Acoustic emission source damage degree evaluation and positioning method based on physical constraint graph convolutional network

Abstract

The application relates to a physical constraint graph convolution network-based acoustic emission source damage degree evaluation and positioning method, which comprises the following steps: collecting multi-channel acoustic emission signals and carrying out pretreatment, segmenting continuous signals of each channel into independent wave packets, composing a multi-path wave packet sequence, and constructing a data set with double labels of coordinates and damage degrees; performing dynamic multi-path feature aggregation based on a main-aid residual gate to generate features of each sensor node; constructing a full-connection directed graph with each sensor as a node, and explicitly encoding observable time difference and relative energy attenuation between sensor pairs into an edge feature vector; performing physical constraint message passing and global feature fusion to obtain a graph-level global feature vector; and synchronously inputting the graph-level global feature vector into two parallel multilayer perceptron branches to obtain a damage source spatial coordinate and a damage degree condition. The application solves the problems of low positioning precision and weak small sample generalization capability, and simultaneously realizes automatic evaluation of the damage degree.

Description

Technical Field

[0001] This invention relates to the field of composite material structure health monitoring technology, specifically a method for assessing and locating the damage level of acoustic emission sources based on dynamic feature fusion and physical constraint graph convolutional networks. Background Technology

[0002] Carbon fiber reinforced polymer (CFRP) composites have been widely used in aerospace, automotive, and civil engineering fields due to their excellent specific strength and corrosion resistance. However, due to manufacturing defects, excessive service loads, or environmental erosion, CFRP structures are prone to internal damage. If not detected and maintained in a timely manner, accumulated damage may lead to catastrophic structural failure. Acoustic emission (AE) technology can passively and in real-time capture transient stress waves released by damage, making it an important means of monitoring the health of composite material structures. Due to limitations in load weight, cost, and wiring complexity, engineering projects typically only allow for the deployment of sparse sensor arrays. How to achieve high-precision positioning of acoustic emission sources and assessment of damage levels using sparse arrays in highly anisotropic CFRP boards is a pressing engineering challenge that needs to be solved.

[0003] Currently, there are three main types of technologies used for locating acoustic emission sources.

[0004] The first category is analytical localization methods based on Time Difference of Arrival (TDOA). These methods assume that sound waves propagate at a constant speed and solve for the sound source coordinates by establishing a system of geometric equations based on the time difference of arrival of the same event received by various sensors. However, the significant anisotropy and inhomogeneity of CFRP cause the wave speed to vary with the propagation direction, accompanied by severe dispersion and attenuation, rendering the constant wave speed assumption invalid. Simultaneously, multipath signals generated by boundary reflections interfere with the accurate acquisition of the first wave's arrival time. Therefore, this type of method suffers from large localization errors under sparse array conditions, typically requiring a dense sensor network to achieve acceptable accuracy.

[0005] The second category is data-driven localization methods based on conventional deep learning models such as Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), or Long Short-Term Memory Networks (LSTMs). These methods achieve localization by learning a nonlinear mapping between waveform data and sound source coordinates. However, they treat multi-channel sensor data as a regular Euclidean grid or a one-dimensional sequence, ignoring the unstructured spatial topology of the sensor network. In sparse arrays, the geometric relationships between sensors contain crucial information about the physical laws of wave propagation; relying solely on local convolution or temporal modeling is insufficient to effectively incorporate these global geometric constraints.

[0006] The third category is the existing technology closest to this invention, namely, localization methods based on graph neural networks (GNN / GCN). These methods use sensors as graph nodes and aggregate information between nodes through graph convolution, enabling them to model the spatial dependencies of sensor networks to some extent. However, existing graph methods have inherent limitations in graph topology construction: their adjacency matrices are typically generated based on Euclidean distance or feature similarity between nodes, representing purely data-driven implicit association modeling, and cannot explicitly encode the underlying physical mechanisms of wave propagation (such as time difference of arrival and energy decay laws). This leads to two problems: first, the model inference process lacks physical interpretability, remaining a "black box"; second, under conditions of small samples and strong noise, it lacks constraints from physical inductive biases, limiting its generalization ability.

[0007] Furthermore, in multipath signal processing, sound waves undergo reflection and mode conversion when propagating within confined boundaries, resulting in complex multipath effects. Existing methods (such as attention-based noise reduction networks and multi-scale filtering networks) generally treat boundary reflections as noise and suppress or filter them out. In fact, reflected waves carry deterministic geometric information related to structural boundaries and damage locations. Blindly suppressing reflected signals will lead to the loss of crucial geometric information, limiting further improvements in positioning accuracy.

[0008] In summary, the existing technology has the following three pressing technical problems: First, the assumption of constant wave velocity in anisotropic media fails, and analytical methods cannot accurately locate waves in sparse arrays; second, existing deep learning methods (including graph methods) rely on data correlation to construct scalar adjacency relationships, which cannot explicitly inject the physical mechanism of wave propagation into the model, resulting in poor interpretability and weak generalization ability for small samples; third, multipath reflected waves are blindly filtered out as noise, and the geometric information contained therein is not utilized. Summary of the Invention

[0009] The purpose of this invention is to provide a method for assessing and locating the damage level of acoustic emission sources based on physical constraint graph convolutional networks. This method addresses the problems of low positioning accuracy, lack of physical interpretability of the model, and weak generalization ability for small samples caused by material anisotropy and multipath effects in existing technologies with sparse sensor arrays, and simultaneously achieves automatic assessment of the damage level.

[0010] The technical solution adopted by this invention to solve its technical problem is as follows: This method for assessing and locating the damage level of acoustic emission sources based on physical constraint graph convolutional networks includes the following steps: Step 1: Acquire multi-channel acoustic emission signals and preprocess them. Divide the continuous signals of each channel into independent wave packets to form a multipath wave packet sequence. The first wave packet is the first wave, and the remaining wave packets are reflected waves. Construct a dataset with dual labels of coordinates and damage degree. Step 2: Dynamic multipath feature aggregation based on master-slave residual gating: The importance weight of each reflected wave packet is dynamically quantified through the confidence evaluation network CEN, and effective geometric information is adaptively selected and fused from the multipath wave packet sequence to generate features of each sensor node. Step 3: Physical edge feature construction: Construct a fully connected directed graph G=(V, E) with each sensor as a node, and explicitly encode the observable arrival time difference and relative energy decay between sensor pairs as edge feature vectors. Step 4: Physical constraint message passing and global feature fusion: The sensor node features output from Step 2 and the physical edge features output from Step 3 are input into the Edge-GCN edge conditional graph convolution module. The physical prior is explicitly guided by additive compensation to achieve the message passing process. Then, the global feature fusion across sensors is completed by the Transformer encoder to obtain the graph-level global feature vector. Step 5, Multi-task Joint Optimization and Prediction: The graph-level global feature vector is synchronously input into two parallel multilayer perceptron branches to obtain the spatial coordinates of the damage source and the degree of damage.

