A method for identifying internal defects of concrete based on a graph neural network

Abstract

The present application belongs to the technical field of nondestructive testing of concrete structures, and particularly relates to a method for identifying the topology of internal defects in concrete based on a graph neural network, comprising: obtaining three-dimensional detection data of a concrete test piece for voxel reconstruction and extracting a three-dimensional defect candidate; constructing an initial graph based on spatial adjacency relationships and extracting node features and edge features; recalibrating the adjacency relationships and edge weights based on the local graph structure topology index of the initial graph to obtain a topology-constrained graph, and performing message passing on the topology-constrained graph while updating the node embedding in combination with adaptive information aggregation weight; constructing a fitness function, optimizing the allocation matrix of nodes to clusters to determine graph coarsening mapping, and generating a multi-layer defect skeleton subgraph; extracting a cross-layer topology description vector from the multi-layer defect skeleton subgraph and outputting the classification and identification result of the defect topology structure. The present application can accurately classify and identify the topology of complex internal defects in concrete.

Description

Technical Field

[0001] This invention relates to the field of non-destructive testing technology for concrete structures. More specifically, this invention relates to a method for identifying the topological structure of internal defects in concrete based on graph neural networks. Background Technology

[0002] With the rapid development of modern civil engineering construction, concrete, as the most widely used building material, has always been a key focus in the engineering field regarding structural safety and durability. Affected by factors such as temperature changes, load effects, and material aging, concrete is prone to various hidden defects such as cracks, voids, and segregation. To promptly identify potential safety hazards in engineering projects, three-dimensional non-destructive testing technologies such as radar and ultrasound have been widely applied to the internal quality inspection of concrete.

[0003] However, internal defects in concrete not only vary greatly in scale but also often exhibit irregular, interconnected forms with multiple levels of branching. Existing 3D reconstruction methods based on image morphology processing or single threshold segmentation can only extract the apparent geometric contours of defects, making it difficult to reconstruct the fine internal structure. This leads to biases in determining the type of complex defects and assessing the degree of structural hazard.

[0004] Graph neural networks, with their significant advantages in non-Euclidean data processing and spatial relationship modeling, have been gradually applied to the field of 3D structure recognition. Among them, a scheme combining hierarchical graph pooling technology can map voxel data to graph nodes, and through graph coarsening mechanisms, progressively reduce dimensionality and extract multi-scale structural skeleton features, providing a new technical approach for topological identification of complex defects inside concrete.

[0005] However, in practical applications, existing technical solutions mostly rely on the spatial distance between nodes to establish adjacent edges during the graph construction stage, failing to effectively incorporate response information unique to the probe signal, such as differences in propagation delay, changes in response gradient, and anisotropic characteristics of the structural tensor. This results in a weak ability of the initial graph structure to represent the essential attributes of defects, and a lack of effective topological constraints and adaptive weight adjustment mechanisms during subsequent message transmission, making it susceptible to signal disturbances caused by internal medium inhomogeneities. Furthermore, in the process of graph coarsening through node discarding or heuristic clustering criteria, the connectivity of micro-scale and bifurcated crack-like defects is easily disrupted. Simultaneously, existing models often rely solely on the embedded features of the terminal graph for classification, failing to collaboratively extract key information reflecting topological differences, such as the continuity characteristics of cross-scale loops and bifurcated hierarchical structures. Consequently, when faced with concrete defects with similar external contours but different internal topological structures, accurate and stable type differentiation and identification are difficult to achieve. Summary of the Invention

[0006] To address the technical problem that existing graph construction methods do not fully incorporate the unique response characteristics of the detection signal, and that the graph coarsening process easily disrupts the connectivity of tiny bifurcated cracks, thus making it difficult to accurately distinguish complex concrete defects with similar appearances but different topological essences, this invention provides a method for identifying the topological structure of internal defects in concrete based on graph neural networks.

[0007] This invention provides a method for identifying the topological structure of internal defects in concrete based on graph neural networks, comprising: acquiring three-dimensional detection data of concrete specimens for voxel reconstruction, and extracting three-dimensional defect candidate bodies composed of voxels; constructing an initial graph based on the spatial adjacency relationships of the voxels of the three-dimensional defect candidate bodies, and combining response gradient difference, propagation delay difference, and structural tensor anisotropy, wherein the initial graph uses voxels as nodes, and extracting node features and edge features; recalibrating adjacency relationships and edge weights based on the local graph structure topology indices of the initial graph to obtain a topological constraint graph, and performing message passing on the topological constraint graph, and updating node embeddings by combining adaptive information aggregation weights; in the hierarchical pooling operation, constructing a fitness function by combining intra-cluster discreteness, inter-cluster connection refinement index, and boundary transition index, optimizing the node-to-cluster allocation matrix to determine the graph coarsening mapping, and generating a multi-layer defect skeleton subgraph; extracting cross-layer topological description vectors from the multi-layer defect skeleton subgraphs, and jointly discriminating them with the final layer graph embeddings, and outputting the classification and identification results of the defect topology structure.

