Bridge network anti-seismic toughness evaluation method based on GAN-Stacking model

Abstract

The invention relates to the technical field of crossing of bridge engineering and machine learning, in particular to a bridge network anti-seismic toughness evaluation method based on a GAN-Stacking model, and the method comprises the following steps: S1, generating a parameterized bridge model and carrying out the vulnerability analysis; s2, constructing a bridge network sample library based on the GAN; s3, bridge network feature calculation; s4, establishing a toughness index; s5, establishing and training a toughness evaluation model based on Stacking; and S6, performing practical application and verification. According to the method, parametric modeling and the GAN technology are combined, a large number of different bridge network samples can be rapidly generated, rich data are provided for a toughness evaluation model, it is guaranteed that sample features conform to an actual network, and the generalization ability of the model is improved. According to the comprehensive toughness index combining the structural toughness and the functional toughness, the recovery capability of the post-earthquake structure and the traffic function of the bridge network is comprehensively considered, so that the evaluation result is more accurate and comprehensive.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bridge engineering and machine learning, in particular to a bridge network seismic resilience evaluation method based on a GAN-Stacking model. BACKGROUND

[0002] As a key node of the transportation network, the seismic resilience of bridges is directly related to the recovery ability of the post-earthquake transportation system and the normal operation of the city. Traditional bridge seismic evaluation methods are often limited to single bridge structure analysis, making it difficult to comprehensively consider the overall performance of the bridge network. With the expansion of city size and the complexity of transportation networks, there is an urgent need for an efficient evaluation method that can comprehensively consider the structural characteristics of the bridge network, traffic characteristics, and seismic impact.

[0003] The development of machine learning technology provides a new approach to solving this problem. Generative Adversarial Networks (GAN) perform well in generating high-quality data samples, and the Stacking ensemble learning model can effectively handle complex relationships between multiple factors and improve prediction accuracy. However, there is currently no mature technology that combines the two organically for bridge network seismic resilience evaluation. SUMMARY

[0004] The present application aims to provide a bridge network seismic resilience evaluation method based on a GAN-Stacking model, achieving rapid and accurate evaluation of bridge network seismic resilience, and providing a scientific basis for bridge network operation and maintenance and city disaster prevention strategy formulation.

[0005] To achieve the above purpose, the technical solution provided is as follows:

[0006] A bridge network seismic resilience evaluation method based on a GAN-Stacking model, characterized by the following steps:

[0007] S1, parameterized bridge model generation and vulnerability analysis;

[0008] S2, GAN-based bridge network sample library construction;

[0009] S3, bridge network feature calculation;

[0010] S4, resilience index establishment;

[0011] S5, Stacking-based resilience evaluation model establishment and training;

[0012] S6, actual application and verification.

[0013] Preferably, in S1, the specific steps of parameterized bridge model generation and vulnerability analysis are as follows:

[0014] Firstly, using professional bridge design software, according to the set bridge structure parameter range, the parameterized automatic modeling is realized by programming, and 500 bridge models with different parameters are generated;

[0015] Then, the finite element analysis module is used to apply different peak ground acceleration seismic waves to each model to simulate the seismic response and obtain the probability data of the bridge in different damage states, and the bridge fragility data set is formed.

[0016] Preferably, in S2, the specific steps of constructing the bridge network sample library based on GAN are as follows:

[0017] Firstly, the Louvain algorithm is used to extract the sub-topological network of the corresponding city in a region and establish a sub-topological network database;

[0018] Secondly, when establishing the virtual database of the sub-topological network, data enhancement is performed first, and then a GAN network model is constructed to generate a virtual sub-topology. The high similarity of the sample to the real sub-topological structure indicates that the performance of the WGAN model meets the expectation. Finally, the virtual sample library is established in combination with the related sub-topological network;

[0019] Finally, according to the sub-topological network sample library, the bridge topological network is formed by matching the same number of parameterized bridge samples according to the number of network nodes, and the bridge network sample library is established. The topology can reflect the actual road network bridge network structure characteristics.

[0020] Preferably, in S3, the bridge network feature calculation includes structure feature calculation and traffic feature calculation.

[0021] Specifically, the structure feature calculation includes clustering coefficient, connectivity, average shortest path, node betweenness and node degree;

[0022] The clustering coefficient calculation is the ratio of the actual number of links between the nodes directly linked around each node in the bridge network to the maximum possible number of links between the nodes around it, and then the average of the clustering coefficients of all nodes in the network is calculated, and the expression is:

[0023]

[0024] In the formula: R e (i) is the actual number of links between the nodes directly linked to node i, and k(i) is the number of nodes directly linked to node i.

