Roadbed and pavement subsidence cause mechanism analysis method based on combined weight

Abstract

The invention relates to a roadbed and pavement subsidence cause mechanism analysis method based on a combined weight. The method comprises the following steps: acquiring a basic factor data set influencing subsidence of a target road section; classifying data of the basic factor data set into a preset influence factor index system to obtain a structured index set; the preset influence factor index system comprises a target, a plurality of criteria and a plurality of indexes; the structured index set comprises a standardized index value and a grade criterion table corresponding to each index; calculating a subsidence influence factor index comprehensive weight according to the structured standard set to obtain a combined weight vector; and based on the combined weight vector, performing roadbed and pavement subsidence cause mechanism sorting and risk identification of the target road section according to the structured index set, and obtaining subsidence contribution degree sequences of the indexes and road section subsidence levels. By adopting the method, the importance of each index in the subsidence cause mechanism can be quantified through the preset influence factor index system, and reference is provided for subsequent engineering disease treatment measure suggestions.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of highway engineering, and particularly relates to a subgrade pavement subsidence cause mechanism analysis method based on combined weights. BACKGROUND

[0002] With the continuous advancement of transportation infrastructure construction, highway engineering is increasingly extended to complex geological conditions and high-density use scenarios, and multi-source data analysis technology for subgrade disease diagnosis and safety evaluation has emerged. Such technology is usually based on field measurement data, structure monitoring data and environmental factors, and combines analysis models to comprehensively judge the performance and safety state of the subgrade structure. Its characteristics lie in emphasizing data-driven, model support and dynamic response, and it has become an important support means for modern highway maintenance and management.

[0003] In the traditional subsidence cause analysis method, finite element simulation, experience interpretation or single-factor regression are usually used in combination with drilling data, geological maps, construction records and other information to trace the causes of subgrade pavement subsidence or deformation.

[0004] However, the above method relies on expert experience for cause factor identification, and lacks systematicity in index selection, thus having problems such as strong subjectivity of evaluation conclusion, difficulty in quantification, and difficulty in decoupling of index coupling effects. There are many factors affecting subsidence, and there may be complex coupling relationships between factors. Traditional methods often lack a systematic index framework, making it difficult to comprehensively cover all key factors; cause analysis based on a single model fails to effectively integrate subjective knowledge and objective data, thus failing to balance reliability and objectivity, affecting the pertinence and effectiveness of subsequent treatment measures. SUMMARY

[0005] Therefore, it is necessary to provide a subgrade pavement subsidence cause mechanism analysis method based on combined weights, which can combine the subjective and objective aspects of the subsidence affecting factors for cause analysis.

[0006] In a first aspect, the application provides a subgrade pavement subsidence cause mechanism analysis method based on combined weights, comprising:

[0007] obtaining a basic factor data set affecting subsidence of a target section;

[0008] classifying the data of the basic factor data set into a preset influence factor index system to obtain a structured index set; the preset influence factor index system includes a target, a plurality of criteria and a plurality of indexes; the structured index set includes a standardized index value and a level criterion table corresponding to each index;

[0009] calculating the subsidence affecting factor index comprehensive weight according to the structured standard set to obtain a combined weight vector;

[0010] Based on the combined weight vector, the subgrade pavement settlement mechanism of the target section is sorted and the risk is identified according to the structured index set, and the index settlement contribution degree sequence and the section settlement grade are obtained.

[0011] In one of the embodiments, the comprehensive weight of the settlement influencing factor index is calculated according to the structured standard set, and the combined weight vector is obtained, including:

[0012] Based on the expert experience index influence network, the subgrade pavement settlement mechanism analysis model is obtained according to the structured standard set; the subgrade pavement settlement mechanism analysis model includes a control layer and a network layer;

[0013] The subjective weight of the index of the subgrade pavement settlement mechanism analysis model is calculated by the network analysis method, and the subjective weight vector is obtained;

[0014] Based on the objective weight assignment method, the objective weight is calculated according to the standardized index value, and the objective weight vector is obtained;

[0015] Based on the game theory, the combined weight vector is obtained according to the subjective weight vector and the objective weight vector.

[0016] In one of the embodiments, the subjective weight of the index of the subgrade pavement settlement mechanism analysis model is calculated by the network analysis method, and the subjective weight vector is obtained, including:

[0017] Based on the criterion framework, the importance of each index is compared by the control layer, and a plurality of judgment matrices are obtained;

[0018] Based on the consistency check, the local weight vector of each index is extracted from each judgment matrix, and the local weight vector matrix is obtained;

[0019] The local weight vector matrix corresponding to a plurality of indexes is integrated by the control layer to obtain a super matrix;

[0020] The super matrix is weighted according to the relative weight of each criterion of the control layer to obtain a weighted super matrix;

[0021] The limit of each weighted super matrix is solved to obtain the subjective weight vector; the subjective weight vector is the weight set of each index of the network layer.

[0022] In one of the embodiments, based on the criterion framework, the indexes are compared by the control layer, and the judgment matrix is obtained, including:

[0023] Under the constraint of the control layer, the importance of each index is compared based on the criterion framework to obtain a comparison matrix;

[0024] The importance ranking index is calculated by calculating the importance ranking in the comparison matrix;

[0025] The judgment matrix is constructed according to the importance ranking index.

[0026] In one of the embodiments, the objective weight vector is obtained by calculating the objective weight according to the standardized index value based on the objective weight assignment method, including:

[0027] The standardized index value is processed by the normalization formula to obtain the standardized matrix.

[0028] The information amount of each index is calculated according to the standardized matrix to obtain the index information amount vector.

[0029] The objective weight vector is obtained according to the index information amount vector.

[0030] The objective weight vector is obtained by the following formula:

[0031]

[0032] Wherein, W j is the objective weight of the jth index, C j is the index information amount vector of the jth index; and n is the total number of indexes.

[0033] In one of the embodiments, the normalization formula is obtained by the following formula:

[0034]

[0035] Wherein, x′ ijmax , x′ ijmin is the normalized standardized value; x ij is the value of the jth index of the ith sample; max(x ij ) is the maximum value of the jth index; and min(x ij ) is the minimum value of the jth index.

