Method for intelligently sensing damage state of vehicle-collided bridge pier based on deep learning and structure monitoring response

By using deep learning and structural monitoring response, a smart perception model for bridge pier damage was constructed using a one-dimensional convolutional neural network and ordinal regression method. This solved the problem of lag in the assessment of bridge pier damage status after a vehicle collision, enabling rapid and accurate identification and early warning of damage status, and improving the efficiency of bridge safety maintenance.

CN121936282APending Publication Date: 2026-04-28SOUTHEAST UNIV
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
SOUTHEAST UNIV
Filing Date
2026-01-14
Publication Date
2026-04-28

AI Technical Summary

Technical Problem

Existing technologies are unable to quickly and automatically assess the damage after a vehicle hits a bridge pier, leading to traffic closures and delays in emergency response.

Method used

By employing deep learning and structural monitoring response, the bridge pier response data is collected in real time through sensors. A damage intelligent perception model is constructed using a one-dimensional convolutional neural network and ordinal regression method to achieve real-time assessment and early warning of damage status.

Benefits of technology

It enables real-time perception and early warning of bridge pier damage, with a recall rate of over 92%, significantly improving the efficiency of bridge safety maintenance and emergency response speed.

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Abstract

The invention discloses a vehicle-collided pier damage state intelligent sensing method based on deep learning and structure monitoring response, and the method comprises the steps: obtaining pier dynamic response and damage state data when a vehicle collides with a pier, and carrying out the classification and arrangement to construct a sample data set; performing normalization preprocessing on the sample data, and dividing data sets and batches; according to the divided data sets, training and verifying the constructed intelligent perception deep learning model for the pier impact damage, storing a deep learning network model with optimal weight parameters in the training process, and deploying the deep learning network model to a remote terminal as a perception and evaluation model; collecting bridge pier response data in real time; and inputting bridge pier response data obtained by the remote terminal into the perception and evaluation model to realize rapid perception and evaluation of the impact damage. The method has the advantages of economy and high efficiency, and the impact damage state of the bridge pier can be accurately and quickly sensed by using the structure response data monitored in real time, so that support is provided for bridge management and maintenance and quick emergency decision making.
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Description

Technical Field

[0001] This invention belongs to the field of highway bridge monitoring and maintenance technology, and relates to the technology for assessing the damage status of bridge piers in vehicle collisions. Specifically, it relates to an intelligent perception method for the damage status of bridge piers in vehicle collisions based on deep learning and structural monitoring response. Background Technology

[0002] With the rapid growth in transportation demand, the risk of collisions between vehicles and bridge piers is increasing, becoming one of the leading causes of sudden damage and even collapse of bridge structures worldwide. Impacts from heavy trucks or high-speed vehicles can not only cause severe damage to the substructure of bridges but also result in injuries and fatalities and partial paralysis of urban transportation systems. Therefore, quickly and accurately assessing the damage to bridge piers after a collision is of significant practical importance for timely emergency response, developing scientific bridge maintenance strategies, and ensuring safe operation in the future.

[0003] Currently, damage perception for vehicle-to-bridge collisions is mainly divided into two categories: pre-collision damage prediction and post-collision damage assessment. Pre-collision prediction primarily targets the bridge design phase, using collision tests or finite element simulations to analyze the impact process, impact force, pier damage, and failure modes, thus providing a basis for crashworthiness design. This method is well-suited for the design phase, but its application in the post-construction operation and maintenance phase has certain limitations. For example, it typically relies on preset parameters such as vehicle mass and impact speed, which are often difficult to obtain in real-time during actual collisions. The second type of assessment method is post-collision assessment, which mainly refers to on-site assessment and analysis of pier damage after an accident. This includes manual visual inspection by technicians or analysis of the accident's causes and the extent of damage based on on-site investigations. Although on-site inspections provide direct evidence for subsequent decision-making, the process is usually time-consuming, labor-intensive, subjective, and carries certain safety risks. Furthermore, the lag in response also affects the golden time for triggering traffic closures and emergency rescue.