[0011] Step one of the above scheme is as follows: A sparse acoustic emission sensor array is arranged on the CFRP board to collect multi-channel acoustic emission signals generated by damage events; based on preset amplitude thresholds and timing gating parameters, the continuous signals of each channel are divided into independent wave packets, and sorted by arrival time to form a multipath wave packet sequence, where the first wave packet is the first wave and the remaining wave packets are reflected waves; 9-dimensional physical features are extracted for each wave packet, including arrival time, amplitude, energy, rise time, duration, count, root mean square value (RMS), average signal level (ASL), and peak frequency, and standardized using the Z-score method; the length of the wave packet sequence of each channel is fixed at K+1, with 1 first wave and K reflected waves, padded with zeros if insufficient and truncated if excessive; each sample is associated with the true coordinates (x, y) of the acoustic emission source and the damage degree category label to construct a dataset with dual labels of coordinates and damage degree.

[0012] Step two in the above scheme is specifically as follows: S21. Map the 9-dimensional physical feature vector p(i,k) of the k-th wave packet of the i-th sensor to the d-dimensional latent feature space via linear projection: (1) In the formula, W is the 9-dimensional physical feature vector extracted from the k-th wave packet of the i-th sensor. p With b p These are the weight matrix and bias term of the projection layer, respectively; h i,k For p i,k The d-dimensional latent feature vector obtained after linear projection; d is the dimension of the latent feature space; Rd Let h represent a d-dimensional real vector space. i,k ∈R d h i,k It is a d-dimensional real column vector; S22. The confidence evaluation network CEN uses a multilayer perceptron and a sigmoid activation function to calculate the importance gating weights of each reflected wave packet. : (2) In the formula, α i,k To evaluate the confidence level of the network CEN, the gating weights α represent the importance of the i-th sensor and the k-th reflected wave packet. i,k ∈(0,1), the larger the value, the more reliable the geometric information carried by the reflected wave packet; σ is the Sigmoid activation function, Here, θ represents a multilayer perceptron, and θ is a learnable parameter of the multilayer perceptron. S23, characterized by the first wave As the baseline primary feature term, the weighted combination of each reflected wave feature is used as an auxiliary correction term, which is then superimposed in the form of residual summation to output the node feature of the i-th sensor. : (3) In the formula, v i h is the node feature vector of the i-th sensor; i,0 Let be the d-dimensional potential feature vector of the first wave from the sensor, serving as the principal feature term; k is the index of the reflected wave, and α i,k with h i,k The importance gate weights obtained from equation (2) and the latent eigenvectors obtained from equation (1) for the k-th reflected wave packet are respectively, and their weighted sum constitutes the auxiliary correction term; K is the total number of extracted reflected waves; when reflection information is missing or noise dominates, it naturally reverts to the first wave reference; when there is effective reflection information, the auxiliary residual term introduces the geometric corrections related to the boundary and propagation path into the node representation.

[0013] Step three in the above plan specifically refers to: S31. For any sensor pair (i, j), calculate the arrival time difference using the first wave arrival times tᵢ and tⱼ obtained from signal feature extraction: (4) In the formula, t i With t j ∆t represents the arrival times of the first wave from sensor i and sensor j, respectively, with the earliest trigger point of the channel in the same acoustic emission event as the relative zero point; ij Let be the time difference between the first wave arrivals of sensor i and sensor j, that is, the difference in their arrival times; S32. The first wave energy of each sensor is obtained by integrating the square of the waveform amplitude within a fixed time window after the arrival of the first wave: (5) In the formula, E i Let be the initial wave energy of the i-th sensor; sᵢ(t) be the waveform signal of the i-th sensor; t be time; t i T represents the arrival time of the first wave from the i-th sensor; w The fixed integration time window is the length taken after the arrival of the first wave, and the integration interval is [t]. i , t i +T w The first wave energy is obtained by integrating the square of the waveform amplitude within this time window. The energy logarithm ratio is used as a characteristic of the relative energy attenuation between sensor pairs: (6) in This represents the relative energy decay characteristics between sensor pairs (i, j). E i With E j The first wave energies of sensor i and sensor j obtained from equation (5) are respectively. S33. Combining the arrival time difference and relative energy attenuation, define the physical edge feature vector connecting node i and node j: (7) In the formula: e ij ∆t is the physical edge feature vector connecting node i and node j. ij Let be the time difference between the first wave arrivals of sensor i and sensor j, where i is the receiving node and j is the source node; The relative energy decay characteristics between sensor pairs (i, j) obtained from equation (6); the superscript T denotes vector transpose, i.e., e ij The arrival time difference ∆t ij With relative energy decay A two-dimensional column vector consisting of two physical quantities.

[0014] Step four in the above scheme is specifically as follows: S41, Source node features With edge features Projected onto the latent feature space of the same dimension respectively: (8) In the formula, h j e is the feature vector of the input node of the source node j; ij W represents the physical edge feature vector connecting node i and node j. h With We Here is the corresponding linear projection weight matrix; ĥ j For the latent features of the source node after projection, ê ij This is projected onto the edge features, which share the same dimension as the node features. S42. Using edge features as additive biases, perform physical propagation compensation on the source node features: (9) In the formula, ĥ j→i The characteristics of the data transmitted from source node j to target node i after physical propagation compensation; ĥ j With ê ij The projected source node features and projected physical edge features are obtained from equation (8), respectively. The edge features apply physical propagation compensation to the source node features in the form of additive bias. Compensated features Represents the theoretical arrival characteristics predicted by the positive physics model; S43. Integrate the compensation features with the inherent observation features of the target node. splicing The multilayer perceptron generates physical perception messages, forcing the network to learn the deviation between the observed values ​​and the predictions of the physical model: (10) In the formula, m ij This refers to the physical sensing message transmitted from source node j to target node i; MLP msg (·) represents a multilayer perceptron for message generation; [·‖·] denotes vector concatenation operation; h i The observed features of target node i itself; ĥ j→i The theoretical arrival characteristics obtained from equation (9) after physical propagation compensation; S44, The target node aggregates its local neighborhood. All physical sensing messages are processed and a nonlinear transformation is applied to complete the node state update: (11) In the formula, h i ′ represents the updated feature of node i; N(i) is the set of neighboring nodes of node i, and j is a neighboring node in this set; m ij The physical sensing message is obtained from equation (10); ReLU(·) is the modified linear unit activation function; S45. Input the updated node feature matrix H into the Transformer encoder, and generate the query matrix Q, key matrix K, and value matrix V through linear transformation: (12) In the formula, H is the node feature matrix composed of the stacked features updated by each node; WQ W K W V Let Q, K, and V be the learnable linear transformation weight matrices that generate the query matrix, key matrix, and value matrix, respectively; Q, K, and V are the query matrix, key matrix, and value matrix, respectively. Calculate multi-head self-attention: (13) In the formula, Attention(Q, K, V) is the self-attention output; Q, K, and V are the query matrix, key matrix, and value matrix, respectively; K T is the transpose of the key matrix; Softmax(·) is the normalized exponential function; The dimension of the key vector is used to scale the dot product result to avoid gradient vanishing. S46. After the feature matrix is ​​fused by a multi-layer Transformer encoder, global average pooling is applied to compress the features of N nodes into a graph-level global feature vector containing global spatiotemporal correlations: (14) In the formula, z global is the graph-level global feature vector obtained by global average pooling; hᵢ is the i-th node feature output by the last layer encoder; and N is the total number of sensors.