[0008] This invention is based on three-dimensional concrete detection data. It extracts defect candidates through voxel reconstruction, integrates spatial adjacency, response gradient difference, propagation delay difference, and structural tensor anisotropy to construct an initial graph and extract node and edge features, fully combining physical detection information with spatial geometric characteristics. A topological constraint graph is obtained by recalibrating based on local topological indices. Adaptive information aggregation weights are used to complete message passing and node embedding updates, suppressing noise interference and enhancing the representation of realistic defect structures. Topology-preserving graph coarsening is achieved by optimizing the fitness function, generating multi-layer defect skeleton subgraphs. Cross-layer topological description vectors are extracted and jointly discriminated with the final layer graph, fully preserving defect connectivity, loops, and bifurcation features. This enables accurate classification and identification of the internal defect topology of concrete, improving the accuracy of identifying complex defect morphologies and the degree of structural detail restoration.

[0009] Preferably, an initial graph is constructed based on the spatial adjacency relationship of the voxels of the three-dimensional defect candidate, combined with the response gradient difference, propagation delay difference, and structural tensor anisotropy. This includes: when the spatial adjacency distance, response gradient difference, propagation delay difference, and structural tensor anisotropy of adjacent voxels all satisfy their respective preset threshold conditions, an undirected connection edge is established between the adjacent voxels to construct the initial graph.

[0010] By incorporating the unique amplitude attenuation, arrival time difference, and local structural tensor direction characteristics of the probe signal into the graph topology construction, the initial graph not only reflects spatial proximity relationships but also accurately expresses the physical connectivity and elongated extension characteristics inside the defect. This effectively suppresses pseudo-connections caused by probe noise or medium inhomogeneity, thereby improving the reliability of subsequent graph structure analysis.

[0011] Preferably, the structural tensor anisotropy is calculated as follows: the structural tensor is calculated by calculating the local spatial response gradient of the nodes; the structural tensor is decomposed into eigenvalues ​​to obtain the principal direction, and the difference between the principal eigenvalues ​​and secondary eigenvalues ​​of the structural tensor is calculated; the difference between the principal eigenvalues ​​and secondary eigenvalues ​​is used to characterize the anisotropy index as the structural tensor anisotropy.

[0012] Preferably, the node features include at least one of the following: a response value based on the average detection response of voxels in the local neighborhood of the node; directional consistency based on the weighted inner product of the principal direction vectors of voxels in the local neighborhood; curvature based on the Gaussian curvature calculated from the fitted surface of the response isosurface in the local neighborhood; and a boundary attenuation gradient based on the spatial attenuation gradient of the defect response intensity calculated by extending outward along the normal of the fitted surface.

[0013] By extracting node features from a multi-dimensional and complementary perspective, where response values ​​reflect the degree of anomaly in the defect medium, directional consistency reflects the regularity of local crack extension, curvature characterizes the concave-convex boundary features of the defect, and boundary attenuation describes the transition characteristics between the defect and the normal concrete area, this multi-feature fusion approach can comprehensively characterize the local physical properties and geometric details of the defect, providing rich and accurate basic node representations for subsequent message passing and feature learning in graph neural networks, and enhancing the ability to distinguish the local features of different types of defects.

[0014] Preferably, the edge features include at least one of the following: the spatial Euclidean distance between the nodes at both ends of the connecting edge; the difference in detection response loss between the two nodes; and the connection rotation angle of the directional consistency vectors of the two nodes.

[0015] By extracting edge features from three dimensions—spatial geometry, physical response, and topological orientation—the actual connection relationships between adjacent defect voxels can be more accurately depicted, making the edge structure of the initial graph more closely match the real connectivity of the defects, and providing reliable edge information support for subsequent message transmission and topological analysis.

[0016] Preferably, the adjacency relationships and edge weights are recalibrated based on the local graph structure topology indices of the initial graph to obtain a topological constraint graph, including: calculating the local clustering coefficients, path reachability density, and edge connection strength of the nodes in the initial graph; calculating the mean of the path reachability density of the nodes at both ends of the connecting edge as a density decay coefficient, multiplying the density decay coefficient by the edge connection strength to obtain a comprehensive edge weight; removing pseudo-connecting edges whose comprehensive edge weight is lower than a preset connection threshold, and updating the initial graph with the retained comprehensive edge weight as edge weights to obtain the topological constraint graph.

[0017] Preferably, the step of performing message passing on the topological constraint graph and updating node embeddings with adaptive information aggregation weights includes: generating message passing vectors based on the node features and edge features; calculating the relevance score using an attention mechanism to obtain edge credibility; calculating the product of node degree centrality and node local clustering coefficients as the node's topological stability; multiplying the edge credibility by the topological stability of the corresponding source node to obtain adaptive information aggregation weights; and performing a weighted summation of the message passing vectors of neighboring nodes based on the adaptive information aggregation weights to update the node embeddings.

[0018] Preferably, the fitness function constructed by combining intra-cluster scatter, inter-cluster connection refinement index, and boundary transition index includes: dividing the nodes of the current layer graph structure into multiple supernode clusters based on the node-to-cluster assignment matrix; calculating the sum of the variances of the node features within each cluster as the intra-cluster scatter; counting the number of cross-cluster connection edges and the sum of their weights between different clusters as the inter-cluster connection refinement index; calculating the angle change rate of the normal vectors of the cluster boundary nodes, and using the proportion of angle change rates greater than a set threshold as the boundary transition index; and constructing the fitness function with the objectives of minimizing the intra-cluster scatter, maximizing the inter-cluster connection refinement index, and retaining high boundary transition indexes.

[0019] Preferably, the optimization of the node-to-cluster allocation matrix determines the graph coarsening mapping to generate a multi-layer defect skeleton subgraph, including: performing matrix multiplication by the transpose of the allocation matrix with the current layer's adjacency matrix and the allocation matrix itself to update the adjacency matrix of the next layer; multiplying the transpose of the allocation matrix with the current layer's node embedding matrix to update the node features of the next layer; and iteratively executing the above graph coarsening mapping process to generate a multi-layer defect skeleton subgraph.