[0004] Overall, current research lacks effective means to achieve rapid and automatic assessment of bridge pier damage in a very short time after an accident. Summary of the Invention

[0005] Purpose of the invention: To overcome the shortcomings of existing technologies for sensing damage to bridge piers after vehicle impacts, this invention provides an intelligent sensing method for the damage status of bridge piers after vehicle impacts based on deep learning and structural monitoring response. This method has the advantages of being economical and efficient, and can accurately and quickly sense the impact damage status of bridge piers using real-time monitored structural response data, thereby providing support for bridge maintenance and rapid emergency decision-making.

[0006] Technical Solution: To achieve the above objectives, this invention provides an intelligent perception method for the damage state of bridge piers in vehicle collisions based on deep learning and structural monitoring response, comprising the following steps:

[0007] S1: Acquire dynamic response and damage status data of the bridge pier when a vehicle collides with it;

[0008] S2: Classify and organize the pier response and damage status data to construct a sample dataset;

[0009] S3: Perform normalization preprocessing on the sample data obtained in step S2, and divide the dataset into datasets and batches;

[0010] S4: Based on the divided dataset, train and validate the constructed intelligent perception deep learning model for bridge pier impact damage, save the deep learning network model with the best weight parameters during training, and deploy it to a remote terminal as a perception and evaluation model.

[0011] S5: When a vehicle collides with a bridge pier, sensors deployed on the bridge pier collect the bridge pier's response data in real time and transmit it to a remote terminal via an industrial router.

[0012] S6: Input the pier response data obtained from the remote terminal into the perception and assessment model to achieve rapid perception and assessment of impact damage.

[0013] Furthermore, in step S1, data on the dynamic response and damage status of the bridge pier when the vehicle collides with it are obtained through finite element simulation or actual monitoring.

[0014] Furthermore, the normalization preprocessing method in step S3 includes mapping the original sequence data to the interval [0,1]. Specifically, this involves first calculating the maximum value X of the original sequence data. max and minimum value X min Then, for each data X in the sequence... i Subtract X min Then divide by (X) max -X min ).

[0015] Furthermore, the intelligent perception deep learning model for bridge pier impact damage in step S4 includes...

[0016] The feature extraction module uses a one-dimensional convolutional neural network to extract data features from the input bridge pier response data;

[0017] The physical characteristic module calculates the following two physical characteristic parameters from the pier top response signal:

[0018] Local peak response R l , which is the peak value of the vibration response at the top of the pier during the continuous impact phase between the vehicle bumper and the engine;

[0019] Global peak response R g , which is the peak value of the entire signal sequence, characterizing the overall vibration amplitude of the structure under vehicle impact;

[0020] The data fusion module combines the data features extracted by the feature extraction module with the two physical features calculated by the physical feature module.

[0021] The classification output module uses ordinal regression to transform the assessment of the N types of damage states of the impacted bridge pier into N-1 binary sub-problems.

[0022] Furthermore, the ordinal regression method in the classification output module includes:

[0023] 1) Label transformation: For a given original training dataset , where x i ∈ X represents the pier response data corresponding to the i-th sample, y i ∈ Y = {DS1, DS2, ..., DS N} represents the impact damage state of the bridge pier corresponding to the sample; label conversion involves constructing a dedicated training dataset for each binary classification sub-problem, and the dedicated training dataset constructed for the k-th binary classification sub-problem is... ,in For binary classification labels, the calculation formula is:

[0024]

[0025] 2) Damage state prediction for unknown samples: The response of unknown bridge piers is predicted using the following formula. Predict the damage status:

[0026]

[0027] In the formula, h(·) represents the mapping relationship between the pier response and the damage state; the calculation formula for the subscript l is as follows:

[0028]

[0029] In the formula, For the k-th binary classifier to handle unknown samples The classification results.

[0030] Furthermore, the model training method in step S4 is as follows: during the backpropagation process of deep learning model training, a loss function is constructed and the model parameters are optimized by gradient descent; the total loss function of the model is composed of the binary cross-entropy loss function corresponding to the ordinal regression model and the loss function corresponding to the physical feature constraints.

[0031] Furthermore, the physical feature constraints used in the model training of step S4 are as follows:

[0032] For any adjacent pier damage state DS k With DS k+1 Higher-order damage state DS k+1 Local peak response R of the corresponding sample l The mean value is significantly higher; mean, the global peak response R0 is also significantly higher. g The mean value also increases with the degree of damage.

