Tunnel lining crack form quantification and expansion trend prediction method and system

Abstract

The invention discloses a tunnel lining crack form quantification and expansion trend prediction method and system, particularly relates to the technical field of network model analysis, and is used for solving the problem that the overall evolution trend of a crack network cannot be predicted when a crack is regarded as an independent individual for analysis in the prior art. The method comprises the following steps: identifying crack contours from a time sequence image, establishing a network topology structure of the crack contours, analyzing connection and spatial configuration between cracks to construct a crack network with a weight, and further extracting topological role features and sub-network cohesion features representing the network structure; constructing a state transition network for representing macroscopic state evolution of the system based on historical data of the features; and finally, deducing a future possible state sequence in the network by taking the current state as a starting point so as to predict the overall evolution trend of the fracture network system.

Description

Technical Field

[0001] This invention relates to the field of network model analysis technology, and more specifically, to a method and system for quantifying the morphology and predicting the propagation trend of tunnel lining cracks. Background Technology

[0002] In the field of structural health monitoring in tunnel engineering, the automated detection and safety assessment of lining cracks mainly rely on computer vision and data analysis technologies to quantify crack morphology and predict trends. A typical process involves: acquiring digital images of the lining surface, using image analysis algorithms to identify and segment crack targets, and then extracting geometric parameters such as length and width to quantify the morphology; subsequently, these quantified parameters are used as time-series data and input into a time-series prediction model for learning and training, ultimately outputting a prediction of the crack's future expansion state. This method aims to transform subjective, qualitative crack descriptions into objective, quantitative analyses, providing a basis for maintenance decisions.

[0003] However, the aforementioned existing technical solutions have limitations: their analysis and prediction models are usually based on the assumption of independent crack evolution, that is, quantifying and inferring trends for each crack in isolation. In actual lining structure damage scenarios, cracks often appear in groups and form complex networks. There are mechanical interactions and influences between cracks. The expansion of a crack will change the stress distribution in its surrounding area, thus significantly affecting the evolutionary behavior of other nearby cracks. Existing technologies treat the crack network as independent individuals, which essentially ignores this crucial group effect. As a result, their prediction models can only reflect the trend of a single crack driven by its own historical data, and cannot accurately characterize and predict the overall evolutionary behavior of the entire crack network as an interacting system. Summary of the Invention

[0004] In order to overcome the above-mentioned defects of the prior art, the present invention provides a method and system for quantifying the crack morphology and predicting the propagation trend of tunnel lining cracks to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for quantifying the morphology and predicting the propagation trend of cracks in tunnel lining includes the following steps:

[0007] S1. Obtain time-series images of the tunnel lining surface, and identify and segment the crack contours from the time-series images;

[0008] S2. For each time series image, establish the crack network topology based on the spatial distance and orientation relationship between each crack contour.

[0009] S3. Based on the analysis of the topological connection and spatial configuration between cracks, the key evolution paths are identified and weighted to obtain a weighted crack network.

[0010] S4. For weighted crack networks, analyze the topological position and connection importance of each crack in the network to extract its topological role features, and identify crack sub-clusters in the network to extract sub-network cohesion features.

[0011] S5. Based on historical time-series data of topological role characteristics and subnetwork cohesion characteristics, construct the state transition network of the crack network system;

[0012] S6. Starting from the system state defined by the topological role characteristics and sub-network cohesion characteristics at the current moment, deduce the possible future state sequence in the state transition network, and predict the overall evolution trend of the crack network based on the state sequence.

[0013] Further, time-series images of the tunnel lining surface are acquired, and crack contours are identified and segmented from the time-series images, including:

[0014] Preprocessing of time-series images enhances the contrast between crack and background areas;

[0015] Pixel regions belonging to the cracks were identified based on the preprocessed image;

[0016] The pixel region belonging to the crack is segmented into a continuous crack outline.

[0017] Furthermore, during the segmentation process, the correlation between images at different times in the temporal image is used to correct and complete the crack contour.

[0018] Furthermore, for each time-series image, a crack network topology is established based on the spatial distance and orientation relationship between each crack contour, including:

[0019] For each time series image, calculate the spatial distance between crack contours.

[0020] Analyze the orientation relationship between crack profiles;

[0021] Determine whether there is a topological connection between crack profiles based on the spatial distance and orientation relationship between crack profiles;

[0022] Generate the crack network topology based on the topological connections between all crack profiles.

[0023] Furthermore, the orientation relationship between crack profiles includes the angle between the main directions of the crack profiles, and the spatial distance includes the shortest distance between the endpoints of the crack profiles.

[0024] Furthermore, based on the analysis of the fracture network topology, the topological connections and spatial configurations between fractures are analyzed, key evolution paths are identified and weighted to obtain a weighted fracture network, including:

[0025] Based on the crack network topology, the topological connectivity and spatial configuration relationships between cracks are analyzed.

[0026] Key evolutionary paths in the crack network were identified based on topological connectivity and spatial configuration relationships;

[0027] Weights are assigned to key evolutionary paths, and the weight values ​​are calculated based on the topological connectivity and spatial configuration relationships of the key evolutionary paths, including the orientation consistency of the key evolutionary paths.

[0028] By assigning weight values ​​to the corresponding critical evolution paths in the fracture network topology, a weighted fracture network is obtained.

[0029] Furthermore, for weighted fracture networks, the topological position and connectivity importance of each fracture in the network are analyzed to extract its topological role features, and fracture sub-clusters in the network are identified to extract sub-network cohesion features, including:

[0030] The connection strength index and bridging function index of each crack are calculated based on the weighted crack network. The connection strength index is determined by the weighted number of connections of the crack in the weighted crack network, and the bridging function index is determined by the frequency of the crack appearing in the shortest path of the weighted crack network.

[0031] The connection strength index and the bridge function index are combined to form the topological role characteristics of each crack;

[0032] The weighted crack network divides cracks into multiple crack sub-clusters with tight internal connections and sparse external connections.

[0033] For each crack sub-cluster, the internal connectivity density and external connectivity sparsity are calculated to form the sub-network cohesion characteristics of each crack sub-cluster.

[0034] Furthermore, based on historical time-series data of topological role characteristics and subnetwork cohesion characteristics, a state transition network for the crack network system is constructed, including:

[0035] The topological role characteristics at each time step are combined with the sub-network cohesive characteristics to form a system feature vector;

[0036] The system feature vector is mapped to the system state in the state set through quantization processing;

[0037] The number of transitions between system states is counted based on the order in which system states appear in historical time-series data.

[0038] A state transition network is constructed based on the number of transitions between system states. The state transition network includes nodes representing system states and directed edges representing transitions between system states. The weight of the directed edges is determined by the number of transitions between system states.

[0039] Furthermore, starting with the system state defined by the current topological role characteristics and subnetwork cohesion characteristics, possible future state sequences are deduced in the state transition network. Based on the state sequences, the overall evolution trend of the crack network is predicted, including:

[0040] The system state corresponding to the current state transition network is determined as the starting point based on the topological role characteristics and subnetwork cohesion characteristics at the current moment;

[0041] In a state transition network, starting from the initial system state, the transition process of the system state along the directed edges is simulated according to the weights of the directed edges in the state transition network, generating multiple future system state sequences.

[0042] Based on the generated multiple system state sequences, the distribution of the frequency of occurrence and evolution path of different system states in the future is statistically analyzed;

[0043] Predict the overall evolution trend of the crack network based on the distribution of occurrence frequency and evolution path.

[0044] On the other hand, the present invention provides a system for quantifying the morphology and predicting the propagation trend of tunnel lining cracks, comprising the following modules:

[0045] The image acquisition module is used to acquire time-series images of the tunnel lining surface and to identify and segment crack contours from the time-series images.

