Cross-bridge type label-domain-free adaptive damage identification method

Abstract

The invention relates to a bridge-crossing type label-domain-free adaptive damage identification method, which belongs to the technical field of bridge structure health monitoring and comprises the following steps of: 1, constructing a three-tower type feature extractor comprising a time domain tower, a frequency domain tower and a modal tower to obtain a cross-modal combined feature; 2, aligning with a modal map through modal consistency constraint; 3, utilizing a multi-scale and dynamic frequency band attention mechanism to adaptively highlight a damage sensitive frequency band; 4, confrontation and cooperation mixed alignment is adopted, feature distribution differences are reduced, and modal physical consistency is kept; 5, a self-training and multi-teacher distillation mechanism guided by modal confidence is designed under the non-labeling condition, and the pseudo label quality and the training stability are improved; and 6, introducing physical constraint regularization to ensure that a result accords with a structural dynamics rule. According to the method, the damage probability distribution, the modal similarity heat map and the reliability index are finally output, target domain labeling is not needed, and the accuracy, the robustness and the engineering applicability of cross-bridge damage identification can be improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of bridge structure health monitoring and intelligent detection, and particularly relates to a cross-bridge type unlabeled domain adaptive damage identification method. BACKGROUND

[0002] During long-term service, bridge structures are prone to cracks, fatigue damage and stiffness degradation due to vehicle load, environmental action and material degradation, etc., which seriously threaten the safety of the structure. Therefore, it is of great significance to develop intelligent damage identification technology based on sensor monitoring data. In recent years, with the development of sensor deployment and machine learning, cross-structure transfer learning and domain adaptive methods have gradually become a research hotspot, aiming to transfer the labeled knowledge of existing bridges to new bridges to reduce the cost of manual labeling and improve the identification efficiency.

[0003] The existing cross-bridge domain adaptive damage identification method mainly has the following problems:

[0004] (1) Strong dependence on labeling: Most methods still need to introduce manual labeling in the target domain, and the application scene is limited;

[0005] (2) Sensitive to sensor layout: When the sensor layout of the source bridge and the target bridge is inconsistent, the transfer performance decreases significantly;

[0006] (3) Lack of physical constraints: Existing methods do not fully combine bridge modal parameters, and the interpretation of the identification results is insufficient;

[0007] (4) Insufficient frequency domain processing: Lack of dynamic frequency band selection mechanism, and insufficient utilization of damage sensitive frequency band;

[0008] (5) Poor robustness of self-training: Pseudo-label error is easy to accumulate, and the transfer result is unstable.

[0009] Therefore, it is urgent to propose a cross-bridge type damage identification method that can adapt to the differences in sensor layout under unlabeled target domain conditions, combine modal consistency constraints, dynamic frequency band attention mechanisms and robust self-training strategies, to significantly improve the accuracy, robustness and engineering applicability of cross-domain transfer identification. SUMMARY

[0010] In order to solve the problems of strong dependence on target domain labeled samples, sensitivity to sensor layout, lack of physical constraints, single frequency domain alignment method and insufficient robustness of self-training in the existing cross-bridge domain adaptive damage identification method, the present application provides a cross-bridge type unlabeled domain adaptive damage identification method, which aims to realize the physical constraint of dynamic parameters by constructing a three-tower feature extraction framework, introducing modal consistency loss and modal atlas alignment mechanism; through the multi-scale and dynamic frequency band attention mechanism, the frequency band most sensitive to damage is adaptively selected; combined with the mixed alignment strategy of confrontation and cooperation, the feature distribution difference between the source bridge and the target bridge is effectively reduced; under the condition of no labeled target domain, the modal confidence guided pseudo-label self-training mechanism is designed, and the multi-teacher cooperative distillation is used to improve the quality of pseudo-label; at the same time, combined with the physical constraint regularization, the identification result is ensured to meet the structural dynamics law.