[0033] Beneficial Effects: Compared with existing technologies, this invention combines deep learning technology with bridge pier monitoring response data to achieve real-time perception and early warning of bridge pier damage status after a vehicle collision. Existing technologies mainly focus on "post-collision assessment," that is, on-site assessment and analysis of bridge pier damage status after an accident, including manual visual inspection by technicians. These methods cannot perceive the bridge pier damage status in real time immediately after the collision, and this lag affects the golden time for triggering traffic closures and emergency rescue. In contrast, this invention focuses on "in-process monitoring" of collisions. By pre-training a deep learning model that maps bridge pier responses to corresponding damage states and deploying it on a remote terminal, the sensors installed on the bridge pier transmit the monitoring response back to the deep learning model in real time as input, outputting the damage state of the bridge pier. This allows for targeted early warnings of different degrees to be triggered immediately, enabling rapid emergency rescue and bridge maintenance measures. The deep learning model of this invention achieves a recall rate (i.e., the proportion of samples that actually belong to a certain damage state correctly identified by the model) of over 92% for each damage state, demonstrating the model's excellent assessment accuracy. Therefore, the method of the present invention can effectively alleviate the problem of delayed response after an accident, significantly improve the efficiency of bridge safety maintenance, and provide rapid and reliable technical support for safety assessment and emergency classification decision-making based on damage status. Attached Figure Description

[0034] Figure 1 This is a schematic flowchart of the method of the present invention;

[0035] Figure 2 This is a diagram of the deep learning model network architecture used in this invention;

[0036] Figure 3 This is a vehicle-pier impact finite element model used for method verification in this embodiment of the invention;

[0037] Figure 4 This is a perception effect diagram of the damage status of a vehicle colliding with a bridge pier obtained in an embodiment of the present invention;

[0038] Figure 5 This is a comparison chart of the evaluation results of different models. Detailed Implementation

[0039] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0040] Example 1:

[0041] like Figure 1 As shown in the figure, this embodiment provides an intelligent perception method for the damage state of a bridge pier in a vehicle collision based on deep learning and structural monitoring response, including the following steps:

[0042] S1: Obtain dynamic response and damage status data of bridge piers when a vehicle collides with a bridge pier through finite element simulation;

[0043] The specific dynamic response data of the bridge pier can be one of the following: acceleration, displacement, strain, etc. at the top of the bridge pier;

[0044] Damage state data can be: the "equivalent plastic strain cloud map" of the bridge pier after being hit by a vehicle, obtained by finite element simulation. This "equivalent plastic strain cloud map" can directly reflect which areas of the bridge pier have entered plasticity and the degree of plasticity, and therefore can be directly used for damage state determination.

[0045] S2: Classify and organize the pier response and damage status data to construct a sample dataset;

[0046] First, using the damage state data from the "equivalent plastic strain cloud map" in step S1, the damage state of all samples is classified into four categories, such as "DS1 (minor damage), DS2 (moderate damage), DS3 (severe damage), and DS4 (major damage)". Then, the dynamic response of the bridge piers is also categorized into four damage states. Based on this, the constructed dataset contains four categories of bridge pier dynamic responses and corresponding labels (the four damage states DS1, DS2, DS3, and DS4). The bridge pier dynamic response serves as the input to the deep learning model, and the labels serve as the model output.

[0047] S3: Perform normalization preprocessing on the sample data obtained in step S2, and divide the dataset into datasets and batches;

[0048] Normalization preprocessing methods include mapping the original sequence data to the interval [0, 1]. Specifically, this involves first calculating the maximum value X of the original sequence data. max and minimum value X min Then, for each data X in the sequence... i Subtract X minThen divide by (X) max -X min ).

[0049] In deep learning models, batching samples is a crucial step in the training process, and its main functions include the following two points: (1) Memory efficiency optimization: Deep learning models usually require a large amount of data for training. Loading all the data into memory (or GPU memory) at once may lead to insufficient memory. By dividing the data into smaller batches, the data can be loaded and processed batch by batch, reducing memory pressure. (2) Training speed and computational efficiency: Using batches can take advantage of the parallel computing capabilities of hardware (such as GPUs). GPUs can perform matrix operations on multiple samples in a batch at the same time, which greatly improves computational efficiency.