[0046] The structure building module is used to build the crack network topology for each time-series image based on the spatial distance and orientation relationship between each crack contour.

[0047] The network generation module is used to analyze the topological connections and spatial configurations between cracks based on the crack network topology, identify key evolution paths, and assign weights to obtain a weighted crack network.

[0048] The feature recognition module is used to analyze the topological position and connection importance of each crack in the weighted crack network to extract its topological role features, and to identify crack sub-clusters in the network to extract sub-network cohesion features.

[0049] The network construction module is used to construct the state transition network of the crack network system based on historical time-series data of topological role characteristics and subnetwork cohesion characteristics;

[0050] The trend prediction module is used to deduce possible future state sequences in the state transition network, starting from the system state defined by the topological role characteristics and sub-network cohesion characteristics at the current moment, and predict the overall evolution trend of the crack network based on the state sequences.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] 1. By analyzing and modeling the crack community as an interconnected dynamic network system, this approach overcomes the limitations of traditional methods that quantify and predict each crack independently. By establishing the crack network topology and analyzing the topological connections and spatial configurations between cracks, it effectively characterizes the interactions and community associations among cracks. Furthermore, by extracting topological role features that represent the importance of individual crack structures and sub-network cohesion features that represent local community structures, it achieves a multi-scale quantitative description of the microstructure and macrostate of the crack network system. This transformation from isolated geometric parameters to network relationship features lays the data foundation for understanding and predicting the cooperative evolutionary behavior of crack systems.

[0053] 2. By constructing a system state transition network based on historical time-series data and extrapolating from it, trend prediction can be carried out within the framework of the overall system state evolution. This not only predicts the expansion of individual cracks but also infers how the structural morphology of the entire crack network will evolve over time. For example, it can determine whether the network tends to become more tightly connected or whether new isolated sub-clusters will emerge. This provides a more comprehensive and accurate basis for decision-making in assessing the overall development trend of lining structure damage, and ultimately improves the reliability and early warning capability of structural health monitoring and analysis based on image data. Attached Figure Description

[0054] Figure 1 This is a flowchart of a method for quantifying the morphology and predicting the propagation trend of tunnel lining cracks according to the present invention.

[0055] Figure 2 This is a schematic diagram of the structure of a tunnel lining crack morphology quantification and propagation trend prediction system according to the present invention. Detailed Implementation

[0056] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0057] Example 1: Figure 1 This invention presents a method for quantifying the morphology and predicting the propagation trend of cracks in tunnel lining, comprising the following steps:

[0058] S1. Obtain time-series images of the tunnel lining surface, and identify and segment the crack contours from the time-series images;

[0059] S2. For each time series image, establish the crack network topology based on the spatial distance and orientation relationship between each crack contour.

[0060] S3. Based on the analysis of the topological connection and spatial configuration between cracks, the key evolution paths are identified and weighted to obtain a weighted crack network.

[0061] S4. For weighted crack networks, analyze the topological position and connection importance of each crack in the network to extract its topological role features, and identify crack sub-clusters in the network to extract sub-network cohesion features.

[0062] S5. Based on historical time-series data of topological role characteristics and subnetwork cohesion characteristics, construct the state transition network of the crack network system;

[0063] S6. Starting from the system state defined by the topological role characteristics and sub-network cohesion characteristics at the current moment, deduce the possible future state sequence in the state transition network, and predict the overall evolution trend of the crack network based on the state sequence.

[0064] S1. Obtain time-series images of the tunnel lining surface, identify and segment crack contours from the time-series images, and implement the following:

[0065] The identification and segmentation process includes image preprocessing, crack pixel region identification, crack contour segmentation, and temporal correction and completion of the crack contour. First, the acquired temporal images of the tunnel lining surface are preprocessed to enhance the contrast between the crack and background areas, enabling more accurate crack identification in subsequent steps. Preprocessing is achieved by adjusting the pixel intensity distribution of the image. Specifically, after reading the temporal images, the color images are converted to grayscale images for subsequent processing. Then, histogram equalization is applied to the grayscale images. Histogram equalization enhances the overall contrast of the image by redistributing the intensity values ​​of image pixels, especially in areas with concentrated grayscale values, such as the textured background of the lining surface and the darker crack areas, effectively widening the intensity difference. Furthermore, to suppress noise that may be introduced during image acquisition, a Gaussian filter is applied to smooth the image after contrast enhancement. A Gaussian filter performs a convolution operation on the image using a convolution kernel of a specified size, such as a 5-pixel × 5-pixel kernel. The weight coefficients in the convolution kernel follow a two-dimensional Gaussian distribution, with the highest weight at the center and decreasing weights at the edges, thus smoothing noise while preserving as much edge information as possible about the cracks. After this preprocessing, the output is an enhanced temporal image, in which the crack features are more pronounced.

[0066] Next, the pixel regions belonging to the cracks are identified based on the preprocessed image. The core of this process is to classify pixels in the image into crack pixels or background pixels according to their intensity values. This is achieved using a threshold segmentation method. First, a grayscale threshold for segmentation needs to be determined. This grayscale threshold is determined based on the global grayscale histogram of the preprocessed image. Specifically, the average and standard deviation of the grayscale values ​​of all pixels in the preprocessed image are calculated, and the grayscale threshold is initially set to the average value minus N times the standard deviation, where N is an empirical coefficient, typically ranging from 0.5 to 2, and in this embodiment, for example, is set to 1. By setting the grayscale threshold using this statistical method, the image can be adapted to different lighting conditions. Then, each pixel in the preprocessed image is traversed. If the grayscale value of a pixel is lower than the determined grayscale threshold, the pixel is determined to belong to the crack; if the grayscale value is higher than or equal to the grayscale threshold, it is determined to be a background pixel. Thus, a binary image is obtained, where pixels marked as cracks have a value of 1, and background pixels have a value of 0. This binary image is the set of pixel regions initially identified as belonging to the cracks.

[0067] Next, the pixel regions belonging to the cracks are segmented into continuous crack contours. Since the crack pixel regions obtained in the previous step may be disconnected points or small regions, and may contain noise points, further processing is needed to form clear contours. First, morphological operations are performed on the binary image to connect neighboring crack pixels and remove small areas of noise. A closing operation is performed first, which is a process of dilation followed by erosion. Using a structuring element, such as a 3-pixel × 3-pixel rectangular structuring element, the binary image is dilated. The dilation operation expands the crack region outward, thereby connecting potentially disconnected neighboring crack pixels. Immediately afterwards, the same structuring element is used for erosion. The erosion operation shrinks the dilated region inward to restore the approximate original size of the crack while maintaining its connectivity. After the morphological operations, the crack pixel regions become more coherent. Subsequently, connected component analysis is used to segment individual crack objects. The processed binary image is scanned, and pixels with a value of 1 are marked. All sets of pixels with adjacent values ​​of 1 are marked as the same connected component. Here, adjacency is defined as eight-neighbor connectivity, meaning a pixel's eight neighboring pixels (top, bottom, left, right, and four diagonal directions). Each identified connected region represents a potential crack target. For each connected region, its outer boundary pixel sequence is extracted. The boundary extraction algorithm is implemented by tracing the outermost pixels of the connected region. Starting from a pixel at the region's edge, it moves along the region boundary in a clockwise or counterclockwise direction until returning to the starting point, recording the coordinates of all traversed boundary pixels. This ordered sequence of coordinates constitutes a continuous crack contour. Thus, multiple crack contours are segmented from a single image.