[0036] In one of the embodiments, the combined weight vector is obtained according to the subjective weight vector and the objective weight vector based on the game theory, including:

[0037] The subjective and objective initial combined vector is set according to the subjective weight vector and the objective weight vector; the subjective and objective initial combined vector includes the subjective linear combination coefficient and the objective linear combination coefficient.

[0038] The Nash equilibrium point of the subjective linear combination coefficient and the objective linear combination coefficient is calculated based on the minimum error objective function of the game theory to obtain the target subjective linear combination coefficient and the target objective linear combination coefficient.

[0039] The target subjective linear combination coefficient and the target objective linear combination coefficient are normalized to obtain a combination weight vector;

[0040] The minimum error target function is obtained by the following formula:

[0041] min‖β1U s +β2U o -U q ‖

[0042] Wherein, β1 is the target subjective linear combination coefficient; β2 is the target objective linear combination coefficient; U s is a subjective weight vector; U o is an objective weight vector; U q is a target vector close to the subjective weight vector and the objective weight vector, q = 1, 2.

[0043] In one of the embodiments, based on the combination weight vector, the roadbed pavement subsidence mechanism of the target section is sorted and the risk is identified according to the structured index set, and the index subsidence contribution degree sequence and the section subsidence grade are obtained, including:

[0044] The overall influence of each index is calculated by using the combination weight vector, and the indexes are arranged in descending order to obtain the index contribution degree sequence;

[0045] The subsidence risk score is calculated according to the combination weight vector and the standardized index value;

[0046] The subsidence risk score is mapped to the corresponding risk grade standard of the grade discrimination table to obtain the section subsidence grade.

[0047] In one of the embodiments, before the roadbed pavement subsidence mechanism analysis model is constructed according to the structured standard set based on the expert experience index influence network, it further includes:

[0048] An expert judgment data set is obtained; the expert judgment data set includes the influence relationship between indexes in the preset influence factor index system;

[0049] An index correlation analysis is performed on the expert judgment data set by using a correlation rule mining algorithm to obtain the support and confidence between indexes;

[0050] Based on the index correlation rule, the influence relationship between indexes is filtered according to the support and confidence to obtain an expert experience index influence network; the index correlation rule corresponds to a strong correlation rule with a minimum support and a minimum confidence threshold; the expert experience index influence network includes index nodes and relationship edges between the index nodes.

[0051] In one of the embodiments, the support and the confidence are obtained by the following formula:

[0052]

[0053] wherein, Support(P) is the support degree; P and Q are the index subsets; σ(P) is the number of index subsets P contained in the expert judgment data set; N is the total number of indexes contained in the expert judgment data set; is the confidence degree; Support(P∪Q) is the frequency of index subsets P and Q mentioned in the expert judgment data set.

[0054] The above-mentioned roadbed pavement subsidence cause mechanism analysis method based on combination weight divides the subsidence related factors into target layer, criterion layer and index layer through the preset influence factor index system, classifies various basic factor data systematically, constructs a structured index set, solves the problem of non-systematic selection and non-uniform classification of cause factors in traditional methods, and improves the comprehensiveness and consistency of analysis. By calculating the comprehensive weight of the structured index set, the importance of each index in the subsidence cause mechanism is quantified, which breaks through the limitation of traditional experience judgment and realizes the comparability analysis of the contribution of each index in the subsidence mechanism. In the cause analysis, the weight of each index is combined with the standardized observation value to calculate the comprehensive risk score, which solves the deviation that may occur in the existing method only according to subjective judgment or only based on data fluctuation analysis, and improves the accuracy of subsidence main cause identification. The combination of the combination weight vector and the standardized index value outputs the subsidence risk score, and the subsidence level is identified according to the set level standard, so that the subsidence analysis result has a clear qualitative output form, and the contribution of the roadbed pavement subsidence cause factor is quantitatively presented, which guides the subsequent engineering repair. Based on the unified index structure and universal analysis process, it can be applied to the subsidence cause analysis of road sections in different regions and under different conditions, and has the adaptability of cross-engineering scenarios. BRIEF DESCRIPTION OF DRAWINGS

[0055] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the related art, the drawings needed to be used in the embodiments or related art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and those skilled in the art can also obtain other drawings according to these drawings without creative labor.

[0056] Figure 1 It is a flowchart of the roadbed pavement subsidence cause mechanism analysis method based on combination weight of the present application;

[0057] Figure 2 It is a flowchart of step S103;

[0058] Figure 3This is a flowchart illustrating the steps of step S204.

[0059] Figure 4 This is a step-by-step flowchart for step S104. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0061] In one embodiment, such as Figure 1 As shown, a method for analyzing the causal mechanism of roadbed and pavement settlement based on combined weights is provided. This embodiment illustrates the application of this method to a terminal. It is understood that this method can also be applied to a server, and to a system including both a terminal and a server, and implemented through interaction between the terminal and the server. In this embodiment, the method includes the following steps:

[0062] S101. Obtain the dataset of basic factors affecting subsidence in the target road section.

[0063] Indicatively, the basic factor dataset refers to a multi-source heterogeneous data set constituting the causes of roadbed subsidence, including observational information on geological conditions, hydrological environment, construction technology, historical seismic activity, climatic factors, and potential geological hazards. Data acquisition can be achieved through methods such as field drilling, engineering experiments, geophysical surveys, surface monitoring, remote sensing image analysis, and historical record retrieval. Specifically, for subsided road sections, the dataset should include at least the following data types: goaf subsidence, earthquakes, frost heave and thaw settlement, construction quality, and drainage conditions. Among these, goaf subsidence includes the number, area, and spatial distribution of collapsed goafs; earthquakes include regional earthquake frequency and magnitude records; frost heave and thaw settlement includes the thickness of the frozen soil layer, the saturated water content of the frozen soil layer, groundwater depth, groundwater corrosivity, and permeability coefficient; construction quality indicators include the quality of fill material, compaction degree, and layer thickness; and drainage conditions include the maximum daily rainfall, surface drainage status, ditch drainage status, and blind ditch drainage status. Optionally, the baseline factor dataset should spatially cover the target subsidence area and temporally be as close as possible to the period of disease occurrence to ensure the real-time nature and accuracy of the assessment.

