A wave damage positioning method for carbon fiber reinforced polymer composite structure

Abstract

This invention discloses a wave damage localization method for carbon fiber reinforced polymer composite structures, relating to the field of damage localization technology, and includes the following steps: Step 1: Complete labeling and spatial hierarchical grouping, and construct dataset x i Step 1: Add binary classification labels to the data in the dataset; Step 2: Construct a path classification model and a distance regression model; First, perform Bayesian optimization of the hyperparameters of the path classification model, and then perform five-fold cross-validation and model deployment and training; Then, based on the optimal hyperparameters of the path classification model, perform Bayesian optimization of the hyperparameters of the distance regression model, and then perform five-fold cross-validation and model deployment and training; Step 3: Perform multi-path damage localization based on the results of the path classification model and the distance regression model, and obtain the predicted coordinates and localization error of the damage point. The method of this invention can improve the interpretability and adaptability of the Lamb wave damage localization process of composite materials.

Description

Technical Field

[0001] This invention relates to the field of damage localization technology, and in particular to a wave damage localization method for carbon fiber reinforced polymer composite structures. Background Technology

[0002] Carbon fiber reinforced polymer (CFRP) composites, due to their lightweight, high strength, and corrosion resistance, have been used in load-bearing structures in aerospace, rail transportation, energy, and marine engineering. However, in actual service, impact, fatigue, and environmental coupling can easily induce damage such as delamination, debonding, and matrix cracking, which are difficult to identify visually in a timely manner. Structural health monitoring technology can provide condition awareness for in-service structures. Among these technologies, Lamb guided wave detection based on piezoelectric sensor networks has become a commonly used method for damage identification and localization in composite materials due to its sensitivity to internal damage. However, guided waves in anisotropic CFRP plates exhibit multimodal strong dispersion propagation, and damage scattering echoes exhibit transient and time-frequency localization characteristics, easily overwhelmed by boundary reflections and mode transitions. Fixed time-frequency front-ends and artificial features are insufficient for consistently extracting damage characteristics. Furthermore, in actual damage detection and localization, the sensitivity of different paths in the sensor network to damage varies significantly. Paths far from the damage or blocked by the wave field carry weak effective damage information. If all of them are included in the inversion without screening, significant noise will be introduced. The information of a single path is not enough to uniquely determine the damage location. The features it carries can only constrain the shortest distance from the damage to the path, corresponding to an equidistant curve on the board, but cannot accurately locate the damage location.

[0003] In summary, the existing technology still has the following technical problems: Problem 1: Traditional CWT front-ends struggle to adaptively extract specific time-frequency features under different damage conditions. Fixed wavelet parameters cannot adapt when damage type, damage location, or propagation path changes. Problem 2: Standard ResNet is prone to overfitting for small sample data. Furthermore, only a small number of frequency bands truly carry damage information in the time-frequency features, meaning that allowing all channels to contribute equally is hampered by noise. Problem 3: Lamb wave damage scattering exhibits multi-scale time-frequency features. Using ResNet's deep feature loss alone results in fine-grained time-frequency localization, while using shallow features alone lacks semantic discrimination capabilities, limiting both classification and regression tasks. Problem 4: The number of damage conditions in actual test data is inherently limited. The identification difficulty varies significantly between damage at the plate center and edge, and between different proportions of positive sample paths. Random five-fold analysis can easily result in damage concentrated almost entirely at the plate center in one fold and concentrated at the edge in another, leading to large inter-fold variance and distorted average indicators. Moreover, damage paths are strongly correlated with damage conditions; distributing multiple paths to the same damage point across different datasets will result in severe data leakage. Question 5: In actual measurements, most paths in the path signals generated by the sensor network carry almost no damage information. If all of them are used for damage localization, they will severely skew the prediction results as noise. At the same time, directly regressing damage coordinates from the original signal end-to-end is highly unconstrained under small sample conditions, prone to overfitting, and the physical meaning is ambiguous. Question 6: Direct coordinate regression methods tend to regress to the centroid of the training set, discarding known point-to-line segment geometric relationships, lacking path-level geometric supervision, resulting in insufficient interpretability of path contributions.

[0004] The above content is only used to help understand the technical solution of the present invention and does not represent an admission that the above content is prior art. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by proposing a wave damage localization method for carbon fiber reinforced polymer composite structures. This method decomposes the damage localization process into stages such as path selection, feature learning, path distance regression, and geometric coordinate recovery. It can utilize path-level physical information and learnable time-frequency features under sparse sensing conditions to improve the interpretability and adaptability of the Lamb wave damage localization process for composite materials.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A wave damage localization method for carbon fiber reinforced polymer composite structures includes the following steps: Step 1: Complete labeling and spatial hierarchical grouping, and construct dataset x. i And add binary classification labels to the data in the dataset; Step 2: Construct a path classification model and a distance regression model; First, perform Bayesian optimization of the hyperparameters of the path classification model, and then perform five-fold cross-validation and model deployment and training; Then, based on the optimal hyperparameters and optimal model of the path classification model, perform Bayesian optimization of the hyperparameters of the distance regression model, and then perform five-fold cross-validation and model deployment and training. Step 3: Based on the results of the path classification model and the distance regression model, perform multipath damage localization to obtain the predicted coordinates and localization error of the damage point.

[0007] Furthermore, in step 2, both the path classification model and the distance regression model include a sequentially connected CWConv network and a lightweight multi-scale feature fusion network. The CWConv network is used to extract physically interpretable time-frequency features from the damage-related scattering signals. The lightweight multi-scale feature fusion network consists of an improved ResNet-18 backbone network and an FPN-PAN network. The improved ResNet-18 backbone network uses a DW-SE-BasicBlock module as its BasicBlock module. The FPN-PAN network of the path classification model is connected to the classification head, and the FPN-PAN network of the distance regression model is connected to the regression head.

[0008] Furthermore, in step 2, the CWConv network extracts time-frequency features, including the following steps: Step A01: Obtain the sampled one-dimensional vibration or acoustic signal sequence x(t); Step A02: Construct the traditional continuous wavelet transform form as the theoretical basis, as follows: ; Where m is the translation parameter, α is the scaling parameter, ξ() is the complex Morse mother wavelet function, and ξ* is the complex conjugate; Step A03: For the k-th convolution kernel, set the translation parameter m of the complex Morse wavelet. k and scale parameter α k The current convolution kernel is generated by the mother wavelet. Performing a sliding inner product between x(t) and the current convolution kernel yields the local response under this scale and translation condition, as follows: ; Step A04: Calculate the gradient of the parameters using the chain rule, as follows: ; Where, m k α k These are the translation parameters and scale parameters of the k-th convolutional kernel, respectively. , mk α k The loss gradient, z k h k This represents the intermediate activation value of the k-th convolutional kernel; Step A05: Subtract the product of gradient δ and learning rate η from the current value, as follows: ; Step A06: After training is completed, the output of the CWConv network is the time-frequency feature learned by data-driven learning, and its frequency band and time localization capabilities are jointly constrained by the task objective.

[0009] Furthermore, in step 2, the DW-SE-BasicBlocks module includes depthwise separable convolution and SE channel attention.

[0010] Furthermore, in step 2, the depthwise separable convolution includes the following steps: Step B01: Obtain input data X∈R^{C in ×H×W}, where C in H represents the number of input channels, and H and W represent the spatial or time-frequency feature map dimensions. Step B02: Perform depthwise convolution, using a k×k convolution kernel for each input channel to extract local spatial features; Step B03: Perform pointwise convolution, using 1×1 convolution to linearly combine the output of depthwise convolution in the channel dimension to achieve cross-channel information fusion and obtain Cout output channels.

