A pre-earthquake reinforcement analysis optimization method for urban bridge network based on dynamic-static intermingled model

Abstract

The present application belongs to the technical field of bridge engineering, and particularly relates to a city bridge network pre-earthquake reinforcement analysis optimization method based on a dynamic and static intermingled model, comprising the following steps: establishing a city bridge network model, i.e. a bridge network topological structure; analyzing the weight of each static topological index by PPR to preliminarily obtain the importance index of each node of the bridge; obtaining the weight information by PPR and then combining the TOPSIS method to comprehensively evaluate all bridge nodes of the upper network; simulating a post-earthquake traffic flow sandpile model; reasonably dynamically correcting the comprehensive evaluation of the network bridge nodes; and optimizing the bridge pre-earthquake reinforcement strategy. The present application establishes a dynamic and static intermingled city bridge network model, adopts the PPR-TOPSIS method when evaluating the static network, and uses the link analysis method to reduce the influence of a certain subjectivity and increase the link tightness between the network structure characteristics and the network itself.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering technology, and specifically relates to a pre-earthquake pre-strengthening analysis and optimization method for urban bridge networks based on a dynamic-static fusion model. Background Technology

[0002] Urban bridges are often located at key transportation hubs and form regional connections. When subjected to earthquakes, their seismic resistance is relatively weak, making them prone to complete destruction or collapse. Bridge damage directly impacts the transportation function of the surrounding road network and severely hinders subsequent rescue and reconstruction efforts. Therefore, how to prioritize reinforcement using limited resources and implement "precise reinforcement" to improve the seismic performance of urban bridge networks is a pressing issue that must be addressed. "Precise reinforcement" involves assessing the seismic performance of the bridge network before an earthquake and then accurately reinforcing each bridge within the network. This effectively improves resource utilization and reduces waste. Earthquakes cause functional losses to bridge components in urban transportation networks, leading to significant traffic congestion, blockages, and even paralysis. Therefore, after obtaining a comprehensive evaluation of the static network bridge nodes, it is necessary to conduct post-earthquake traffic simulations and further refine the evaluation of bridge nodes through dynamic traffic congestion analysis to guide pre-earthquake bridge reinforcement work. Summary of the Invention

[0003] The purpose of this invention is to provide an optimization method for pre-earthquake reinforcement analysis of urban bridge networks based on a dynamic-static integrated model, so as to solve the problem of determining the priority of reinforcement under the premise of limited resources and to improve the seismic performance of urban bridge networks through "precise reinforcement".

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] A pre-earthquake reinforcement analysis and optimization method for urban bridge networks based on a dynamic-static fusion model, characterized by the following steps:

[0006] Step 1: Establish a city bridge network model, i.e., the bridge network topology;

[0007] Step 2: Analyze the weight of each static topology index using PPR to obtain preliminary importance indices for each node of the bridge.

[0008] Step 3: Use PPR to obtain weight information, and then combine it with the TOPSIS method to comprehensively evaluate all bridge nodes in the upper layer network;

[0009] Step 4: Simulate a post-earthquake traffic quicksand pile model;

[0010] Step 5: Make reasonable dynamic adjustments to the comprehensive evaluation of network bridge nodes;

[0011] Step 6: Optimization of pre-earthquake reinforcement strategies for bridges.

[0012] Preferably, in step one, a topology network diagram is established in layers when performing analysis of key bridge nodes.

[0013] Specifically, the method for establishing the urban bridge network model, i.e., the bridge network topology, is as follows: When performing static structural characteristic analysis (upper layer) on the bridge network topology, the Dual Approach method is used to establish an undirected bridge network to fully restore the original characteristics of the bridge network; when performing simulated post-earthquake dynamic traffic flow congestion sand pile model analysis (lower layer) on the bridge network topology, the Primal Approach method is used to establish the topology to ensure that the traffic characteristics of the bridge network remain unchanged after the earthquake.