[0015] Step five in the above scheme is specifically as follows: S51. The localization regression branch uses a multilayer perceptron to achieve a nonlinear mapping from global features to sound source coordinates, outputting predicted coordinates (x̂, ŷ). A Smooth L1 loss is employed to enhance robustness against noise and anomalous samples. (15) In the formula, L reg The L1 loss function is used for localization regression; SmoothL1(·) is the smoothing L1 loss function. and These represent the sound source coordinate vectors predicted by the model and the actual sound source coordinate vectors, respectively. S52. The damage severity classification branch predicts the damage severity category using a multilayer perceptron parallel to the regression branch. It employs cross-entropy loss to impose discriminative constraints on the shared feature space, guiding the encoder to learn essential difference representations related to different damage mechanisms. (16) In the formula, L cls Cross-entropy loss for classifying damage severity; C is the total number of damage severity categories. In this invention, C=2, corresponding to mild and severe damage severity, respectively. One-hot encoding for the real label; Predict the probability that a sample belongs to class c for the model; S53. Combine the regression loss and classification loss in a weighted manner to form the overall objective function: (17) In the formula, L total The overall objective function for a single sample; L reg L is the localization regression loss obtained from equation (15); cls The damage classification loss is obtained from equation (16); λ is the balance coefficient, which is used to adjust the gradient contributions of the two tasks in backpropagation. The spatial coordinates and damage level category of the acoustic emission source are output synchronously using the overall objective function.

[0016] In the above scheme, the number of sensors in the sparse sensor array in step one is 4, which are respectively arranged in the four corner areas of the CFRP board; the total number of reflected waves K per channel is 7, that is, the wave packet sequence length is fixed at 8.

[0017] In the above scheme, the Edge-GCN module contains two edge-conditional graph convolutional layers, and the output dimensions of the two layers are kept consistent to avoid the loss of key physical geometric information; the Transformer encoder contains two stacked encoding layers, adopts a 4-head self-attention mechanism, and the hidden layer dimension is 64.

[0018] Beneficial effects: (1) This invention constructs a dynamic multipath feature aggregation mechanism based on a master-slave residual gating structure, adopts a strategy of "first wave dominance + reflected wave gating correction", and realizes course learning through negative bias initialization of the confidence evaluation network. Existing technologies treat boundary reflected waves as noise filtering, while this invention adaptively decouples the geometric information of the boundary and propagation path contained in the reflected wave and injects it into the node representation, turning interference into gain, and directly solving the problem that multipath reflected waves are blindly treated as noise filtering and the geometric information contained therein is not utilized. Experiments show that on a strongly anisotropic CFRP board with only 4 sensors, the average positioning error of the test set of this invention is as low as 0.59cm, the minimum error is only 0.04cm, the positioning error of 80% of the samples is less than 0.88cm, and the positioning error of 95% of the samples is less than 1.28cm.

[0019] (2) This invention constructs an Edge-GCN architecture for explicit physical geometric reasoning, abandoning the scalar adjacency matrix based on Euclidean distance or feature similarity. The observable wave propagation physical quantity—the arrival time difference calculated by Equation (4) and the logarithmic ratio of energy attenuation calculated by Equation (6)—is explicitly encoded into a high-dimensional edge feature vector as shown in Equation (7). The network is forced to learn the deviation between the observation and the physical forward model through additive compensation message passing of Equations (9) and (10). This design injects the wave propagation control law as a strong inductive bias into the graph topology, making the model reasoning process physically interpretable. It breaks through the limitations of the pure data-driven "black box" model and directly solves the problem of poor interpretability and weak generalization ability for small samples due to the inability to explicitly inject the physical mechanism of wave propagation into the model. Ablation experiments show that after removing physical edge features, the average positioning distance error increases from 1.00cm to 1.14cm; after removing the graph convolution module, the error further increases to 2.42cm, which fully demonstrates the substantial contribution of physical edge features and graph structure reasoning to positioning accuracy. Compared with the traditional TDOA method that relies on the assumption of constant wave velocity (which has a positioning error of 3.919 cm and 5.523 cm on the same typical measurement point of the specimen), the positioning error of the present invention is reduced by about an order of magnitude, directly solving the problem that the analytical method cannot accurately locate under sparse array.

[0020] (3) This invention integrates Edge-GCN with Transformer global attention and adopts a multi-task framework that jointly optimizes localization regression and damage classification. Transformer breaks through the limitation of local receptive field of graph convolution, and the classification task, as a structured regularization, forces the shared encoder to learn essential features with physical discriminative power. Experiments show that the structure achieves 100% accuracy in damage classification tasks, and the average localization error differs by only 0.085cm (0.651cm vs. 0.736cm) between mild and severe excitation intensities, demonstrating strong robustness to changes in damage severity; at the same time, ablation experiments show that the average distance error increases from 1.00cm to 1.11cm after removing the Transformer module. Attached Figure Description

[0021] Figure 1 This is a flowchart of the steps of the method of the present invention; Figure 2 This is a schematic diagram of the acoustic emission data acquisition experiment setup in an embodiment of the present invention; Figure 3 This is a schematic diagram of the structure and data flow of the dynamic multipath feature aggregation module of the present invention; Figure 4 This is a schematic diagram comparing the physical edge feature construction method of the present invention with the traditional scalar adjacency matrix; Figure 5 This is a schematic diagram of the physical constraint edge condition message passing mechanism of the present invention; Figure 6 This is a schematic diagram of the overall network architecture of the Edge-GCN-Transformer of this invention; Figure 7 This is a schematic diagram of the positioning performance verification results in an embodiment of the present invention. Detailed Implementation