[0064] S102. Classify the data of the basic factor dataset into the preset influencing factor indicator system to obtain a structured indicator set; the preset influencing factor indicator system includes objectives, multiple criteria and multiple indicators; the structured indicator set includes the standardized indicator value and grade criterion table corresponding to each indicator.

[0065] Illustratively, the preset influencing factor index system is a multi-level index system established according to existing disease experience, industry standards and expert consensus. The system is composed of a target layer, a criterion layer and an index layer. The target layer is a general description of the causes of subgrade pavement settlement. The criterion layer represents the key dimensions affecting the settlement, covering five categories of factors, namely, goaf collapse, earthquake, frost heaving and thawing settlement, construction quality and drainage condition. Each criterion layer is further refined into several index layers, such as the number of collapse holes, collapse hole area and spatial distribution under goaf collapse, and the maximum daily rainfall, surface drainage, ditch drainage and blind ditch drainage condition under drainage condition, a total of 17 index items. This system ensures the systematic coverage of the influencing factors of settlement causes, the relative independence of the indexes and their engineering measurability.

[0066] Further, the data classification process is to map the collected basic factor data set to each index item in the index system, ensuring that the data is highly aligned with the evaluation model in structure. Further, in order to realize the horizontal comparison between different indexes, the index values are standardized to obtain standardized index values. Combined with actual engineering experience and industry standards, the grade criterion table of each index is formulated to divide the standardized values into four grade intervals for qualitative judgment of risk degree. Illustratively, the grade criterion of the number of collapse holes may be 0, (0, 10), [10, 30), [30, 100), corresponding to the influence degrees I, II, III and IV, and the four safety risk levels of very safe, relatively safe, relatively dangerous and very dangerous, respectively.

[0067] S103, calculating the comprehensive weight of the settlement influencing factor index according to the structured standard set to obtain a combined weight vector.

[0068] Illustratively, according to the structured index set constructed, the comprehensive weight of the settlement influencing factor is calculated by using the combined weighting mechanism, and then the complete combined weight vector is obtained, including the subjective weight, the objective weight and the game combined weight.

[0069] The subjective weight is calculated based on an ANP (Analytic Network Process) method. The method considers the interdependence and feedback structure between indexes based on a traditional analytic hierarchy process (AHP). Specifically, an ANP network structure is constructed, the expert transaction data is mined for association rules by using an Apriori algorithm based on the judgments of multiple experts on the dependence relationship between indexes, a high-frequency and reliable index influence path is identified, redundant and weakly related relationships are removed, and a directed dependence network diagram is constructed. Based on the directed dependence network diagram, a pair-wise comparison judgment matrix between indexes is constructed with each criterion as a control node. After consistency checking, a feature vector is extracted or a local weight vector is calculated by using a geometric mean method. Multiple local weight vectors are assembled into a super matrix in accordance with the ANP network structure, and a relative weight of a control layer criterion is introduced for weighted processing to obtain a normalized weighted super matrix. Finally, a subjective weight vector is obtained through power multiplication convergence.

[0070] The objective weight is calculated based on a CRITIC (Criteria Importance Though Intercrieria Correlation) method. The core idea is to automatically determine the weight based on data volatility and correlation between indexes. Specifically, the standard deviation of the standardized data of each index is calculated to reflect its discrimination ability in each sample. A correlation coefficient matrix is constructed based on the standard deviation to quantify the information redundancy degree between indexes. The information quantity of each index, i.e., its objective importance, is obtained by product operation. The objective weight vector is obtained by normalizing the information quantity. Compared with the subjective method, the CRITIC weighting process is completely based on data volatility and structure, without the need for manual judgment, thereby enhancing the objectivity and robustness of the model.

[0071] Further, to fuse the subjective and objective weights, a game theory combination idea is used to construct a target function. Under the condition of linearly additive combination weights, the Nash equilibrium point is derived to solve the optimal combination coefficients β1 and β2, which are substituted into the combination expression U = β1U s + β2U o , so as to obtain the final combination weight of each index in the global. The combination weight vector takes into account both expert knowledge and data rules, thereby improving the adaptability and reliability of the model in different road sections.

[0072] In S104, based on the combination weight vector, the roadbed and pavement subsidence cause mechanism of the target road section is sorted and risk is identified according to the structured index set, so as to obtain a subsidence contribution degree sequence of each index and a road section subsidence grade.

[0073] Illustratively, the standardized value of each index is multiplied by its combination weight, and the sum is obtained to obtain a comprehensive subsidence risk score where w j is the combination weight of the jth index, x j is its normalized value. The resulting R value is in the interval [0, 1], which is mapped to a preset level criterion to classify and identify the road section subsidence state. For example, the criterion can be set to four levels, R ∈ [0, 0.25) is level I (very safe), R ∈ [0.25, 0.5) is level II (relatively safe), R ∈ [0.5, 0.75) is level III (relatively dangerous), and R ∈ [0.75, 1.0] is level IV (very dangerous). By sorting the weight values of the contributions of each index to the score, a contribution sequence of the cause mechanism can be output, revealing the dominant cause of the subsidence and providing a basis for subsequent treatment measures.

[0074] In the above roadbed and pavement subsidence cause mechanism analysis method based on combination weight, the subsidence-related basic factor data of the target road section is collected and classified into a preset influence factor index system, realizing the structured modeling and standardized expression of the roadbed subsidence problem, enabling multi-source heterogeneous data to be analyzed and compared under a unified framework, and improving the adaptability and universality of the evaluation system. Using the preset index system to organize the observation data can ensure that the factors considered in the analysis process are systematic and comprehensive, avoiding the bias in cause identification caused by factor omission or arbitrary selection, and improving the scientificity of the subsidence analysis. By calculating the comprehensive weight of the structured index set, the combination weight vector of each index is obtained, so that the subsidence cause analysis can reflect the importance of the index and its current state, thereby realizing the logical interpretability of index sorting and the sensitivity of risk identification. Based on the combination weight vector, the contribution of each index to the target road section is sorted, and the comprehensive risk score is calculated combined with the structured index value to identify the level, realizing the quantitative determination of the main cause of subsidence and the hierarchical output of the road section risk level, and improving the decision support capability of the subsidence analysis result.