[0014] Preferably, in step two, four static topology indicators are selected to study the topological characteristics of the bridge network, achieving a more favorable comprehensive evaluation of the bridge nodes; the four static topology indicators are node degree value, betweenness coefficient, clustering coefficient, and economic cost; the calculation formulas for each indicator are as follows:

[0015] Node degree value: ;

[0016] In the formula: Represents a node All surrounding nodes;

[0017] Betweenness: ;

[0018] In the formula: Represents bridge nodes , Among all shortest distances between nodes The number; express , The number of all shortest distances between them;

[0019] Clustering coefficient: ;

[0020] In the formula: For nodes The actual number of links between directly linked nodes; For nodes The number of directly linked nodes; economic costs calculated based on actual circumstances.

[0021] Preferably, in step two, the steps for analyzing the weights of each static topology index using PPR are as follows:

[0022] Step 1: Define the initial value of the importance of each bridge node to each indicator;

[0023] Step 2: Determine the link probability using link analysis. Specifically, define the node link probability as a combination of the topological link probability and the average capacity loss rate between bridge nodes, expressed as:

[0024] ;

[0025] In the formula: , representing the node degree value, Represents a node All surrounding nodes;

[0026]

[0027] This link analysis method can reduce the influence of subjectivity to a certain extent and increase the tightness of the link between network structure characteristics and the network itself;

[0028] Step 3: Determine the weight of each indicator; Since the initial values ​​of each indicator to the importance of the node are different, the iteration results are also different. Define the PageRank score of a certain bridge node for each indicator as its weight reference.

[0029] Specifically, to ensure the universality of the results, six bridge nodes are randomly selected, and their weights for each indicator are calculated. Then, the average of the six weights for each indicator is calculated and normalized to obtain the weights of each indicator.

[0030] Preferably, in step two, the performance index for evaluating the overall bridge network is defined by combining the network's global efficiency with the bridge's traffic capacity, expressed as:

[0031]

[0032] In the formula: This represents the number of bridges contained in the network. This represents the total number of all non-bridge nodes in the lower-level network. for , Shortest distance between; To ensure the bridge's traffic capacity before the earthquake; This represents the expected capacity of the bridge. For nodes , The number of bridges included in the area.

[0033] Preferably, in step three, the method for comprehensive evaluation of PPR-TOPSIS is as follows:

[0034] Step 1: Combine the obtained weights of each indicator with the bridge node indicators to form a weighted, standardized evaluation matrix. The expression is as follows:

[0035]

[0036] In the formula: Indicates the weight of each indicator; These are the standardized node degree value, betweenness, clustering coefficient, and economic cost, respectively.

[0037] Step 2, according to The optimal and inferior solutions can be directly calculated using the following expressions:

[0038]

[0039] Step 3, Define the first The distances between each target node and the optimal and inferior solutions are expressed as follows:

[0040]

[0041] Step 4: Use the proximity formula The importance of all bridge nodes is ranked.

[0042] All network static indicators in this invention are extremely large, so the process of positiveizing the indicators is omitted; and because there is no need to process the dimensions.

[0043] Preferably, in step four, the sand pile model differs from the traditional queuing model because it considers the reduced bridge capacity and decreased vehicle efficiency after an earthquake. However, the cumulative speed of vehicles queuing upstream of the bridge remains unchanged, resulting in congestion on the upstream section of the bridge. The sand pile model also considers bridge damage; in damaged sections, reduced capacity leads to a decrease in the transmission speed of the initiation wave, thus reducing the queue length during the transmission of the initiation wave from the head of the queue to the tail when the green light turns on. It will decrease, assuming the number of sudden changes in vehicle queue length during the alternation of traffic lights. as well as The reduction is determined by the loss of traffic capacity, and its expression is:

[0044]

[0045]

[0046] In the formula: The rate of loss of traffic capacity of a road segment, i.e., compared with quite;

[0047] Therefore, the length of the convoy when it dissipates is:

[0048] In the formula: The length of the queue when the green light is on; This represents the speed at which the last vehicle in the convoy arrives.

[0049] Preferably, in step five, when dynamically correcting the comprehensive evaluation of bridge network nodes, the importance correction value is defined as:

[0050]

[0051] In the formula: Represents a node The global network efficiency loss rate caused by failure. For nodes Network efficiency during failure; Represents a node The proportion of network collapses to all network collapses, of which This indicates the total number of times a node collapses during the simulation;

[0052] The obtained result is normalized and added to the static result to obtain the corrected final result.