[0011] In order to achieve the above purpose, the specific schemes of the present application are as follows:

[0012] A cross-bridge type unlabeled domain adaptive damage identification method, comprising the following steps:

[0013] Step 1, multi-tower feature extraction: a three-tower feature extractor including a time domain tower, a frequency domain tower and a modal tower is constructed, and the features output by the time domain tower, the frequency domain tower and the modal tower are spliced in the embedding space to obtain cross-modal joint features;

[0014] Step 2, modal consistency loss and modal atlas alignment: using the modal parameters extracted by the modal tower in step 1, a modal consistency loss function is defined, a modal atlas is constructed with the modal order as the node and the correlation between modes as the edge, and a graph neural network is used to realize the alignment of cross-domain modal relationship;

[0015] Step 3, multi-scale and dynamic frequency band attention alignment: the frequency domain features extracted by the frequency domain tower in step 1 are divided into multiple frequency bands, and the attention mechanism is used to assign weights to different frequency bands to highlight the frequency interval sensitive to damage; a dynamic frequency band mask mechanism is introduced, which adaptively selects and highlights the frequency band most sensitive to damage according to the actual vibration characteristics of the target bridge, while suppressing the interference signals of non-critical frequency bands;

[0016] Step 4, confrontation and cooperation mixed alignment: using the cross-modal joint features obtained in step 1, both confrontation and cooperation mechanisms are used to define a comprehensive loss function including domain adversarial loss and modal cooperation loss, and the aligned features are obtained by optimizing the comprehensive loss function;

[0017] Step 5, Modal confidence-guided multi-teacher self-training: On the unlabeled data in the target domain, using the alignment features obtained in Step 4, a modal confidence-guided pseudo-label self-training mechanism is introduced. Samples with high confidence in pseudo-labels are selected to participate in iterative training. When there are multiple source bridges, a multi-teacher collaborative distillation mechanism is introduced. Pseudo-labels are generated by the teacher models of each source bridge, and weight coefficients are set according to the performance scores of each teacher model on the source domain validation set. The pseudo-label results generated by each teacher model are weighted and averaged to generate pseudo-label self-training results.

[0018] Step 6, Physical Constraint Regularization and Multidimensional Output: During the training process, the pseudo-label self-training results obtained in Step 5 are used to introduce a physical constraint regularization term to make the modal features satisfy the structural dynamics equilibrium equation. The physical constraint regularization term is integrated into the comprehensive optimization objective function defined in Step 4 to form an updated comprehensive optimization objective function. The model is trained by optimizing the updated comprehensive optimization objective function, and the output includes multidimensional damage identification results including damage probability map, modal similarity heatmap, bridge reliability index and uncertainty distribution map.

[0019] Further, the time-domain tower described in step 1 is used to input the acceleration time-history signal of the bridge structure and extract time-domain features using a one-dimensional convolutional neural network; the frequency-domain tower is used to perform a fast Fourier transform on the time-history signal to obtain the power spectral density and extract frequency-domain features using convolution and attention mechanisms; the modal tower is used to extract the modal parameters of the bridge, including natural frequencies, damping ratios, and mode shape vectors, through a random subtraction method or a subspace recognition method, forming a modal feature representation.

[0020] Furthermore, the modal consistency loss function defined in step 2 is used to constrain the differences between the source and target domains in terms of frequency, damping ratio, and mode shape parameters, and is defined as follows:

[0021] (1),

[0022] In the formula: L modal Represents the modal consistency loss function; , These represent the intrinsic frequency vectors of the source and target domains, respectively. , Let represent the damping ratio vectors of the source domain and the target domain, respectively; , These represent the modal shape vectors of the source domain and the target domain, respectively. , , These are the weighting coefficients for the loss term, used to balance the importance of the three types of constraints: frequency, damping ratio, and mode shape.

[0023] Furthermore, the frequency domain features extracted by the frequency domain tower in step 3 are divided into multiple frequency bands, and weights are assigned to different frequency bands through an attention mechanism, specifically including the following steps:

[0024] Step 31, divide the spectrum into low-frequency bands [0, ... ], mid-frequency band , ] and high frequency band [ , ];

[0025] Step 32: Extract the feature vectors for each frequency band and define the attention weights:

[0026] (2),

[0027] In the formula: Let the attention weights of the i-th frequency band satisfy the following condition: ; This represents the learnable parameter corresponding to the i-th frequency band; This represents the learnable parameter corresponding to the j-th frequency band; This represents the feature vector of the i-th frequency band; This represents the feature vector of the j-th frequency band;

[0028] Step 33, the frequency band features are weighted and fused to obtain the final frequency domain features, which are represented as follows:

[0029] (3),

[0030] In the formula: This represents the frequency domain characteristics after weighted fusion; Let the attention weights of the i-th frequency band satisfy the following condition: ; This represents the feature vector of the i-th frequency band;

[0031] The steps of introducing a dynamic frequency band masking mechanism, which adaptively selects and highlights the frequency bands most sensitive to damage based on the actual vibration characteristics of the target bridge, while suppressing interference signals in non-critical frequency bands, include:

[0032] (1) Frequency band selection: The spectrum is divided into multiple frequency bands using a multi-scale method;

[0033] (2) Characteristic response evaluation: Calculate the damage sensitivity index for each frequency band. The sensitivity of each frequency band to damage response is evaluated by the characteristic changes of each frequency band on the sample set.