[0050] S4: Based on the divided dataset, train and validate the constructed intelligent perception deep learning model for bridge pier impact damage, save the deep learning network model with the best weight parameters during training, and deploy it to a remote terminal as a perception and evaluation model.

[0051] like Figure 2 As shown, the intelligent perception deep learning model for bridge pier impact damage includes...

[0052] The feature extraction module uses a one-dimensional convolutional neural network to extract data features from the input bridge pier response data;

[0053] The physical characteristic module calculates the following two physical characteristic parameters from the pier top response signal:

[0054] Local peak response R l The peak value of the vibration response at the top of the pier during the continuous impact phase between the vehicle bumper and the engine is calculated using the following formula:

[0055]

[0056] In the formula, R(t) is the vibration response signal of the pier top at time t; t a and t b These are the impact start time and impact end time, respectively, taking into account the continuous impact phase between the vehicle bumper and engine. This indicates taking the absolute value, ensuring that positive and negative peak values ​​are considered; the max operation operates within the specified interval [t]. a , t b Find the maximum absolute value within ] .

[0057] Global peak response R g , representing the peak value of the entire signal sequence, characterizes the overall vibration amplitude of the structure under vehicle impact, and is calculated using the following formula:

[0058]

[0059] In the formula, T is the total signal recording duration; the max operation finds the maximum absolute value within the entire signal duration [0, T].

[0060] The data fusion module combines the data features extracted by the feature extraction module with the two physical features calculated by the physical feature module.

[0061] The role of splicing and fusing data features and physical features is to enhance the accuracy of damage state assessment of deep learning models through physical constraints.

[0062] The classification output module uses ordinal regression to transform the assessment of the N types of damage states of the impacted bridge pier into N-1 binary sub-problems.

[0063] The ordinal regression methods in the classification output module include:

[0064] 1) Label transformation: For a given original training dataset , where x i ∈ X represents the pier response data corresponding to the i-th sample, y i ∈ Y = {DS1, DS2, ..., DS N} represents the impact damage state of the bridge pier corresponding to the sample; label conversion involves constructing a dedicated training dataset for each binary classification sub-problem, and the dedicated training dataset constructed for the k-th binary classification sub-problem is... ,in For binary classification labels, the calculation formula is:

[0065]

[0066] 2) Damage state prediction for unknown samples: The response of unknown bridge piers is predicted using the following formula. Predict the damage status:

[0067]

[0068] In the formula, h(·) represents the mapping relationship between the pier response and the damage state; the calculation formula for the subscript l is as follows:

[0069]

[0070] In the formula, For the k-th binary classifier to handle unknown samples The classification results.

[0071] The "binary classifier" mentioned here is equivalent to the "binary sub-classification problem" mentioned in the label conversion section. Here, "binary classifier" refers to a binary classifier trained using a deep learning model, where the input sample is x during training. iThe output is the binary classification label (obtained from the label conversion part).

[0072] The model training method is as follows: During the backpropagation process of deep learning model training, a loss function is constructed and the model parameters are optimized using gradient descent. The total loss function of the model is composed of the binary cross-entropy loss function corresponding to the ordinal regression model and the loss function corresponding to the physical feature constraints, and its expression is:

[0073]

[0074] In the formula, and These are the loss functions corresponding to the ordinal regression model and the physical feature constraints, respectively. α is a tradeoff hyperparameter, whose optimal value can be determined based on the classification accuracy of the validation set within a pre-defined range using a grid search method.

[0075] The physical feature constraints used in model training are as follows:

[0076] For any adjacent pier damage state DS k With DS k+1 Higher-order damage state DS k+1 Local peak response R of the corresponding sample l The mean value is significantly higher; mean, the global peak response R0 is also significantly higher. g The mean value also increases with the degree of damage.

[0077] The optimal weights are those that perform best on the validation set to ensure the model's generalization ability on unseen data. Their determination is monitored using the validation set, and the steps are as follows:

[0078] (1) Divide the data into independent validation sets: Divide the data into training set, validation set, and test set. The validation set is not used in training and is only used to evaluate the model's performance during training.

[0079] (2) Selection of evaluation metrics: Select appropriate evaluation metrics. This invention uses "accuracy," which is commonly used to evaluate the performance of deep learning classification models, as the evaluation metric.