[0011] Furthermore, in step 2, the SE attention mechanism includes the following steps: Step C01: Perform global average pooling on the feature map to obtain the global average pooling description for each channel, as shown in the following formula: ; Among them, z c This describes the global average pooling for the c-th channel. This is the feature map of the c-th channel; Step C02: Generate channel weights s through two layers of fully connected mapping and activation functions. c The formula is as follows: ; in, For the sigmoid function, W1 and W2 are non-linear activation functions, and W1 and W2 are the weights of the two fully connected layers in the SE attention mechanism. Step C03: Multiply the weights back to the corresponding channels, using the following formula: ; Step C04: Add the features recalibrated by the SE attention mechanism to the residual branch, and then pass them through the activation function to obtain the output Y.

[0012] Furthermore, in step 2, the FPN-PAN network includes the following steps: Step D01: Obtain the multi-scale features C2, C3, and C4 output from different stages of the improved ResNet-18 backbone network; Step D02: Apply lateral 1×1 convolution to C2, C3, and C4 respectively to give the features of different levels a unified channel dimension; Step D03: Perform top-down fusion using FPN, upsampling high-level features to the size of adjacent low-level features and adding them to the low-level lateral features to obtain the fused feature F. i The formula is as follows: ; Among them, F i The features of the i-th layer after top-down fusion of FPN are... It is a 1×1 convolution, and Up(·) is an upsampling operation; Step D04: Perform bottom-up PAN fusion, downsample the lower-level fused features and add them to the adjacent higher-level features, then perform smoothing and local fusion through 3×3 convolution to obtain the enhanced feature P. i The formula is as follows: ; Among them, P i This represents the output characteristics of the i-th layer after bottom-up enhancement of PAN. It is a 3×3 convolution, and Down(·) is a downsampling operation; Step D05: Output P2, P3, and P4, respectively retaining semantic information, local structural information, and cross-scale fusion information at different resolutions.

[0013] Furthermore, in step 2, the Bayesian optimization of the hyperparameters of the path classification model and the Bayesian optimization of the hyperparameters of the distance regression model are performed through a two-stage cascaded learning process with feature transfer, including the following steps: Step E01: Define the search space and evaluation objective. The inputs are the training set, validation set, model structure, and hyperparameter space A. The output is the hyperparameter combination that performs best on the validation set, as shown in the following formula: ; Where a(t) is the acquisition function, used to evaluate whether the hyperparameter combination t is worth calculating; Step E02: Construct a tree-structured Parzen estimator. The tree-structured Parzen estimator divides the historical trials into better and worse regions according to a threshold q*, and estimates the conditional density, as shown in the following formula: ; ; ; Where a is the combination of hyperparameters in a single trial, q is the validation set evaluation value of a single trial, and l(a) and g(a) are the conditional density estimates corresponding to the better and worse regions in the tree-structured Parzen estimator. Step E03: Perform the Bayesian optimization phase search for the hyperparameters of the path classification model, inputting the classification training data, classification validation data, the complete model, and the search space A. cls After training each candidate combination for several rounds, a classification metric is calculated on the validation set, and trials with significantly poor performance are terminated early using a pruning strategy, as shown in the following formula: ; Where F1(a) is the validation set judgment criterion for this stage; Step E04: Output the optimal configuration for this stage, including the optimal hyperparameter a. cls * The corresponding model weights and the learned CWConv network parameters serve as the initialization source for the next stage; Step E05: Perform the Bayesian optimization phase search for the hyperparameters of the distance regression model, inputting the source model obtained in the previous phase, the regression training data, the regression validation data, and the search space A for this phase. reg In this stage, the CWConv network parameters are fixed, limiting the search scope to fine-tuning the hyperparameters, as shown in the following formula: ; Among them, R 2 (a) is the validation set judgment criterion for this stage; Step E06: Output the final model and hyperparameters, including the optimal fine-tuned hyperparameter a. reg * and the final distance regression model, used for subsequent testing or deployment.

[0014] Furthermore, step 3 includes the following steps: Step F01: Based on the path validity label S given by the path classification model, where S={0,1} is the binary classification result label, assign different weight coefficients w to it. i The formula is as follows: ; Step F02: Calculate the Euclidean distance t from any damage point (x, y) to the i-th line segment. i The formula is as follows: ; Among them, P i S iSensor coordinates; Step F03: Obtain the residual function J(x,y) by weighting, and realize the fusion of multi-path distance constraints, as shown in the following formula: ; Where K represents the K effective paths selected from group D for the same damage point. Geometric prediction value, This is the distance prediction value; Step F04: Use the L-BFGS-B algorithm to solve the residual function, complete the optimization solution with boundary constraints, and obtain the predicted coordinates. The formula is as follows: ; Where L is the size of the plate; Step F05: Calculate the positioning error e to complete the positioning error assessment. The formula is as follows: ; Where (x*, y*) are the true values ​​of the damage coordinates.

[0015] Compared with the prior art, the beneficial effects of this invention are as follows: 1. The shape parameters β and γ of the Morse wavelet are used as hyperparameters for Bayesian optimization. At the same time, the scale and translation parameters (α and m) are constructed into a learnable convolution so that the time-frequency features of the signal can be adaptively focused on the most sensitive A0 / S0 mode frequency band of the current dataset.

[0016] 2. Replace the standard 3×3 convolution with depthwise separable convolution to significantly compress the number of parameters and alleviate overfitting. Then, concatenate SE channel attention to automatically amplify sensitive frequency bands and suppress irrelevant channels.

[0017] 3. Add a feature pyramid network module for multi-scale feature fusion to the standard ResNet. Through bidirectional multi-scale fusion, the FPN transmits strong semantics from top to bottom and the PAN feeds back fine location information from bottom to top, so that the final features have both semantic abstraction ability and time-frequency localization accuracy.

[0018] 4. Using Group D (damage condition points) as the grouping unit and "spatial location type × positive sample ratio binning" as the hierarchical label, StratifiedGroupKFold is called to ensure that each fold is consistent in spatial distribution and sample difficulty while ensuring that the same damage point does not cross folds, thus providing a stable and reliable performance estimate.

[0019] 5. First, train the path classification model to obtain path labels carrying a large amount of damage information, and then assign different weights to them and transfer them to the distance regression model learning, which alleviates the fundamental contradiction of overfitting on small samples. It is divided into two stages, which can not only ensure that a robust damage feature representation is learned, but also transfer the backbone weight to the regression stage, so that the localization task can be carried out on a high signal-to-noise ratio subset.

[0020] 6. The task is broken down into distance regression and classical least squares geometric localization. Information from multiple paths is fused and weighted according to the signal-to-noise ratio. This preserves the model's learning ability and adds geometric constraints to enhance physical interpretability. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of a Lamb wave damage localization method for carbon fiber reinforced polymer composite structures; where (a) shows Labels and spatial hierarchical grouping, (b) shows two-stage transfer training, and (c) shows multi-path geometric coordinate localization. Figure 2 This is a schematic diagram of a CWConv network. Figure 3 The schematic diagram of the DW-SE-BasicBlocks module; Figure 4 This is a schematic diagram of the principle of depthwise separable convolution. Figure 5 This is a schematic diagram of the SE attention mechanism. Figure 6 This is a schematic diagram of an FPN-PAN network. Figure 7 Schematic diagram for Bayesian optimization; Figure 8 Ultrasonic guided wave propagation using PZT actuators and receivers; Figure 9 The signals are Lamb signals at different center frequencies; where (a) is the excitation signal at different frequencies and (b) is the received signal at different frequencies. Figure 10 This is a schematic diagram of the scattered signal; Figure 11 Optimize the history of Bayesian methods during the classification phase; Figure 12 Optimize the history for the Bayesian regression phase; Figure 13 Rank the importance of each hyperparameter in the classification stage; Figure 14 Rank the hyperparameters by importance during the regression phase; Figure 15 Sensitivity analysis of training hyperparameters for the classification stage; Figure 16Sensitivity analysis of training hyperparameters for the regression phase; Figure 17 Sensitivity analysis of cwconv parameters and training hyperparameters during the classification phase; Figure 18 Sensitivity analysis of cwconv parameters during the classification phase; Figure 19 A graph showing the multi-index threshold tradeoff analysis of the classification model; Figure 20 The confusion matrix is ​​the optimal one below. Figure 21 The training metric curve for the final model; Figure 22 The regression line represents the difference between the actual distance and the predicted distance. Figure 23 This represents the residual distribution during the regression phase. Figure 24 This is a diagram showing the comparison between the actual value and the predicted value. Figure 25 This is a schematic diagram showing the distribution of the final positioning error values. Detailed Implementation

[0022] 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 only some embodiments of the present invention, and not all embodiments.