[0075] In one embodiment, as shown in FIG. 1, the subsidence influence factor index comprehensive weight is calculated according to the structured standard set to obtain a combination weight vector, including: Figure 2

[0076] S201, based on the expert experience index influence network, a roadbed and pavement subsidence cause mechanism analysis model is obtained according to the structured standard set; the roadbed and pavement subsidence cause mechanism analysis model includes a control layer and a network layer.

[0077] ​Illustratively, a subgrade pavement subsidence mechanism analysis model is established according to a structured standard set and field expert experience. The model adopts a two-layer structure, namely a control layer and a network layer. The control layer corresponds to the criterion layer in the index system, is used to decompose the main influence dimensions involved in the overall subsidence target, and includes five types of criteria, namely goaf collapse, earthquake, frost heaving and thawing settlement, construction quality and drainage condition. The network layer is further refined to the index layer and is composed of 17 index nodes, each of which represents a quantifiable subsidence influencing factor. Specifically, in the model construction process, the dependence relationship and feedback path between the nodes of the network layer are determined based on expert experience.

[0078] S202. Subjective weight vector of the subgrade pavement subsidence mechanism analysis model is calculated by the network analysis method, and the subjective weight vector is obtained.

[0079] Illustratively, for the constructed subgrade pavement subsidence mechanism analysis model, ANP is applied to calculate the subjective weight of each index. Specifically, taking each control layer criterion as the center, a pair-wise comparison judgment matrix is constructed for the subordinate indexes. Based on the relative importance between each pair of indexes, a judgment matrix is formed by scale assignment. Further, the judgment matrix is subjected to consistency check to ensure that the expert judgment logic is self-consistent. Then, the local weight vector is extracted by the eigenvalue method or the geometric mean method, and the relative weight of each index under the criterion is obtained. After obtaining the local weight of each criterion, the local weight is combined into an initial supermatrix, and the corresponding submatrix is filled according to the dependence path between the indexes in the subgrade pavement subsidence mechanism analysis model. Further, the global weight of the control layer criterion is introduced to weight the supermatrix, and a weighted supermatrix is formed, and each column of the weighted supermatrix is normalized to reflect the global importance. The weighted supermatrix is subjected to power operation until convergence, and the obtained result is the subjective weight vector of all indexes, which reflects the relative contribution of each index to the subsidence mechanism under the expert knowledge cognition.

[0080] S203. Objective weight vector is calculated based on the objective weight assignment method according to the standardized index value, and the objective weight vector is obtained.

[0081] Illustratively, to overcome the problem that the subjective weight vector is easily affected by the subjective bias of experts, the CRITIC method is used to calculate the weight of each index in a data-driven manner. Specifically, the index values are subjected to dimensionless normalization processing to unify the data magnitude and directionality; the standard deviation of each index is calculated to reflect its discrimination ability in different road sections; and a correlation coefficient matrix is further constructed to evaluate the information redundancy degree between the indexes. On this basis, the information amount of each index is defined as the product of its standard deviation and independence, so as to obtain the weight contribution ability of the index. Through normalization processing, the objective weight vector is formed, which represents the importance ranking of each factor revealed by the data itself without relying on expert judgment.

[0082] S204, obtaining a combined weight vector according to the subjective weight vector and the objective weight vector based on game theory.

[0083] Illustratively, the final combined weight vector is constructed by the linear combination idea of game theory to coordinate the deviation between the two types of weights, so that the final result can reflect both the structural knowledge between the indicators and the objectivity obtained by data analysis. Specifically, the subjective weight is U s , the objective weight is U o , and the combined weight is U = β1U s + β2U o . To solve the optimal combination coefficients β1and β2, an error minimization objective function is constructed, with the sum of the Euclidean distances between the combined weight and the subjective and objective weights as the objective term. Under the condition of β1+ β2 = 1, the Nash equilibrium point is obtained by derivation and least squares optimization to determine the optimal weight coefficients, and the combined weight vector U obtained comprehensively reflects the structural cognition of experts and the objective data law, has both structural explainability and numerical rationality, and provides a scientific basis for subsidence cause identification and treatment.

[0084] In one embodiment, the subjective weight of the roadbed and pavement subsidence cause mechanism analysis model is calculated by network analysis method to obtain a subjective weight vector, including:

[0085] S11, based on the criterion framework, the importance of each indicator is compared in pairs by the control layer to obtain a plurality of judgment matrices.

[0086] Illustratively, the criteria in the structured index system are taken as the analysis framework, and according to the hierarchical structure of the control layer and the network layer in the roadbed and pavement subsidence cause mechanism analysis model, a number of index nodes under each criterion are compared in pairs in turn. The comparison process is judged by experts according to experience. Illustratively, a three-level scale method is used to quantitatively assign the importance between any two indicators, i.e. when an expert thinks that indicator i is slightly more important than indicator j in the subsidence mechanism, a comparison value of 2 is assigned, and vice versa. If they are equally important, the value is 1. All pairwise comparison results form an n x n judgment matrix, where n is the number of indicators under the criterion layer, and the element in the (i, j) position of the matrix represents the importance ratio of indicator i to indicator j. Illustratively, the judgment matrix is

[0087] S12, based on consistency checking, the local weight vector of each indicator is extracted from each judgment matrix to obtain a local weight vector matrix.

[0088] Illustratively, in order to ensure the reliability of the weight result, the consistency index (CI) and the consistency ratio (CR) of each judgment matrix need to be calculated due to the possible logical inconsistency of expert judgment. Specifically, the maximum eigenvalue λ max of the judgment matrix is determined and the corresponding random consistency index RI is determined by looking up the table to obtain the consistency ratio Illustratively, when the CR value is less than the preset threshold 0.1, the judgment matrix is considered to meet the consistency requirement; otherwise, the comparison value needs to be adjusted. On the premise of passing the consistency, the eigenvector corresponding to λ max is extracted and normalized by the eigenvector method, or the local weight vector is extracted by multiplying the product of each row element by n times and then normalizing by the geometric mean method. The vector reflects the relative importance of each index in the local structure under the criterion layer. The local weight vectors corresponding to all criterion layers form a local weight vector matrix

[0089] S13, integrating the local weight vector matrix corresponding to multiple indexes by the control layer to obtain a super matrix.