[0080] (3) Monitoring and determination of optimal weight parameters: After each training round or a certain number of iterations, the model is evaluated on the validation set, and the evaluation metrics are recorded. Throughout the process, the weight parameters at which the evaluation metrics on the validation set are optimal are selected and saved as the best model obtained during the training process.

[0081] S5: Structural response sensors are deployed on the piers of operating bridges. When a vehicle collides with a pier, the structural response sensors collect the pier's response data in real time and transmit it to a remote terminal via an industrial router;

[0082] S6: Input the pier response data obtained from the remote terminal into the perception and assessment model to achieve rapid perception and assessment of impact damage.

[0083] Example 2:

[0084] To verify the effectiveness of the method of this invention in intelligent perception of vehicle-pier impact damage, a finite element model of the vehicle-pier impact was used to generate pier displacement response data and corresponding damage states. The vehicle-pier impact finite element model is as follows: Figure 3 As shown.

[0085] The injury status is divided into four types: DS1 (minor injury), DS2 (moderate injury), DS3 (severe injury) and DS4 (major injury), and a dataset is constructed accordingly.

[0086] The deep learning model of this invention was validated using the constructed dataset:

[0087] Obtain Figure 4 The results, based on the perceived data, show that the model's recall rates for damage states DS1 to DS4 on the validation set were 87.5%, 95.0%, 91.3%, and 85.7%, respectively, demonstrating high recognition completeness for different damage states. On the test set, the corresponding recall rates were 96.0%, 92.0%, 96.7%, and 97.1%, further validating the model's good generalization ability and predictive stability on unseen data. Therefore, it is evident that the deep learning model of this invention can provide reliable technical support for rapid safety assessment and graded decision-making based on damage levels in bridge health monitoring systems.

[0088] Example 3:

[0089] To verify the role of the deep learning model of this invention in assessing damage status by integrating data features and physical features, and the effect of ordinal regression, two model evaluation metrics, accuracy and recall, were used to compare the performance of three models: the deep learning model of this invention considering both physical features and ordinal regression (P-OR), the deep learning model using only ordinal regression (OR), and the traditional classification model (SC) that considers neither physical features nor ordinal regression. The results are as follows: Figure 5 As shown.

[0090] The two model evaluation metrics used are accuracy and recall, and their calculation formulas are as follows:

[0091]

[0092]

[0093] In the formula, i = 1, 2, 3, 4 represent the four damage states; N is the total number of damage samples participating in the assessment; n i TP represents the number of true samples of the i-th type of damage state; i FN represents the number of samples where the i-th damage state is correctly identified as that state by the model; i This represents the number of samples that actually belong to the i-th type of damage state but were not identified by the model.

[0094] Figure 5 The results show that, in both the validation and test sets, the three models exhibit significant differences in their assessment of the four damage states of bridge piers: the P-OR model of this invention performs best, with both evaluation indicators exceeding 90%; the OR model is second, with all indicators above 85%; and the SC model achieves over 80% for all indicators. These results demonstrate the effective role of physical feature fusion and ordinal regression methods in improving the reliability of deep learning models in assessing damage states.

Claims

1. A method for intelligent perception of damage status of bridge piers in vehicle collisions based on deep learning and structural monitoring response, characterized in that, Includes the following steps: S1: Acquire dynamic response and damage status data of the bridge pier when a vehicle collides with it; S2: Classify and organize the pier response and damage status data to construct a sample dataset; S3: Perform normalization preprocessing on the sample data obtained in step S2, and divide the dataset into datasets and batches; S4: Based on the divided dataset, train and validate the constructed intelligent perception deep learning model for bridge pier impact damage, save the deep learning network model with the best weight parameters during training, and deploy it to a remote terminal as a perception and evaluation model. S5: When a vehicle collides with a bridge pier, sensors deployed on the bridge pier collect the bridge pier's response data in real time and transmit it to a remote terminal via an industrial router. S6: Input the pier response data obtained from the remote terminal into the perception and assessment model to achieve rapid perception and assessment of impact damage.

2. The intelligent perception method for vehicle-collision bridge pier damage state based on deep learning and structural monitoring response as described in claim 1, characterized in that, In step S1, data on the dynamic response and damage status of the bridge pier when a vehicle collides with it are obtained through finite element simulation or actual monitoring.