[0068] Finally, during the segmentation process, the correlation between images at different times in the temporal images is used to correct and complete the crack contour. Since a single image may be affected by noise, sudden changes in illumination, or local occlusion, the segmented crack contour may be incomplete or contain errors. Temporal images refer to multiple images continuously acquired in chronological order at the same location on the tunnel lining surface. Temporal correlation is used to optimize the segmentation result at the current time by utilizing the continuity and gradual change in the spatial position and morphology of the crack in adjacent time-series images. The specific correction and completion process is as follows: For a crack contour obtained from the current time-series image, a corresponding crack contour is found in the adjacent previous time-series image. The correspondence is determined based on the spatial overlap and centroid distance between the two contours. The minimum bounding rectangle of the crack contour at the current time is calculated, and among all crack contours in the previous time-series image, contours whose minimum bounding rectangle overlaps with the current contour's bounding rectangle by more than a preset overlap area ratio threshold, such as 50%, are found. Simultaneously, the Euclidean distance between the centroids of the two contours is calculated; this distance must be less than a preset distance threshold, such as 5% of the image width. If a corresponding contour that meets the conditions is found, they are considered to be images of the same crack at different times. Correction or completion is performed by comparing the completeness of the current contour with the corresponding contour at the previous time. If the length of the current contour (i.e., the length calculated from the area of ​​the pixel region enclosed by the contour) is significantly shorter than the length of the corresponding contour at the previous time (e.g., more than 20% shorter), and the current contour has an unnatural truncated shape, it is judged that the current contour may be incompletely segmented. In this case, the geometric information of the corresponding contour at the previous time is used as a reference, and region growing is performed near the corresponding spatial position of the current image, using a local grayscale threshold as a standard, to complete the crack. The local grayscale threshold is set based on the pixel grayscale statistics of the region where the contour is located at the previous time; for example, 80% of the average grayscale value of the region can be used as the local grayscale threshold. During the completion process, the shape of the contour at the previous time is also smoothly transitioned to the current time to ensure the temporal continuity of the contour. On the other hand, if an isolated contour with a very small area that has not appeared in the images of previous time steps is segmented at the current time step, such as a contour with an area of ​​less than 10 pixels, it may be identified as noise and removed. Through this cross-time step verification and correction, the final output is a more accurate and complete set of crack contours after temporal correction and completion, laying the foundation for establishing an accurate crack network topology in subsequent steps.

[0069] S2. For each time series image, establish the crack network topology based on the spatial distance and orientation relationship between each crack contour, as follows:

[0070] The process of establishing the crack network topology consists of four main parts: calculating the spatial distance between crack contours, analyzing the orientation relationship between crack contours, determining topological connectivity based on spatial distance and orientation relationship, and finally generating the crack network topology. First, for each crack contour identified in a time-series image, the spatial distance between every two crack contours is calculated. Here, a crack contour refers to the continuous boundary curve obtained in step S1 after correction and completion. The specific measure of spatial distance is the shortest distance between the endpoints of the crack contour. For a crack contour, its endpoints are defined as the coordinates of the two furthest pixels at the ends of the contour curve. The method for calculating the shortest distance between the endpoints of two crack contours is to select one endpoint from all endpoints of the first crack contour and one endpoint from all endpoints of the second crack contour, calculate the Euclidean distance between each pair of endpoints, and then find the minimum value among all calculated pairs of Euclidean distances. This minimum value is recorded as the spatial distance between the two crack contours. The Euclidean distance is calculated based on pixel coordinates; the input is the horizontal and vertical coordinates of the two endpoints, and the output is a distance scalar in pixels. By traversing all crack contour pairs in the current time series image, a spatial distance matrix can be obtained, which records the spatial proximity between any two crack contours.

[0071] Next, we analyze the orientation relationship between crack contours. The orientation relationship is used to quantify the correlation of crack contours in their spatial extension direction, and its core is calculating the angle between the principal directions of the crack contours. For a crack contour, its principal direction refers to the direction of its overall extension trend. First, we need to obtain the principal direction of the crack contour. We use the least squares method to fit a straight line to approximate the overall orientation of the crack contour. Specifically, we take the coordinate set of all pixels on the crack contour as input and calculate an optimal fitted line through least squares linear regression, minimizing the sum of the squares of the vertical distances from all points on the contour to this line. The tilt angle of this fitted line, i.e., the angle between the line and the positive direction of the horizontal axis of the image, is calculated using the arctangent function and transformed to the range of 0 to 180 degrees, which is defined as the principal direction of the crack contour. For two crack contours, after calculating their principal directions, we calculate the absolute value of the difference between these two angle values. Since crack directions have 180-degree rotational symmetry, meaning a crack is still considered to have the same orientation after rotating 180 degrees, we need to process the calculated angle difference. If the absolute value of the angle difference is greater than 90 degrees, subtract this absolute value from 180 degrees. The result is the angle between the principal directions of the two crack profiles, which ranges from 0 to 90 degrees. The smaller this angle, the more parallel the two crack profiles are; the larger the angle, the greater the difference in their directions, and the more perpendicular or intersecting at a large angle.

[0072] Then, the existence of topological connections between crack contours is determined based on the spatial distance and orientation relationship between them. This is a decision-making process based on dual thresholds, aiming to identify crack contour pairs that are spatially close and have a certain correlation in orientation, considering them as connected in the topological network. First, a spatial distance threshold and an angle difference threshold need to be set. The setting of the spatial distance threshold depends on the image resolution and the estimated actual physical scale of the cracks. For example, a certain percentile of the distance values ​​calculated based on the spatial distance matrix between all crack contours can be used as the threshold, such as the 20th percentile. This means that approximately 20% of the closest crack contour pairs are initially considered as potential connection candidates. The setting of the angle difference threshold is based on the understanding of the geometric characteristics that crack networks typically exhibit. For example, in a lining crack network, interfering cracks are more likely to exist in a way that is approximately parallel or intersects at a small angle. Therefore, the angle difference threshold can be set as an empirical value, such as 30 degrees. The specific logic for determining the connection is that for any pair of crack contours, it is checked whether their spatial distance is less than or equal to the set spatial distance threshold, and whether the angle between their principal directions is less than or equal to the set angle difference threshold. A topological connection between two crack contours is determined only when both conditions are met. If only one condition is met or neither condition is met, no direct topological connection is determined. This determination process traverses all crack contour pairs in the image, outputting a series of connection pairs, each recording which two crack contours are determined to be connected.

[0073] Finally, the crack network topology is generated based on the topological connections between all crack contours. Each crack contour is abstracted as a node, and the topological connections identified in the previous step are abstracted as edges connecting two nodes. Thus, a graph theory data structure is used to represent the crack network topology. The specific generation process is as follows: First, an empty undirected graph is created. Then, each crack contour in the current time series image is added to this graph as a uniquely identified node. Next, all connection pairs obtained in step three are traversed, and for each connection pair, an undirected edge is added between the corresponding two nodes in the graph. This constructs a graph model with crack contours as nodes and topological connections as edges; this graph model is the desired crack network topology. This structure clearly depicts the connections between individual cracks, integrating the originally isolated crack contours into a unified network, providing a foundation for subsequent analysis of the collective behavior and evolution patterns of the crack network.