[0025] The connectivity calculation is the ratio of the actual value of the number of edges in the network to the theoretical maximum value, and the expression is:

[0026]

[0027] Wherein: L is the total number of edges of the network, N is the total number of nodes of the network.

[0028] The average shortest path is the average value of the shortest path length between two points in the network, and the expression is:

[0029]

[0030] Wherein: d ij is the shortest path length between i and j;

[0031] The node betweenness is the proportion of the number of paths passing through the node in all shortest paths in the network, and the average value of all nodes is taken, and the expression is:

[0032]

[0033] Wherein: m inj is the number of shortest paths between nodes i and j passing through node n, m ij is the number of shortest paths between nodes i and j, and N is the total number of nodes in the network.

[0034] The node degree represents the number of edges directly linked between a node and other nodes, and the average value of all node degrees is taken, and the expression is:

[0035]

[0036] Wherein: R(i) represents all nodes around node i, and N is the total number of nodes in the network;

[0037]

[0038] Specifically, the traffic feature is calculated as the total traffic demand of the bridge network and the expected value of the bridge network function loss rate, and the total traffic demand of the bridge network is the sum of the elements of the bridge network traffic demand matrix, and the expression is:

[0039] D={q ij},T=∑ qij (6)

[0040] Wherein: D is the bridge network traffic demand matrix, T is the total traffic demand of the bridge network, q ij is the traffic demand between nodes i and j.

[0041] Considering the impact of bridge damage on network function after an earthquake, ignoring road function loss, the expected value of bridge network function loss rate is obtained by taking the average value of the product of the probability expectation value corresponding to different damage states of all bridges in the network and the function loss rate, and the expression is:

[0042]

[0043] wherein: ξ is the loss rate of the traffic capacity of the bridge b in the k damage state under the action of the earthquake EM; P k|EM (b) is the probability of the bridge b being in the k damage state under the action of the earthquake EM, obtained by the vulnerability analysis; wherein k = 1, 2, 3, 4 respectively represent four states of the bridge being in a slight damage, a moderate damage, a severe damage and a basic collapse.

[0044] Preferably, in S4, the resilience index establishment comprises structural resilience, functional resilience and comprehensive resilience.

[0045] The structural resilience is defined as the ratio of the post-earthquake bridge network efficiency to the pre-earthquake bridge network efficiency; the pre-earthquake bridge network efficiency is the ratio of the sum of the shortest paths between any two points in the network to the maximum number of edges, and the expression is:

[0046]

[0047] wherein: d ij represents the shortest distance between nodes i and j, and N is the total number of network nodes.

[0048] The post-earthquake bridge network efficiency takes into account the loss of traffic capacity caused by the damage of the bridge, and the network efficiency is improved by introducing the bridge function loss rate and the damage exceeding probability;

[0049]

[0050] wherein: Q ij is defined as the expected value of the network function retention rate between nodes i and j; H represents the number of shortest paths between nodes i and j, and m n represents the number of bridge nodes on the nth shortest path.

[0051] Based on the above, the expression of the structural resilience is:

[0052]

[0053] The functional resilience takes the driving time resilience as an index, and the driving time resilience is calculated based on the traffic flow borne by the road section before and after the earthquake and the driving time change through the road section, wherein the traffic flow before and after the earthquake is obtained by using the incremental distribution method according to the traffic demand, and the driving time is calculated according to the BPR function proposed by the United States Federal Highway Administration. The expression of the network function resilience is:

[0054]

[0055] wherein: x0(i), x d (i) respectively represent the traffic flow borne by the road section i before and after the earthquake; t0(i), t d (i) respectively represent the driving time through the road section i before and after the earthquake.

[0056] The comprehensive resilience is combined with the improved network efficiency index and system travel time, and the bridge network seismic resilience evaluation index is defined as

[0057]

[0058] The evaluation index quantifies the seismic resilience of the bridge network by multiplying the ratio of the pre-earthquake and post-earthquake bridge network efficiency and system travel time.

[0059] Preferably, in S5, the specific steps of building and training the Stacking-based resilience evaluation model are as follows:

[0060] S51, model configuration: build a Stacking integrated learning model, select AdaBoost, CatBoost, DecisionTree, GBoost, LightGBM, Random Forest, XGBoost, Extra Tree, etc. As a basic learning machine, LinearRegression is used as a meta-learner; the meta-learner integrates the prediction results of different basic learning machines and outputs the final bridge network seismic resilience prediction value;

[0061] S52, model training and optimization: using the built bridge network sample library, extract the clustering coefficient, connectivity, average shortest path, node betweenness, node degree, calculate the bridge network traffic demand, bridge network function loss rate expectation value and seismic intensity (PGA) and the resilience results corresponding to the 8 characteristic parameters, establish the training set; adopt the method of grid tuning combined with 10 times cross validation to train the model for many times, find the optimal model configuration, and improve the prediction accuracy of the model;

[0062] S53, model evaluation: use Prediction Accuracy, MSPE and MAPE three indexes to evaluate the prediction effect of the model, through training, make the model reach lower MSPE and MAPE value, at the same time have higher Prediction Accuracy, ensure the reliability of the model.