[0022] The invention will be further described below with reference to the accompanying drawings: This method for assessing and locating the damage level of acoustic emission sources based on physical constraint graph convolutional networks includes the following steps: Step 1: Data Acquisition and Preprocessing: A sparse acoustic emission sensor array is deployed on the CFRP board to acquire multi-channel acoustic emission signals generated by damage events. Based on preset amplitude thresholds and timing gating parameters, the continuous signal of each channel is segmented into independent wave packets (Hits), and sorted by arrival time to form a multipath wave packet sequence, where the first wave packet is the first wave and the remaining wave packets are reflected waves. Nine-dimensional physical features are extracted from each wave packet, including arrival time, amplitude, energy, rise time, duration, count, root mean square (RMS), average signal level (ASL), and peak frequency, and standardized using the Z-score method. The length of the wave packet sequence for each channel is fixed at K+1 (1 first wave and K reflected waves, padded with zeros if insufficient, truncated if excessive). Each sample is associated with the true coordinates (x, y) of the acoustic emission source and the damage severity category label to construct a dataset. Step 2: Dynamic Multipath Feature Aggregation Based on Master-Auxiliary Residual Gating: Construct a confidence evaluation network (CEN) to dynamically quantify the importance weights of each reflected wave packet. Using the first wave as the primary feature term and the reflected wave as the auxiliary correction term, adaptively filter and fuse effective geometric information from the multipath sequence to generate node features for each sensor; specifically including: S21. Map the 9-dimensional physical feature vector p(i,k) of the k-th wave packet of the i-th sensor to the d-dimensional latent feature space via linear projection: (1) In the formula, W is the 9-dimensional physical feature vector extracted from the k-th wave packet of the i-th sensor. p With b p These are the weight matrix and bias term of the projection layer, respectively; h i,k For p i,k The d-dimensional latent feature vector obtained after linear projection; d is the dimension of the latent feature space; R d Let h represent a d-dimensional real vector space. i,k ∈R d h i,k It is a d-dimensional real column vector; S22. The confidence evaluation network CEN uses a multilayer perceptron and a sigmoid activation function to calculate the importance gating weights of each reflected wave packet. : (2) In the formula, α i,k To evaluate the confidence level of the network CEN, the gating weights α represent the importance of the i-th sensor and the k-th reflected wave packet. i,k ∈(0,1), the larger the value, the more reliable the geometric information carried by the reflected wave packet; σ is the Sigmoid activation function, Here, θ represents a multilayer perceptron, and h represents the learnable parameters of this multilayer perceptron. i,k The d-dimensional latent feature vector of the wave packet obtained by equation (1); the bias parameter of the CEN is initialized with negative bias to realize course learning: in the early stage of training, the gate output is suppressed to near zero, and the model only relies on the reliable first wave to converge; as training progresses, the weight of the high confidence reflection wave packet is gradually increased to achieve a smooth transition from "first wave dominance" to "multipath information enhancement", avoiding the introduction of gradient interference by multipath noise in the early stage of training; S23, characterized by the first wave As the baseline primary feature term, the weighted combination of each reflected wave feature is used as an auxiliary correction term, which is then superimposed in the form of residual summation to output the node feature of the i-th sensor. : (3) In the formula, v i h is the node feature vector of the i-th sensor; i,0 Let α be the d-dimensional latent eigenvector of the first wave (k=0) of the sensor, serving as the principal feature term; k is the index of the reflected wave, and α is the eigenvector of the first wave (k=0). i,k with h i,k Let K be the importance gating weight obtained from Equation (2) and the latent eigenvector obtained from Equation (1) for the k-th reflected wave packet, respectively. The weighted sum of the two constitutes the auxiliary correction term; K is the total number of extracted reflected waves; when reflection information is missing or noise dominates, the model naturally reverts to the first wave reference; when there is effective reflection information, the auxiliary residual term introduces geometric corrections related to the boundary and propagation path into the node representation; the upper limit of the summation in Equation (3) is K. i That is, the total number of reflected waves K extracted by the i-th sensor.

[0023] Step 3: Physical Edge Feature Construction: Construct a fully connected directed graph G=(V, E) with each sensor as a node. Abandoning the traditional scalar adjacency matrix, the observable arrival time difference and relative energy attenuation between sensor pairs are explicitly encoded as edge feature vectors; specifically including: S31. For any sensor pair (i, j), the arrival times tᵢ and tᵢ of the first wave are obtained using signal feature extraction. j Calculate the time difference of arrival: (4) In the formula, t i With t j ∆t represents the arrival times of the first wave from sensor i and sensor j, respectively, with the earliest trigger point of the channel in the same acoustic emission event as the relative zero point; ij Let be the time difference between the first wave arrivals of sensor i and sensor j, that is, the difference in their arrival times.

[0024] S32. The first wave energy of each sensor is obtained by integrating the square of the waveform amplitude within a fixed time window after the arrival of the first wave: (5) In the formula, E i Let be the initial wave energy of the i-th sensor; sᵢ(t) be the waveform signal of the i-th sensor; t be time; t i T represents the arrival time of the first wave from the i-th sensor; w The fixed integration time window is the length taken after the arrival of the first wave, and the integration interval is [t]. i , t i +T w The first wave energy is obtained by integrating the square of the waveform amplitude within the time window.

[0025] The energy logarithm ratio is used as a characteristic of the relative energy attenuation between sensor pairs: (6) in This represents the relative energy decay characteristics between sensor pairs (i, j). E is a minimal constant term; i With E j Let E be the initial wave energy of sensor i and sensor j obtained from equation (5); the relative energy attenuation characteristic is denoted as E in equation (7). ij .

[0026] S33. Combining the arrival time difference and relative energy attenuation, define the physical edge feature vector connecting node i and node j: (7) In the formula: e ij ∆t is the physical edge feature vector connecting node i and node j. ij E represents the first wave arrival time difference between sensor i and sensor j, obtained from equation (4); ijThe relative energy decay characteristics between sensor pairs (i, j) obtained from equation (6) are given by equation (6). The superscript T indicates vector transpose, that is, the physical edge characteristics are two-dimensional column vectors composed of two physical quantities: arrival time difference and relative energy decay.

[0027] Step 4: Physical Constraint Message Passing and Global Feature Fusion: The node features output from Step 2 and the physical edge features output from Step 3 are input into the Edge-GCN edge-conditional graph convolutional module. Additive compensation is used to explicitly guide the message passing process based on physical priors. Then, the Transformer encoder completes cross-sensor global feature fusion. The Edge-GCN module contains two edge-conditional graph convolutional layers, with the output dimensions of both layers kept consistent to avoid loss of key physical geometric information. The Transformer encoder contains two stacked encoding layers, employing a 4-head self-attention mechanism, with a hidden layer dimension of 64. Specifically, it includes: S41, Source node features With edge features Projected onto the latent feature space of the same dimension respectively: (8) In the formula, h j The input node feature vector of source node j is the node feature v output in step two during the convolution of the first layer graph. j ;e ij W represents the physical edge feature vector connecting node i and node j. h With W e Here is the corresponding linear projection weight matrix; ĥ j For the latent features of the source node after projection, ê ij This is projected onto the edge features, which are in the same dimension as the node features.