[0074] S3. Based on the analysis of the fracture network topology, the topological connections and spatial configurations between fractures are analyzed, key evolution paths are identified and weighted to obtain a weighted fracture network. The specific implementation is as follows:

[0075] First, based on the crack network topology generated in step S2, the topological connectivity and spatial configuration relationships between cracks are analyzed. The crack network topology is a graph, where nodes represent crack profiles and edges represent topological connections determined to exist between crack profiles. Analyzing the topological connectivity relationships involves quantifying the connectivity characteristics of the graph. Specifically, the degree of each node in the graph is calculated, i.e., the number of edges connected to that node, which reflects the number of direct connections of a single crack profile in the topological network. Simultaneously, the clustering coefficient of the entire network is calculated, which measures the tendency of nodes in the network to cluster together. The clustering coefficient is calculated as follows: for each node in the graph, all its neighboring nodes are first identified; the ratio of the actual number of edges between these neighboring nodes to the maximum possible number of edges is the local clustering coefficient of that node; then, the average of the local clustering coefficients of all nodes is taken to obtain the clustering coefficient of the entire network. Furthermore, the average path length of the network is calculated, i.e., the average number of edges traversed by the shortest path between all pairs of nodes in the network, which reflects the connectivity efficiency of the network. These calculations are all based on the adjacency matrix of the graph. The adjacency matrix is ​​a square matrix whose rows and columns correspond to nodes in the network. If two nodes are connected by an edge, the corresponding matrix element is 1; otherwise, it is 0. By traversing the adjacency matrix, the connection number (degree) of each node can be counted. By analyzing the connections between a node's neighboring nodes, the local clustering coefficient can be calculated. The shortest path length between any two nodes can be calculated using a breadth-first search algorithm. In analyzing spatial configuration relationships, the core is to evaluate the consistency of the crack profiles in spatial geometric arrangement, especially the orientation consistency. Spatial configuration relationships include the orientation consistency of key evolution paths, but in this analysis stage, we first need to obtain the spatial geometric properties related to the edges in the network. For each edge, i.e., each pair of crack profiles determined to be connected, we obtain two feature quantities calculated in step S2: the spatial distance between the two crack profiles and the angle between the principal directions of the two crack profiles. The angle between the principal directions has been obtained in step S2 by calculating the angle difference between the principal directions of the two crack profiles and normalizing it to the range of 0 to 90 degrees. Based on this data, the average spatial distance and average principal direction angle of all edges in the entire network can be calculated to characterize the overall spatial proximity and orientation alignment of the network. Furthermore, the relationship between spatial distance and topological connectivity can be analyzed, for example, checking whether the spatial distances corresponding to connecting edges are generally small. The distribution of principal direction angles can also be analyzed, for example, by statistically analyzing the proportion of edges with principal direction angles less than a certain threshold, such as 30 degrees, to assess the overall consistency of crack orientations within the network. These analytical results lay the foundation for subsequent identification of paths that are important in both topological and spatial terms.

[0076] Next, critical evolutionary paths in the crack network are identified based on topological connectivity and spatial configuration. A critical evolutionary path refers to a sequence of nodes in the crack network topology that is connected by a series of continuous edges, exhibiting strong topological connectivity and high spatial consistency. The identification process requires comprehensive consideration of both the topological and spatial geometric properties of the path. First, paths meeting the criteria need to be searched within the crack network topology. The search employs a depth-first search algorithm, starting from each node in the network and expanding along its connected edges to adjacent nodes, gradually constructing a path. During the expansion process, constraints need to be applied to filter out path segments with spatial consistency. Specifically, for a newly added edge on the path, the angle between the principal directions of the two crack profiles connected by that edge must be less than a preset spatial consistency angle threshold. This spatial consistency angle threshold controls the variation in crack orientation along the path, and its setting is based on the understanding of the physical mechanism of crack propagation; that is, crack segments on the same evolutionary path often have similar propagation directions. This threshold can be set as an empirical value, such as 20 degrees. To prevent paths from extending indefinitely or containing too many irrelevant gaps, a maximum path length constraint must be set, meaning the number of nodes in a path cannot exceed a maximum value, such as 10 nodes. Furthermore, paths should avoid repeatedly visiting the same node. This constrained depth-first search can initially filter out a large number of candidate paths that meet the spatial consistency condition from the network. Then, these candidate paths need to be further filtered to select those with high topological importance. The topological importance of a path can be measured by the topological importance of the nodes it encompasses. A node's topological importance can be characterized by its degree centrality; higher degree centrality indicates more connections and greater importance in the network topology. Therefore, for each candidate path, the average degree of all nodes on the path is calculated as its topological importance score. Simultaneously, a spatial consistency score is calculated, defined as the reciprocal of the average angle between the principal directions of all edges on the path, with paths having smaller average angles receiving higher scores. The topological importance score and spatial consistency score of each candidate path are then weighted and fused to obtain a comprehensive score. During weighted fusion, a weight coefficient is assigned to both the topological importance score and the spatial consistency score; for example, both weight coefficients are 0.5, indicating that they are equally important. Then, all candidate paths are sorted in descending order based on the comprehensive score, and the top-ranked paths, such as the top 15 paths, are selected as the final identified critical evolution paths. These critical evolution paths represent the main channels in the fracture network most likely to undergo co-evolution or stress transfer.

[0077] Then, weights are assigned to critical evolutionary paths, calculated based on their topological connectivity and spatial configuration. The purpose of weighting is to quantify the relative importance of each critical evolutionary path throughout the entire fracture network evolution process. Weight calculation requires comprehensive utilization of both the topological and spatial attributes of the paths. Specifically, for each identified critical evolutionary path, two normalized sub-scores are calculated. The first is a normalized topological importance score, calculated by taking the path's topological importance score (the average of the path's node degrees) and dividing it by the maximum value among all critical evolutionary paths' topological importance scores, thus normalizing the score to between 0 and 1. The second is a normalized spatial consistency score, calculated by taking the path's spatial consistency score (the reciprocal of the average angle between the principal directions of the path's edges) and dividing it by the maximum value among all critical evolutionary paths' spatial consistency scores, also normalizing this score to between 0 and 1. Finally, these two normalized scores are linearly combined to obtain the path's original weight. The formula for linear combination is: the original weight of a path equals the topological importance weight coefficient multiplied by the normalized topological importance score, plus the spatial consistency weight coefficient multiplied by the normalized spatial consistency score. Here, the topological importance weight coefficient and the spatial consistency weight coefficient are two adjustable parameters, and their sum is usually 1. For example, they can both be set to 0.5, indicating equal emphasis on both attributes. Through this calculation, each critical evolution path obtains an original weight value. Finally, the original weight values ​​of all critical evolution paths are normalized so that their sum is 1. The normalization method is to divide the original weight value of each path by the sum of the original weight values ​​of all paths. The value obtained after normalization is the final weight value of that critical evolution path. This weight value is a number between 0 and 1, and its magnitude directly reflects the relative importance that the path should be considered when predicting the overall evolution trend of the fracture network. The larger the weight value, the more critical the path is in the historical evolution pattern, and the greater its potential impact on future trends.

[0078] Finally, weights are assigned to the corresponding critical evolution paths in the crack network topology to obtain a weighted crack network. This process maps abstract path weights back to specific network topologies, transforming the original, unweighted crack network topology into a network with weighted edges. Specifically, a graph identical to the original crack network topology is first created, but each edge is initialized to a weight of 0. Then, each critical evolution path is traversed. A critical evolution path consists of a series of consecutive edges. The final weight of this path is accumulated to the current weight of each edge it contains. If an edge is shared by multiple different critical evolution paths, its weight will be the sum of the weights of all paths containing it. After traversing all critical evolution paths and accumulating the weights, a crack network topology with weighted edges is obtained—the weighted crack network. In this weighted crack network, the edge weights have a clear physical meaning: they represent the frequency and importance of the connections between the crack profiles represented by that edge in the historical critical evolution paths. Edges with higher weight values ​​indicate that the crack profiles they connect to appear more frequently on important, spatially consistent evolutionary pathways, and therefore may play a more active role in future network evolution. This weighted crack network will serve as the direct input to step S4 to extract more refined topological role features and subnetwork cohesion features, thereby completing the transformation from network structure to quantified features.