[0063] The beneficial effects of the present application are:

[0064] 1、The present application combines parameterized modeling and GAN technology, can quickly generate a large number of bridge network samples with differences, provides rich data for resilience evaluation model, and ensures that the sample features are consistent with the actual network, improves the generalization ability of the model.

[0065] 2、The comprehensive resilience index combining structural resilience and functional resilience is proposed, which comprehensively considers the recovery ability of the structure and traffic function of the bridge network after the earthquake, so that the evaluation result is more accurate and comprehensive.

[0066] 3. The stacking ensemble learning model effectively handles the complex relationship of multiple factors and improves the prediction accuracy of the seismic resilience of the bridge network, which can quickly evaluate the comprehensive resilience of the bridge network and provide strong support for the operation and maintenance of the bridge network and the formulation of urban disaster prevention strategies. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 The flowchart of the bridge network seismic resilience evaluation method based on the GAN-Stacking model of the application;

[0068] Figure 2 The Anaheim road network and sub-topology in the application;

[0069] Figure 3 The GAN network generated topology example and bridge topology network example in example one of the application;

[0070] Figure 4 The traffic demand heat map of the application;

[0071] Figure 5 The expected value of the function loss rate of the bridge network;

[0072] Figure 6 The structural resilience and functional resilience map of the application;

[0073] Figure 7 The comprehensive resilience prediction value and actual value comparison curve of the application. DETAILED DESCRIPTION

[0074] The technical solutions in the embodiments of the application will be described clearly and completely below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments of the application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the application.

[0075] Example one

[0076] A bridge network seismic resilience evaluation method based on a GAN-Stacking model, as shown in Figure 1 The steps are as follows:

[0077] S1, Parameterized bridge model generation and vulnerability analysis: Using professional bridge design software (such as OpenSees), according to the set bridge structure parameter range (such as span in 20-100 meters, beam height in 1-5 meters, number of piers in 3-10, etc.), through programming to realize parameterized automatic modeling, generate 500 bridge models with different parameters. Using the finite element analysis module, different peak ground acceleration (PGA) seismic waves (such as El Centro wave, Taft wave, etc.) are applied to each model to simulate seismic response and obtain probability data of the bridge under different damage states (slight damage, moderate damage, severe damage, and basic collapse). The bridge vulnerability data set is formed.

[0078] S2, Bridge network sample library construction based on GAN: Taking a region in Anaheim as an example, the Louvain algorithm is used to extract the sub-topological network of 14 cities and establish a sub-topological network database; the sub-topological network extracted from the Anaheim road network is optimized as Figure 2 When establishing the virtual database of sub-topological network, data enhancement is performed first, and then the GAN network model is constructed to generate virtual sub-topology. The high similarity of the sample to the real sub-topological structure indicates that the performance of the WGAN model meets the expectation. Finally, a virtual sample library is established in combination with related sub-topological networks; according to the sub-topological network sample library, the same number of parameterized bridge samples are matched according to the number of network nodes to form a bridge topological network, and a bridge network sample library is established. This topology can more truly reflect the structural characteristics of the bridge network in the actual road network. For example, Figure 3 (Left) shows a randomly extracted generated sub-topological sample, which has high similarity to the real sub-topological structure, indicating that the performance of the trained WGAN model meets the expectation. For example, Figure 3 (Right) shows a bridge topological network sample. This topology can more truly reflect the structural characteristics of the bridge network in the actual road network.

[0079] S3, Bridge network feature calculation: For each network sample in the bridge network sample library, a Python program is written to call the Network-X library to calculate the structural characteristics. The traffic demand matrix is processed using the NumPy library, and the traffic characteristics are calculated. The structural characteristics of the bridge topological network are calculated according to formulas (1)-(5) as shown in Figure 2 The results of each feature calculation are shown in Table 1. The traffic demand between nodes of the bridge network is calculated according to formula (6), Figure 4 which is the traffic demand heat map of the bridge network. The values in the figure are the traffic demand between nodes. The expected value of the functional loss rate of the bridge network under each PGA can be obtained by calculating formula (7), Figure 5 Due to the damage caused by seismic motion to the bridge, this value increases continuously with the increase of PGA, i.e., the functional loss becomes larger and larger.