[0053] Preferably, in step six, reinforcement strategies are formulated based on the static evaluation results, the dynamic simulation of the collapse, and the dynamic correction results, respectively, and are implemented according to the formula... Calculate the toughness of the bridge network system after pre-strengthening.

[0054] The present invention has the following beneficial effects: It establishes a dynamic and static integrated urban bridge network model. When evaluating the static network, the PPR-TOPSIS method is adopted. The use of link analysis can reduce the influence of subjectivity and increase the tightness of the connection between the network structure characteristics and the network itself. When conducting post-earthquake traffic simulation at the lower level, the queuing model incorporates the consideration of bridge damage, which is more in line with the characteristics of post-earthquake traffic. It is also reasonably modified in combination with the sand pile model. Based on this, it helps decision-makers to formulate more reasonable pre-earthquake reinforcement strategies, so that the seismic performance of the urban bridge network can be maximized under limited resource conditions. Attached Figure Description

[0055] Figure 1 This is a traffic network layout diagram in an embodiment of the present invention;

[0056] Figure 2 This is the dual topology graph established using the Dual Approach method in this embodiment of the invention;

[0057] Figure 3 These are diagrams illustrating the collapse conditions of various bridge sections in embodiments of the present invention.

[0058] Figure 4 This is a diagram showing the importance correction values ​​of each bridge node in the embodiments of the present invention;

[0059] Figure 5These are three different pre-reinforcement strategies in this invention, with a comparison of toughness before and after pre-reinforcement. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0061] Example 1

[0062] This embodiment uses a simplified traffic network map of a certain area as an example to illustrate in detail the pre-earthquake reinforcement analysis and optimization method for urban bridge networks based on a dynamic-static fusion model, as described in this invention.

[0063] The local transportation network information is as follows: It has 12 road intersections and 17 two-way road sections, including 17 bridge sections. Five intersections are earthquake focal points, and nine are emergency rescue points. Figure 1 As shown.

[0064] Step 1: Using the Dual Approach, based on the upper-level structure, establish a topology graph focusing on bridges for analysis, such as... Figure 2 As shown, there are a total of 17 bridge nodes. Based on this, four static index characteristics of the bridge nodes, namely the standard initial values, are obtained, including degree value, betweenness coefficient, clustering coefficient, and economic cost. The calculation formulas for each index are as follows:

[0065] Node degree value: ;

[0066] In the formula: Represents a node All surrounding nodes;

[0067] Betweenness: ;

[0068] In the formula: Represents bridge nodes , Among all shortest distances between nodes The number; express , The number of all shortest distances between them;

[0069] Clustering coefficient: ;

[0070] In the formula: For nodes The actual number of links between directly linked nodes; For nodes The number of directly linked nodes; economic costs calculated based on actual circumstances.

[0071] Step 2: Based on the initial values ​​of each indicator, use the PPR method to obtain the relative importance of each indicator to each bridge node;

[0072] Step 3: Randomly select nodes 1, 3, 6, 9, 12, and 17. Using the TOPSIS method, obtain the standard mean PageRank values ​​of each indicator at the nodes as follows: 0.032, 0.041, 0.024, and 0.036. After normalization, obtain the weights of each indicator as follows: =0.24、 =0.31、 =0.18、 =0.27.

[0073] By organizing the indicators and corresponding weights of each node, a standardized matrix is ​​obtained. The distance between the advantages and disadvantages of each node is calculated to obtain the final score. The higher the score, the higher the importance of the node. Based on the scores of each bridge node in the traffic network, the importance of the upper structure with static characteristics is evaluated. Through the evaluation of the importance of the upper structure with static characteristics, it is found that 3, 14, 13, 4, 9, and 1 are more important. Solving for superior and inferior solutions and the first The distance expressions between each target node and the optimal and inferior solutions are as follows:

[0074]

[0075] In the formula: Indicates the weight of each indicator; These represent the standardized node degree, betweenness, clustering coefficient, and economic cost, respectively.