[0023] Example 1: A wave damage localization method for carbon fiber reinforced polymer composite structures, referenced Figure 1 As shown, it includes the following steps: Step 1: Complete labeling and spatial hierarchical grouping, and construct dataset x. i And add binary classification labels to the data in the dataset.

[0024] In this embodiment, in step 1, the binary classification labels 0 and 1 represent whether the distance between the sensor path and the damage point exceeds a given threshold. If the distance is less than the threshold, the path is considered to be closer to the damage point and carries more damage information.

[0025] Step 2: Construct a path classification model and a distance regression model; First, perform Bayesian optimization of the hyperparameters of the path classification model, and then perform five-fold cross-validation and model deployment and training; Then, based on the optimal hyperparameters and optimal model of the path classification model, perform Bayesian optimization of the hyperparameters of the distance regression model, and then perform five-fold cross-validation and model deployment and training.

[0026] Directly regressing damage coordinates end-to-end from the original signal is highly unconstrained and prone to overfitting in small samples and complex wavefields, and it cannot identify invalid paths far from the damage—these paths contain almost no damage information and become systematic noise sources once directly entered into coordinate regression. Therefore, in this embodiment, step 2 constructs a path classification model (for damage identification) and a distance regression model (to allow the model that has already identified damage to learn to estimate distance). The purpose of these two stages is to break down this task into two sub-tasks: first, determine which paths carry damage information (classification), and then estimate how far the damage is from the path for credible paths (regression). Based on this, the following benefits are gained: 1. The classification task has clear boundaries and sufficient supervision, allowing general damage features to be learned in advance; after the classification features are extracted, they can be used as the initial weights for transfer learning in the regression stage, significantly saving samples and time compared to training from scratch, and significantly reducing the risk of overfitting in small sample regression. 2. Invalid paths with low signal-to-noise ratios are screened out before entering geometric inversion, avoiding their serious interference with the prediction results.

[0027] In this embodiment, in step 2, both the path classification model and the distance regression model include a sequentially connected CWConv network (continuous wavelet convolution) and a lightweight multi-scale feature fusion network. The CWConv network is used to extract physically interpretable time-frequency features from the damage-related scattering signals. The resolution of these time-frequency features can be adjusted by wavelet parameters and scale settings, thereby providing a unified input for subsequent processing. The lightweight multi-scale feature fusion network consists of an improved ResNet-18 backbone network and an FPN-PAN network. The improved ResNet-18 backbone network uses a DW-SE-BasicBlock module as its BasicBlock module. The FPN-PAN network of the path classification model is connected to the classification head, and the FPN-PAN network of the distance regression model is connected to the regression head.

[0028] Guided wave signals in composite material structures are inherently dispersive and contain complex wave components. The presence of damage can cause scattering, attenuation, and local waveform distortion. Therefore, an effective front-end module is needed to simultaneously preserve time-domain and frequency-domain information before high-level feature extraction. Traditional methods typically use continuous wavelet transform (CWT) as an offline preprocessing step, where the one-dimensional guided wave signal is first converted into a two-dimensional time-frequency representation, which is then input into a backbone network based on a convolutional neural network (CNN).

[0029] In this embodiment, the core function of the CWConv network in step 2 is to embed the interpretable time-frequency analysis concept from continuous wavelet transform into the convolutional layer. Traditional continuous wavelet transform requires manual specification of parameters such as wavelet type, scale, and translation, which can affect time-frequency resolution and task adaptability. The CWConv network in this embodiment uses complex Morse wavelets as learnable convolutional kernels, allowing the translation and scale parameters of the wavelets to be updated through backpropagation. Each convolutional kernel corresponds to a time-frequency atom with temporal positioning and frequency selection characteristics, thus its response can characterize the local correlation of a signal at a specific time location and within a specific frequency band. In this way, the multi-channel features output by the CWConv network retain the physical meaning of wavelet analysis while automatically adjusting key wavelet parameters according to classification or regression objectives, thereby reducing reliance on manually specified continuous wavelet transform parameters and providing a more suitable data representation for subsequent lightweight multi-scale feature extraction and fusion modules.

[0030] In this embodiment, reference Figure 2 In step 2, the CWConv network extracts time-frequency features, including the following steps: Step A01: Obtain the sampled one-dimensional vibration or acoustic signal sequence x(t).

[0031] Step A02: Construct the traditional continuous wavelet transform form as the theoretical basis, as follows: ; Where m is the translation parameter, which controls the position of the wavelet on the time axis, α is the scaling parameter, which controls the degree of wavelet scaling, ξ() is the complex Morse mother wavelet function, and ξ* is the complex conjugate.

[0032] Step A03: For the k-th convolution kernel, set the translation parameter m of the complex Morse wavelet. k and scale parameter α k The current convolution kernel is generated by the mother wavelet. Performing a sliding inner product between x(t) and the current convolution kernel yields the local response under this scale and translation condition, as follows: .

[0033] In this embodiment, step A03 is to rewrite the k-th convolutional kernel transformation into a learnable convolutional kernel.

[0034] Step A04: Calculate the gradient of the parameters using the chain rule, as follows: ; Where, m k α k These are the translation parameters and scale parameters of the k-th convolutional kernel, respectively. , m k α k The loss gradient, z k h k This represents the intermediate activation value of the k-th convolutional kernel.

[0035] In this embodiment, step A04 is used to adaptively optimize the parameters through backpropagation.

[0036] Step A05: Subtract the product of gradient δ and learning rate η from the current value, as follows: .

[0037] In this embodiment, step A05 is used for the reverse update of wavelet parameters.

[0038] Step A06: After training is completed, the output of the CWConv network is the time-frequency feature learned by data-driven learning, and its frequency band and time localization capabilities are jointly constrained by the task objective.

[0039] In this embodiment, in step 2, after the time-frequency representation is generated by the CWConv network, a lightweight multi-scale feature fusion network is used to further extract and fuse damage-related features. This network includes two complementary sub-networks: an improved ResNet-18 backbone network equipped with DW-SE-BasicBlocks modules and an FPN-PAN network. The improved ResNet-18 backbone network extracts compact hierarchical features from the time-frequency input with higher channel selectivity and lower computational cost. The FPN-PAN network combines low-level spatial details with high-level semantic features through bidirectional cross-scale fusion, combining low-level features with rich local details with high-level features with stronger semantic information, providing a discriminative multi-scale representation for subsequent damage identification and localization tasks.

[0040] In this embodiment, reference Figure 3 In step 2, the DW-SE-BasicBlocks module includes depthwise separable convolutions and SE channel attention. Depthwise separable convolutions are used to reduce computational overhead, and SE channel attention is used to enhance channel feature representation.

[0041] The original BasicBlock in ResNet-18 consists of two standard 3×3 convolutional layers. While this structure has proven effective in general image recognition tasks, it can introduce unnecessary computational overhead when applied to the time-frequency representation of guided wave signals. Furthermore, damage-induced scattering responses often exhibit localized high-energy regions, requiring the backbone network to capture local patterns efficiently and selectively.