[0028] S42. Using edge features as additive biases, perform physical propagation compensation on the source node features: (9) In the formula, ĥ j→i The characteristics of the data transmitted from source node j to target node i after physical propagation compensation; ĥ j With ê ij The projected source node features and projected physical edge features are obtained from equation (8), respectively. The edge features apply physical propagation compensation to the source node features in the form of additive bias.

[0029] Compensated features Represents the theoretical arrival characteristics predicted by the positive physics model; S43. Integrate the compensation features with the inherent observation features of the target node. splicing The multilayer perceptron generates physical perception messages, forcing the network to learn the deviation between the observed values ​​and the predictions of the physical model: (10) In the formula, m ij This refers to the physical sensing message transmitted from source node j to target node i; MLP msg (·) represents a multilayer perceptron for message generation; [·‖·] denotes vector concatenation operation; h i The observed features of target node i itself; ĥ j→i The theoretical arrival characteristics obtained from equation (9) after physical propagation compensation are given.

[0030] S44, The target node aggregates its local neighborhood. All physical sensing messages are processed and a nonlinear transformation is applied to complete the node state update: (11) In the formula, h i ′ represents the updated feature of node i; N(i) is the set of neighboring nodes of node i, and j is a neighboring node in this set; m ij The physical sensing message is obtained from equation (10); ReLU(·) is the modified linear unit activation function.

[0031] S45. Input the updated node feature matrix H into the Transformer encoder, and generate the query matrix Q, key matrix K, and value matrix V through linear transformation: (12) In the formula, H is the node feature matrix composed of the stacked features updated by each node; W Q W K W V Q, K, and V are the learnable linear transformation weight matrices that generate the query matrix, key matrix, and value matrix, respectively; Q, K, and V are the query matrix, key matrix, and value matrix, respectively.

[0032] And calculate the multi-head self-attention using the following formula: (13) In the formula, Attention(Q, K, V) is the self-attention output; Q, K, and V are the query matrix, key matrix, and value matrix, respectively; K T is the transpose of the key matrix; Softmax(·) is the normalized exponential function; The dimension of the key vector is used to scale the dot product result to avoid gradient vanishing. S46. After the feature matrix is ​​fused by a multi-layer Transformer encoder, global average pooling is applied to compress the features of N nodes into a graph-level global feature vector containing global spatiotemporal correlations: (14) In the formula, z global is the graph-level global feature vector obtained by global average pooling; hᵢ is the i-th node feature output by the last layer encoder; N is the total number of sensors; Step 5, Multi-task Joint Optimization and Prediction: Graph-level global feature vectors... Two parallel multilayer perceptron branches are input simultaneously to perform spatial coordinate regression of the injury source and classification of the injury severity. Both the regression and classification branches of the multilayer perceptron contain a 32-neuron hidden layer, after which ReLU activation and Dropout regularization are applied sequentially. The balance coefficient λ is set to 0.1. Specifically, the following steps are included: S51. The localization regression branch uses a multilayer perceptron to achieve a nonlinear mapping from global features to sound source coordinates, outputting predicted coordinates (x̂, ŷ). A Smooth L1 loss is employed to enhance robustness against noise and anomalous samples. (15) In the formula, L reg The L1 loss function is used for localization regression; SmoothL1(·) is the smoothing L1 loss function. and These represent the sound source coordinate vectors predicted by the model and the actual sound source coordinate vectors, respectively. S52. The damage severity classification branch predicts the damage severity category using a multilayer perceptron parallel to the regression branch. It employs cross-entropy loss to impose discriminative constraints on the shared feature space, guiding the encoder to learn essential difference representations related to different damage mechanisms. (16) In the formula, L cls Cross-entropy loss for classifying damage severity; C is the total number of damage severity categories. In this invention, C=2, corresponding to mild and severe damage severity, respectively. One-hot encoding for the real label; Predict the probability that a sample belongs to class c for the model; S53. Combine the regression loss and classification loss in a weighted manner to form the overall objective function: (17) In the formula, L total The overall objective function for a single sample; L reg L is the localization regression loss obtained from equation (15); clsThe damage classification loss is obtained from equation (16); λ is the balance coefficient, which is used to adjust the gradient contribution of the two tasks in backpropagation; the network parameters are updated by minimizing the overall objective function through backpropagation; after training, the acoustic emission event to be tested is processed according to steps one to four and then input into the model, that is, the spatial coordinates of the acoustic emission source and the damage category are output synchronously. Example

[0033] See Figure 1 The method for assessing and locating the damage level of acoustic emission sources based on dynamic feature fusion and physical constraint graph convolutional networks is as follows: (I) Experimental Platform and Data Acquisition (Step 1) See Figure 2 In this embodiment, a T700s carbon fiber reinforced composite material plate was selected as the test object. The specimen size was 200mm×200mm×1mm, and the layup method was [0 / 90]4s, with a total of 16 layers. Its main mechanical parameters are shown in Table 1. An acoustic emission sensor (model PK3I) was arranged in the four corner areas 20mm away from each edge of the CFRP composite material plate 1, forming a rectangular sparse array surrounding the monitoring area. Vacuum silicone grease was uniformly coated between the acoustic emission sensor and the surface of the specimen as a coupling agent layer to reduce energy loss caused by acoustic impedance mismatch. The output of each acoustic emission sensor was connected to a multi-channel acoustic emission acquisition system (PCI-Express type) via a preamplifier, and the acquired data was recorded and processed by a computer. The system sampling rate was set to 2MSPS, the hardware trigger threshold was 35dB, and the key timing parameters for waveform feature extraction (peak definition time PDT, impact definition time HDT, and impact lockout time HLT) were configured according to Table 2 to ensure accurate segmentation of the multipath wave packet sequence generated by a single physical event.

[0034] Table 1: Material parameters of T700s CFRP composite panels

[0035]

[0036] To construct a dataset labeled with damage levels, two excitation schemes were used to simulate different degrees of damage events on the specimen surface: Mild excitation involved controlled tapping of predetermined measurement points with a hard pen tip, generating low-energy and low-amplitude acoustic emission signals to simulate early-stage matrix microcracks or low-energy surface impact events in composite materials; Severe excitation involved breaking a 0.5mm diameter HB lead core at a 30° angle on the material surface (Hsu-Nielsen lead breaking test), releasing a broadband, high-amplitude transient stress wave at the moment of fracture to simulate high-energy acoustic emission events such as carbon fiber fracture or severe delamination. The effective monitoring area within the sensor array was divided into 60 recognition regions using a 20mm × 20mm grid. Nine measurement points with a 0.5mm spacing were evenly selected within each region, resulting in 540 discrete coordinate points. Mild and severe excitations were sequentially applied to each measurement point, with each mode repeated nine times and recorded simultaneously by four sensors, yielding 9720 sets of multi-channel acoustic emission samples. After wave packet segmentation and feature extraction, a feature dataset containing 162,700 records was constructed.