[0090] Illustratively, the super matrix is a weight structure specific to the ANP method, which is based on all index nodes in the network layer and integrates all local weight information into a large block matrix structure, i.e., a super matrix Each sub-block in the super matrix represents the influence weight of a group of indexes on another group of indexes, and the entire super matrix is arranged and organized according to the dependent path in the network model, forming a comprehensive characterization of the influence path between the control layer and the network layer. Unlike traditional hierarchical structures, the super matrix can contain horizontal dependencies, self-feedback, and cross-layer effects between elements, thereby effectively modeling the coupling relationship between indexes in a complex subsidence system.

[0091] S14, weighting the super matrix according to the relative weights of the criteria of the control layer to obtain a weighted super matrix.

[0092] Illustratively, in order to incorporate the relative importance between the criteria of the control layer into the overall weight system of the indexes, the super matrix is weighted to obtain a weighted super matrix. Specifically, the global importance value of each criterion in the control layer is determined, wherein the global importance value can be determined by expert judgment, AHP method, or prior weighting method. Further, each column in the super matrix is proportionally weighted according to the importance of the upper control criterion, adjusting the influence strength of different control paths, so that the weighted super matrix retains the network dependency information in structure while achieving normalization of each column in value, having global comparability.

[0093] S15, limit solving is performed on each weighted super matrix to obtain a subjective weight vector; the subjective weight vector is a weight set of each index of the network layer.

[0094] Illustratively, limit solving is performed based on the weighted super matrix to extract a final subjective weight vector. Specifically, by performing a continuous power multiplication operation on the weighted super matrix, the propagation and balance process of information in the entire model structure is simulated. When the matrix power tends to be stable, that is, the change of the result matrix tends to be close to zero between two adjacent times, it is considered to have converged, and the obtained matrix is the limit super matrix. Each column vector of the limit super matrix is the stable weight of each index in the network layer, reflecting its comprehensive subjective contribution in the entire system. The corresponding column vector in the limit super matrix is extracted and normalized to obtain the subjective weight vector required by the present application, which is used for subsequent combination weight fusion and subsidence cause ordering analysis. Illustratively, wherein W ∞ is the limit super matrix, that is, the stable form of the super matrix after power multiplication convergence; is the kth power of the weighted super matrix; k is the power; N is the total number of elements, that is, the total number of indexes; s is the criterion.

[0095] In one embodiment, based on the criterion framework, the control layer compares each index pairwise to obtain a judgment matrix, including:

[0096] S21, under the constraint of the control layer, the importance of each index is compared pairwise based on the criterion framework to obtain a comparison matrix.

[0097] Illustratively, according to the constructed index system, the specific index items belonging to each control layer criterion are determined. Within this constraint framework, all indexes under any criterion layer are systematically compared pairwise, that is, all possible index pairs are combined and listed, and the relative importance relationship between these indexes is valued through expert investigation, standard specification reference or engineering experience judgment. Illustratively, a three-scale system is used for pairwise comparison, that is, wherein if i is more important than j, the value is 2, otherwise 0, and if they are equally important, the value is 1. This comparison process forms a set of pairwise comparison values, wherein n is the number of indexes under the current criterion layer.

[0098] S22, the importance ordering index is calculated to obtain the importance ordering index.

[0099] To convert the pairwise comparison result into a matrix form structure expression, the above comparison relationship needs to be formed into a consistent ordering basis, that is, the importance ordering index. The importance ordering index reflects the comprehensive comparison result of each index relative to other indexes, which can be realized by various methods, including but not limited to arithmetic mean method, geometric mean method, eigenvalue method, etc. Illustratively, the importance ordering index is wherein r i is the sum of the elements in the i-th row of the comparison matrix C, c ij is the value of the importance of index i relative to index j; and n is the order of the comparison matrix, i.e., the number of indexes.

[0100] S23, constructing a judgment matrix according to the importance ranking index.

[0101] According to the obtained importance ranking index, a final judgment matrix A = {a ij} is constructed, wherein The judgment matrix is an n x n positive reciprocal matrix, i.e., the elements on the main diagonal are all 1, and any one set of reciprocal relations satisfies Each element a ij of the judgment matrix represents the importance of index i relative to index j.

[0102] The above method, the judgment matrix construction process is based on the control layer criterion logic structure, relying on the pair comparison mechanism, through the importance ranking index conversion and matrix construction, the original judgment result is structured and quantified, and the subjective relative importance between indexes is accurately expressed. Both the interpretability of the weight source is guaranteed, and the data basis and structural support for subsequent weight extraction, consistency check and super matrix construction are provided.

[0103] In one of the embodiments, based on the objective weight assignment method, the objective weight vector is obtained according to the standardized index value, including:

[0104] S31, performing dimensionless processing on the standardized index value through a normalization formula to obtain a standardized matrix.

[0105] Illustratively, the observation values of all indexes in the structured index set are normalized to eliminate the influence of the original dimensions and value ranges of the indexes, and a standardized matrix with unified dimensions and unified direction is constructed. Specifically, different normalization formulas are used to process different properties of indexes, i.e., for the more serious impact class index, a positive normalization method is used, i.e. And for the more serious impact class index, a reverse normalization method is used, i.e. wherein x ij represents the original value of the i-th sample on the j-th index, x′ ijmax , x′ ijmin are the normalized standardized values. The normalization result constitutes an n x m-dimensional standardized matrix X′, wherein n is the number of samples and m is the number of indexes.

[0106] S32, calculating the information amount of each index according to the standardized matrix to obtain an index information amount vector.