[0042] In this embodiment, the DW-SE-BasicBlocks module introduces depthwise separable convolution and SE channel attention into the residual framework of ResNetBasicBlock. Its goal is to reduce the number of convolution parameters and enhance the key channel feature response while preserving the ability to extract local features and the stability of residual training.

[0043] In this embodiment, reference Figure 4 In step 2, depthwise separable convolution includes the following steps: Step B01: Obtain input data X∈R^{C in ×H×W}, where C in H represents the number of input channels, and H and W represent the spatial or time-frequency feature map dimensions.

[0044] In this embodiment, the input data for step B01 is the output data of the CWConv network.

[0045] Step B02: Perform depthwise convolution, using a k×k convolution kernel (k is the side length of the convolution kernel) to extract local spatial features for each input channel. Channels are not mixed at this time.

[0046] In this embodiment, in step B02, depthwise convolution is performed, that is, convolution operation is performed independently on each channel of the input feature map to extract spatial features.

[0047] Step B03: Perform standard pointwise convolution, using 1×1 convolution to linearly combine the output of depthwise convolution in the channel dimension to achieve cross-channel information fusion and obtain Cout output channels.

[0048] In this embodiment, in step B03, a 1x1 convolution kernel is used to perform channel fusion on the output of depthwise convolution to extract channel features.

[0049] In this embodiment, the number of parameters is significantly reduced by decomposing the depthwise separable convolution, to approximately 1 / Cout + 1 / k2 of the standard convolution.

[0050]

[0051] In this embodiment, reference Figure 5 In step 2, the SE attention mechanism includes the following steps: Step C01: Perform global average pooling on the feature map to obtain the global average pooling description for each channel, as shown in the following formula: ; Among them, z cThis describes the global average pooling for the c-th channel. This is the feature map of the c-th channel.

[0052] In this embodiment, the feature map processed in step C01 is the result of depthwise separable convolution.

[0053] Step C02: Generate channel weights s through two layers of fully connected mapping and activation functions. c The formula is as follows: ; in, For the sigmoid function, W1 and W2 are the weights of the two fully connected layers in the SE attention mechanism, where W1 and W2 are non-linear activation functions, i.e., ReLU.

[0054] Step C03: Multiply the weights back to the corresponding channels, using the following formula: .

[0055] Step C04: Add the features recalibrated by the SE attention mechanism to the residual branch, and then pass them through the activation function to obtain the output Y.

[0056] In this embodiment, although DW-SE-BasicBlock improves the efficiency and selectivity of feature extraction, a single network stage is still insufficient to represent damage-related patterns. In guided wave detection, the scattering response is simultaneously affected by damage size, damage location, and boundary reflection, causing useful information to appear at different spatial and frequency scales. Therefore, a multi-scale fusion structure is needed to integrate features from different levels of the backbone network.

[0057] In this embodiment, the FPN-PAN network receives multi-scale features output from different stages of the improved ResNet-18 backbone network, supplements high-level semantic information through a top-down path, and enhances low-level localization information and fine-grained structural representation through a bottom-up path. This structure enables features of different resolutions to complement each other, thereby improving the ability of subsequent classification or regression tasks to perceive multi-scale fault modes.

[0058] In this embodiment, reference Figure 6 In step 2, the FPN-PAN network includes the following steps: Step D01: Obtain the multi-scale features C2, C3, and C4 from different stages of the improved ResNet-18 backbone network. These three features have different spatial resolutions and semantic levels.

[0059] Step D02: Apply lateral 1×1 convolution to C2, C3, and C4 respectively to give the features of different levels a unified channel dimension.

[0060] Step D03: Perform top-down fusion using FPN, upsampling high-level features to the size of adjacent low-level features and adding them to the low-level lateral features to obtain the fused feature F. i The formula is as follows: ; Among them, F i The features of the i-th layer after top-down fusion of FPN are... 1×1 convolution is used for channel alignment and dimensionality reduction, and Up(·) is an upsampling operation used to amplify high-level features to low-level resolution.

[0061] Step D04: Perform bottom-up PAN fusion, downsample the lower-level fused features and add them to the adjacent higher-level features, then perform smoothing and local fusion through 3×3 convolution to obtain the enhanced feature P. i The formula is as follows: ; Among them, P i This represents the output characteristics of the i-th layer after bottom-up enhancement of PAN. The 3×3 convolution is used for local smoothing and feature extraction after fusion. Down(·) is a downsampling operation used to compress low-level features to high-level resolution.

[0062] Step D05: Output P2, P3, and P4, retaining semantic information, local structural information, and cross-scale fusion information at different resolutions, respectively. Subsequent prediction heads can then be input.

[0063] In this embodiment, in step 2, the Bayesian optimization of hyperparameters of the path classification model and the Bayesian optimization of hyperparameters of the distance regression model are performed through a two-stage cascaded learning with feature transfer. In the Bayesian optimization stage of the path classification model, the training hyperparameters and parameters related to the CWConv network are searched to obtain a more stable feature extractor. In the Bayesian optimization stage of the distance regression model, the path classification model is used as the source model, the CWConv network parameters are fixed, and only the hyperparameters are searched and fine-tuned.

[0064] In this embodiment, the above design reduces the search space of the second stage, decreases the complexity of the joint search, and reduces the disturbance of the second stage to the underlying time-frequency representation.

[0065] In this embodiment, reference Figure 7 As shown in Table 1, step 2, the two-stage cascaded learning with feature transfer includes the following steps: Step E01: Define the search space and evaluation objective. The inputs are the training set, validation set, model structure, and hyperparameter space A. The output is the hyperparameter combination that performs best on the validation set, as shown in the following formula: .

[0066] Step E02: Construct a tree-structured Parzen estimator. The tree-structured Parzen estimator divides the historical trials into better and worse regions according to a threshold q*, and estimates the conditional density, as shown in the following formula: ; ; ; Where a is the combination of hyperparameters in a single trial, q is the validation set evaluation value of a single trial, and l(a) and g(a) are the conditional density estimates corresponding to the better and worse regions in the tree-structured Parzen estimator.

[0067] Step E03: Perform the Bayesian optimization phase search for the hyperparameters of the path classification model, inputting the classification training data, classification validation data, the complete model, and the search space A. cls After training each candidate combination for several rounds, a classification metric is calculated on the validation set, and trials with significantly poor performance are terminated early using a pruning strategy, as shown in the following formula: ; F1(a) is the validation set judgment criterion for this stage.

[0068] Step E04: Output the optimal configuration for this stage, including the optimal hyperparameter a. cls * The corresponding model weights and the learned CWConv network parameters serve as the initialization source for the next stage.

[0069] Step E05: Perform the Bayesian optimization phase search for the hyperparameters of the distance regression model, inputting the source model obtained in the previous phase, the regression training data, the regression validation data, and the search space A for this phase. reg In this stage, the CWConv network parameters are fixed, limiting the search scope to fine-tuning the hyperparameters, as shown in the following formula: ; Among them, R 2 (a) is the validation set judgment criterion for this stage.

[0070] Step E06: Output the final model and hyperparameters, including the optimal fine-tuned hyperparameter a. reg * and the final distance regression model, used for subsequent testing or deployment.

[0071] Table 1. Search space of hyperparameters for Bayesian optimization of two-stage networks.

[0072] In this embodiment, in step 2, for the five-fold cross-validation and path classification model, the obtained optimal hyperparameters are used to perform a full version of Stratified-GroupKFold five-fold training. Each fold is trained from zero for a full number of epochs. The model is grouped by D groups (D groups are grouped according to the damage point D (containing 56 paths), ensuring all paths of each D are in one dataset; and stratified according to the distance of the damage point D from the center of the board, ensuring that a dataset contains both edge and center cases). The best_epoch and all classification metrics for each fold are recorded. The purpose is to confirm that the hyperparameters remain stable under normal training and to provide a reliable performance estimate of the variance. For the distance regression model, the five-fold cross-validation is reloaded and initialized from the classification backbone, and fine-tuned by grouping according to differentiated learning rates. Regarding the training method, for the path classification model, all layers are trained with full gradients from random initialization, the learning rate is a single base learning rate for the entire network, and the loss function is the BCE loss function. For the distance regression model, the model is reloaded and initialized from the classification backbone, fine-tuned by grouping according to differentiated learning rates, and the loss function is the MSE loss function.