[0020] Preferably, the method involves extracting cross-layer topological description vectors from the multi-layer defect skeleton subgraphs and jointly discriminating them with the embedding of the last-layer graph to output the classification and recognition results of the defect topology structure. This includes: extracting connectivity features, loop persistence features, and bifurcation level features from each layer skeleton subgraph, concatenating them to reduce dimensionality and form the cross-layer topological description vector; concatenating the cross-layer topological description vector with the embedding of the last-layer graph generated from the last-layer defect skeleton subgraph to obtain joint features; inputting the joint features into a classifier to calculate the probability distribution, extracting the category index corresponding to the maximum probability value, and outputting the classification and recognition results of the defect topology structure.

[0021] By extracting connectivity, loop persistence, and bifurcation hierarchy features from multi-layer defect skeleton subgraphs, and concatenating and reducing the dimensionality to obtain cross-layer topological description vectors, this vector is then fused with the feature embedding of the final layer graph and input into a classifier for identification. This method can uncover the topological patterns of defects at different scales, fully preserving key details such as defect connectivity, pore structure, and branch hierarchy. It compensates for the shortcomings of relying solely on the final layer graph embedding, which easily loses fine-grained topological information. It can effectively distinguish concrete internal defects that are similar in shape but different in topological nature, thus improving the accuracy of classification and identification.

[0022] The technical solution of the present invention has the following beneficial technical effects: This invention constructs an initial graph by fusing multi-dimensional physical and geometric information such as response gradient difference, propagation delay difference, and structural tensor, extracting rich node and edge features. It then recalibrates adjacency relationships and edge weights using local topological indices to generate a topological constraint graph. Adaptive information aggregation weights are adjusted based on edge credibility and topological stability to update node embeddings. A multi-index optimized hierarchical pooling method is introduced to generate multi-layer defect skeleton subgraphs, extracting cross-layer topological description vectors and jointly discriminating them with the final layer graph embedding. This invention enhances the completeness of defect information representation, suppresses false edges and noise interference, preserves key topological details such as defect bifurcation and transitions, and uncovers the structural patterns of defects at multiple scales. It solves the problems of weak initial graph representation, graph coarsening leading to morphological distortion, and difficulty in distinguishing defects with similar shapes but different topological essences in existing technologies, achieving accurate classification and identification of complex defect topological structures within concrete. Attached Figure Description

[0023] Figure 1 This is a flowchart of a method for identifying the topological structure of internal defects in concrete based on graph neural networks, as described in this invention. Figure 2 This is a graph showing the relationship between edge connection strength and node distance. Figure 3 This is a schematic diagram showing the comparison curves of the model classification accuracy. Detailed Implementation

[0024] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0025] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0026] This invention discloses a method for identifying the topological structure of internal defects in concrete based on graph neural networks, referring to... Figure 1 This includes the following steps: S1. Reconstruct the three-dimensional detection data and extract three-dimensional defect candidates.

[0027] Load the three-dimensional detection matrix data of concrete specimens acquired by ground-penetrating radar or industrial computed tomography (CT) equipment. Voxel reconstruction is performed on this three-dimensional detection data using a multi-dimensional image processing module. A maximum-minimum normalization algorithm is applied to map the detection intensity values ​​of all voxels to the 0-1 range, eliminating signal amplitude differences between different detection devices and operating conditions. An adaptive threshold is automatically calculated using the Otsu method's global threshold segmentation algorithm, extracting the set of voxels with detection intensity values ​​higher than this threshold as three-dimensional defect candidates characterizing potential internal defects in the concrete.

[0028] S2. Integrate multi-dimensional physical properties to construct an initial graph and extract features.

[0029] Based on the spatial adjacency relationship of three-dimensional defect candidate voxels, and combined with the response gradient difference, propagation delay difference and structural tensor anisotropy, an initial graph is constructed. The initial graph uses voxels as nodes, and node features and edge features are extracted.

[0030] In an optional embodiment, the step of constructing the initial graph specifically includes: The bounding box containing the three-dimensional defect candidate is divided into a multi-scale three-dimensional spatial grid. The preferred grid resolution range is 2mm×2mm×2mm to 10mm×10mm×10mm, in order to discretize the spatial distribution of defects.

[0031] The peak difference in probe amplitude between a grid node and its neighboring nodes is calculated, and the ratio of this difference to the corresponding Euclidean distance is taken as the response gradient difference. As an example, the absolute difference in the probe signal amplitude at two adjacent nodes is extracted and denoted as 0.4. Dividing this by the Euclidean distance between the nodes, 2.83 mm, yields a response gradient difference of approximately 0.14 / mm.

[0032] The arrival time difference of the detection signal between the node and its neighboring nodes is calculated as the propagation delay difference. The arrival time of ultrasonic or ground-penetrating radar waves can be extracted using a threshold method or a cross-correlation algorithm. This difference is typically between 0.5 μs and 2 μs.