[0034] The damage sensitivity index The calculation formula is as follows:

[0035] (4),

[0036] In the formula: Indicates the first The damage sensitivity coefficient for each frequency band is used to measure the response sensitivity of that frequency band to damage. Indicates the first Each frequency band in the sample Eigenvalues ​​on; Indicates the first Each frequency band in the sample Feature changes; Indicates all frequency bands in the sample Feature changes; The number of samples;

[0037] (3) Dynamic band mask generation: based on the sensitivity index Generate dynamic frequency band mask The features of each frequency band are weighted according to the mask, and the mask is defined as follows:

[0038] (5),

[0039] In the formula: Indicates the first Dynamic frequency band mask for each frequency band; Indicates the first Damage sensitivity index for each frequency band; It is the total number of frequency bands;

[0040] (4) Weighted fusion: The final weighted frequency domain features are expressed as:

[0041] (6),

[0042] In the formula: This represents the final weighted frequency domain feature, which is the result of feature fusion after weighting all frequency bands; Indicates the first Dynamic frequency band mask for each frequency band; It is the first Feature vectors of each frequency band; These are the corresponding mask weights; It represents the total number of frequency bands.

[0043] Furthermore, the comprehensive loss function described in step 4 is defined as follows:

[0044] (7),

[0045] In the formula: L align This represents the alignment loss resulting from a mixture of adversarial and collaborative actions. Domain adversarial loss is used to reduce the distributional differences between the source and target domains. This represents the modal cooperation loss, used to maintain the consistency of modal parameters; , This represents the balance coefficient, used to adjust the contribution of the two types of losses.

[0046] Furthermore, the confidence level of the pseudo-label described in step 5 is jointly determined by the predicted probability and modal similarity, and is defined as follows:

[0047] (8),

[0048] In the formula: Indicates the confidence level of the pseudo-label; Indicates the balance factor; This represents the probability predicted by the classifier; The similarity is calculated based on the modal parameters of the source and target domains;

[0049] The pseudo-label is only They were selected to participate in the training, among which This is the preset confidence threshold.

[0050] Furthermore, the constraint equation for the physical constraint regularization term in step 6 is defined as follows:

[0051] (9),

[0052] In the formula: L phy This represents the physical constraint regularization term; Represents the stiffness matrix of the bridge structure; This represents the corresponding mode shape vector; The mass matrix representing the bridge structure; This represents the modal natural frequency.

[0053] Furthermore, the updated comprehensive optimization objective function described in step 6 is:

[0054] (10)

[0055] In the formula: L represents the updated comprehensive optimization objective function; Represents the classification loss of the source domain; This represents the modal consistency loss; This represents the alignment loss resulting from a mixture of adversarial and collaborative actions. This represents the loss due to physical constraint regularization. , , This represents the balance coefficient, used to adjust the contribution of each loss term.

[0056] Advantages of the present invention

[0057] (1) Achieving bridge migration under unlabeled conditions: This invention does not rely on manually labeled data of the target bridge, and can complete damage identification only through unlabeled vibration signals collected in situ. This breaks through the limitation of existing methods that must rely on labeled samples of the target domain, significantly reduces the cost of data collection and labeling, and improves the engineering feasibility of the method.

[0058] (2) Enhanced generalization capability across bridges: This invention, through a multi-scale and dynamic frequency band attention mechanism, can automatically identify the frequency range most sensitive to damage and adaptively allocate weights, thereby effectively addressing the differences in sensor deployment and structural dynamic characteristics among different bridges. This enables the method to achieve robust transfer between different bridge types (such as steel box girder bridges and concrete beam bridges), overcoming the limitation of existing methods that are only applicable to isomorphic sensor deployments.

[0059] (3) Introducing modal consistency and modal spectrum alignment to enhance physical interpretability: This invention not only aligns the data distributions of the source and target domains in the feature space, but also introduces modal consistency loss (frequency, damping ratio, mode shape) and modal spectrum alignment mechanism to ensure that cross-domain features remain consistent in the sense of bridge dynamics. Compared with existing schemes that rely solely on statistical feature alignment, the results of this invention are more consistent with the laws of structural dynamics and have stronger physical interpretability and engineering credibility.