[0079] S4. For weighted crack networks, analyze the topological location and connectivity importance of each crack in the network to extract its topological role features, and identify crack sub-clusters in the network to extract sub-network agglomeration features. The specific implementation is as follows:

[0080] The input to this step is the weighted crack network output from step S3, which is an undirected weighted graph where nodes represent crack profiles, edges represent topological connections between crack profiles, and each edge has a weight value reflecting the importance of this connection in historical key evolutionary paths. This step aims to extract two types of core features from this weighted network: firstly, topological role features describing the structural position of each individual crack in the network; and secondly, subnetwork cohesion features describing the local community structure of the network. The entire process first calculates the connection strength index and bridging role index for each crack. The connection strength index aims to quantify the sum of the strengths of direct connections of a crack in the weighted network, and its calculation is based on the weighted crack network. Specifically, for each node in the network, i.e., each crack profile, its connection strength index is obtained by calculating the weighted degree centrality of that node. The method for calculating the weighted degree centrality is to first obtain the weight values ​​of all edges connected to the node, and then sum these weight values. This summation result is the connection strength index of that node. The physical meaning is that if a crack is connected to multiple other cracks, and the weights of these connections are all high, it indicates that the crack is located in a densely connected and important region of the network, and its direct influence is strong. For example, if a crack is connected to three other cracks, and the weights of the three edges are 0.2, 0.3, and 0.15 respectively, then the connection strength index of the crack is 0.2 + 0.3 + 0.15 = 0.65. Next, the bridge function index is calculated, which aims to quantify the importance of a crack as a hub or bridge connecting different parts of the network. The bridge function index is obtained by calculating the betweenness centrality of the node in the weighted crack network. The core of betweenness centrality calculation is to count the frequency of the node appearing on all shortest paths in the network. In weighted networks, the definition of the shortest path is based on the edge weight, but usually the weight represents the connection strength or importance, so it needs to be converted into the concept of distance. A common conversion method is to take the reciprocal of the edge weight, or to subtract the weight value from a large number, so that the edge with the larger weight has a smaller distance cost. Specifically, in this embodiment, the weight value of each edge is converted into a distance cost using the formula: distance cost = 1 / weight value of the edge. If the weight value is 0, a maximum value is set as its distance cost. After the conversion, the network becomes a graph with edge distance costs. Then, the shortest path between all pairs of nodes in the network is calculated. For each pair of nodes, the shortest path based on distance cost is found using, for example, Dijkstra's algorithm. Next, all shortest paths are traversed, and for each shortest path, it is checked whether the current node is located on that path. The total number of times the current node appears on all shortest paths is counted. Finally, this count is normalized to obtain the betweenness centrality value.Normalization typically involves dividing the number of times a node can theoretically appear on all shortest paths by the maximum possible number of times. This maximum number is related to the network size; for example, for an undirected graph with n nodes, this maximum number is (n-1)×(n-2) / 2. After normalization, the bridging index is a value between 0 and 1. A higher index means that the crack plays a more crucial bridging role in the network's information or stress transmission. For example, a crack located between two dense subclusters is likely to be on the shortest paths of many node pairs, thus having a high bridging index. After calculating both indices for all nodes, proceed to the next step.

[0081] The connection strength index and bridging function index are combined to form the topological role feature of each crack. The purpose of this combination is to characterize the role of each crack in the topological structure using a comprehensive feature vector. Specifically, for each crack, its connection strength index and bridging function index are treated as two components of a two-dimensional vector. Before combination, these two indices are usually standardized to eliminate the influence of differences in dimensions and numerical ranges. Standardization can be achieved using the Z-score standardization method: for all cracks in the network, the mean and standard deviation of the connection strength index are calculated; then, for each original connection strength index value, the mean is subtracted and the result is divided by the standard deviation to obtain the standardized connection strength index. The bridging function index is processed in the same way. After standardization, the value of each index will follow a distribution with a mean of 0 and a standard deviation of 1. The two standardized indices are then combined sequentially to form a two-dimensional vector, which represents the topological role feature of the crack. This two-dimensional feature vector comprehensively reflects the structural properties of the crack in both local connection strength and global bridging function dimensions. For example, a crack with high connectivity but low bridging function may be a central node within a tightly knit cluster; while a crack with medium connectivity but high bridging function may be a key hub connecting different clusters. The set of topological role characteristics of all cracks constitutes a quantitative description of the individual network structure.

[0082] The weighted fracture network divides fractures into multiple fracture sub-clusters with tightly connected internal connections and sparse external connections. This process, known as community detection or graph clustering, aims to identify naturally formed, densely connected groups of nodes within the network. This embodiment employs a modularity optimization-based method to divide fracture sub-clusters. Modularity is a metric for measuring the quality of network community partitioning; a higher value indicates tighter internal connections and sparser connections between communities. In practice, the network is first initialized, treating each node as an independent sub-cluster. Then, a greedy algorithm iteratively moves nodes to improve the overall modularity. In each iteration, each node is moved from its current sub-cluster to the sub-cluster of each of its neighbors, and the modularity gain for each move is calculated. The modularity gain calculation relies on the current network's modularity definition formula, which considers the difference between the actual weights of edges within a sub-cluster and their expected weights in a random network. For each node, the neighboring sub-cluster that yields the maximum positive modularity gain is selected for movement. If, for a given node, no possible movement yields a positive modularity gain, the node remains in the atomic cluster. This process iterates until it becomes impossible to improve the overall modularity by moving any nodes. Ultimately, the network is divided into several crack sub-clusters. Nodes within each crack sub-cluster are connected by edges, and these edges have a relatively high average weight. Edges between nodes belonging to different crack sub-clusters have a relatively low average weight. This partitioning decomposes the entire complex crack network into several structurally independent sub-units. For example, the crack network in a tunnel lining might be divided into crack sub-clusters in the arch region, crack sub-clusters in the sidewall region, and so on.

[0083] For each crack sub-cluster, the internal connectivity density and external connectivity sparsity are calculated to form the sub-network cohesion characteristics of each crack sub-cluster. Internal connectivity density quantifies the strength and density of connections between nodes within a sub-cluster. The calculation method is as follows: for a crack sub-cluster, the corresponding sub-network is first extracted, which is the graph consisting of all nodes within the sub-cluster and all edges between these nodes. Internal connectivity density can be comprehensively characterized by calculating the average edge weight and internal edge density of the sub-network. The average edge weight is the arithmetic mean of the weights of all edges in the sub-network. The internal edge density is the ratio of the actual number of edges in the sub-network to the theoretically maximum number of edges. For a sub-network containing k nodes, the theoretically maximum number of edges is k×(k-1) / 2. Dividing the actual number of edges by this maximum possible number yields the internal edge density. Finally, internal connectivity density can be defined as the product of the average edge weight and the internal edge density, or a weighted sum. For example, internal connectivity density can be set as 0.6×average edge weight + 0.4×internal edge density. The higher the value obtained, the stronger and denser the internal connections of the sub-cluster. External connection sparsity is used to quantify the density of connections between a sub-cluster and other parts of the network. It is calculated by first identifying all edges connecting nodes within the sub-cluster to nodes outside the sub-cluster; these edges are called cut edges. External connection sparsity can be characterized by calculating the average weight of these cut edges; the lower the average weight, the weaker and sparser the connection between the sub-cluster and the outside world. Alternatively, it can be calculated by combining the number of cut edges with the number of nodes within the sub-cluster. For example, external connection sparsity can be defined as the ratio of the external connection sparsity coefficient to the average weight of the cut edges, where the external connection sparsity coefficient is a constant greater than 0, such as 1. Thus, the smaller the average weight of the cut edges, the larger the external connection sparsity value, indicating that the sub-cluster is more distant from the outside world. Finally, the calculated internal connection density and external connection sparsity are combined into a two-dimensional vector, which serves as the sub-network cohesion feature of the cracked sub-cluster. For example, a subcluster with an internal connectivity density of 0.85 and an external connectivity sparseness of 2.5 has a subnetwork cohesion feature vector of (0.85, 2.5). This feature vector characterizes the cohesion of the internal structure and the independence of its external connections within the subcluster as a module in the network. The set of subnetwork cohesion features for all crack subclusters provides a quantitative basis for the structural characteristics of its components in subsequent analysis of the overall state of the network system. The output of the entire step S4 is the topological role features of all cracks and the subnetwork cohesion features of all crack subclusters, which together constitute a fine-grained state description of the crack network at a single moment.