3. The intelligent perception method for vehicle-collision bridge pier damage state based on deep learning and structural monitoring response as described in claim 1, characterized in that, The normalization preprocessing method in step S3 includes mapping the original sequence data to the interval [0, 1]. Specifically, the maximum value X of the original sequence data is first calculated. max and minimum value X min Then, for each data X in the sequence... i Subtract X min Then divide by (X) max -X min ).

4. The intelligent perception method for vehicle-collision bridge pier damage state based on deep learning and structural monitoring response as described in claim 1, characterized in that, The bridge pier impact damage intelligent perception deep learning model in step S4 includes... The feature extraction module uses a one-dimensional convolutional neural network to extract data features from the input bridge pier response data; The physical characteristic module calculates the following two physical characteristic parameters from the pier top response signal: Local peak response R l , which is the peak value of the vibration response at the top of the pier during the continuous impact phase between the vehicle bumper and the engine; Global peak response R g , which is the peak value of the entire signal sequence, characterizing the overall vibration amplitude of the structure under vehicle impact; The data fusion module combines the data features extracted by the feature extraction module with the two physical features calculated by the physical feature module. The classification output module uses ordinal regression to transform the assessment of the N types of damage states of the impacted bridge pier into N-1 binary sub-problems.

5. The intelligent perception method for vehicle-collision bridge pier damage state based on deep learning and structural monitoring response according to claim 4, characterized in that, In the physical feature module: Local peak response R l The calculation formula is: ; In the formula, R(t) is the vibration response signal of the pier top at time t; t a and t b These are the impact start time and impact end time, respectively, taking into account the continuous impact phase between the vehicle bumper and engine. This indicates taking the absolute value, ensuring that positive and negative peak values ​​are considered; the max operation operates within the specified interval [t]. a , t b Find the maximum absolute value within the range; Global peak response R g The calculation formula is: ; In the formula, T is the total signal recording duration; the max operation finds the maximum absolute value within the entire signal duration [0, T].

6. The intelligent perception method for vehicle-collision bridge pier damage state based on deep learning and structural monitoring response according to claim 4, characterized in that, The ordinal regression method in the classification output module includes: 1) Label transformation: For a given original training dataset , where x i ∈ X represents the pier response data corresponding to the i-th sample, y i ∈ Y = {DS1, DS2, ..., DS N } represents the impact damage state of the bridge pier corresponding to this sample; label conversion involves constructing a dedicated training dataset for each binary classification sub-problem, and the dedicated training dataset constructed for the k-th binary classification sub-problem is... ,in For binary classification labels, the calculation formula is: ; 2) Damage state prediction for unknown samples: The response of unknown bridge piers is predicted using the following formula. Predict the damage status: ; In the formula, h(·) represents the mapping relationship between the pier response and the damage state; the calculation formula for the subscript l is as follows: ; In the formula, For the k-th binary classifier to handle unknown samples The classification results.

7. The intelligent perception method for vehicle-collision bridge pier damage state based on deep learning and structural monitoring response according to claim 6, characterized in that, The model training method in step S4 is as follows: during the backpropagation process of deep learning model training, the model parameters are optimized by constructing a loss function and using gradient descent; the total loss function of the model is composed of the binary cross-entropy loss function corresponding to the ordinal regression model and the loss function corresponding to the physical feature constraints.

8. The intelligent perception method for vehicle-collision bridge pier damage state based on deep learning and structural monitoring response according to claim 7, characterized in that, In step S4, during model training, the expression for the model's total loss function is: ; In the formula, and These are the loss functions corresponding to the ordinal regression model and the physical feature constraints, respectively. α is a tradeoff hyperparameter, whose optimal value is determined based on the classification accuracy of the validation set within a pre-defined range using a grid search method.

9. The intelligent perception method for vehicle-collision bridge pier damage state based on deep learning and structural monitoring response according to claim 8, characterized in that, In the model training of step S4, the physical feature constraints used are as follows: For any adjacent pier damage state DS k With DS k+1 Higher-order damage state DS k+1 Local peak response R of the corresponding sample l The mean value is significantly higher; mean, the global peak response R0 is also significantly higher. g The mean value also increases with the degree of damage.