[0107] Illustratively, the information quantity of each indicator is calculated based on the standardized matrix. The essence of the information quantity is the product of the distinguishing strength and the independence degree of an indicator in multiple samples. Specifically, the standard deviation σ j The numerical fluctuation of each indicator in all samples is measured, reflecting its distinguishing strength for the evaluation system; a correlation matrix is constructed to calculate the correlation coefficient r ji between each pair of indicators, to assess the information overlap with other indicators. Illustratively, if an indicator has a high correlation with multiple other indicators, it means that its information is redundant and its relative weight should be reduced. After combining the standard deviation and the correlation coefficient, the information quantity of each indicator is where C j is the information quantity of the jth indicator, x′ ij is the element in the standardized matrix; is the mean of the indicators; m is the number of indicators; r ij is the correlation coefficient between indicator i and indicator j. Finally, an m-dimensional information quantity vector C j is obtained to describe the relative strength of all indicators in information contribution. Further, the greater the information quantity, the stronger the distinguishing ability and the more independent the information content, so a higher weight should be given.

[0108] S33, the objective weight vector is calculated according to the indicator information quantity vector.

[0109] The objective weight vector is obtained by the following formula:

[0110]

[0111] where W j is the objective weight of the jth indicator, C j is the indicator information quantity vector of the jth indicator; and n is the total number of indicators.

[0112] Illustratively, the information quantity vector is normalized to ensure that the sum of the weights obtained is 1, and to form the final objective weight vector. The normalized objective weight vector not only retains the objective performance of each indicator in the data, but also automatically suppresses the weight proportion of indicators with insufficient fluctuation or high correlation in the overall evaluation, thereby constructing a non-biased weight system based on data characteristics.

[0113] The above method, the CRITIC weighting process effectively realizes the objective recognition of the importance of indicators through standardization, diversity measurement and redundancy correction, etc. It does not require manual intervention and is suitable for weight calculation under different data distribution conditions, with good universality, repeatability and data sensitivity, providing objective and robust weight support for subsidence mechanism analysis.

[0114] In one embodiment, the normalization formula is obtained by the following formula:

[0115]

[0116] wherein x′ ijmax , x′ ijmin is the normalized standardized value; x ij is the value of the jth index of the ith sample; max(x ij ) is the maximum value of the jth index; and min(x ij ) is the minimum value of the jth index.

[0117] In one embodiment, as shown in formula (1), the combined weight vector is obtained based on game theory according to the subjective weight vector and the objective weight vector, including: Figure 3

[0118] S301, setting the subjective and objective initial combined vector according to the subjective weight vector and the objective weight vector; the subjective and objective initial combined vector includes a subjective linear combination coefficient and an objective linear combination coefficient.

[0119] Illustratively, according to the obtained subjective weight vector and the objective weight vector , the subjective and objective initial combined vector is set as U = β1U s + β2U o , wherein β1 is the subjective linear combination coefficient, and β2 is the objective linear combination coefficient. Illustratively, the initial combined vector can be configured with equal weights, i.e., β1 = β2 = 0.5, or set according to historical experience. The combination coefficients need to satisfy the weight conservation constraint condition β1 + β2 = 1, and β1 ≥ 0, β2 ≥ 0.

[0120] S302, calculating the Nash equilibrium point of the subjective linear combination coefficient and the objective linear combination coefficient based on the minimum error objective function of game theory, to obtain the target subjective linear combination coefficient and the target objective linear combination coefficient.

[0121] The minimum error objective function is obtained by the following formula:

[0122] min‖β1U s + β2U o - U q ‖

[0123] wherein β1 is the target subjective linear combination coefficient; β2 is the target objective linear combination coefficient; U s is the subjective weight vector; U o is the objective weight vector; and U q ​q = 1, 2 for the target vector close to the subjective weight vector and the objective weight vector.

[0124] Illustratively, to find the optimal coefficient pair of the subjective and objective combination, an optimization model is constructed to minimize the combination error. Specifically, the Euclidean distance is introduced as an error measurement tool, and the deviation between the combination weight and the original subjective and objective weight vectors is taken as the core content of the optimization objective function. Illustratively, the objective function is F(β1, β2) = ‖U - U S ‖ 2 +‖U - U O ‖ 2 That is, the objective function is minimized to make the combination weight close to the subjective weight vector and the objective weight vector. That is, if the combination weight can approach the subjective weight vector and the objective weight vector at the same time, it means that the compromise degree of the two in the game is optimal. The initial combination expression U = β1U s + β2U o is substituted into the objective function, which is further expanded and simplified into a quadratic function about β1 and β2. By taking the partial derivative of F(β1, β2) with respect to β1 and β2 and setting it to zero, a linear equation group is constructed. Then the combination coefficients β1 and β2 corresponding to the minimum point are solved, that is, the target subjective linear combination coefficient and the target objective linear combination coefficient. The solution is the Nash equilibrium point of the subjective linear combination coefficient and the objective linear combination coefficient, which represents the optimal cooperative strategy reached by the two parties in the game under the premise of mutual restraint and information sharing.

[0125] S303, normalize the target subjective linear combination coefficient and the target objective linear combination coefficient to obtain the combination weight vector.

[0126] Illustratively, considering that β1 + β2 ≠ 1 may be caused by numerical accuracy or initial coefficient setting in actual calculation, in order to ensure the normalization and interpretability of the weight result, the above optimal combination coefficients need to be normalized to obtain the combination weight vector U = β1'U s + β2'U o which has structural rationality and data sensitivity, and reflects the comprehensive contribution strength of each index in the subsidence mechanism.

[0127] The above method, the game theory combination weight method, is based on a mathematical optimization model, and through the balance and coordination mechanism between the weights, a weight integration framework is constructed to integrate the advantages of subjective and objective evaluation, which significantly improves the stability, objectivity and reliability of the weight result, and provides a scientific and reliable input basis for subsequent subsidence mechanism identification and grade evaluation.

[0128] In one of the embodiments, as Figure 4As shown, based on the combined weight vector, the subgrade pavement subsidence mechanism of the target section is sorted and risk is identified according to the structured index set, and the index subsidence contribution degree sequence and the section subsidence grade are obtained, including:

[0129] S401, the overall influence of each index is calculated by using the combined weight vector, and is arranged in descending order, and the index contribution degree sequence is obtained.