[0060] (4) A hybrid alignment mechanism combining adversarial and cooperative approaches is adopted: This invention reduces the distribution difference between the source and target domains through adversarial loss, while introducing modal cooperative loss to maintain the consistency of modal parameters, thus achieving dual protection of distribution alignment and physical consistency. This mechanism avoids the "modal drift" problem that may be caused by purely adversarial learning, making cross-domain recognition more stable and reliable.

[0061] (5) Higher robustness of pseudo-label self-training: This invention proposes a pseudo-label screening method guided by modal confidence, which weights and fuses classification prediction probability with modal similarity to ensure that only high-confidence samples participate in training, thus avoiding noise accumulation caused by low-quality pseudo-labels. At the same time, a multi-teacher collaborative distillation mechanism is introduced in the multi-source bridge scenario to further improve the accuracy and robustness of pseudo-labels, thereby enhancing the stability of target domain self-training.

[0062] (6) Introducing physical constraint regularization to ensure dynamic rationality: This invention adds a physical constraint regularization term during the training process to ensure that the learned modal features satisfy the dynamic equilibrium equation. This design effectively avoids the "non-physical" results that may occur in deep learning models under unconstrained conditions, ensuring that the damage identification results are not only numerically accurate, but also reasonable in terms of mechanical mechanism.

[0063] (7) Provides multi-dimensional damage identification results: The final output of this invention includes not only a damage probability map, but also a modal similarity heatmap, a bridge reliability index, and an uncertainty distribution map, which can comprehensively evaluate the results of bridge damage identification from multiple perspectives. Unlike existing methods that only provide a single damage probability, the results of this invention are more comprehensive and more conducive to engineers' diagnosis and decision-making.

[0064] (8) Improved overall recognition performance and engineering practicality: This invention achieves high-precision, interpretable and robust bridge damage recognition under unlabeled conditions by jointly optimizing classification performance, modal consistency, domain alignment effect and physical rationality through a comprehensive loss function. Experimental verification shows that this method outperforms existing technologies in terms of cross-domain F1 score, AUROC and other indicators, significantly improving the accuracy and practicality of bridge damage recognition.

[0065] In summary, compared with existing technologies, this invention can adapt to different bridge types and sensor deployment differences under unlabeled conditions, significantly improving the accuracy, robustness, and engineering applicability of bridge damage identification. It not only solves the problems of label dependence, poor adaptability, and insufficient physical interpretability in existing bridge migration damage identification methods, but also significantly improves the accuracy, stability, and engineering applicability of bridge damage identification by innovatively introducing mechanisms such as modal consistency, dynamic frequency band attention, physical constraint regularization, and multi-dimensional result output. It possesses significant technical advantages and promotional value. Attached Figure Description

[0066] Figure 1 This is a flowchart of the cross-bridge type unlabeled domain adaptive damage identification method of the present invention. Detailed Implementation

[0067] The following explanation and description are provided in conjunction with the accompanying drawings and specific embodiments. However, it should be noted that these specific embodiments are not intended to limit the scope of the invention.

[0068] like Figure 1 As shown in the figure, this embodiment provides a bridge-type unlabeled domain adaptive damage identification method, which includes the following steps: A bridge-type unlabeled domain adaptive damage identification method, characterized in that it includes the following steps:

[0069] Step 1, Multi-tower feature extraction: Construct a three-tower feature extractor including a time-domain tower, a frequency-domain tower, and a modality tower;

[0070] The time-domain tower is used to input the acceleration time-history signal of the bridge structure, and a one-dimensional convolutional neural network (1D-CNN) is used to extract time-domain features;

[0071] The frequency domain tower is used to perform a fast Fourier transform (FFT) on the time-history signal to obtain the power spectral density, and to extract frequency domain features using convolution and attention mechanisms.

[0072] The modal tower is used to extract the modal parameters of the bridge, including natural frequencies, damping ratios, and mode shape vectors, through random subtraction or subspace identification methods, to form a modal feature representation.