[0033] The structure tensor of the local spatial response gradients of nodes is computed, and its principal directions are obtained through eigenvalue decomposition. Fractional anisotropy is then calculated as the anisotropy parameter of the structure tensor. Specifically, the response gradient structure tensor matrix within the local neighborhood (e.g., a 3×3 neighborhood) of each node can be constructed, and after eigenvalue decomposition, three eigenvalues ​​arranged in descending order are obtained. , and Extracting the largest eigenvalue The corresponding eigenvectors are used as the principal directions, and the fractional anisotropy values ​​are calculated as the anisotropy parameters of the structure tensor according to the following relationship: ; in, , , These are the three eigenvalues ​​of the structure tensor, arranged from largest to smallest after eigenvalue decomposition. The value ranges from 0 to 1. The larger the value, the stronger the directionality of the local response gradient distribution, and the more the corresponding defect morphology tends to be a narrow crack. The closer the value is to 0, the more isotropic it is, corresponding to a void or a uniform region.

[0034] For example, when 0.8 0.15 When the value is 0.05, the calculated anisotropy value of the structural tensor is 0.87. This parameter is used to characterize the elongated shape of the defect.

[0035] Set thresholds for spatial distance, gradient difference, time delay error, and anisotropy. To control the graph size and avoid creating false connections, the spatial distance threshold can be set to 2 to 3 times the grid size (e.g., 10 mm), the time delay error threshold can be set to the theoretical propagation time of the signal at that distance plus a certain tolerance (e.g., 2.5 μs), the gradient difference threshold can be set to 0.2 / mm, and the anisotropy threshold can be set to 0.6. A connection edge is established between a pair of candidate voxels only if the spatial adjacency distance between adjacent voxels meets the spatial distance threshold condition, the propagation time delay difference meets the time delay error threshold condition, the response gradient difference meets the gradient difference threshold condition (e.g., the previously calculated 0.14 per mm is less than 0.2 per mm to ensure the continuity of the internal response), and the structural tensor anisotropy meets the anisotropy threshold condition (e.g., the previously calculated 0.87 is greater than 0.6 to preferentially capture the direction of crack extension). This process constructs an initial graph that not only includes spatial relationships but also maps the connectivity and geometric topology of the physical response to defects.

[0036] Based on the constructed initial graph, node features of each node in the initial graph are further extracted. In an optional embodiment, the step of extracting node features includes: The average value of the detection response of all voxels within the local neighborhood of the node is calculated as the response value of that node. The local neighborhood can be selected as a 5×5×5 voxel three-dimensional spatial window centered on the current node. For example, the average value of the detection response intensity of 125 voxels within this window is calculated, resulting in a normalized average response value of 0.65.

[0037] The principal direction vectors of each voxel within the local neighborhood are calculated, and the weighted inner product sum of the direction vectors of all neighboring voxels is used to represent the directional consistency of the node. Principal component analysis can be used to extract the principal directions of each voxel, and a distance-decaying Gaussian function is used as the weight to calculate the weighted inner product sum of the direction vectors of all neighboring voxels and the direction vector of the central node. Its value ranges from 0 to 1, reflecting the regularity of the local crack extension.

[0038] The response isosurfaces of voxels within the local neighborhood are extracted and fitted with a quadratic surface. The Gaussian curvature of the fitted surface is calculated as the curvature of that node. Isosurfaces with a response value equal to 0.5 within the local neighborhood can be extracted, and a quadratic surface is fitted using the least squares method. The model is as follows: ; The Gaussian curvature of the fitted surface at the vertex is calculated as a curvature parameter to identify the concave and convex boundaries of the defect.

[0039] Extending outward along the normal direction of the fitted surface, the spatial attenuation gradient of the defect response intensity within the local spatial range is calculated, which serves as the boundary attenuation gradient of that node. For example, with a step size of 1 mm, extending outward along the normal direction to 6 mm, the change in defect response intensity from 0.65 to 0.2 is recorded, and its ratio to the extension distance is calculated, yielding a boundary attenuation gradient value of 0.075 / mm.

[0040] The calculated response values, directional consistency, curvature, and boundary decay are normalized and scaled to the range of 0 to 1, then concatenated into a single feature vector, which serves as the node feature for that node. For example, the concatenation results in a 1×4 dimensional initial feature vector containing the values ​​[0.65, 0.82, 0.04, 0.075].

[0041] For edge feature extraction, the Euclidean distance between the three-dimensional coordinates of the two ends of the edge is calculated as the distance between the nodes; the absolute difference of the response values ​​of the two ends of the edge is calculated as the loss difference; the cosine similarity of the directional consistency vectors of the two ends of the edge is calculated and converted into an angle value as the connection angle. The three are then concatenated to obtain the edge feature vector.

[0042] Thus, the above steps complete the initial graph construction that integrates physical detection information and spatial geometric information, and provide basic features for describing the local characteristics of defects for subsequent graph neural network processing.

[0043] S3. Recalibrate the topology constraint graph and adaptively update node embeddings.

[0044] Based on the initial graph, the adjacency relationships and edge weights are recalibrated using the local graph structure topology index to obtain the topological constraint graph. Message passing is then performed on the topological constraint graph, and node embeddings are updated by combining adaptive information aggregation weights.

[0045] First, the adjacency relationships and edge weights of the initial graph are recalibrated to generate a topologically constrained graph. The specific steps include: The local clustering coefficient of a node is the ratio of the actual number of edges connecting its first-order neighbors to the theoretically maximum number of edges that can exist. For example, for a node with 6 first-order neighbors, theoretically, there can be a maximum of 15 edges connecting these neighbors. If the actual number of edges connecting the neighbors is 5, then the local clustering coefficient of this node is... It is used to characterize the density of local defect agglomerations.