[0130] Illustratively, the combined weight vector is Wherein, The comprehensive weight of the jth index, that is, its relative contribution degree in the subsidence mechanism. According to the weight vector itself, the indexes are sorted in descending order, that is, arranged in descending order The contribution degree sequence Seq=[b (1) ,b (2) ,…b (n) ] is obtained, where b (i) Indicates the key influence index of the ith position. The sequence reflects the structural influence degree of each index on the subsidence risk under the current weight system, which provides reference for subsequent diagnosis.

[0131] S402, the subsidence risk score is calculated according to the combined weight vector and the standardized index value.

[0132] Illustratively, the subsidence risk score of the section is calculated by comprehensively considering the actual index performance of the current section and its relative importance. The scoring index quantifies the overall risk level of the subsidence mechanism under the current state, which is defined as the weighted average value of the standardized value of each index and the corresponding combined weight, that is Wherein, x j ′ is the standardized value of the jth index, reflecting the severity of the index in the current section, The combined weight of the jth index, indicating the importance of the index. The result of multiplying the weight and the standardized value is the weighted risk item, and the accumulation is the comprehensive subsidence risk score R of the whole section under the existing structural influence. Since all indexes have been standardized to the interval [0, 1], the weight sum is 1, so the R value is also between [0, 1].

[0133] S403, the subsidence risk score is mapped to the contrast risk level standard of the grade judgment table to obtain the subsidence grade of the section.

[0134] Illustratively, the risk score R is mapped to the preset grade judgment table to complete the classification and identification of the subsidence risk grade of the target section. Illustratively, the grade judgment table can be set according to engineering experience, industry standard or statistical plan result, and is usually divided into four grades corresponding to different risk degree intervals.

[0135] The above method couples and integrates the combination weight and the field data in structure, provides the index main cause identification and the road section level division two dimensions of conclusions in output, and improves the explainability, operability and engineering guidance value of the subsidence cause analysis result.

[0136] In one of the embodiments, before the roadbed pavement subsidence cause mechanism analysis model is constructed according to the structured standard set, the method further includes:

[0137] S41, acquiring an expert judgment data set; the expert judgment data set includes the influence relationship between indexes in the preset influence factor index system.

[0138] The influence relationship between the subsidence mechanism related indexes is obtained by constructing the structured expert judgment data set. The expert judgment data set is derived from the interview investigation of a plurality of professional and technical personnel with backgrounds of highway engineering, geological disasters, construction management and the like. The investigation content is around the 17 index items in the preset influence factor index system, and the expert is required to provide the index pairs that he believes have direct or indirect causal relationship. Each expert forms a judgment transaction, which includes a group of indexes that he believes have influence relationship with each other. For example, the expert may point out that the number of goaf collapse holes will affect the ground surface drainage condition, or the underground water level depth may have linkage with the frost heaving layer thickness. A plurality of expert judgment transactions together constitute the expert judgment data set S, which is essentially a transaction set composed of index items, and provides a discrete input for subsequent relationship mining. Further, in order to avoid relationship redundancy or omission caused by human cognitive differences, the Apriori association rule algorithm is used to optimize and screen the index influence relationship provided by the expert, and to mine the index correlation pairs that have high frequency co-occurrence and have causal logic in the expert opinions. The algorithm retains the strong correlation relationship with stable statistical significance by analyzing the support and confidence between the item sets in the expert transaction data set, so as to construct a simple and reasonable directed index network diagram as the input structure for subsequent network analysis. Optionally, the Apriori association rule algorithm can be used to optimize and screen the index influence relationship provided by the expert, which can be pre-screened once when constructing the roadbed pavement subsidence cause mechanism analysis, or can be individually screened for different target road sections.

[0139] S42, using an association rule mining algorithm to perform index correlation analysis on the expert judgment data set, to obtain the support and confidence between the indexes.

[0140] Illustratively, the Apriori algorithm performs frequent itemset analysis on the dataset S. The algorithm recursively mines all frequent itemsets that satisfy a support threshold by using an enumeration method from bottom to top, and generates possible inter-index association rules accordingly. For any two indexes P and Q, if they appear simultaneously in multiple expert transactions and satisfy the defined strong rule, i.e., the conditional support Support(P) represents the proportion of transactions that contain both P and Q; and the confidence represents the probability of containing Q in the transactions containing P.

[0141] S43, based on the index association rules, filtering the influence relationship between indexes according to the support and confidence, obtaining an expert experience index influence network; the index association rules correspond to strong association rules with minimum support and minimum confidence thresholds; the expert experience index influence network includes index nodes and relationship edges between the index nodes.

[0142] According to the set minimum support threshold MIN support(P) and the minimum confidence threshold , all the mined index association rules are filtered, and only the rules that satisfy the double threshold conditions are retained as strong association rules, representing the influence relationship between indexes that is recognized by most experts and has a clear logical causal direction under expert knowledge. Based on this, an expert experience index influence network is constructed, wherein the nodes represent each index in the structured index system, and the edges represent the direct influence relationship between the indexes, with the direction from cause to effect The existence of the edges is based on the strong association rules that are filtered and retained. Optionally, the network structure can be represented as a directed graph G=(V, E), where V is the index set, and E is the dependent relationship set that satisfies the threshold rule.

[0143] The above method not only depicts the structural influence logic in the subsidence cause system, but also greatly simplifies the connection complexity in the network analysis model, avoiding the model redundancy caused by invalid dependent paths. The constructed expert experience index influence network will be used as the basic structure input for subsequent ANP subjective weight calculation, ensuring that the model structure has both engineering logic and statistical stability. The construction process of the expert experience index influence network realizes the formal transformation from experience knowledge to model structure through structured expert cognition, algorithmic dependence extraction, and logical rule filtering, providing scientific, controllable, and reasonable topological support for the construction of the subsidence mechanism analysis model.

[0144] In one embodiment, the support and confidence are obtained by the following formula:

[0145]

[0146] Support (P) is the support degree; P and Q are the index subsets; σ (P) is the number of index subsets P contained in the expert judgment data set; N is the total number of indexes contained in the expert judgment data set; is the confidence degree; Support (P∪Q) is the frequency of index subsets P and Q mentioned in the expert judgment data set.