[0073] The features output from the time-domain tower, frequency-domain tower, and modality tower are concatenated in the embedding space to obtain cross-modal joint features;

[0074] Step 2, Modal consistency loss and modal graph alignment: To ensure the consistency of modal dynamics between the source and target domains, a modal consistency loss function is defined using the modal parameters extracted from the modal tower described in Step 1;

[0075] The defined modal consistency loss function is used to constrain the differences between the source and target domains in terms of frequency, damping ratio, and mode shape parameters. Its definition is as follows:

[0076] (1),

[0077] In the formula: L modal Represents the modal consistency loss function; , These represent the intrinsic frequency vectors of the source and target domains, respectively. , Let represent the damping ratio vectors of the source domain and the target domain, respectively; , These represent the modal shape vectors of the source domain and the target domain, respectively. , , These are the weighting coefficients for the loss term, used to balance the importance of the three types of constraints: frequency, damping ratio, and mode shape.

[0078] The loss ensures that the source domain and the target domain are as close as possible in terms of frequency, damping, and mode shape.

[0079] Modal parameters are used to construct a modal graph, with modal order as nodes and intermodal correlation as edges. A graph neural network (GNN) is used to align cross-domain modal relationships. This design ensures that the aligned modal features are not only close in numerical terms, but also maintain topological consistency between modalities.

[0080] Step 3, Multi-scale and dynamic frequency band attention alignment: Divide the frequency domain features extracted by the frequency domain tower in Step 1 into multiple frequency bands, and assign weights to different frequency bands through an attention mechanism to highlight the frequency ranges that are sensitive to damage;

[0081] The frequency domain features extracted by the frequency domain tower are divided into multiple frequency bands, and weights are assigned to different frequency bands through an attention mechanism. Specifically, the steps include:

[0082] Step 31, divide the spectrum into low-frequency bands [0, ... ], mid-frequency band , ] and high frequency band [ , ];

[0083] Step 32: Extract the feature vectors for each frequency band and define the attention weights:

[0084] (2),

[0085] In the formula: Let the attention weights of the i-th frequency band satisfy the following condition: ; This represents the learnable parameter corresponding to the i-th frequency band; This represents the learnable parameter corresponding to the j-th frequency band; This represents the feature vector of the i-th frequency band; This represents the feature vector of the j-th frequency band;

[0086] Step 33, the frequency band features are weighted and fused to obtain the final frequency domain features, which are represented as follows:

[0087] (3),

[0088] In the formula: This represents the frequency domain characteristics after weighted fusion; Let the attention weights of the i-th frequency band satisfy the following condition: ; This represents the feature vector of the i-th frequency band;

[0089] Based on multi-scale frequency band division and attention weighting, a dynamic frequency band masking mechanism is introduced. According to the actual vibration characteristics of the target bridge, the mechanism adaptively selects and highlights the frequency bands most sensitive to damage, while suppressing interference signals in non-critical frequency bands, thereby enhancing the adaptability and robustness during bridge migration. Through the dynamic frequency band masking mechanism, even when different bridges have significantly different frequency distributions, the model can still accurately align key damage information, thus significantly enhancing the adaptability and robustness of bridge migration. The specific implementation steps are as follows:

[0090] (1) Frequency band selection: The spectrum is divided into multiple frequency bands using a multi-scale method. For example: low frequency band [0, ], mid-frequency band , ], high frequency band , ],in This indicates the upper limit frequency of the low-frequency band, which is usually determined by experiments or signal characteristics; This indicates the upper limit frequency of the mid-frequency band, which is usually determined by experiments or signal characteristics; Indicates the maximum frequency of the entire spectrum;

[0091] (2) Characteristic response evaluation: Calculate the damage sensitivity index for each frequency band. The sensitivity of each frequency band to damage response is evaluated by the characteristic changes of each frequency band on the sample set.

[0092] The damage sensitivity index The calculation formula is as follows:

[0093] (4),

[0094] In the formula: Indicates the first The damage sensitivity coefficient for each frequency band is used to measure the response sensitivity of that frequency band to damage. Indicates the first Each frequency band in the sample Eigenvalues ​​on; Indicates the first Each frequency band in the sample Feature changes; Indicates all frequency bands in the sample Feature changes; This represents the number of samples.

[0095] (3) Dynamic band mask generation: based on the sensitivity index Generate dynamic frequency band mask The features of each frequency band are then weighted according to this mask. The mask is defined as follows:

[0096] (5),

[0097] In the formula: Indicates the first Dynamic frequency band mask for each frequency band; Indicates the first Damage sensitivity index for each frequency band; It is the total number of frequency bands; through the mask It can highlight the frequency bands most sensitive to damage and suppress interference in non-critical frequency bands.