[0046] The path reachability density of a node is calculated as the ratio of the total number of reachable nodes within a specified hop count range to the theoretical total number of nodes within that range. The preferred hop count range is 2 to 3 hops. For example, with a hop count of 2, a breadth-first search yields 24 actually reachable nodes, while the theoretical maximum number of connected nodes within this hop count range for the spatial grid is 33. Therefore, the path reachability density of this node is calculated as follows: , used to represent the branch richness of a local defect network.

[0047] Calculate the characteristic differences and Euclidean distances between the nodes at both ends of the connecting edge in the local coordinate system. The dimensionless exponential decay value is then used as the edge connection strength. The specific calculation formula is as follows: ; in, For edge connection strength; The L2 norm difference value of the feature vectors of the two nodes is calculated from the existing multidimensional feature vectors of the nodes; This is the dimensionless value of the spatial Euclidean distance between the two nodes. and These are the feature difference smoothing factor and the distance smoothing factor, respectively. Both are empirical hyperparameters that can be determined through a grid search on the validation set; typically... The selected range is 0.2 to 0.8. The selection range is from 1 to 2.5. The smoothing factor controls the sensitivity of exponential decay; the smaller the value, the faster the decay and the more sensitive it is to changes in feature differences and distances.

[0048] For example, the L2 difference of the feature vectors of the nodes at both ends of the connecting edge is 0.15, and the physical Euclidean distance between the nodes is 5 mm. After dimensionless mesh scaling, this value is substituted into the Gaussian kernel decay function for calculation. (Refer to...) Figure 2 The figure illustrates that, with varying feature differences, edge connection strength decreases exponentially with increasing node distance. Furthermore, the greater the feature difference, the lower the edge connection strength at the same distance. The 0.4 truncation threshold marked in the figure serves as the criterion for eliminating pseudo-connections in the construction of the topological constraint graph, visually demonstrating the basis for adjacency relationship selection. Setting smoothing factors of 0.5 for feature difference and 1.5 for distance, the connection strength obtained after exponential decay calculation is 0.82.

[0049] To prevent false connections caused by probe noise, the mean of the path reachability density of the nodes at both ends of a connecting edge is calculated as a density attenuation coefficient. This density attenuation coefficient is then multiplied by the edge connection strength to obtain the overall edge weight. For example, if the path reachability density of one node is 0.73 and that of the other node is 0.67, the density attenuation coefficient is the average of the two, 0.70. Multiplying this coefficient 0.70 by the edge connection strength 0.82 yields an overall edge weight of 0.574. A connection threshold is preset, preferably in the range of 0.3 to 0.5, for example, set to 0.4. False connecting edges with an overall edge weight lower than 0.4 are removed, and the overall edge weight of the remaining edges is used as the new edge weight to update the initial graph, thus obtaining the topologically constrained graph.

[0050] After obtaining the topological constraint graph, message passing is performed on the graph to update node embeddings. In an optional embodiment, the process includes: For each connecting edge in the topological constraint graph, its source node feature vector (e.g., 64-dimensional), target node feature vector (e.g., 64-dimensional), and edge features (e.g., expanded to 16-dimensional) are concatenated along the feature channel dimension to form a fused feature vector (e.g., 144-dimensional).

[0051] The fused feature vector is input into a multilayer perceptron for feature mapping to generate a message passing vector. This multilayer perceptron consists of an input layer, hidden layers, and an output layer, and its computational relationship is as follows: ; in, This represents the fused feature vector obtained by concatenating the source node features, target node features, and edge features along the channel dimension. and The weight matrix is ​​a learnable matrix. and For bias terms; The activation function is a non-linear activation function, such as ReLU or GELU. This is the output of the multilayer perceptron. This is a message passing vector that captures the high-dimensional nonlinear interaction features between adjacent defective nodes. Its dimension is usually set to be consistent with the node embedding dimension so that subsequent weighted aggregation can be performed.

[0052] The message passing vector is input into the attention mechanism to calculate the edge confidence. The calculation formula for this attention mechanism is: ; in, This is a learnable attention weight vector, whose dimension is the same as the message vector. The dimensions are consistent; the negative slope coefficient in the LeakyReLU activation function can be taken as 0.2; For nodes With nodes Message passing vectors between them Represents a node The set of first-order neighbor nodes. The output of this attention mechanism. The edge confidence score represents the relative importance of the neighbor node's information relative to all its neighbors during the aggregation process. This score is automatically optimized through backpropagation during training.

[0053] The topological stability of a node is calculated as the product of its degree centrality and its local clustering coefficients within the local graph structure. Degree centrality is calculated by dividing the current node's degree by the maximum degree in the graph.

[0054] In an alternative implementation, the node's topological stability can be obtained by adding or weighting the node's degree centrality to its local linearity (the proportion of the largest eigenvalues ​​in the node's local feature covariance matrix). The product of the edge confidence and the source node's topological stability is used as the adaptive information aggregation weight for that connection edge. The local linearity is calculated by collecting data from the current node and its... The feature vectors of the nearest neighbor nodes are used to construct a local feature matrix, and the covariance matrix of this matrix is ​​calculated. Eigenvalue decomposition is performed on this covariance matrix, and the ratio of the largest eigenvalue to the sum of all eigenvalues ​​is used as the local linearity. This index reflects the concentration of the local node feature distribution along the main direction; a larger value indicates a more significant extension of the local region along a single direction, consistent with the morphology of crack-like defects.

