayesian network model, construct its inference method and establish a dynamic Bayesian network model for predicting the time series curve of tunnel surrounding rock displacement. S6. Input the measured values ​​of influencing factors to predict the time series curve of tunnel surrounding rock displacement; In S4, based on the validated static Bayesian network model, the structure construction method and parameter learning method of the dynamic Bayesian network model are improved. The specific process is as follows: (1) Examine all displacement time series curves, take the longest time series curve as the standard, use extrapolation to extend the time axis of all other displacement time series curves, and divide the time axis into several time nodes; (2) Based on the reverse time sequence, the displacement value of each time node is set as the transition node of the dynamic Bayesian network model, as follows: , ... , ... Based on the settings of the transfer nodes, the sample library is updated, and the displacement value of each time node is used as a variable in the sample library. (3) Based on the node order and transition node order determined by the static Bayesian network model, determine the value of the K2 algorithm number i and q. i The possible values ​​of ; (4) Determine the part of the K2 algorithm based on the directional connections determined by the static Bayesian network model. The value of is consistent with the directional connections in the static Bayesian network model; (5) Optimize the K2 algorithm based on the network structure and transition node order of the static Bayesian network model; establish the transition node order using the optimized K2 algorithm. , ... , ... By establishing directional connections with influencing factors, a dynamic Bayesian network model structure can be constructed. (6) Based on the structure of the completed dynamic Bayesian network model, the training sample set of the sample library is substituted into it, and the parameters of the dynamic Bayesian network model are learned through the maximum likelihood estimation method to form a complete conditional probability table. In S5, it is assumed that the displacement at time t is only related to the displacement at time t-1 and the influencing factors, and is independent of the displacement before time t-1 and the displacement after time t. By comprehensively applying Bayes' theorem, Markov chain rule formula, and conditional independence formula, the posterior probability distribution of the surrounding rock displacement level at the current time is derived. The specific process is as follows: (1) Given the influencing factors and the displacement at time t-1, find the displacement at time t. The expression is as follows: in, As influencing factor nodes, , For transfer nodes; (2) Apply Bayes' theorem to derive the above formula. The formula is as follows: In the formula, X represents the evidence item, and Y represents the target item; Here, is the posterior probability, which is the probability of Y occurring given some new evidence e of X. The prior probability is the probability of variable Y before considering new evidence e of X, which is learned from historical data. The likelihood of Y is also a conditional probability, calculated based on historical data. The probability of new evidence for X occurring; According to Bayes' theorem, we get: (3) At this time, because A, B, ..., M, N, , The variables are not independent of each other. and Since it cannot be computed, the classic Bayesian formula cannot be applied; therefore, the Markov chain rule formula is introduced as follows: in, Represents the variables of each node in a Bayesian network; Therefore, we can obtain: (4) In the above formula, the prior probability Conditional independence can be obtained from the conditional probability table, while other conditional probabilities cannot. Therefore, the conditional independence formula is introduced as follows: in, For variables The set of parent nodes; Therefore, we can obtain: (5) At this point, all conditional probability terms retain only the parent node terms of the nodes, which can be directly obtained from the conditional probability table, thus enabling the calculation of the formula: (6) Extract the probability of each surrounding rock displacement level from the posterior probability distribution of the surrounding rock displacement level at each time point, using the following formula: in, The probability of the displacement is given for the eight possible value intervals; based on the maximum membership principle, the surrounding rock displacement at each time step is obtained. (7) Starting from the first time node, the unique values ​​at each time point are obtained sequentially through the above calculation method to obtain the time series curve of tunnel surrounding rock displacement.

2. The method for predicting tunnel surrounding rock displacement time series curves based on dynamic Bayesian networks as described in claim 1, characterized in that, In S1, the influencing factors include 14 factors such as surrounding rock grade, surrounding rock lithology, surrounding rock structure, initial ground stress state, dip angle of main structural plane, tunnel depth, tunnel excavation span, stratum water content, groundwater control, advanced support method, excavation method, degree of surrounding rock disturbance, support timing and support strength.