[0098] (4) Weighted fusion: The final weighted frequency domain features are expressed as:

[0099] (6),

[0100] In the formula: This represents the final weighted frequency domain feature, which is the result of feature fusion after weighting all frequency bands; Indicates the first Dynamic frequency band mask for each frequency band; It is the first Feature vectors of each frequency band; These are the corresponding mask weights; It represents the total number of frequency bands.

[0101] By introducing a dynamic frequency band masking mechanism, this embodiment can adaptively select and highlight the frequency bands most sensitive to damage based on the vibration characteristics of different bridges, while suppressing interference signals in non-critical frequency bands, thereby significantly enhancing the adaptability and robustness during bridge relocation.

[0102] Step 4, Hybrid Alignment of Adversarial and Collaborative Mechanisms: To achieve robust alignment of the feature space, the cross-modal joint features obtained in Step 1 are utilized, and both adversarial and collaborative mechanisms are employed. A comprehensive loss function is defined, comprising domain adversarial loss and modal collaborative loss. The adversarial mechanism reduces the feature distribution differences between the source and target domains, while the collaborative mechanism ensures consistency in modal parameters between the two domains. Aligned features are obtained by optimizing the comprehensive loss function.

[0103] The comprehensive loss function is defined as follows:

[0104] (7),

[0105] In the formula: L align This represents the alignment loss resulting from a mixture of adversarial and collaborative actions. Domain adversarial loss is used to reduce the distributional differences between the source and target domains. This represents the modal cooperation loss, used to maintain the consistency of modal parameters; , This represents the balance coefficient, used to adjust the contribution of the two types of losses.

[0106] The adversarial and collaborative hybrid alignment ensures that cross-domain alignment considers both data distribution consistency and physical interpretability.

[0107] Step 5, Modal confidence-guided multi-teacher self-training: On unlabeled data in the target domain, the transfer effect is further improved through a pseudo-label self-training mechanism. Using the alignment features obtained in Step 4, a modal confidence-guided pseudo-label self-training mechanism is introduced to select samples with high pseudo-label confidence to participate in iterative training.

[0108] The confidence level of the pseudo-label is determined by both the predicted probability and modal similarity, and is defined as follows:

[0109] (8),

[0110] In the formula: Indicates the confidence level of the pseudo-label; Indicates the balance factor; This represents the probability predicted by the classifier; The similarity is calculated based on the modal parameters of the source and target domains;

[0111] The pseudo-label is only When adopted for training, this reduces the introduction of noise. This is the preset confidence threshold.

[0112] When there are multiple source bridges, a multi-teacher collaborative distillation mechanism is introduced. Pseudo-labels are generated by the teacher model of each source bridge, and weight coefficients are set according to the performance scores of each teacher model on the source domain validation set. The pseudo-label results generated by each teacher model are weighted and averaged to generate pseudo-label self-training results.

[0113] The multi-teacher collaborative distillation mechanism avoids the bias that may be caused by the differences in bridge characteristics of a single teacher. By integrating the decisions of multiple teacher models, it improves the consistency and robustness of pseudo-labels, thereby significantly improving the stability and accuracy of target domain self-training.

[0114] Step 6, Physical constraint regularization term and multidimensional result output: During the training process, the pseudo-label self-training result obtained in step 5 is used to introduce a physical constraint regularization term to make the modal features satisfy the structural dynamics equilibrium equation.

[0115] The constraint equation for the physical constraint regularization term is defined as follows:

[0116] (9),

[0117] In the formula: L phy This represents the physical constraint regularization term; Represents the stiffness matrix of the bridge structure; This represents the corresponding mode shape vector; The mass matrix representing the bridge structure; This represents the modal natural frequency.

[0118] The physical constraint regularization term ensures that the learned modal features satisfy the dynamic equilibrium equation, thereby guaranteeing the physical rationality of the recognition results.

[0119] The classification loss, modality consistency loss, cross-domain alignment loss and physical constraint regularization mentioned above are uniformly optimized and integrated into the comprehensive optimization objective function defined in step 4 to form the updated comprehensive optimization objective function.

[0120] The updated comprehensive optimization objective function is:

[0121] (10)

[0122] In the formula: L represents the updated comprehensive optimization objective function; Represents the classification loss of the source domain; This represents the modal consistency loss; This represents the alignment loss resulting from a mixture of adversarial and collaborative actions. This represents the loss due to physical constraint regularization. , , This represents the balance coefficient, used to adjust the contribution of each loss term.