[0073] In this embodiment, in step 2, the path classification model has the following impact on the distance regression model: 1. The path classification model has determined the parameters of DW-SE, FPN-PAN, and CWConv. The distance regression model directly inherits these structural switches and no longer searches for them. Therefore, its search dimension is greatly reduced, saving computing power and maintaining architectural consistency.

[0074] 2. The stability of the five-fold cross-validation in the path classification model determines the degree of adjustment for hyperparameter optimization in the distance regression model. If the path classification model has small inter-fold variance and a stable feature extractor, the backbone fine-tuning range can be widened and the upper limit of BACKBONE_LR_RATIO can be increased during hyperparameter optimization in the distance regression model; conversely, backbone fine-tuning should be tightened to protect existing features. The five-fold cross-validation in the path classification model also indirectly predicts the number of training epochs required for feature learning, which can be used as a reference to determine the number of training epochs in the regression phase.

[0075] 3. The weights of the path classification model determine the initial values ​​of the distance regression model's parameters and the differential learning rate grouping. This affects the Bayesian hyperparameter optimization of the distance regression model, the five-fold cross-validation of transfer learning, each trial and fold during training and deployment, and ultimately, the parameter initialization and optimizer grouping of the model. This is the most direct and critical impact of the path classification model on the distance regression model, specifically manifested on two levels: (1) Parameter initialization: CWConv, ResNet backbone, and FPN-PAN of the path regression model all inherit the weights of the classification stage. Only RegressionHeadWithGeom (regression head) is newly trained. This means that the path regression model has the ability to identify the time-frequency features of damage scattering from the beginning. It only needs to learn the new mapping of "damage features → distance".

[0076] (2) Differential Learning Rates: The learning rates for the path regression model must be grouped hierarchically, with each group trained using a different learning rate, rather than the entire network sharing a single learning rate. In the path classification model, the backbone represents different weights at different levels, i.e., the BACKBONE_LR_RATIO for regression optimization. Shallow backbones have already learned general waveform features and only require fine-tuning, so their learning rates should be small; newly added regression heads have completely random initial parameters, so their learning rates should be large. If the path classification model's training results are poor, the entire set of differential learning rates loses its basis and degenerates into a single learning rate, leading to a significant drop in regression performance.

[0077] Step 3: Based on the results of the path classification model and the distance regression model, perform multipath damage localization to obtain the predicted coordinates and localization error of the damage point.

[0078] Distance observation along a single path can only constrain the damage to an equidistant curve on the board with the path segments as its skeleton, failing to provide a unique location. Furthermore, allowing the neural network to directly regress coordinates would require relearning known point-to-line segment geometric relationships, wasting capacity and becoming contaminated by small sample errors. Therefore, in this embodiment, step 3, multi-path geometric constraint, utilizes multi-view observations from the sensor network to fuse multi-path information using closed geometric relationships, obtaining a unique and noise-resistant coordinate solution.

[0079] In this embodiment, step 3 includes the following steps: Step F01: Based on the path validity label S given by the path classification model, where S={0,1} is the binary classification result label, assign different weight coefficients w to it. i The formula is as follows: .

[0080] In this embodiment, the label in step F01 is obtained by the path classification model.

[0081] Step F02: Calculate the Euclidean distance t from any damage point (x, y) to the i-th line segment. i The formula is as follows: ; Among them, P i Si For sensor coordinates, the clip operation ensures that "if the line segment is outside the line segment, the endpoint is taken".

[0082] Step F03: Obtain the residual function J(x,y) by weighting, and realize the fusion of multi-path distance constraints, as shown in the following formula: ; Where K represents the K effective paths selected from group D for the same damage point. Geometric prediction value, This is the distance prediction value.

[0083] In this embodiment, in step F03, the distance prediction value Obtained from the path regression model.

[0084] In this embodiment, in step 3, the geometric prediction value is adjusted by adjusting the predicted value (x,y) to... and distance prediction values The goal is to minimize the residual, i.e., to find a (x,y) such that its geometric distance to each path is as close as possible to the predicted distance.

[0085] Step F04: Use the L-BFGS-B algorithm to solve the residual function, complete the optimization solution with boundary constraints, and obtain the predicted coordinates. The formula is as follows: ; Where L is the size of the plate.

[0086] Step F05: Calculate the positioning error e to complete the positioning error assessment. The formula is as follows: ; Where (x*, y*) are the true values ​​of the damage coordinates.

[0087] In this embodiment, step 3 achieves the following effects: by using least squares, multiple equidistant curves intersect at a single point, and multi-view observation converges the multiple solutions of a single view to a unique solution, which is physically interpretable; the precise geometric relationship of the distance from a point to a line segment is directly incorporated into the objective function, so the training model does not need to learn geometry and focuses more on wave field characteristics; when the distance prediction of individual paths is biased, it can be averaged by the geometric constraints of other paths, and the impact of single-point errors is small.

[0088] This embodiment presents a wave damage localization method for carbon fiber reinforced polymer composite structures, addressing the problems existing in the prior art: For problem 1: The shape parameters β and γ of the Morse wavelet are used as hyperparameters for Bayesian optimization. At the same time, the scale and translation parameters (α and m) are constructed into a learnable convolution so that the time-frequency features of the signal can be adaptively focused on the most sensitive A0 / S0 mode frequency band of the current dataset.

[0089] To address issue 2: replace the standard 3×3 convolution with depthwise separable convolution to significantly compress the number of parameters and alleviate overfitting, and then concatenate SE channel attention to automatically amplify sensitive frequency bands and suppress irrelevant channels.

[0090] To address issue 3: A feature pyramid network module for multi-scale feature fusion is added to the standard ResNet. Through bidirectional multi-scale fusion, strong semantics are passed down from top to bottom by FPN and fine location information is fed back from bottom to top by PAN, so that the final features have both semantic abstraction capabilities and time-frequency localization accuracy.

[0091] Regarding question 4: Using Group D (Group D refers to the damage condition, i.e., the location of the damage, which is a group consisting of 56 paths) as the grouping unit and "spatial location type × positive sample ratio binning" as the hierarchical label, StratifiedGroupKFold is called to ensure that each fold is consistent in spatial distribution and sample difficulty while ensuring that the same damage point does not cross folds, thus providing a stable and reliable performance estimate.

[0092] Regarding question 5: First, a path classification model is trained to obtain path labels carrying a large amount of damage information. Then, different weights are assigned to them and transferred to the distance regression model learning, which alleviates the fundamental contradiction of overfitting with small samples. It is divided into two stages, which can ensure that a robust damage feature representation is learned, and the backbone weights can be transferred to the regression stage, allowing the localization task to be performed on a high signal-to-noise ratio subset.

[0093] To address question 6: the task is broken down into distance regression and classical least squares geometric localization. Information from multiple paths is fused and weighted according to the signal-to-noise ratio, which preserves the model's learning ability and adds geometric constraints to enhance physical interpretability.