3. The method for predicting tunnel surrounding rock displacement time series curves based on dynamic Bayesian networks as described in claim 1, characterized in that, In S2, there are 15 variables, including surrounding rock displacement and influencing factors. Based on the results of the variable correlation analysis, a mutual influence matrix of the variables is established to construct the explanatory structural model. Variables are considered correlated if the Pearson correlation coefficient is less than 0.05; otherwise, they are not correlated. The construction of the explanatory structural model includes the following steps: (1) Based on the results of the correlation analysis, construct the mutual influence matrix of the variables; (2) Transform the mutual influence matrix into an adjacency matrix A: in Representing variables right Influence relationship, =1 means right There is an impact. =0 indicates that there is no effect; (3) Perform an exponentiation operation on the adjacency matrix to obtain the reachability matrix M; the reachability matrix is ​​a matrix that represents the reachability of any two variables in the system after traversing a path of arbitrary length. Its specific calculation process is as follows: in for The path is long. It is the identity matrix; (4) Divide the reachability matrix into hierarchical parts to form a skeleton matrix; Reachability matrix The Middle The set of variables represented by columns with a row value of 1 is called the reachable set. , No. The set of variables represented by rows with a column value of 1 is called the antecedent set. Variable set Let represent the set of variables that exist simultaneously in both the reachability set and the antecedent set. Determine whether the set of variables is a set of highest-level variables based on whether it satisfies the following formula: (5) Find the set For the first level variable in the hierarchy, delete... middle The new matrix is ​​obtained by determining the row and column of the corresponding variable. And then Repeat the above steps to obtain For the second level of variables, delete them again. middle The corresponding row and column of the variable can be obtained by analogy. Determine the hierarchy of all variables to form a skeleton matrix; (6) Based on the skeleton matrix structure, according to the interaction relationship of variables in the same or adjacent levels, and following the rule that higher-level elements point to lower-level elements and higher-level variables are above and lower-level variables are below, a multi-level directed topology graph is drawn by connecting the lines in sequence, ignoring the relationship between cross-level variables, and finally establishing an explanatory structure model.

4. The method for predicting tunnel surrounding rock displacement time series curves based on dynamic Bayesian networks as described in claim 1, characterized in that, In S3, based on the interpreted structural model, the construction method of the K2 algorithm for improving the static Bayesian network model structure is as follows: (1) Determine the scoring function, using As a scoring function, the formula is: The variables in the scoring function have the following meanings: D: dataset; G: proposed network model; n: number of variables; P(G): prior probability distribution of network structure G; r i :node The number of possible values; i: node number; j: node The value number of the parent node; :node The set of parent nodes; q i : The number of possible values ​​for N; ijk :node parent node set Take the j-th value, The number of samples when taking the k-th value; N ij :node Parent node set The number of samples corresponding to the j-th state combination; (2) Based on the interpretable structural model, determine the value of node number i and q. i The possible values ​​of ; (3) Based on the explanatory structural model, determine part of the The possible values ​​of ; (4) The search strategy is determined to be a greedy search algorithm; the search puts the parent node variable with the largest score function into the set; when the score function cannot be increased, the search stops, and the optimal model is found; (5) Based on the sample data of the training set, a static Bayesian network model structure is established through the above-mentioned optimized K2 algorithm.

5. The method for predicting tunnel surrounding rock displacement time series curves based on dynamic Bayesian networks as described in claim 1, characterized in that, In S3, the maximum likelihood estimation method is used to learn the parameters of the static Bayesian network model. The specific process is as follows: (1) The logarithmic function form for determining the likelihood is: Where N is the sample data size, and n is the number of nodes. The number of nodes; let the nodes The set of parent nodes is q i parent node set The number of possible values ​​for r i For nodes The number of possible values ​​for N; ijk For nodes parent node set Take the j-th value, The number of samples when taking the k-th value; θ ijk For nodes parent node set Take the j-th value, The parameter value corresponding to the k-th value. ; (2) Find the maximum value of the above logarithmic function, that is, find the maximum value by taking the derivative with respect to the parameter θ. This will give us the parameter θ. ijk The value can be: (3) Based on the sample data of the training set, the conditional probability table of the static Bayesian network model is established by the above method.

6. The method for predicting tunnel surrounding rock displacement time series curves based on dynamic Bayesian networks as described in claim 1, characterized in that, In S3, inference analysis is performed based on Bayes' theorem, Markov chain theorem, and conditional independence theorem to establish a static Bayesian network model; the model is then trained and tested to verify its correctness.

Images