[0076]

[0077]

[0078] Step 4: Employ the Primal Approach to establish a dynamic simulation of the lower-level traffic network. Specifically, each node of the city's bridge topology network and its upstream road segment are considered a sandpile, and each vehicle is considered a grain of sand. When the length of the queued vehicles exceeds the length of the road segment, congestion spreads, i.e., the sandpile collapses. The excess sand grains are optimally distributed to other sandpiles, thus affecting them and forming a network avalanche. All road segments and nodes in the entire topology network constitute a complete sandpile model. Traffic information at 0, 3, 6, and 9 hours after the earthquake is input to simulate the traffic situation within 12 hours after the earthquake, and the starting wave velocity is set. R'=1.5g, and then the network was simulated for post-earthquake traffic sand piles.

[0079] Step 5: Based on the simulation results, discuss the statistical characteristics of the simulation results for 3, 6, 9, and 12 hours, including counting the number of avalanches on each bridge section and calculating the sand pile dynamics correction value, using the number of collapses on the section where bridge 8 is located as the standard value. The results are as follows: Figure 3 and Figure 4 As shown in the figure, the more times the node collapses, the more likely it is to become congested after an earthquake; while the larger the correction value, the more times the node collapses in the long-term sand pile collapse model, and the greater the impact of each collapse on the overall network.

[0080] The obtained correction value is added to the superstructure importance evaluation based on static characteristics to obtain the comprehensive evaluation of the bridge node.

[0081] Step 6: Based on the static evaluation results (a), the dynamic simulation of the collapse (b), and the dynamic correction results (c), formulate reinforcement strategies. Define the pre-reinforcement strategy as an evaluation result greater than or equal to 50%. The pre-reinforcement strategies are shown in the table below:

[0082] (a) 1、3、4、7、9、12、13、14 (b) 8、10、16 (c) 1、3、4、7、8、9、10、12、13、14

[0083] According to the formula Calculate the toughness of the bridge network system after pre-strengthening;

[0084] The results of the three pre-hardening strategies are as follows Figure 5 As shown; by Figure 5 It can be seen that the resilience of strategy (c) after dynamic correction reaches 0.543, the resilience of strategy (b) after only dynamic evaluation is 0.225, and the resilience of strategy (a) after only static evaluation is 0.498. Compared with the network without pre-reinforcement, the resilience of each strategy has increased by 194.67%, 33.14%, and 221.3% respectively, indicating that the present invention can effectively improve the seismic resilience of bridge networks and is feasible.

[0085] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A pre-earthquake pre-strengthening analysis and optimization method for urban bridge networks based on a dynamic-static fusion model, characterized in that, Includes the following steps: Step 1: Establish the urban bridge network model, i.e., the bridge network topology. When analyzing key bridge nodes, a layered topology network diagram is established. The method for establishing the urban bridge network model, i.e., the bridge network topology, is as follows: When performing static structural characteristic analysis on the upper-level bridge network topology, to fully restore the original characteristics of the bridge network, the Dual Approach method is used to establish an undirected bridge network. When performing simulated post-earthquake dynamic traffic flow congestion sand pile model analysis on the lower-level bridge network topology, to ensure that the traffic characteristics of the bridge network remain unchanged after the earthquake, the Primal Approach method is used to establish the topology diagram. Step 2: Analyze the weight of each static topology index using PPR to obtain preliminary importance indices for each node of the bridge. Step 3: Use PPR to obtain weight information, and then combine it with the TOPSIS method to comprehensively evaluate all bridge nodes in the upper layer network; Step 4: Simulate a post-earthquake traffic flow sandpile model. This sandpile model differs from traditional queuing models because it considers the reduced bridge capacity and decreased vehicle efficiency after an earthquake. However, the cumulative speed of vehicles queuing upstream of the bridge remains unchanged, resulting in congestion in the upstream sections of the bridge. The sandpile model also considers bridge damage; in damaged sections, reduced capacity leads to a slower propagation speed of the initiation wave. Therefore, when the green light illuminates, the length of the queue decreases as the initiation wave travels from the head of the queue to the tail. It will decrease, assuming the number of sudden changes in vehicle queue length during the alternation of traffic lights. as well as The reduction is determined by the loss of traffic capacity, and its expression is: In the formula: The rate of loss of traffic capacity of a road segment, i.e., compared with quite; Therefore, the length of the convoy when it dissipates is: In the formula: The length of the queue when the green light is on; The speed at which the last vehicle in the convoy arrives; Step 5: Make reasonable dynamic adjustments to the comprehensive evaluation of network bridge nodes; when making dynamic adjustments to the comprehensive evaluation of bridge network nodes, the importance adjustment value is defined as: In the formula: Represents a node The global network efficiency loss rate caused by failure. For nodes Network efficiency during failure; Represents a node The proportion of network collapses to all network collapses, of which This indicates the total number of times a node collapses during the simulation; The obtained result is normalized and added to the static result to obtain the corrected final result; Step 6: Optimization of pre-earthquake reinforcement strategies for bridges.