[0080] Table 1. Bridge topological network structure characteristics

[0081]

[0082] S4, Resilience index establishment: the structure and function resilience of the network can be obtained by calculating formula (8)-formula (12). As Figure 6 , due to the destruction of the bridge after the earthquake, the increase of the shortest travel path between the network nodes leads to the decrease of the network efficiency, so the structure resilience is constantly decreasing with the increase of PGA; at the same time, the decrease of the bridge capacity after the earthquake causes the increase of the total driving time of the system, so the function resilience is also constantly decreasing with the increase of PGA. By calculating the network structure resilience and function resilience, the comprehensive seismic resilience of the bridge network can be obtained by using formula (13). For a bridge network sample in Anaheim, when PGA is 0.3g, the structure resilience is calculated to be 0.6, the function resilience is 0.7, and the comprehensive resilience is 0.65.

[0083] S5, Stacking-based resilience evaluation model establishment and training: use Python's scikit-learn library to build a Stacking model, configure the base learner and meta-learner. Select 5000 samples from the bridge network sample library as the training set, set the grid search parameter range (such as the learning rate of AdaBoost in 0.01-0.1, the maximum depth of decision tree in 3-10, etc.), and perform 10-fold cross-validation training. After multiple training, the optimal model configuration is obtained, at this time the PredictionAccuracy of the model reaches 0.9134, the MSPE is 0.0145, and the MAPE is 0.0698.

[0084] Using the structure characteristics, traffic characteristics and seismic intensity of the network as input, the seismic resilience prediction value of the network can be obtained by using the resilience evaluation model. Figure 7 That is, by comparing the calculated resilience and the predicted resilience, it can be seen that the calculated resilience curve and the predicted resilience curve have the same characteristics. It is found that the calculated resilience curve and the predicted resilience curve have the same trend, the maximum relative error is 8.74%, and the maximum absolute error is 0.025, which verifies the effectiveness of the present application.

[0085] For those skilled in the art, it is obvious that the present application is not limited to the details of the above exemplary embodiments, and can be implemented in other specific forms without departing from the spirit or essential characteristics of the present application. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting, the scope of the present application is defined by the appended claims rather than the above description, and therefore all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present application. Any reference signs in the claims should not be regarded as limiting the claims involved.

Claims

1. A method for evaluating the seismic resilience of a bridge network based on a GAN-Stacking model, characterized in that, The steps include the following: S1, parameterized bridge model generation and vulnerability analysis; S2, bridge network sample library construction based on GAN; S3, bridge network feature calculation; S4, resilience index establishment; S5, resilience evaluation model establishment and training based on stacking; S6, actual application and verification.

2. The method of claim 1, wherein the method is characterized by, In S1, the specific steps of the parameterized bridge model generation and vulnerability analysis are as follows: First, use professional bridge design software to generate 500 bridge models with different parameters by programming according to the set bridge structure parameter range; Then, use the finite element analysis module to apply different peak ground acceleration seismic waves to each model to simulate seismic response and obtain probability data of the bridge in different damage states, and organize to form a bridge vulnerability data set.

3. The method of claim 1, wherein the method is characterized by, In S2, the specific steps of the bridge network sample library construction based on GAN are as follows: First, use Louvain algorithm to extract and establish a sub-topological network database for the corresponding city in a certain region; Second, when establishing the virtual database of the sub-topological network, first perform data enhancement, then construct a GAN network model to generate a virtual sub-topology, and the high similarity of the sample to the real sub-topological structure indicates that the performance of the WGAN model meets the expectation. Finally, combine related sub-topological networks to establish a virtual sample library; Finally, according to the sub-topological network sample library, match the same number of parameterized bridge samples according to the number of network nodes to form a bridge topological network, and establish a bridge network sample library. This topology can more truly reflect the structural characteristics of the bridge network in the actual road network.

4. The method of claim 1, wherein the method is characterized by, In S3, the bridge network feature calculation includes structure feature calculation and traffic feature calculation.