[0094] Verification Implementation Examples To verify the effectiveness of the method in Example 1, the following specific examples were conducted: 1. Obtaining the dataset through waveguide experiments The specimen was a CFRP plate with dimensions of 500×500×1.2 mm and a symmetrical ply density of [45 / -45 / 0 / 90]s. Eight piezoelectric sensors were arranged along the boundary of a central 300 mm × 300 mm square region, defined as the damage monitoring area. The experimental system consisted of a Tektronix arbitrary waveform generator, a PZT array, and an acquisition system. The excitation signal generated by the arbitrary waveform generator was applied to a selected PZT exciter, and the resulting guided wave propagated in the composite plate and was recorded by the remaining PZT receivers. Before acquisition, the received signal was amplified with a 40 dB gain to enhance the detectability of weakly scattered wave components. The amplified response was then collected by a DS-8B acoustic emission acquisition system and transmitted to a computer for further processing.

[0095] The excitation signal applied to the actuator must generate a wave field with concentrated frequency components and pure modal composition, while avoiding severe dispersion and multimodal aliasing. A sinusoidal tone pulse modulated by a 5-cycle Hanning window is used as the excitation source, and its waveform is as follows: ; Among them, f c Where is the center frequency, and N is the number of modulation cycles.

[0096] To determine the center frequency of the excitation frequency, subsequent experiments used... Figure 8 The transmission and reception configuration shown is as follows. Two piezoelectric sensors (PZTs) are used to form a sensing path, with one PZT acting as an actuator to excite the guided wave, and the other acting as a sensor to record the received signal. Figure 9 Displays a range of center frequencies f covering the selected 100-350kHz range. c As shown in the figure, the modes are purest when the center frequency is 150kHz, thus avoiding interference caused by mode superposition and facilitating the extraction of monitoring information.

[0097] After determining the excitation parameters, the guided wave experiment was formally conducted. During signal acquisition, each sensor was selected sequentially as the exciter, and the remaining PZTs acted as receivers. In this way, the eight PZT networks formed 8×7=56 directed excitation-receiver paths. The directed path configuration was retained because the Lamb wave response in the anisotropic CFRP structure varies with the propagation direction. This direction dependence affects wave velocity, attenuation, and scattering behavior. Therefore, each directed excitation-receiver pair was considered an independent path-level signal channel.

[0098] Ninety damage conditions were specified within a 300mm × 300mm monitoring area. Considering the significant multipath propagation and boundary reflection in anisotropic composite structures, both healthy and damaged state responses were acquired. (Reference) Figure 10 As shown, the scattered signals are then obtained by subtracting the healthy state response from the corresponding damaged state response. These scattered signals highlight the damage-induced fluctuation component and provide more discriminative information for damage determination and localization. For each path-level sample, its supervision label is generated by the geometric relationship between the sensing path and the damage center. The formula for calculating the shortest Euclidean distance from the damage center to the path segment is as follows: ; Among them, the j-th directed path is generated by exciter S. a (x a ,y a ) and receiver S b (x b ,yb The damage is defined as D(x) d ,y d Geometric distance value It is used in both the path-level binary classification stage and the subsequent distance regression stage. In the classification stage, this distance is used to define the binary label. In the regression stage, it serves as a continuous objective to learn the mapping between the path response and the distance from the sensing path to the lesion center.

[0099] For each damage condition, responses from all 56 directed sensing paths are extracted, resulting in 90 × 56 = 5040 path-level samples. This data organization preserves the physical association between each damage location and the corresponding multipath Lamb wave response. Unlike treating all path signals as single, unrelated samples, the dataset is constructed at the damage condition level, where the 56 path responses associated with the same damage condition collectively describe the interaction between the damage and the sensing network. Therefore, the dataset partitioning is also performed at the damage condition level rather than the single path level. This grouping strategy prevents highly correlated path responses from the same damage location from appearing in different subsets. Furthermore, spatial stratification is introduced at the grouping level to account for the differences between central and peripheral damage locations, thus maintaining a balanced spatial distribution of damage conditions in each fold. A stratified grouped five-fold cross-validation strategy is used to evaluate the reliability of the mean performance and variation of the proposed model. The spatially stratified samples are divided into five subsets with similar spatial coverage. In each fold, four subsets are used for model training, and the remaining subset is used for evaluation; the final performance is reported as the average of the five folds. This strategy reduces the reliance of the evaluation results on a single partition and provides a more stable assessment of the model's generalization ability across different damage locations.

[0100] 2. Results Analysis 2.1 Analysis of Ablation Test Results of Model Components To evaluate the contributions of each component in the proposed framework, a series of ablation studies were conducted. Specifically, three key modules were considered: the multi-scale feature fusion structure (FPN-PAN), the lightweight channel enhancement unit (DW-SE), and the time-frequency feature extraction module (CWConv). Each module was removed or modified while maintaining the training protocol and data partitioning. Performance was then compared under the same evaluation metrics, and the results are summarized in Table 2. Overall, the complete model achieved the best performance across all metrics, indicating that the proposed components function in a complementary manner. A significant performance degradation was observed when the multi-scale fusion structure was removed, particularly in terms of F1-score and localization error. This suggests that the lack of cross-scale feature interaction limits the model's ability to simultaneously capture local details and global structural patterns in complex scattered wave signals. When the DW-SE module was removed, precision decreased slightly, while recall remained relatively stable. This indicates that the channel recalibration mechanism primarily improves feature discriminativity by suppressing false positives, with limited impact on detection sensitivity. Therefore, DW-SE plays a supporting role in feature refinement, rather than being the dominant contributing factor. Furthermore, removing the CWConv-based time-frequency representation leads to further performance degradation. This indicates that learning directly from the original signal is insufficient to capture the complex time-frequency characteristics of the scattered wave, and explicit time-frequency modeling is necessary for effective feature representation.

[0101] Table 2 Summary of Ablation Experiments

[0102] In summary, the multi-scale fusion structure plays a dominant role in capturing the cross-scale features of scattered wave signals, while DW-SE and CWConv provide complementary enhancements through feature refinement and representation transformation, respectively. The combined effect of these modules enables the model to learn robust and discriminative representations under complex signal conditions.

[0103] 2.2 Analysis of Hyperparameter Optimization Results Bayesian optimization (BO) was used for hyperparameter tuning in both stages. Compared to grid search and random search, BO has higher sample efficiency by constructing a probabilistic surrogate model of the target landscape. This embodiment uses a tree-structured Parzen estimator as the surrogate model. To reduce sampling bias, each candidate configuration was evaluated using five-fold cross-validation. The resulting cross-validation F1-score and R... 2 These serve as the objective functions to be maximized in the classification and regression phases, respectively. The optimal configurations obtained are listed in Table 3.

[0104] Table 3 Optimal hyperparameter configurations for the classification and regression phases

[0105] To further evaluate the effectiveness of the Bayesian optimization strategy, Figures 11-14 The optimization history and the corresponding importance ranking obtained through functional ANOVA are presented. During the classification phase ( Figure 11 The average cross-validation F1-score increased from 0.831 to 0.896 in the first eight trials, then stabilized, indicating rapid convergence of the search process. In contrast, the regression phase ( Figure 12 R showed greater variability between different trials, with R in the 4th trial. 2 It dropped significantly to approximately 0.893. Even so, the best R to date... 2 It continued to increase steadily, reaching 0.952 in the 13th trial.

[0106] Based on the above fANOVA importance ranking, sensitivity analysis was conducted to evaluate the interactive effects of dominant hyperparameters on positioning accuracy and optimization efficiency. Specifically, these representative couplings include the training hyperparameters in both stages and the structural hyperparameters of CWConv, such as... Figures 15-18 As shown.