[0037] Nine physical features were extracted for each wave packet, including arrival time, amplitude, energy, rise time, duration, count, root mean square (RMS), average signal level (ASL), and peak frequency. The arrival time was set to the earliest trigger time of the channel within the same event as the relative zero point. All features were Z-score standardized based on the mean and standard deviation of the training set, and this standardization parameter remained consistent during the testing phase. Multiple wave packets within each channel were sorted by arrival time, with the first wave packet defined as the first wave (direct wave), and the rest as potential reflected or diffracted waves. The maximum length of the wave packet sequence was fixed at 8 (1 first wave and K=7 reflected waves), with zeros padded if insufficient and the earliest 8 retained if exceeding the limit. Finally, a fully connected directed graph was constructed using four sensors as nodes, with the true coordinates (x, y) of the acoustic emission source as the regression label and the excitation intensity category (mild / severe, corresponding to different degrees of damage) as the classification label, forming a dual-label dataset that supports multi-task joint optimization.

[0038] (II) Dynamic Multipath Feature Aggregation (Step 2) See Figure 3The dynamic multipath feature aggregation module includes a linear projection unit, a confidence evaluation network, and a master-slave residual aggregation unit. The 9-dimensional physical feature vectors of the first wave and each reflected wave in the multipath wave packet sequence are first mapped to the d-dimensional latent space by the linear projection unit according to Equation (1); the confidence evaluation network is composed of a multilayer perceptron and a sigmoid activation function, and calculates the importance gating weights for each reflected wave packet according to Equation (2). Its bias parameter is initialized to a significantly negative value: the gating output is close to zero in the early stage of training, and the model only relies on the first wave feature to converge stably. As training progresses, the weights of high-confidence reflected waves are gradually increased to achieve a smooth transition in a course-like learning manner; the master-slave residual aggregation unit outputs the features of each sensor node by superimposing the residuals with the first wave feature as the benchmark and the weighted sum of the reflected waves as the auxiliary correction term according to Equation (3).

[0039] (III) Construction of physical edge features (Step 3) See Figure 4 For any sensor pair (i, j), the physical edge feature construction module calculates the arrival time difference from the arrival time of the first wave according to Equation (4), integrates the first wave energy within a fixed time window after the arrival of the first wave according to Equation (5), calculates the energy logarithm ratio as the relative energy attenuation feature according to Equation (6), and finally combines the two into the physical edge feature vector of the edge according to Equation (7). Figure 4 The left side shows the scalar adjacency matrix construction method of the traditional graph method, while the right side shows the physical edge feature construction method of the present invention. The essential difference between the two is that the former only adjusts the aggregation strength and does not contain physical semantics; the latter explicitly injects the observable physical quantities of wave propagation into the graph topology, providing physically consistent geometric constraints for message passing.

[0040] (iv) Physical constraint message passing and global feature fusion (step four) See Figure 5 In the Edge-GCN graph convolution module, the feature linear projection unit projects the source node features and edge features to the same latent space according to equation (8); the additive compensation unit uses the edge features as additive biases to perform physical propagation compensation on the source node features according to equation (9), obtaining the theoretical arrival features for physical forward prediction; the physical perception message generation unit concatenates the compensated features and the target node observation features according to equation (10) and generates a message through a multilayer perceptron, reducing the deviation between the network learning observations and the physical model; the neighborhood aggregation unit aggregates neighborhood messages according to equation (11) and performs nonlinear updates. See below for further details. Figure 6 The updated node features are input into the Transformer global fusion module, which contains two encoders, adopts a 4-head self-attention mechanism, and has a hidden layer dimension of 64. The global attention interaction across sensors is calculated according to Equation (12) and Equation (13), and finally, the graph-level global feature vector is generated by global average pooling according to Equation (14).

[0041] (V) Multi-task joint optimization and training (Step 5) See Figure 6 The multi-task output module includes a parallel localization regression branch and a damage classification branch, both of which share the same feature encoder. The multilayer perceptron of both branches contains a 32-neuron hidden layer, after which ReLU activation and Dropout regularization are applied. The localization regression branch uses Smooth L1 loss to constrain coordinate prediction according to Equation (15); the damage classification branch uses cross-entropy loss to constrain class prediction according to Equation (16); the overall objective function is weighted and combined according to Equation (17), with a balance coefficient λ of 0.1. The dataset is randomly divided into a training set (113,890 samples), a validation set (32,540 samples), and a test set (16,270 samples) in a 7:2:1 ratio; the Adam optimizer is used, with a batch size of 128, a maximum number of training rounds of 500, and an initial learning rate of 0.001. If the training loss does not improve significantly for 10 consecutive rounds, the learning rate is reduced to 0.5 times the original value; to reduce the uncertainty introduced by random initialization, 5 independent repeated experiments are conducted. During training, the validation loss and training loss converged rapidly with a small difference, indicating that the model was not overfitting. The validation set MAE and RMSE stabilized at approximately 0.6 cm and 1.2 cm, respectively, and the coefficient of determination R² stabilized above 0.93. The classification accuracy quickly reached and remained at 100%.

[0042] (vi) Verification of implementation results See Figure 7 The trained model is then systematically validated.

[0043] 1. Positioning Accuracy: 100 samples were randomly selected from 540 excitation locations in the test set for independent positioning analysis. The overall average positioning error of the test set was 0.59cm, with a maximum error of 1.48cm (true coordinates (12.50cm, 6.50cm), predicted (13.93cm, 6.11cm)) and a minimum error of only 0.04cm (true coordinates (13.50cm, 13.50cm), predicted (13.54cm, 13.50cm)). The cumulative error distribution statistics show that 80% of the test samples had a positioning error of less than 0.88cm, 90% were less than 1.12cm, and 95% were less than 1.28cm.

[0044] 2. Ablation Experiment: Three variant models were constructed for comparison—NE model (removing physical constraint edge features), NG model (removing GCN module), and NT model (removing Transformer module). The results of five random initializations and repeated experiments are shown in Table 3. After removing physical edge features, the average distance error increased from 1.00cm to 1.14cm, proving the substantial contribution of the physical edge features constructed by equations (4) to (7); after removing the GCN module, the error increased to 2.42cm, proving that spatial geometric reasoning based on graph structure is indispensable; after removing the Transformer, the error increased to 1.11cm, proving the necessity of global attention fusion.