[0084] S5. Based on historical time-series data of topological role characteristics and sub-network cohesion characteristics, construct the state transition network of the crack network system. The specific implementation is as follows:

[0085] The input to this step is the topological role features and subnetwork cohesion features at multiple time points, arranged chronologically, output from step S4. These data together constitute the historical time-series observation sequence of the crack network system. The purpose of constructing the state transition network is to abstract and characterize the dynamic pattern of the system state evolution over time. This process first combines the topological role features and subnetwork cohesion features at each time point into a system feature vector. The topological role feature is a set of two-dimensional vectors, where each vector corresponds to the topological role of a crack. The subnetwork cohesion feature is also a set of two-dimensional vectors, where each vector corresponds to the structural characteristics of a crack subcluster. To form features representing the global state of the entire network system at a certain time point, these features need to be aggregated. Specifically, for each time point, the statistics of the topological role feature vectors of all cracks at that time point are first calculated. The mean and standard deviation of the connectivity strength index of all cracks are calculated, as well as the mean and standard deviation of the bridging function index of all cracks. This yields four statistics. Next, the statistics of the subnetwork cohesion feature vectors of all crack subclusters at that time point are calculated. The mean and standard deviation of the internal connectivity of all crack subclusters are calculated, as are the mean and standard deviation of the external connectivity of all crack subclusters. This yields four more statistics. Finally, these eight statistics are arranged in a predetermined order to form an eight-dimensional system feature vector. This eight-dimensional vector comprehensively characterizes the macroscopic state of the crack network system at a given moment from multiple dimensions, including the overall connectivity strength distribution, bridging effect distribution, subcluster cohesion distribution, and subcluster independence distribution. For example, the system feature vector at a given moment might be represented as (mean connectivity strength 0.75, connectivity strength standard deviation 0.12, mean bridging effect 0.33, bridging effect standard deviation 0.08, mean cohesion 0.68, cohesion standard deviation 0.15, mean independence 2.1, independence standard deviation 0.9).

[0086] Next, the system feature vectors are mapped to the system states in the state set through quantization. Since the system feature vectors are continuous values, while the state transition network requires discrete state nodes, quantization is necessary. This embodiment uses a cluster-based quantization method. First, the system feature vectors of all times in the historical time series data are collected to form a sample set. Then, cluster analysis is performed on this sample set to group similar continuous feature vectors into the same discrete state. Cluster analysis requires pre-specifying the desired number of clusters, i.e., the number of states. The number of states can be determined based on the size of the sample set and the analysis requirements; for example, it can be determined using the elbow rule. The elbow rule involves trying different numbers of clusters, calculating the sum of squared distances from all sample points to their respective cluster centers for each number, plotting the sum of squared distances as a function of the number of clusters, and selecting the number corresponding to the inflection point of the curve as the final number of states. For example, if analysis shows a clear inflection point when the number of clusters is 5, then the number of states is set to 5. After determining the number of states, an iterative optimization clustering algorithm, such as the K-means algorithm, is used to partition the sample set. The algorithm first randomly initializes five cluster centers and then iterates. In each iteration, each system feature vector sample is assigned to its nearest cluster center, typically using Euclidean distance. Then, based on all samples assigned to each cluster, the cluster center is recalculated, i.e., the average of all samples within that cluster across all dimensions is used as the new center. This process of sample assignment and center update is repeated until the cluster center positions no longer change significantly or a predetermined number of iterations is reached. After clustering, each cluster is defined as a system state. Each system state is characterized by its cluster center vector and the time points of the included samples. Finally, a mapping relationship is established: for each time point in the historical time series data, a corresponding system state label is assigned based on the cluster to which its system feature vector is assigned. Thus, continuous historical time series feature data is transformed into a discrete sequence of system states.

[0087] Then, the number of transitions between system states is counted based on the order of occurrence of system states in the historical time series data. The system state sequence is arranged in chronological order, such as state A, state B, state A, state C, etc. A state transition refers to the change of the system state from one moment to the next adjacent moment. The method for counting the number of transitions is as follows: First, a counting matrix is ​​initialized, where the row and column indices correspond to all possible system states. If there are 5 system states, a 5x5 matrix is ​​created, with all elements initialized to 0. Next, the system state sequence is traversed chronologically. For each pair of adjacent moments in the sequence, the state of the previous moment is extracted as the starting state of the transition, and the state of the next moment is extracted as the target state. In the counting matrix, the row corresponding to the starting state and the column corresponding to the target state are found, and the count value at that position is incremented by 1. After traversing the entire state sequence, the element values ​​in the counting matrix represent the number of times a transition from one specific state to another occurred in historical observations. For example, a value of 5 in the 2nd row and 3rd column of the counting matrix indicates that the event of transitioning from state 2 to state 3 occurred 5 times in the historical data. This statistical method objectively records the empirical patterns of system state evolution.

[0088] Finally, a state transition network is constructed based on the number of transitions between system states. The state transition network is a directed weighted graph where nodes represent system states, directed edges represent transition relationships between states, and the weight of an edge represents the frequency of the transition. The specific construction process is as follows: First, each system state is created as a network node. Nodes can be identified using their corresponding state label or the index of their cluster center vector. Then, directed edges are created based on the counting matrix obtained in the previous step. Each non-zero element in the counting matrix is ​​traversed. For the non-zero element in the i-th row and j-th column of the counting matrix, its value represents the number of times state i transitions to state j. In the state transition network, a directed edge is created in the direction from node i to node j. The weight of this directed edge is set to this number of transitions. If the number of transitions is 0, it means that no transition in that direction has been observed in history, so no corresponding edge is created. For ease of subsequent analysis, the edge weights are usually normalized, converting them into transition probabilities. The normalization method involves calculating the sum of the weights of all directed edges originating from each initial state node, and then dividing the weight of each outgoing edge by this sum. This yields the estimated probability of transitioning from that state to various target states. For example, if state node i has three outgoing edges with weights of 3, 1, and 1, totaling 5, the normalized weights would be 0.6, 0.2, and 0.2. The normalized weight values ​​represent the probability distribution of transitioning to various possible states at the next moment, given that the system is currently in state i. The resulting state transition network contains nodes representing various possible macroscopic patterns of the system, and its edges quantify the probability and trend of transitions between these patterns. This network abstracts and encapsulates the dynamic knowledge of the historical evolution of the crack network system, providing a probability-based reasoning model for predicting future evolution trends. The entire construction process, through the aggregation, discretization, statistical analysis, and graph modeling of high-dimensional temporal features, achieves a leap from microscopic crack characteristics to macroscopic system dynamics, forming a structured description of the time-varying behavior of the tunnel lining crack system.