[0107] During the classification phase, when the learning rate is between 1e -3 and 2e -3 A high F1 score region can be observed when the dropout probability is between 0.15 and 0.25, indicating that classification performance is jointly controlled by the optimization step size and regularization strength. Within this range, the network can effectively capture stable differences in guided wave packet morphology, energy distribution, and damage-induced scattering modes. In contrast, when the dropout probability exceeds approximately 0.35, the F1 score drops significantly, suggesting that excessive regularization suppresses useful discriminative features in the guided wave response. Compared to classification, the regression stage requires a more refined representation of the continuous changes in the guided wave response. These subtle features are primarily encoded in the deep backbone network layers inherited from the classification stage. Therefore, the backbone network fine-tuning strategy constitutes another factor affecting regression performance. When the learning rate is maintained at 1e... -3 up to 2e -3 Within the range, and when the backbone network learning rate ratio is between 0.50 and 0.70, R 2 The values ​​are relatively high. This distribution also confirms that regression performance depends on the fine-tuning step size and the adaptive strength of the backbone network transitioning from the classification stage.

[0108] Furthermore, the proposed framework uses the CWConv layer as the front-end feature extractor. The learnable wavelet parameters gamma and beta in this layer directly control the temporal-frequency resolution of the extracted features, and these two parameters are updated together with all other trainable parameters during backpropagation. Therefore, further analysis is needed to examine their interaction with the learning rate and the pairwise coupling between them.

[0109] η-γ0 response surface ( Figure 17 This indicates that when gamma is between 4 and 6 and the learning rate is approximately 1.5e... -3 up to 2e -3 At this point, classification performance improved, with the F1-score exceeding 0.89. This result indicates that the optimization step size must be coordinated with wavelet parameterization to ensure that the front-end representation remains well aligned with the damage-related transient guided wave response. Conversely, when gamma is below 4 or above 7, the F1-score drops below 0.86 regardless of the learning rate. This can be attributed to the wavelet scaling parameter determining the time-frequency resolution of the extracted features. β0-γ0 contour map ( Figure 18 This further demonstrates the significant coupled impact of wavelet parameterization on classification performance. High F1-scores are concentrated in the region with beta of 5 to 15 and gamma of 5 to 8. In contrast, the F1-score drops significantly when beta exceeds approximately 25 and gamma falls below 4. From a physical perspective, this combination broadens the wavelet kernel in the time domain and narrows its frequency bandwidth, thereby reducing sensitivity to short-term, broadband scattering events characteristic of local damage. This trend suggests that beta and gamma must be jointly tuned to maintain appropriate time-frequency resolution. A well-matched combination can better distinguish local wave packet distortion and frequency-dependent propagation behavior caused by damage, thus providing a more informative front-end representation for subsequent classification and regression stages.

[0110] Combined with the above network-level sensitivity analysis, these results confirm that the proposed multi-stage framework benefits from stage-specific and component-specific hyperparameter optimization, and the identified optimal configuration is used in all subsequent training and validation processes.

[0111] 2.3 Damage localization results based on experimental dataset The proposed framework comprises two tasks: injury-sensitive signal identification and injury localization; therefore, task-specific evaluation metrics are employed. Identification performance is assessed using classification metrics, including Accuracy, Precision, Recall, F1-score, and Area Under the Receiver Operating Characteristic (AUC). These metrics collectively characterize the accuracy of predictions and class balance. Localization performance is assessed using regression metrics, including Mean Absolute Error (MAE), Mean Squared Error (MSE), and Coefficient of Determination (R²). These metrics quantify the deviation between predicted injury coordinates and actual injury coordinates. The complete definitions of these metrics are summarized in Table 4.

[0112] Table 4. List of metrics used to evaluate the model

[0113] 2.3.1 Analysis of Classification Damage Detection Results A binary classification stage was introduced before localization to identify damage-sensitive paths, and the cross-validation results are summarized in Table 5. From the perspective of guided wave propagation, the high precision and AUC indicate that the responses of damage-sensitive and damage-insensitive paths are well separated in the learned feature space. This separation suggests that the network captures consistent damage-related variations in the signal, such as scattering, attenuation, and waveform distortion. Precision and recall provide complementary evidence for the reliability of the selected path set. The high precision indicates that most of the selected paths contain informative damage-related perturbations, which reduces the impact of irrelevant paths on the downstream regression stage. The high recall indicates that most informative paths are retained, which helps to maintain sufficient path constraints for localization. The F1-score further confirms the balance between path selection accuracy and path retention.

[0114] Table 5 Summary of classification performance under five-fold cross-validation

[0115] Based on cross-validation evaluation, the final classification model is retrained using the complete training dataset. To determine the classifier's operating point, a classification threshold is selected on the validation set, and the corresponding threshold-F1 curve is shown below. Figure 19 As shown, the selected threshold achieved the highest F1-score on the validation set, indicating that the classifier was not biased towards either precision or recall. Instead, it maintained a balanced path selection strategy. This balance is important for the proposed two-stage framework because it reduces the number of non-informative paths passed to the downstream regression and geometric localization stages while preserving most of the impairment-sensitive paths.

[0116] The final training results of the deployable classification model are as follows Figures 20-21 As shown, the error distribution corresponds to a high F1-score and a small number of omitted informative paths, indicating that most true damage-sensitive paths are preserved. This property is important for guided wave-based localization because false negatives correspond to paths that pass through the damaged area but are incorrectly discarded. The damage-induced scattering and waveform distortion carried by these paths will be unusable in downstream localization stages. In contrast, false positives mainly introduce redundant paths, the impact of which can be reduced by multi-path constraints used in subsequent stages. Therefore, the confusion matrix is ​​consistent with the goal of the two-stage framework, namely, that the classification stage retains a sufficiently informative set of paths while suppressing obviously irrelevant paths. Overall, these results demonstrate that the classifier provides a reliable set of informative paths for subsequent localization stages.

[0117] 2.3.2 Analysis of Coordinate Regression Results After path selection, the regression phase predicts the Euclidean distance between each retained propagation path and the damage location, and reconstructs the final damage coordinates through multipath geometric localization. This design separates local distance estimation from global coordinate reconstruction, allowing regression performance to be evaluated simultaneously at the path and localization levels.

[0118] To maintain consistency with the classification phase, the regression phase employed the same grouped, spatially hierarchical five-fold cross-validation protocol. Table 6 reports the path-level regression indices and the localization errors obtained after multi-path geometric fusion. The regression indices assess the model's stability across different data partitions and demonstrate that the path responses provide sufficient distance-related information to support stable regression. Although path-level distance predictions still contain non-negligible errors, the geometric fusion step integrates local distance estimates from multiple paths and transforms them into more stable coordinate constraints. This result indicates that the localization phase suppresses single-path regression bias through multi-path consistency.

[0119] Table 6 Summary of classification performance under five-fold cross-validation

[0120] After cross-validation evaluation, the final regression model was trained on the complete dataset, and the corresponding path-level distance regression results are as follows: Figures 22-23 As shown, the predicted distances approximate the ideal diagonal, indicating that the model has learned reliable continuous mappings over a wide distance range. These results demonstrate that distance-related information can be reliably recovered from both direct damage scattering paths and weaker indirect response paths. Once the path-level distances are predicted, the final damage coordinates are reconstructed using multipath geometric localization, as shown in the figure. Figures 24-25 As shown. Figure 24 The results show that most of the predicted points are close to the actual damage locations. Figure 25 Further analysis shows that the positioning error is mainly distributed within a small radius, and no significant systematic directional deviation was observed. The final coordinate error is significantly smaller compared to the path-level distance error. This confirms that geometric positioning does not simply accumulate errors from a single path, but rather suppresses local deviations through multi-path constraints.