[0055] For example, if an edge has a confidence level of 0.45, its corresponding source node has a degree centrality of 0.4, a local linearity of 0.85, and a topological stability of 1.25, then the adaptive information aggregation weight of that edge is: .

[0056] Based on the adaptive information aggregation weight, the message passing vectors from each neighbor node are weighted and summed. The summation result is then processed by a nonlinear activation function (such as an exponential linear unit function), and combined with residual connections and layer normalization operations to output the updated node embedding.

[0057] Thus, through the above steps, by utilizing topological constraints and adaptive weight adjustment mechanisms, we can enhance the real defect structure information while suppressing noise interference, thereby obtaining a more accurate node embedding representation.

[0058] S4. Optimize the fitness function to determine graph coarsening and generate a multi-layer skeleton.

[0059] In the hierarchical pooling operation, a fitness function is constructed by combining intra-cluster discreteness, inter-cluster connection refinement index and boundary transition index. The node-to-cluster allocation matrix determines the graph coarsening mapping and generates a multi-layer defect skeleton subgraph.

[0060] The nodes in the current layer graph structure are divided into multiple supernode clusters based on the node-to-cluster assignment matrix. For each cluster, the sum of the variances of the feature vectors of all nodes within it in each dimension is calculated as the intra-cluster dispersion. For example, for a cluster containing 20 nodes with a feature dimension of 64, the sum of the mean squared errors of the variances in each dimension is 12.5. The smaller this value, the higher the homogeneity within the cluster.

[0061] The number of cross-cluster connections between different supernode clusters is counted, and the weights of these edges are summed to serve as a refinement index for inter-cluster connectivity. For example, if there are 15 cross-cluster edges with a total weight of 12.8, this index reflects the connectivity density of the inter-cluster topology.

[0062] The rate of change of the angle between the direction vectors of the cluster boundary nodes along the spatial connection is calculated, and the proportion of nodes with an angle change rate greater than a set threshold is used as the boundary turning point index. Specifically, principal component analysis is used to calculate the spatial distribution covariance matrix of the boundary node and its local neighboring nodes, and the eigenvector corresponding to the minimum eigenvalue is extracted as the normal vector of the local boundary surface. The variance of the angle between the normal vectors of all boundary nodes within the cluster is calculated. The angle threshold is set to 45°. (Radians), which is the proportion of nodes whose angle change rate is greater than a certain threshold to the total number of boundary nodes. For example, if there are 10 boundary nodes, and 3 of them show a sharp turn, then the boundary turn index of this cluster is 0.3.

[0063] A linearly weighted fitness function is constructed with the objectives of minimizing intra-cluster dispersion, maximizing inter-cluster connection refinement, and preserving high-boundary transition indices. This fitness function is optimized using backpropagation gradient descent with an adaptive moment estimation algorithm. An auxiliary graph neural network is trained to output the probability distribution of each node to the next layer of coarsened cluster nodes, serving as the soft assignment matrix from node to cluster. This matrix has dimensions of [original number of nodes] × [number of supernode clusters]. Pooling multiplication of graph features and the adjacency matrix is ​​performed based on this assignment matrix to complete the graph coarsening mapping. Preferably, the graph coarsening mapping process is iterated twice to generate a three-layer, multi-layer defect skeleton subgraph containing the original layer and two pooling layers. The preferred downsampling ratio for each pooling is 5:1; for example, the number of nodes steadily decreases from 1000 in the first layer to 200 in the second layer, and then to 40 in the third layer.

[0064] In this way, while reducing the graph size, key topological details such as defective forks and turns are effectively preserved through constraints such as boundary transition indices, thus avoiding distortion of the skeleton shape.

[0065] S5. Combine cross-layer vectors and final layer graph embedding to output recognition results.

[0066] Cross-layer topological description vectors are extracted from multi-layer defect skeleton subgraphs and jointly discriminated with the embedding of the last layer graph to output the classification and recognition results of the defect topology structure. Feature extraction is performed on each layer skeleton subgraph to form cross-layer topological description vectors. Specific steps include: A depth-first search algorithm is used to traverse each layer of the skeleton subgraph, counting the total number of independent connected components that are not connected to each other and the size of the nodes in each component, as connectivity features. For example, if three independent connected components are identified in a certain layer of the skeleton with node sizes of 150, 40 and 10 respectively, these values ​​can be sorted and filled into a feature vector of a preset dimension.

[0067] The generation and destruction processes of holes and loops in a graph structure are calculated using a persistent homology algorithm, and the lifetime length of the topological features is extracted as the loop persistence feature. Specifically, a simplex complex is constructed and the persistent homology algorithm is executed to monitor the change of one-dimensional homology features with increasing filtering thresholds. The filtering thresholds at the time of generation and at the time of destruction of each loop or hole feature are recorded, and the difference between the two is the lifetime length of that feature. For example, the longest lifetime is 0.65, indicating the existence of a highly stable closed hole. The top 5 longest lifetime values ​​can be selected as the loop persistence features.

[0068] The degree distribution of each node in each layer of the skeleton subgraph is calculated, and the number of branch nodes with a degree greater than or equal to three and their hierarchical distribution in the multi-layer graph are extracted as the branching level feature. For example, 45 branching nodes are detected in the fine-grained layer, 12 in the medium-grained layer, and 3 in the coarse-grained layer. These values ​​are used to construct a sequence representing the structural complexity.