[0089] S6. Starting from the system state defined by the topological role characteristics and sub-network cohesion characteristics at the current moment, deduce the possible future state sequence in the state transition network, and predict the overall evolution trend of the crack network based on the state sequence. The specific implementation is as follows:

[0090] This step is the core of the prediction process. Its inputs include the current topological role characteristics and subnetwork cohesion characteristics, as well as the state transition network constructed in step S5. Its goal is to simulate and predict the system's possible future development based on historical evolution patterns. First, the system state corresponding to the current moment in the state transition network is determined as the starting point based on the current topological role characteristics and subnetwork cohesion characteristics. Specifically, the current topological role characteristics and subnetwork cohesion characteristics are combined to form the current system feature vector. The combination method is completely consistent with historical data processing, i.e., calculating the average and standard deviation of the connection strength index of all cracks, the average and standard deviation of the bridge function index, the average and standard deviation of the internal connection tightness of all crack sub-clusters, and the average and standard deviation of the external connection sparsity. These eight statistics are arranged in the same order to form an eight-dimensional system feature vector. After obtaining the current system feature vector, it needs to be mapped to a specific state in the system state set defined in the state transition network. The mapping is based on the similarity between this vector and the cluster centers of each system state obtained through clustering in step S5. Calculate the Euclidean distance between the current system feature vector and the cluster center vector of each system state. The Euclidean distance is calculated by summing the squares of the differences between the corresponding dimensions of the two vectors, and then taking the square root of the sum. Select the system state corresponding to the cluster center with the smallest Euclidean distance to the current system feature vector; this is determined as the system state at the current moment. If multiple equal and smallest distances exist, one can be chosen at random, or determined according to other rules, such as selecting the state that appears more frequently in history. The output of this step is a specific state label, such as "State 3," which will serve as the starting point for subsequent simulations.

[0091] Next, in the state transition network, starting from the initial system state, the transition process along the directed edges is simulated based on the weights of the directed edges in the state transition network, generating multiple future system state sequences. The state transition network is a directed weighted graph, where nodes are system states, and the weights of the directed edges represent the strength or empirical probability of transitioning from one state to another. The simulation process uses a random walk approach. First, the predicted future time step needs to be set, for example, predicting the system state evolution at 5 future moments. Second, the number of simulated paths needs to be set, i.e., how many possible state evolution sequences to generate to cover the future possibility space, for example, generating 1000 independent state sequences. The generation of each state sequence is an iterative random process. The specific steps are: using the determined initial system state as the first state of the sequence. Then, the iterative process begins, for the current system state node, examining all its outgoing edges in the state transition network. Each outgoing edge points to a possible next state, and each outgoing edge carries a weight. These weights are typically normalized to transition probabilities in step S5, which are the probability values ​​of transitioning from the current state to each possible next state, with the sum of the probabilities of all outgoing edges being 1. Based on these probability values, a roulette wheel selection method is used to randomly select the next state. The roulette wheel selection method works as follows: first, all possible next states and their corresponding transition probabilities are listed; then, a uniformly distributed random number between 0 and 1 is generated; next, the probabilities of each state are accumulated in probability order until the sum is greater than or equal to the generated random number for the first time. The state corresponding to this sum is then selected as the next state. The selected state is added to the current sequence, and this state is used as the new current state. This selection process is repeated until the length of the generated sequence reaches a preset future time step, for example, a sequence length of 5 states. This completes the simulation of a future state sequence. This process is repeated to independently generate a specified number of sequences, for example, 1000. Finally, a set of 1000 future system state sequences, each of length 5, is obtained. These sequences reflect the various state evolution paths the system may experience in the future, starting from the current state, based on historical transition patterns.

[0092] Then, based on the generated multiple system state sequences, the frequency of occurrence and evolution path distribution of different system states in the predicted future are statistically analyzed. Statistical analysis of a large number of simulated state sequences aims to extract statistical patterns of future evolution. First, the frequency of occurrence of different system states at each predicted time in the future is statistically analyzed. For the first time in the future, all simulated sequences are traversed, and the system state appearing at the first position in each sequence (i.e., the next time immediately following the current time) is counted. The number of occurrences of each state is calculated, and then divided by the total number of sequences to obtain the frequency of occurrence of each state at the first time in the future. For example, if state A occurs 300 times and there are 1000 sequences in total, then the frequency of occurrence of state A at the first time in the future is 0.3. The same statistical analysis is performed on the second, third, fourth, and fifth time in the future to obtain the frequency distribution of each state at different future times. This distribution shows the probabilistic trend of system state evolution over time. Second, the distribution of evolution paths is statistically analyzed. An evolution path refers to a complete state sequence, such as "state 3 -> state 1 -> state 4 -> state 2 -> state 5". In all simulated state sequences, the frequency of each unique path is counted. Since the path space can be large, typically only typical or frequent paths that appear frequently are considered. A minimum occurrence threshold can be set to filter meaningful paths, for example, only paths appearing more than 10 times are retained. This threshold is set based on the total number of simulated paths, usually a small proportion, such as 1%. The resulting paths and their occurrence frequencies constitute a discrete distribution description of possible future evolutionary patterns. For example, the path "state 3->state 1->state 1->state 2->state 2" might be found to have the highest frequency, at 8%, indicating that this path is one of the most likely future evolutionary patterns.

[0093] Finally, the overall evolution trend of the fracture network is predicted based on the distribution of occurrence frequency and evolution path. The aforementioned statistical analysis results are transformed into qualitative or semi-quantitative predictions of the macroscopic evolution direction of the fracture network. The prediction of the overall evolution trend can be carried out on two levels. The first level is state trend prediction, which identifies states with significantly increased or decreased frequencies based on the occurrence frequency of each state at different future times. For example, if the analysis finds that the occurrence frequency of "state 5" continuously increases from 0.1 at time 1 to 0.6 at time 5, while the frequency of "state 1" continuously decreases from 0.5 to 0.1, then the overall evolution trend of the system can be predicted to be from the network pattern represented by "state 1" to the network pattern represented by "state 5". The network pattern represented by each system state is defined by eight-dimensional statistics of its cluster centers. These statistics correspond to the overall connection strength, bridging effect, cohesion, and independence of the fracture network, respectively. Therefore, the trend of the state can be directly interpreted as the trend of the network structure characteristics. For example, if "State 5" is characterized by high average connectivity and low average cohesion, while "State 1" is characterized by medium connectivity and high cohesion, then the aforementioned trend implies that the predicted crack network will evolve towards a macroscopic direction of tighter overall connectivity but looser sub-cluster structure. The second level is path stability prediction, based on the distribution of evolution paths. If statistics show that future evolution paths are highly concentrated on a few paths, for example, the cumulative frequency of the first three paths exceeds 70%, then the predicted evolution path of the system is relatively certain, and the trend is clear. Conversely, if the path distribution is very dispersed, with no dominant path, then the predicted future evolution has multiple possibilities, and the trend is unclear. Combining the analysis of state trends and path stability, a comprehensive predictive conclusion on the overall evolution trend of the crack network can be formed, such as "In the next five monitoring periods, the crack network has a high probability of evolving from its current relatively loose sub-cluster structure to a structure with strengthened global connectivity but weakened local cohesion, and the evolution path is relatively concentrated, with a clear trend." This prediction result provides a key basis for the structural safety assessment and maintenance decisions of tunnel linings based on a data-driven model.

[0094] Example 2: Figure 2 A schematic diagram of the structure of a tunnel lining crack morphology quantification and propagation trend prediction system according to the present invention is provided. The system includes the following modules:

[0095] The image acquisition module is used to acquire time-series images of the tunnel lining surface and to identify and segment crack contours from the time-series images.