[0045]

[0046] 3. Comparison with traditional TDOA methods: Based on the least squares TDOA algorithm, the theoretical group velocity of the A0 mode (approximately 1.4 mm / μs), which dominates the low-frequency band, is selected for calculation according to the T700s plate group velocity dispersion curve. Randomly selected measurement points D1 (7.5 cm, 8.5 cm) in the central region and D2 (6.5 cm, 0.5 cm) near the edge are shown in Table 4. The positioning errors are 3.919 cm and 5.523 cm, respectively. This is mainly due to the inability of the constant wave velocity assumption to adapt to the direction-dependent wave velocity changes of CFRP, and the interference of boundary reflection multipath on the first wave arrival time. In contrast, the average error of this invention on the same dataset is only 0.59 cm, which is about an order of magnitude lower.

[0047]

[0048] 4. Comparison with other deep learning models: Under the same hyperparameters and data partitioning conditions, this invention is compared with three representative benchmark models: LSTM, conventional GCN, and Transformer. The results show that conventional GCN, which only captures static geometric relationships, has the highest error; the pure Transformer, which lacks physical prior constraints, has a slightly higher error than LSTM; this invention has the lowest error across all evaluation metrics, and its overall performance is significantly better than each single-mechanism model.

[0049] 5. Robustness under Different Damage Degrees: The histogram and cumulative distribution function (CDF) of the localization error were further analyzed. The distribution pattern shows that the error is highly concentrated in the low error range, exhibiting a slightly right-skewed long-tail characteristic. The overall average error of the test set is as low as 0.59 cm. The CDF statistical curve shows that 80% of the test samples have a localization error below 0.88 cm, 90% of the samples have an error controlled within 1.12 cm, and as many as 95% of the samples have an error less than 1.28 cm. This result indicates that the localization error of the vast majority of samples is concentrated in a low range, and the cumulative distribution curve shows that a high proportion of samples can be controlled within 1.5 cm, indicating that the Edge-GCN-Transformer model has good spatial localization ability and certain predictive stability under unknown damage signals.

[0050] The verification in this embodiment is based on a flat plate structure under controlled experimental conditions. For more complex geometric structures and actual engineering conditions, the data acquisition, feature construction and model training process of the present invention are also applicable.

Claims

1. A method for assessing and locating the damage level of an acoustic emission source based on a physical constraint graph convolutional network, characterized in that... Includes the following steps: Step 1: Acquire multi-channel acoustic emission signals and preprocess them. Divide the continuous signals of each channel into independent wave packets to form a multipath wave packet sequence. The first wave packet is the first wave, and the remaining wave packets are reflected waves. Construct a dataset with dual labels of coordinates and damage degree. Step 2: Dynamic multipath feature aggregation based on master-slave residual gating: The importance weight of each reflected wave packet is dynamically quantified through the confidence evaluation network CEN, and effective geometric information is adaptively selected and fused from the multipath wave packet sequence to generate features of each sensor node. Step 3: Physical edge feature construction: Construct a fully connected directed graph G=(V, E) with each sensor as a node, and explicitly encode the observable arrival time difference and relative energy decay between sensor pairs as edge feature vectors. Step 4: Physical constraint message passing and global feature fusion: The sensor node features output from Step 2 and the physical edge features output from Step 3 are input into the Edge-GCN edge conditional graph convolution module. The physical prior is explicitly guided by additive compensation to achieve the message passing process. Then, the global feature fusion across sensors is completed by the Transformer encoder to obtain the graph-level global feature vector. Step 5, Multi-task Joint Optimization and Prediction: The graph-level global feature vector is synchronously input into two parallel multilayer perceptron branches to obtain the spatial coordinates of the damage source and the degree of damage.

2. The method for assessing and locating the damage level of acoustic emission sources based on physical constraint graph convolutional networks according to claim 1, characterized in that: Step one specifically involves: deploying a sparse acoustic emission sensor array on a CFRP board to collect multi-channel acoustic emission signals generated by damage events; based on preset amplitude thresholds and timing gating parameters, dividing the continuous signal of each channel into independent wave packets, and sorting them by arrival time to form a multipath wave packet sequence, where the first wave packet is the first wave and the remaining wave packets are reflected waves; extracting 9-dimensional physical features for each wave packet, including arrival time, amplitude, energy, rise time, duration, count, root mean square (RMS) value, average signal level (ASL), and peak frequency, and standardizing them using the Z-score method; fixing the length of the wave packet sequence for each channel to K+1, with 1 first wave and K reflected waves, padding with zeros if insufficient and truncating if excessive; associating each sample with the true coordinates (x, y) of the acoustic emission source and the damage degree category label to construct a dataset with dual labels of coordinates and damage degree.

3. The method for assessing and locating the damage level of acoustic emission sources based on physical constraint graph convolutional networks according to claim 2, characterized in that: Step two specifically involves: S21. Map the 9-dimensional physical feature vector p(i,k) of the k-th wave packet of the i-th sensor to the d-dimensional latent feature space via linear projection: （1） In the formula, W is the 9-dimensional physical feature vector extracted from the k-th wave packet of the i-th sensor. p With b p These are the weight matrix and bias term of the projection layer, respectively; h i,k For p i,k The d-dimensional latent feature vector obtained after linear projection; d is the dimension of the latent feature space; R d Let h represent a d-dimensional real vector space. i,k ∈R d h i,k It is a d-dimensional real column vector; S22. The confidence evaluation network CEN uses a multilayer perceptron and a sigmoid activation function to calculate the importance gating weights of each reflected wave packet. : (2) In the formula, α i,k To evaluate the confidence level of the network CEN, the gating weights α represent the importance of the i-th sensor and the k-th reflected wave packet. i,k ∈(0,1), the larger the value, the more reliable the geometric information carried by the reflected wave packet; σ is the Sigmoid activation function, Here, θ represents a multilayer perceptron, and θ is a learnable parameter of the multilayer perceptron. S23, characterized by the first wave As the baseline primary feature term, the weighted combination of each reflected wave feature is used as an auxiliary correction term, which is then superimposed in the form of residual summation to output the node feature of the i-th sensor. : (3) In the formula, v i h is the node feature vector of the i-th sensor; i,0 Let be the d-dimensional potential feature vector of the first wave from the sensor, serving as the principal feature term; k is the index of the reflected wave, and α i,k with h i,k The importance gate weights obtained from equation (2) and the latent eigenvectors obtained from equation (1) for the k-th reflected wave packet are respectively, and their weighted sum constitutes the auxiliary correction term; K is the total number of extracted reflected waves; when reflection information is missing or noise dominates, it naturally reverts to the first wave reference; when there is effective reflection information, the auxiliary residual term introduces the geometric corrections related to the boundary and propagation path into the node representation.