[0069] The connectivity features, loop persistence features, and bifurcation level features extracted from each layer's skeleton subgraph are concatenated to form a composite vector. For example, 10-dimensional connectivity features, 5-dimensional loop persistence features, and 5-dimensional bifurcation level features are concatenated into a 20-dimensional composite vector. A fully connected network is then used to reduce the dimensionality of this composite vector. The computational formula for this fully connected network is as follows: ; in, The input is a 20-dimensional composite vector. This is the weight matrix. This is the bias vector. The output of this fully connected network. This is the compact cross-layer topology description vector after dimensionality reduction.

[0070] Finally, for the defect skeleton subgraph of the final layer (i.e., the coarsest layer), global average pooling and global max pooling operations are used to process and concatenate all node embeddings to generate the final layer graph embedding. This final layer graph embedding is concatenated with the cross-layer topology description vector generated in the previous steps along the feature dimension, and the concatenated joint feature vector is input into a fully connected neural network classifier that includes a random deactivation mechanism and a linear rectified activation function. A Softmax multi-classifier is used to calculate the probability distribution of each category (such as cracks, holes, or peeling defects) of the input vector, and the category index corresponding to the maximum probability value is extracted as the final defect topology structure classification and recognition result, which is then output.

[0071] To verify the beneficial effects of the technical solution provided in this application, experiments were conducted based on a 3D ground-penetrating radar concrete defect detection test dataset containing 2000 annotated 3D defect samples (divided into three categories: cracks, cavities, and impurities). The dataset was divided into training, validation, and test sets in an 8:1:1 ratio. The experiments were run on a computing server equipped with a dual-processor high-performance graphics processor, and a deep learning framework was used for model building. The network optimizer used was adaptive moment estimation, with an initial learning rate set to 0.001, a batch size of 32, and 100 iterations of training. Evaluation metrics included overall classification accuracy, average F1 score, and 3D defect segmentation intersection-union ratio (IUU).

[0072] The experiment set up five models for comparative testing, see [link / reference]. Figure 3The figure compares the training and convergence processes of the basic graph neural network, the intermediate model with each core module of the present invention superimposed sequentially, and the complete solution of the present invention. It can be seen that each module of the present invention can significantly improve the model accuracy and convergence speed, and the complete solution ultimately achieves the best performance, verifying the superiority of the technical solution of the present invention. Basic model: It only uses traditional grid construction and basic message passing mechanism. Its classification accuracy is 0.795, F1 score is 0.77, and intersection-over-union ratio is 0.684.

[0073] By introducing a multi-dimensional node feature and topological constraint graph recalibration module on the basic model, the classification accuracy was improved to 0.842, the F1 score reached 0.82, and the intersection-over-union ratio was increased to 0.731. This indicates that by recalibrating the graph structure using physical and topological indicators such as response gradient difference, propagation delay difference, and clustering coefficient, pseudo-connections caused by probe noise were eliminated, thus improving the quality of the graph structure.

[0074] Further incorporating an adaptive information aggregation weighting message passing mechanism resulted in a classification accuracy of 0.887, an F1 score of 0.87, and an intersection-over-union ratio (IoU) of 0.785. This demonstrates that dynamically adjusting message passing weights based on edge credibility and topological stability enhances the nonlinear representation of the elongated local morphological features of defects.

[0075] Adding a hierarchical pooling graph coarsening module optimized with boundary inflection indicators further improved classification accuracy to 0.923, F1 score to 0.91, and intersection-over-union ratio to 0.846. This demonstrates that the optimized hierarchical pooling strategy, leveraging boundary inflection indicators, preserves the details of branches with high curvature, preventing the loss of shape in the defective skeleton during graph coarsening.

[0076] The complete solution of this invention (integrating cross-layer topology description vector module) achieves a classification accuracy of 0.958, an F1 score of 0.95, and an intersection-over-union ratio of 0.892. This demonstrates that the cross-layer topology description vector, combined with the hole and loop lifetime and connectivity features extracted by the continuous homology algorithm, effectively mines complex three-dimensional spatial geometric information at multiple scales, resulting in higher accuracy in both defect classification and boundary segmentation tasks.

[0077] In summary, the method provided by this invention achieves high-precision classification and identification of complex defect topology structures inside concrete by fusing detection physical features and topological structure information, and sequentially performing graph construction and recalibration, adaptive message passing, topology-preserving hierarchical pooling, and cross-layer topological feature extraction.

[0078] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for identifying the topological structure of internal defects in concrete based on graph neural networks, characterized in that, include: Three-dimensional detection data of concrete specimens were acquired for voxel reconstruction, and three-dimensional defect candidates composed of voxels were extracted. Based on the spatial adjacency relationship of the voxels of the three-dimensional defect candidate, and combined with the response gradient difference, propagation delay difference and structural tensor anisotropy, an initial graph is constructed. The initial graph uses voxels as nodes, and node features and edge features are extracted. Based on the local graph structure topology index of the initial graph, the adjacency relationship and edge weight are recalibrated to obtain the topological constraint graph. Message passing is then performed on the topological constraint graph, and the node embedding is updated by combining adaptive information aggregation weights. In the hierarchical pooling operation, a fitness function is constructed by combining intra-cluster discreteness, inter-cluster connection refinement index and boundary transition index, and the node-to-cluster allocation matrix is ​​optimized to determine the graph coarsening mapping and generate a multi-layer defect skeleton subgraph. Extract cross-layer topological description vectors from the multi-layer defect skeleton subgraph, and jointly discriminate them with the embedding of the last layer graph to output the classification and recognition results of the defect topological structure.