5. The method of claim 4, wherein the method is characterized by, The structure feature calculation includes clustering coefficient, connectivity, average shortest path, node betweenness, and node degree; The clustering coefficient calculation is for each node in the bridge network, that is, the ratio of the actual number of links between the node and the surrounding nodes to the maximum possible number of links between the surrounding nodes. Then, the average of the clustering coefficients of all nodes in the network is calculated, and the expression is: where: R e (i) is the actual number of links between nodes directly linked to node i, k(i) is the number of nodes directly linked to node i; The connectivity calculation is the ratio of the actual value of the number of edges in the network to the theoretical maximum value, and the expression is: In the formula, L is the total number of edges, and N is the total number of nodes; The average shortest path is the average value of the shortest path length between two points in the network, and the expression is: where: d ij is the shortest path length between i, j The node betweenness is the proportion of the number of paths passing through the node in all shortest paths, and the average of all nodes is taken, and the expression is: where: m inj is the number of shortest paths between nodes i, j through node n, m ij is the number of shortest paths between nodes i, j, and N is the total number of nodes in the network. The node degree represents the number of edges directly linked between a node and other nodes, and the average of all node degrees is taken, and the expression is: In the formula, R(i) represents all nodes around node i, and N is the total number of nodes; 6. The method of claim 4, wherein the method is characterized by, The traffic feature calculation is to calculate the total traffic demand of the bridge network and the expected value of the function loss rate of the bridge network. The total traffic demand of the bridge network is the sum of the elements of the bridge network traffic demand matrix, and the expression is: D = {q ij}, T = Σq ij (6) where D is the bridge network traffic demand matrix, T is the total traffic demand of the bridge network, q ij is the traffic demand between nodes i, j. Considering the impact of bridge damage on network function after earthquake, the expected value of bridge network function loss rate is calculated by the average value of the product of the probability expectation value corresponding to different damage states of all bridges in the network and the function loss rate, which is expressed as: In the formula, ξ is the loss rate of the traffic capacity of the bridge b in the earthquake EM effect, P k|EM (b) is the probability of the bridge b in the k damage state under the earthquake EM effect, obtained by vulnerability analysis; wherein k = 1, 2, 3, 4, respectively, indicating that the bridge is in four states of slight damage, moderate damage, severe damage, and basic collapse.

7. The method of claim 1, wherein the method is characterized by, In S4, the resilience index is established, including structural resilience, functional resilience and comprehensive resilience. The structural resilience is defined as the ratio of post-earthquake to pre-earthquake bridge network efficiency, and the pre-earthquake bridge network efficiency is the ratio of the sum of the shortest paths between any two points in the network to the maximum number of edges, which is expressed as: where: d ij represents the shortest distance between nodes i, j, and N is the total number of nodes in the network. The post-earthquake bridge network efficiency takes into account the loss of traffic capacity caused by bridge damage, and is improved by introducing the bridge function loss rate and the damage exceeding probability. In the formula, Q ij The definition is the expected value of network function retention rate between nodes i, j; H represents the number of shortest paths between nodes i, j, m n The number of bridge nodes on the nth shortest path is represented. Therefore, the expression of the structural resilience is: The functional resilience takes the travel time resilience as an index, which is calculated based on the traffic flow on the road section before and after the earthquake and the change of travel time through the road section, where the traffic flow before and after the earthquake is obtained by using the incremental distribution method according to traffic demand, and the travel time is calculated according to the BPR function proposed by the US Federal Highway Administration; the expression of the network function resilience is: wherein: x0(i), x d (i) represent the traffic flow on link i before and after the earthquake, respectively; t0(i), t d (i) represent the travel time on link i before and after the earthquake, respectively; The comprehensive resilience combines the improved network efficiency index and the system travel time, and the bridge network seismic resilience evaluation index is defined as This evaluation index quantifies the seismic resilience of the bridge network by multiplying the pre-earthquake and post-earthquake bridge network efficiency and the system travel time.

8. The method of claim 1, wherein the method is characterized by, In S5, the specific steps of building and training the Stacking-based resilience evaluation model are as follows: S51, model configuration: build a Stacking ensemble learning model, select AdaBoost, CatBoost, DecisionTree, GBoost, LightGBM, Random Forest, XGBoost, Extra Tree, etc. as the base learner, and LinearRegression as the meta-learner; the meta-learner integrates the prediction results of different base learners and outputs the final bridge network seismic resilience prediction value; S52, model training and optimization: use the built bridge network sample library to extract the clustering coefficient, connectivity, average shortest path, node betweenness, node degree, calculate the total traffic demand of the bridge network, the expected value of the bridge network function loss rate, and the seismic intensity (PGA) corresponding to the resilience results of 8 characteristic parameters, and establish the training set; use grid tuning combined with 10-fold cross-validation method to train the model multiple times to find the optimal model configuration to improve the prediction accuracy of the model; S53, model evaluation: use Prediction Accuracy, MSPE, MAPE three indexes to evaluate the prediction effect of the model, through training, make the model have lower MSPE and MAPE value, and at the same time have higher Prediction Accuracy, to ensure the reliability of the model.

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