[0123] By training the model using the optimized and updated comprehensive objective function, the final output is a multi-dimensional damage identification result, which includes:

[0124] Damage probability maps are used to reflect the damage probability distribution of different structural parts;

[0125] Modal similarity heatmaps are used to visualize the alignment of modal features between the source bridge and the target bridge;

[0126] The bridge reliability index is used to combine the F1 score, AUROC, and modal consistency score to output a single reliability index.

[0127] Uncertainty distribution is used to reflect the difference in the reliability of prediction results at different locations.

[0128] The updated comprehensive optimization objective function ensures the accuracy, stability, and interpretability of bridge damage identification under unlabeled conditions by jointly optimizing classification performance, modal consistency, domain alignment effect, and physical rationality.

Claims

1. A bridge-type unlabeled domain adaptive damage identification method, characterized in that, Includes the following steps: Step 1, Multi-tower feature extraction: Construct a three-tower feature extractor including a time-domain tower, a frequency-domain tower, and a modal tower. Concatenate the features output by the time-domain tower, the frequency-domain tower, and the modal tower in the embedding space to obtain cross-modal joint features. Step 2, Modality Consistency Loss and Modality Graph Alignment: Using the modal parameters extracted from the modality tower described in Step 1, a modality consistency loss function is defined, and a modality graph is constructed from the modal parameters. With modality order as nodes and intermodal correlation as edges, a graph neural network is used to align cross-domain modal relationships. Step 3, Multi-scale and Dynamic Frequency Band Attention Alignment: The frequency domain features extracted by the frequency domain tower in Step 1 are divided into multiple frequency bands. Weights are assigned to different frequency bands through an attention mechanism to highlight the frequency ranges that are sensitive to damage. A dynamic frequency band masking mechanism is introduced to adaptively select and highlight the frequency bands that are most sensitive to damage based on the actual vibration characteristics of the target bridge, while suppressing interference signals in non-critical frequency bands. Step 4, Hybrid Alignment of Adversarial and Collaborative Approaches: Utilizing the cross-modal joint features obtained in Step 1, a comprehensive loss function is defined that includes domain adversarial loss and modal collaborative loss. By optimizing the comprehensive loss function, alignment features are obtained. Step 5, Modal confidence-guided multi-teacher self-training: On the unlabeled data in the target domain, using the alignment features obtained in Step 4, a modal confidence-guided pseudo-label self-training mechanism is introduced. Samples with high confidence in pseudo-labels are selected to participate in iterative training. When there are multiple source bridges, a multi-teacher collaborative distillation mechanism is introduced. Pseudo-labels are generated by the teacher models of each source bridge, and weight coefficients are set according to the performance scores of each teacher model on the source domain validation set. The pseudo-label results generated by each teacher model are weighted and averaged to generate pseudo-label self-training results. Step 6, Physical Constraint Regularization and Multidimensional Output: During the training process, the pseudo-label self-training results obtained in Step 5 are used to introduce a physical constraint regularization term to make the modal features satisfy the structural dynamics equilibrium equation. The physical constraint regularization term is integrated into the comprehensive optimization objective function defined in Step 4 to form an updated comprehensive optimization objective function. The model is trained by optimizing the updated comprehensive optimization objective function, and the output includes multidimensional damage identification results including damage probability map, modal similarity heatmap, bridge reliability index and uncertainty distribution map.

2. The method according to claim 1, characterized in that, The time-domain tower described in step 1 is used to input the acceleration time-history signal of the bridge structure and extract time-domain features using a one-dimensional convolutional neural network; the frequency-domain tower is used to perform a fast Fourier transform on the time-history signal to obtain the power spectral density and extract frequency-domain features using convolution and attention mechanisms; the modal tower is used to extract the modal parameters of the bridge, including natural frequencies, damping ratios, and mode shape vectors, through random subtraction or subspace recognition methods, forming a modal feature representation.

3. The method according to claim 1, characterized in that, The modal consistency loss function defined in step 2 is used to constrain the differences between the source and target domains in terms of frequency, damping ratio, and mode shape parameters. Its definition is: （1）， In the formula: L modal Represents the modal consistency loss function; , These represent the intrinsic frequency vectors of the source and target domains, respectively. , Let represent the damping ratio vectors of the source domain and the target domain, respectively; , These represent the modal shape vectors of the source domain and the target domain, respectively. , , These are the weighting coefficients for the loss term, used to balance the importance of the three types of constraints: frequency, damping ratio, and mode shape.