[0147] It should be understood that, although each step in the flowchart involved in each embodiment as described above is shown in sequence according to the arrow, these steps are not necessarily executed in the order indicated by the arrow. Unless explicitly stated herein, the execution of these steps is not strictly limited in sequence, and these steps can be executed in other orders. Moreover, at least part of the steps in the flowchart involved in each embodiment as described above can include multiple steps or multiple stages, which are not necessarily executed at the same time, but can be executed at different times, and the execution sequence of these steps or stages is not necessarily sequential, but can be executed in rotation or alternation with at least part of other steps or steps or stages in other steps.

[0148] The above-described embodiments only express several implementation manners of the application, and the description is relatively specific and detailed, but it should not be understood as a limitation on the patent scope of the application. It should be pointed out that, for those skilled in the art, without departing from the concept of the application, several modifications and improvements can be made, which are all within the protection scope of the application.

Claims

1. A method for analyzing the mechanism of subgrade pavement settlement causes based on combined weights, characterized in that, The method comprises: obtaining a basic factor data set of a target section affecting subsidence; classifying data of the basic factor data set into a preset influence factor index system to obtain a structured index set; the preset influence factor index system comprises a target, a plurality of criteria and a plurality of indexes; the structured index set comprises a standardized index value and a grade criterion table corresponding to each index; calculating a subsidence influence factor index comprehensive weight according to the structured index set to obtain a combination weight vector; based on the combination weight vector, performing roadbed and pavement subsidence mechanism sorting and risk identification of the target section according to the structured index set to obtain a subsidence contribution degree sequence of each index and a section subsidence grade.

2. The method of claim 1, wherein, The method comprises: based on an expert experience index influence network, obtaining a roadbed and pavement subsidence mechanism analysis model according to the structured index set; the roadbed and pavement subsidence mechanism analysis model comprises a control layer and a network layer; performing index subjective weight calculation on the roadbed and pavement subsidence mechanism analysis model by a network analysis method to obtain a subjective weight vector; based on an objective weight assignment method, performing objective weight calculation according to the standardized index value to obtain an objective weight vector; based on game theory, obtaining the combination weight vector according to the subjective weight vector and the objective weight vector.

3. The method of claim 2, wherein, The method comprises: based on the criterion framework, performing importance pairwise comparison on each index by the control layer to obtain a plurality of judgment matrices; based on consistency checking, extracting a local weight vector of each index from each judgment matrix to obtain a local weight vector matrix; integrating the local weight vector matrices corresponding to a plurality of indexes by the control layer to obtain a super matrix; performing weighted processing on the super matrix according to the relative weights of each criterion of the control layer to obtain a weighted super matrix; performing limit solving on each weighted super matrix to obtain the subjective weight vector; the subjective weight vector is a weight set of each index of the network layer.

4. The method of claim 3, wherein, The method comprises: under the constraint of the control layer, performing importance pairwise comparison on each index based on the criterion framework to obtain a comparison matrix; calculating an importance ranking index by calculating the importance ranking of the comparison matrix; constructing the judgment matrix according to the importance ranking index.

5. The method of claim 2, wherein, The method comprises: performing non-dimensionalization processing on the standardized index value by a normalization formula to obtain a standardized matrix; calculating the information amount of each index according to the standardized matrix to obtain an index information amount vector; calculating the objective weight vector according to the index information amount vector; the objective weight vector is obtained by the following formula: Wherein, W j is the objective weight of the jth index, C j is the index information quantity vector of the jth index; and n is the total number of indexes.

6. The method of claim 5, wherein: the normalization formula is obtained by the following formula: wherein x′ ijmax , x′ ijmin are normalized standardized values; x ij is the value of the jth index of the ith sample; max(x ij ) is the maximum value of the jth index; and min(x ij ) is the minimum value of the jth index.

7. The method of claim 2, wherein, the combination weight vector is obtained based on the game theory according to the subjective weight vector and the objective weight vector, and the combination weight vector comprises: an initial subjective-objective combination vector is set according to the subjective weight vector and the objective weight vector, and the initial subjective-objective combination vector comprises a subjective linear combination coefficient and an objective linear combination coefficient; a Nash equilibrium point of the subjective linear combination coefficient and the objective linear combination coefficient is calculated based on a game theory minimum error objective function to obtain a target subjective linear combination coefficient and a target objective linear combination coefficient; the target subjective linear combination coefficient and the target objective linear combination coefficient are normalized to obtain the combination weight vector; the minimum error objective function is obtained by the following formula: min || β1U s + β2U o - U q ‖ where β1is the target subjective linear combination coefficient; β2is the target objective linear combination coefficient; U s is the subjective weight vector; U o is the objective weight vector; U q is the target vector close to the subjective weight vector and the objective weight vector, q = 1, 2.

8. The method of claim 1, wherein, the combination weight vector is used to perform roadbed and pavement settlement mechanism sorting and risk identification on the target road section according to the structured index set to obtain an index settlement contribution degree sequence and a road section settlement grade, and the combination weight vector comprises: the overall influence of each index is calculated, and the indexes are arranged in descending order to obtain an index contribution degree sequence; a settlement risk score is calculated according to the combination weight vector and the standardized index value; the settlement risk score is mapped to a corresponding risk grade standard of the grade discrimination table to obtain the road section settlement grade.

9. The method of claim 2, wherein, Before the roadbed and pavement settlement mechanism analysis model is constructed according to the structured index set, the method further comprises: an expert judgment data set is obtained, and the expert judgment data set comprises influence relationships between indexes in the preset influence factor index system; an index correlation analysis is performed on the expert judgment data set by using a correlation rule mining algorithm to obtain support and confidence between indexes; the influence relationships between indexes are filtered according to the support and the confidence based on an index correlation rule to obtain the expert experience index influence network; the index correlation rule corresponds to a strong correlation rule of a minimum support threshold and a minimum confidence threshold; and the expert experience index influence network comprises index nodes and relationship edges between the index nodes.

10. The method of claim 9, wherein: the support and the confidence are obtained by the following formula: Wherein, Support(P) is the support degree; P and Q are the index subsets; σ(P) is the number of index subsets P contained in the expert judgment data set; N is the total number of indexes contained in the expert judgment data set; is the confidence degree; Support(P∪Q) is the frequency of index subsets P and Q mentioned in the expert judgment data set.

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