[0096] The structure building module is used to build the crack network topology for each time-series image based on the spatial distance and orientation relationship between each crack contour.

[0097] The network generation module is used to analyze the topological connections and spatial configurations between cracks based on the crack network topology, identify key evolution paths, and assign weights to obtain a weighted crack network.

[0098] The feature recognition module is used to analyze the topological position and connection importance of each crack in the weighted crack network to extract its topological role features, and to identify crack sub-clusters in the network to extract sub-network cohesion features.

[0099] The network construction module is used to construct the state transition network of the crack network system based on historical time-series data of topological role characteristics and subnetwork cohesion characteristics;

[0100] The trend prediction module is used to deduce possible future state sequences in the state transition network, starting from the system state defined by the topological role characteristics and sub-network cohesion characteristics at the current moment, and predict the overall evolution trend of the crack network based on the state sequences.

[0101] All calculations involved in the embodiments are dimensionless numerical calculations, and the preset parameters and thresholds in the calculations are set by those skilled in the art according to the actual situation.

[0102] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, in the form of a computer program product.

[0103] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and inventive constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0104] In addition, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0105] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or modules may be electrical, mechanical, or other forms.

[0106] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0107] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for quantifying the morphology and predicting the propagation trend of cracks in tunnel lining, characterized in that, Includes the following steps: S1. Obtain time-series images of the tunnel lining surface, and identify and segment the crack contours from the time-series images; S2. For each time series image, establish the crack network topology based on the spatial distance and orientation relationship between each crack contour. S3. Based on the analysis of the topological connections and spatial configurations between cracks, the key evolution paths are identified and weighted to obtain a weighted crack network. S4. For weighted crack networks, analyze the topological position and connection importance of each crack in the network to extract its topological role features, and identify crack sub-clusters in the network to extract sub-network cohesion features. S5. Based on historical time-series data of topological role characteristics and subnetwork cohesion characteristics, construct the state transition network of the crack network system; S6. Starting from the system state defined by the topological role characteristics and sub-network cohesion characteristics at the current moment, deduce the possible future state sequence in the state transition network, and predict the overall evolution trend of the crack network based on the state sequence.

2. The method for quantifying the morphology and predicting the propagation trend of tunnel lining cracks according to claim 1, characterized in that, Acquire time-series images of the tunnel lining surface, identify and segment crack contours from the time-series images, including: Preprocessing of time-series images enhances the contrast between crack and background areas; Pixel regions belonging to the cracks were identified based on the preprocessed image; The pixel region belonging to the crack is segmented into a continuous crack outline.

3. The method for quantifying the morphology and predicting the propagation trend of tunnel lining cracks according to claim 2, characterized in that, in, During the segmentation process, the correlation between images at different times in the time series image is used to correct and complete the crack contour.

4. The method for quantifying the morphology and predicting the propagation trend of tunnel lining cracks according to claim 1, characterized in that, For each time-series image, a crack network topology is established based on the spatial distance and orientation relationship between each crack contour, including: For each time series image, calculate the spatial distance between crack contours. Analyze the orientation relationship between crack profiles; Determine whether there is a topological connection between crack profiles based on the spatial distance and orientation relationship between crack profiles; Generate the crack network topology based on the topological connections between all crack profiles.

5. The method for quantifying the morphology and predicting the propagation trend of tunnel lining cracks according to claim 4, characterized in that, in, The orientation relationship between crack profiles includes the angle between the main directions of the crack profiles, and the spatial distance includes the shortest distance between the endpoints of the crack profiles.

6. The method for quantifying the morphology and predicting the propagation trend of tunnel lining cracks according to claim 1, characterized in that, Based on the analysis of fracture network topology, the topological connections and spatial configurations between fractures are analyzed, key evolution paths are identified and weighted to obtain a weighted fracture network, including: Based on the crack network topology, the topological connectivity and spatial configuration relationships between cracks are analyzed. Key evolutionary paths in the crack network were identified based on topological connectivity and spatial configuration relationships; Weights are assigned to key evolutionary paths, and the weight values ​​are calculated based on the topological connectivity and spatial configuration relationships of the key evolutionary paths, including the orientation consistency of the key evolutionary paths. By assigning weight values ​​to the corresponding critical evolution paths in the fracture network topology, a weighted fracture network is obtained.

7. The method for quantifying the morphology and predicting the propagation trend of tunnel lining cracks according to claim 1, characterized in that, For weighted crack networks, we analyze the topological location and connectivity importance of each crack in the network to extract its topological role features. And identify crack sub-clusters in the network to extract sub-network cohesive features, including: The connection strength index and bridging function index of each crack are calculated based on the weighted crack network. The connection strength index is determined by the weighted number of connections of the crack in the weighted crack network, and the bridging function index is determined by the frequency of the crack appearing in the shortest path of the weighted crack network. The connection strength index and the bridge function index are combined to form the topological role characteristics of each crack; The weighted crack network divides cracks into multiple crack sub-clusters with tight internal connections and sparse external connections. For each crack sub-cluster, the internal connectivity density and external connectivity sparsity are calculated to form the sub-network cohesion characteristics of each crack sub-cluster.

8. The method for quantifying the morphology and predicting the propagation trend of tunnel lining cracks according to claim 1, characterized in that, Based on historical time-series data of topological role characteristics and subnetwork cohesion characteristics, a state transition network for a crack network system is constructed, including: The topological role characteristics at each time step are combined with the sub-network cohesive characteristics to form a system feature vector; The system feature vector is mapped to the system state in the state set through quantization processing; The number of transitions between system states is counted based on the order in which system states appear in historical time-series data. A state transition network is constructed based on the number of transitions between system states. The state transition network includes nodes representing system states and directed edges representing transitions between system states. The weight of the directed edges is determined by the number of transitions between system states.

9. The method for quantifying the morphology and predicting the propagation trend of tunnel lining cracks according to claim 1, characterized in that, Starting with the system state defined by the current topological role characteristics and subnetwork cohesion characteristics, we extrapolate possible future state sequences in the state transition network, and predict the overall evolution trend of the crack network based on the state sequences, including: The system state corresponding to the current state transition network is determined as the starting point based on the topological role characteristics and subnetwork cohesion characteristics at the current moment; In a state transition network, starting from the initial system state, the transition process of the system state along the directed edges is simulated according to the weights of the directed edges in the state transition network, generating multiple future system state sequences. Based on the generated multiple system state sequences, the distribution of the frequency of occurrence and evolution path of different system states in the future is statistically analyzed; Predict the overall evolution trend of the crack network based on the distribution of occurrence frequency and evolution path.

10. A system for quantifying the morphology and predicting the propagation trend of tunnel lining cracks, used to implement the method for quantifying the morphology and predicting the propagation trend of tunnel lining cracks as described in any one of claims 1-9, characterized in that, Includes the following modules: The image acquisition module is used to acquire time-series images of the tunnel lining surface and to identify and segment crack contours from the time-series images. The structure building module is used to build the crack network topology for each time-series image based on the spatial distance and orientation relationship between each crack contour. The network generation module is used to analyze the topological connections and spatial configurations between cracks based on the crack network topology, identify key evolution paths, and assign weights to obtain a weighted crack network. The feature recognition module is used to analyze the topological position and connection importance of each crack in the weighted crack network to extract its topological role features, and to identify crack sub-clusters in the network to extract sub-network cohesion features. The network construction module is used to construct the state transition network of the crack network system based on historical time-series data of topological role characteristics and subnetwork cohesion characteristics; The trend prediction module is used to deduce possible future state sequences in the state transition network, starting from the system state defined by the topological role characteristics and sub-network cohesion characteristics at the current moment, and predict the overall evolution trend of the crack network based on the state sequences.

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