4. The method according to claim 1, characterized in that, The frequency domain features extracted by the frequency domain tower in step 3 are divided into multiple frequency bands. Weights are assigned to different frequency bands through an attention mechanism, specifically including the following steps: Step 31, divide the spectrum into low-frequency bands [0, ... ], mid-frequency band , ] and high frequency band [ , ]; Step 32: Extract the feature vectors for each frequency band and define the attention weights: （2）， In the formula: Let the attention weights of the i-th frequency band satisfy the following condition: ; This represents the learnable parameter corresponding to the i-th frequency band; This represents the learnable parameter corresponding to the j-th frequency band; This represents the feature vector of the i-th frequency band; This represents the feature vector of the j-th frequency band; Step 33, the frequency band features are weighted and fused to obtain the final frequency domain features, which are represented as follows: （3）， In the formula: This represents the frequency domain characteristics after weighted fusion; Let the attention weights of the i-th frequency band satisfy the following condition: ; This represents the feature vector of the i-th frequency band; The steps of introducing a dynamic frequency band masking mechanism, which adaptively selects and highlights the frequency bands most sensitive to damage based on the actual vibration characteristics of the target bridge, while suppressing interference signals in non-critical frequency bands, include: (1) Frequency band selection: The spectrum is divided into multiple frequency bands using a multi-scale method; (2) Characteristic response evaluation: Calculate the damage sensitivity index for each frequency band. The sensitivity of each frequency band to damage response is evaluated by the characteristic changes of each frequency band on the sample set. The damage sensitivity index The calculation formula is as follows: （4）， In the formula: Indicates the first The damage sensitivity coefficient for each frequency band is used to measure the response sensitivity of that frequency band to damage. Indicates the first Each frequency band in the sample Eigenvalues ​​on; Indicates the first Each frequency band in the sample Feature changes; Indicates all frequency bands in the sample Feature changes; The number of samples; (3) Dynamic band mask generation: based on the sensitivity index Generate dynamic frequency band mask The features of each frequency band are weighted according to the mask, and the mask is defined as follows: （5）， In the formula: Indicates the first Dynamic frequency band mask for each frequency band; Indicates the first Damage sensitivity index for each frequency band; It is the total number of frequency bands; (4) Weighted fusion: The final weighted frequency domain features are expressed as: （6）， In the formula: This represents the final weighted frequency domain feature, which is the result of feature fusion after weighting all frequency bands; Indicates the first Dynamic frequency band mask for each frequency band; It is the first Feature vectors of each frequency band; These are the corresponding mask weights; It represents the total number of frequency bands.

5. The method according to claim 1, characterized in that, The comprehensive loss function mentioned in step 4 is defined as follows: （7）， In the formula: L align This represents the alignment loss resulting from a mixture of adversarial and collaborative actions. Domain adversarial loss is used to reduce the distributional differences between the source and target domains. This represents the modal cooperation loss, used to maintain the consistency of modal parameters; , This represents the balance coefficient, used to adjust the contribution of the two types of losses.

6. The method according to claim 1, characterized in that, The confidence level of the pseudo-labels mentioned in step 5 is determined by both the predicted probability and modal similarity, and is defined as follows: （8）， In the formula: Indicates the confidence level of the pseudo-label; Indicates the balance factor; This represents the probability predicted by the classifier; The similarity is calculated based on the modal parameters of the source and target domains; The pseudo-label is only They were selected to participate in the training, among which This is the preset confidence threshold.

7. The method according to claim 1, characterized in that, The constraint equation for the physical constraint regularization term in step 6 is defined as follows: （9）， In the formula: L phy This represents the physical constraint regularization term; Represents the stiffness matrix of the bridge structure; This represents the corresponding mode shape vector; The mass matrix representing the bridge structure; This represents the modal natural frequency.

8. The method according to claim 1, characterized in that, The updated comprehensive optimization objective function described in step 6 is: （10）， In the formula: L represents the updated comprehensive optimization objective function; Represents the classification loss of the source domain; This represents the modal consistency loss; This represents the alignment loss resulting from a mixture of adversarial and collaborative actions. This represents the loss due to physical constraint regularization. , , This represents the balance coefficient, used to adjust the contribution of each loss term.

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