4. The method for assessing and locating the damage level of acoustic emission sources based on physical constraint graph convolutional networks according to claim 3, characterized in that: Step three specifically involves: S31. For any sensor pair (i, j), calculate the arrival time difference using the first wave arrival times tᵢ and tⱼ obtained from signal feature extraction: (4) In the formula, t i With t j ∆t represents the arrival times of the first wave from sensor i and sensor j, respectively, with the earliest trigger point of the channel in the same acoustic emission event as the relative zero point; ij Let be the time difference between the first wave arrivals of sensor i and sensor j, that is, the difference in their arrival times; S32. The first wave energy of each sensor is obtained by integrating the square of the waveform amplitude within a fixed time window after the arrival of the first wave: (5) In the formula, E i Let be the initial energy of the i-th sensor; sᵢ(t) be the waveform signal of the i-th sensor; t represents time; t i T represents the arrival time of the first wave from the i-th sensor; w The fixed integration time window is the length taken after the arrival of the first wave, and the integration interval is [t]. i ,t i +T w The first wave energy is obtained by integrating the square of the waveform amplitude within this time window. The energy logarithm ratio is used as a characteristic of the relative energy attenuation between sensor pairs: (6) in This represents the relative energy decay characteristics between sensor pairs (i, j). E i With E j The first wave energies of sensor i and sensor j obtained from equation (5) are respectively. S33. Combining the arrival time difference and relative energy attenuation, define the physical edge feature vector connecting node i and node j: (7) In the formula: e ij ∆t is the physical edge feature vector connecting node i and node j. ij Let be the time difference between the first wave arrivals of sensor i and sensor j, where i is the receiving node and j is the source node; The relative energy decay characteristics between sensor pairs (i, j) obtained from equation (6); The superscript T denotes the vector transpose, i.e., e ij The arrival time difference ∆t ij With relative energy decay A two-dimensional column vector consisting of two physical quantities.

5. The method for assessing and locating the damage level of acoustic emission sources based on physical constraint graph convolutional networks according to claim 4, characterized in that: Step four specifically involves: S41, Source node features With edge features Projected onto the latent feature space of the same dimension respectively: （8） In the formula, h j e is the feature vector of the input node of the source node j; ij W represents the physical edge feature vector connecting node i and node j. h With W e Here is the corresponding linear projection weight matrix; ĥ j For the latent features of the source node after projection, ê ij This is projected onto the edge features, which share the same dimension as the node features. S42. Using edge features as additive biases, perform physical propagation compensation on the source node features: （9） In the formula, ĥ j→i The characteristics of the data transmitted from source node j to target node i after physical propagation compensation; ĥ j With ê ij The projected source node features and projected physical edge features are obtained from equation (8), respectively. The edge features apply physical propagation compensation to the source node features in the form of additive bias. Compensated features Represents the theoretical arrival characteristics predicted by the positive physics model; S43. Integrate the compensation features with the inherent observation features of the target node. splicing The multilayer perceptron generates physical perception messages, forcing the network to learn the deviation between the observed values ​​and the predictions of the physical model: （10） In the formula, m ij This refers to the physical sensing message transmitted from source node j to target node i; MLP msg (·) represents a multilayer perceptron for message generation; [·‖·] denotes vector concatenation operation; h i The observed features of target node i itself; ĥ j→i The theoretical arrival characteristics obtained from equation (9) after physical propagation compensation; S44, The target node aggregates its local neighborhood. All physical sensing messages are processed and a nonlinear transformation is applied to complete the node state update: （11） In the formula, h i ′ represents the updated feature of node i; N(i) is the set of neighboring nodes of node i, and j is a neighboring node in this set; m ij The physical sensing message is obtained from equation (10); ReLU(·) is the modified linear unit activation function; S45. Input the updated node feature matrix H into the Transformer encoder, and generate the query matrix Q, key matrix K, and value matrix V through linear transformation: （12） In the formula, H is the node feature matrix composed of the stacked features updated by each node; W Q W K W V Let Q, K, and V be the learnable linear transformation weight matrices that generate the query matrix, key matrix, and value matrix, respectively; Q, K, and V are the query matrix, key matrix, and value matrix, respectively. Calculate multi-head self-attention: （13） In the formula, Attention(Q, K, V) is the self-attention output; Q, K, and V are the query matrix, key matrix, and value matrix, respectively; K T is the transpose of the key matrix; Softmax(·) is the normalized exponential function; The dimension of the key vector is used to scale the dot product result to avoid gradient vanishing. S46. After the feature matrix is ​​fused by a multi-layer Transformer encoder, global average pooling is applied to compress the features of N nodes into a graph-level global feature vector containing global spatiotemporal correlations: （14） In the formula, z global is the graph-level global feature vector obtained by global average pooling; hᵢ is the i-th node feature output by the last layer encoder; and N is the total number of sensors.

6. The method for assessing and locating the damage level of acoustic emission sources based on physical constraint graph convolutional networks according to claim 5, characterized in that: Step five specifically involves: S51. The localization regression branch uses a multilayer perceptron to achieve a nonlinear mapping from global features to sound source coordinates, outputting predicted coordinates (x̂, ŷ). A Smooth L1 loss is employed to enhance robustness against noise and anomalous samples. （15） In the formula, L reg The L1 loss function is used for localization regression; SmoothL1(·) is the smoothing L1 loss function. and These represent the sound source coordinate vectors predicted by the model and the actual sound source coordinate vectors, respectively. S52. The damage severity classification branch predicts the damage severity category using a multilayer perceptron parallel to the regression branch. It employs cross-entropy loss to impose discriminative constraints on the shared feature space, guiding the encoder to learn essential difference representations related to different damage mechanisms. （16） In the formula, L cls Cross-entropy loss for classifying damage severity; C is the total number of damage severity categories. In this invention, C=2, corresponding to mild and severe damage severity, respectively. One-hot encoding for the real label; Predict the probability that a sample belongs to class c for the model; S53. Combine the regression loss and classification loss in a weighted manner to form the overall objective function: （17） In the formula, L total The overall objective function for a single sample; L reg L is the localization regression loss obtained from equation (15); cls The damage level classification loss is obtained from equation (16); λ is the balancing coefficient, used to adjust the gradient contributions of the two tasks during backpropagation; The spatial coordinates and damage level category of the acoustic emission source are output synchronously using the overall objective function.

7. The method for assessing and locating the damage level of acoustic emission sources based on physical constraint graph convolutional networks according to claim 6, characterized in that: In step one, the sparse sensor array has four sensors, which are arranged in the four corner regions of the CFRP board; the total number of reflected waves K per channel is 7, that is, the wave packet sequence length is fixed at 8.

8. The method for assessing and locating the damage level of acoustic emission sources based on physical constraint graph convolutional networks according to claim 7, characterized in that: The Edge-GCN edge-conditional graph convolutional module contains two edge-conditional graph convolutional layers, with the output dimensions of the two layers remaining consistent to avoid loss of key physical geometric information; the Transformer encoder contains two stacked encoding layers, employing a 4-head self-attention mechanism, with a hidden layer dimension of 64.

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