[0121] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A wave damage localization method for carbon fiber reinforced polymer composite structures, characterized in that, Includes the following steps: Step 1: Complete labeling and spatial hierarchical grouping, and construct dataset x. i And add binary classification labels to the data in the dataset; Step 2: Construct a path classification model and a distance regression model; First, perform Bayesian optimization of the hyperparameters of the path classification model, and then perform five-fold cross-validation, model deployment, and training; Then, based on the optimal hyperparameters and optimal model of the path classification model, perform Bayesian optimization of the hyperparameters of the distance regression model, and then perform five-fold cross-validation, model deployment, and training; Both the path classification model and the distance regression model include a sequentially connected CWConv network and a lightweight multi-scale feature fusion network; The CWConv network is used to extract physically interpretable time-frequency features from damage-related scattering signals. The lightweight multi-scale feature fusion network consists of an improved ResNet-18 backbone network and an FPN-PAN network. The improved ResNet-18 backbone network uses a DW-SE-BasicBlock module instead of a DW-SE-BasicBlock module. The FPN-PAN network in the path classification model is connected to the classification head, and the FPN-PAN network in the distance regression model is connected to the regression head. The DW-SE-BasicBlocks module includes depthwise separable convolutions and SE channel attention. Step 3: Based on the results of the path classification model and the distance regression model, perform multipath damage localization to obtain the predicted coordinates and localization error of the damage point.

2. The wave damage localization method for carbon fiber reinforced polymer composite structures according to claim 1, characterized in that, In step 2, the CWConv network extracts time-frequency features, including the following steps: Step A01: Obtain the sampled one-dimensional vibration or acoustic signal sequence x(t); Step A02: Construct the traditional continuous wavelet transform form as the theoretical basis, as follows: ； Where m is the translation parameter, α is the scaling parameter, ξ() is the complex Morse mother wavelet function, and ξ* is the complex conjugate; Step A03: For the k-th convolution kernel, set the translation parameter m of the complex Morse wavelet. k and scale parameter α k The current convolution kernel is generated by the mother wavelet. Performing a sliding inner product between x(t) and the current convolution kernel yields the local response under this scale and translation condition, as follows: ； Step A04: Calculate the gradient of the parameters using the chain rule, as follows: ； Where, m k α k These are the translation parameters and scale parameters of the k-th convolutional kernel, respectively. , m k α k The loss gradient, z k h k This represents the intermediate activation value of the k-th convolutional kernel; Step A05: Subtract the product of gradient δ and learning rate η from the current value, as follows: ； Step A06: After training is completed, the output of the CWConv network is the time-frequency feature learned by data-driven learning, and its frequency band and time localization capabilities are jointly constrained by the task objective.

3. The wave damage localization method for carbon fiber reinforced polymer composite structures according to claim 1, characterized in that, In step 2, depthwise separable convolution includes the following steps: Step B01: Obtain input data X∈R^{C in ×H×W}, where C in H represents the number of input channels, and H and W represent the spatial or time-frequency feature map dimensions. Step B02: Perform depthwise convolution, using a k×k convolution kernel for each input channel to extract local spatial features; Step B03: Perform pointwise convolution, using 1×1 convolution to linearly combine the output of depthwise convolution in the channel dimension to achieve cross-channel information fusion and obtain Cout output channels.

4. The wave damage localization method for carbon fiber reinforced polymer composite structures according to claim 1, characterized in that, In step 2, the SE attention mechanism includes the following steps: Step C01: Perform global average pooling on the feature map to obtain the global average pooling description for each channel, as shown in the following formula: ； Among them, z c This describes the global average pooling for the c-th channel. This is the feature map of the c-th channel; Step C02: Generate channel weights s through two layers of fully connected mapping and activation functions. c The formula is as follows: ； in, For the sigmoid function, W1 and W2 are non-linear activation functions, and W1 and W2 are the weights of the two fully connected layers in the SE attention mechanism. Step C03: Multiply the weights back to the corresponding channels, using the following formula: ； Step C04: Add the features recalibrated by the SE attention mechanism to the residual branch, and then pass them through the activation function to obtain the output Y.

5. The wave damage localization method for carbon fiber reinforced polymer composite structures according to claim 1, characterized in that, Step 2, the FPN-PAN network includes the following steps: Step D01: Obtain the multi-scale features C2, C3, and C4 output from different stages of the improved ResNet-18 backbone network; Step D02: Apply lateral 1×1 convolution to C2, C3, and C4 respectively to give the features of different levels a unified channel dimension; Step D03: Perform top-down fusion using FPN, upsampling high-level features to the size of adjacent low-level features and adding them to the low-level lateral features to obtain the fused feature F. i The formula is as follows: ； Among them, F i The features of the i-th layer after top-down fusion of FPN are... It is a 1×1 convolution, and Up(·) is an upsampling operation; Step D04: Perform bottom-up PAN fusion, downsample the lower-level fused features and add them to the adjacent higher-level features, then perform smoothing and local fusion through 3×3 convolution to obtain the enhanced feature P. i The formula is as follows: ； Among them, P i This represents the output characteristics of the i-th layer after bottom-up enhancement of PAN. It is a 3×3 convolution, and Down(·) is a downsampling operation; Step D05: Output P2, P3, and P4, respectively retaining semantic information, local structural information, and cross-scale fusion information at different resolutions.

6. The wave damage localization method for carbon fiber reinforced polymer composite structures according to claim 1, characterized in that, In step 2, the Bayesian optimization of the hyperparameters of the path classification model and the distance regression model are performed through a two-stage cascaded learning process with feature transfer, including the following steps: Step E01: Define the search space and evaluation objective. The inputs are the training set, validation set, model structure, and hyperparameter space A. The output is the hyperparameter combination that performs best on the validation set, as shown in the following formula: ； Where a(t) is the acquisition function, used to evaluate whether the hyperparameter combination t is worth calculating; Step E02: Construct a tree-structured Parzen estimator. The tree-structured Parzen estimator divides the historical trials into better and worse regions according to a threshold q*, and estimates the conditional density, as shown in the following formula: ； ； ； Where a is the combination of hyperparameters in a single trial, q is the validation set evaluation value of a single trial, and l(a) and g(a) are the conditional density estimates corresponding to the better and worse regions in the tree-structured Parzen estimator. Step E03: Perform the Bayesian optimization phase search for the hyperparameters of the path classification model, inputting the classification training data, classification validation data, the complete model, and the search space A. cls After training each candidate combination for several rounds, a classification metric is calculated on the validation set, and trials with significantly poor performance are terminated early using a pruning strategy, as shown in the following formula: ； Where F1(a) is the validation set judgment criterion for this stage; Step E04: Output the optimal configuration for this stage, including the optimal hyperparameter a. cls * The corresponding model weights and the learned CWConv network parameters serve as the initialization source for the next stage; Step E05: Perform the Bayesian optimization phase search for the hyperparameters of the distance regression model, inputting the source model obtained in the previous phase, the regression training data, the regression validation data, and the search space A for this phase. reg In this stage, the CWConv network parameters are fixed, limiting the search scope to fine-tuning the hyperparameters, as shown in the following formula: ； Among them, R 2 (a) is the validation set judgment criterion for this stage; Step E06: Output the final model and hyperparameters, including the optimal fine-tuned hyperparameter a. reg * and the final distance regression model, used for subsequent testing or deployment.

7. The wave damage localization method for carbon fiber reinforced polymer composite structures according to claim 1, characterized in that, Step 3 includes the following steps: Step F01: Based on the path validity label S given by the path classification model, where S={0,1} is the binary classification result label, assign different weight coefficients w to it. i The formula is as follows: ； Step F02: Calculate the Euclidean distance t from any damage point (x, y) to the i-th line segment. i The formula is as follows: ； Among them, P i S i Sensor coordinates; Step F03: Obtain the residual function J(x,y) by weighting, and realize the fusion of multi-path distance constraints, as shown in the following formula: ； Where K represents the K effective paths selected from the D groups for the same damage point. Geometric prediction value, This is the distance prediction value; Step F04: Use the L-BFGS-B algorithm to solve the residual function, complete the optimization solution with boundary constraints, and obtain the predicted coordinates. The formula is as follows: ； Where L is the size of the plate; Step F05: Calculate the positioning error e to complete the positioning error assessment. The formula is as follows: ； Where (x*, y*) are the true values ​​of the damage coordinates.

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