2. The method for identifying the topological structure of internal defects in concrete based on graph neural networks according to claim 1, characterized in that, Based on the spatial adjacency relationship of the voxels of the three-dimensional defect candidate, and combined with the response gradient difference, propagation delay difference and structural tensor anisotropy, an initial graph is constructed, including: when the spatial adjacency distance, response gradient difference, propagation delay difference and structural tensor anisotropy of adjacent voxels all meet their respective preset threshold conditions, an undirected connection edge is established between the adjacent voxels to construct the initial graph.

3. The method for identifying the topological structure of internal defects in concrete based on graph neural networks according to claim 1, characterized in that, The structural tensor anisotropy is calculated by calculating the structural tensor of the node's local spatial response gradient; The principal direction is obtained by performing eigenvalue decomposition on the structure tensor, and the difference between the principal eigenvalue and the secondary eigenvalue of the structure tensor is calculated. The anisotropy index is characterized by the difference between the principal eigenvalue and the secondary eigenvalue, and is used as the anisotropy of the structure tensor.

4. The method for identifying the topological structure of internal defects in concrete based on graph neural networks according to claim 1, characterized in that, The node features include at least one of the following: The response value is based on the average detection response of voxels in the local neighborhood of the node. The directional consistency is based on the weighted inner product of the principal direction vectors of voxels within the local neighborhood; Curvature based on Gaussian curvature calculated from the fitted surface of the response isosurface in the local neighborhood; The boundary attenuation gradient is formed by the spatial attenuation gradient of the defect response intensity calculated by extending outward along the normal of the fitted surface.

5. The method for identifying the topological structure of internal defects in concrete based on graph neural networks according to claim 1, characterized in that, The edge features include at least one of the following: the spatial Euclidean distance between the nodes at both ends of the connecting edge; the difference in detection response loss between the two nodes; The connection angle of the directional consistency vectors at both ends of the node.

6. The method for identifying the topological structure of internal defects in concrete based on graph neural networks according to claim 1, characterized in that, Based on the local graph structure topology indices of the initial graph, adjacency relationships and edge weights are recalibrated to obtain a topologically constrained graph, including: Calculate the local clustering coefficients, path reachability density, and edge connectivity strength of the nodes in the initial graph; The mean of the path reachability density of the nodes at both ends of the connecting edge is calculated as the density decay coefficient. The density decay coefficient is multiplied by the edge connection strength to obtain the comprehensive edge weight. False connections with a combined edge weight lower than a preset connection threshold are removed, and the retained combined edge weights are used as edge weights to update the initial graph, thus obtaining the topological constraint graph.

7. The method for identifying the topological structure of internal defects in concrete based on graph neural networks according to claim 1, characterized in that, The step of performing message passing on the topological constraint graph and updating node embedding by combining adaptive information aggregation weights includes: generating a message passing vector based on the node features and edge features, and calculating the relevance score by inputting an attention mechanism to obtain the edge credibility. The product of the node's degree centrality and its local clustering coefficient is used as the node's topological stability. The edge credibility is multiplied by the topological stability of the corresponding source node to obtain the adaptive information aggregation weight. The message passing vectors of neighboring nodes are then weighted and summed according to the adaptive information aggregation weight to update the node embedding.

8. The method for identifying the topological structure of internal defects in concrete based on graph neural networks according to claim 1, characterized in that, The fitness function is constructed by combining intra-cluster discreteness, inter-cluster connection refinement index and boundary transition index, including: dividing the nodes of the current layer graph structure into multiple supernode clusters based on the node-to-cluster assignment matrix, and calculating the sum of the variances of the node features within the cluster as the intra-cluster discreteness. The number of cross-cluster connection edges and the sum of edge weights between different clusters are counted as the refinement index of inter-cluster connections; the angle change rate of the normal vector of the cluster boundary node is calculated, and the proportion of the angle change rate greater than a set threshold is used as the boundary turning index. A fitness function is constructed with the objectives of minimizing the intra-cluster dispersion, maximizing the inter-cluster connection refinement index, and preserving the high boundary transition index.

9. The method for identifying the topological structure of internal defects in concrete based on graph neural networks according to claim 1, characterized in that, The optimization of the node-to-cluster allocation matrix determines the graph coarsening mapping and generates a multi-layer defect skeleton subgraph, including: performing matrix multiplication by the transpose of the allocation matrix with the current layer's adjacency matrix and the allocation matrix itself to update the adjacency matrix of the next layer; multiplying the transpose of the allocation matrix with the current layer's node embedding matrix to update the node features of the next layer; and iteratively executing the above graph coarsening mapping process to generate a multi-layer defect skeleton subgraph.

10. The method for identifying the topological structure of internal defects in concrete based on graph neural networks according to claim 1, characterized in that, The process involves extracting cross-layer topological description vectors from the multi-layer defect skeleton subgraphs and jointly discriminating them with the embedding of the last-layer graph to output the classification and recognition results of the defect topology. This includes: extracting connectivity features, loop persistence features, and bifurcation level features from each layer skeleton subgraph and concatenating them to reduce dimensionality and form the cross-layer topological description vector; concatenating the cross-layer topological description vector with the embedding of the last-layer graph generated from the last-layer defect skeleton subgraph to obtain joint features; inputting the joint features into a classifier to calculate the probability distribution, extracting the category index corresponding to the maximum probability value, and outputting the classification and recognition results of the defect topology.

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