2. The pre-earthquake pre-strengthening analysis and optimization method for urban bridge networks based on a dynamic-static fusion model as described in claim 1, characterized in that: In step two, four static topology indicators are selected to study the topological characteristics of the bridge network, achieving a more favorable comprehensive evaluation of the bridge nodes. These four static topology indicators are node degree, betweenness coefficient, clustering coefficient, and economic cost. The calculation formulas for each indicator are as follows: Node degree value: ; In the formula: Represents a node All surrounding nodes; Number of intermediaries: ; In the formula: Represents bridge nodes , Among all shortest distances between nodes The number; express , The number of all shortest distances between them; Clustering coefficient: ; In the formula: For nodes The actual number of links between directly linked nodes; For nodes The number of directly linked nodes; economic costs calculated based on actual circumstances.

3. The pre-earthquake pre-strengthening analysis and optimization method for urban bridge networks based on a dynamic-static fusion model according to claim 2, characterized in that: In step two, the steps for analyzing the weights of each static topology index using PPR are as follows: Step 1: Define the initial value of the importance of each bridge node to each indicator; Step 2: Determine the link probability using link analysis. Specifically, define the node link probability as a combination of the topological link probability and the average capacity loss rate between bridge nodes, expressed as: ； In the formula: , representing the node degree value, Represents a node All surrounding nodes; This link analysis method can reduce the influence of subjectivity and increase the tightness of the link between network structure characteristics and the network itself; Step 3: Determine the weight of each indicator; Since the initial values ​​of each indicator to the importance of the node are different, the iteration results are also different. Define the PageRank score of a certain bridge node for each indicator as its weight reference.

4. The pre-earthquake pre-strengthening analysis and optimization method for urban bridge networks based on a dynamic-static fusion model according to claim 3, characterized in that: To ensure the generalizability of the results, six bridge nodes were randomly selected, and their weights for each indicator were calculated. Then, the mean of the six weights for each indicator was calculated and normalized to obtain the weights of each indicator.

5. The pre-earthquake pre-strengthening analysis and optimization method for urban bridge networks based on a dynamic-static fusion model according to claim 4, characterized in that: In step two, the performance index for evaluating the overall bridge network is defined by combining the network's global efficiency with the bridge's traffic capacity, expressed as: In the formula: This represents the number of bridges contained in the network. This represents the total number of all non-bridge nodes in the lower-level network. for , Shortest distance between; To ensure the bridge's traffic capacity before the earthquake; This represents the expected capacity of the bridge. For nodes , The number of bridges included in the area.

6. The pre-earthquake pre-strengthening analysis and optimization method for urban bridge networks based on a dynamic-static fusion model according to claim 5, characterized in that: In step three, the method for comprehensive evaluation of PPR-TOPSIS is as follows: Step 1: Combine the obtained weights of each indicator with the bridge node indicators to form a weighted, standardized evaluation matrix. The expression is as follows: In the formula: Indicates the weight of each indicator; These are the standardized node degree value, betweenness, clustering coefficient, and economic cost, respectively. Step 2, according to The optimal and inferior solutions can be directly calculated using the following expressions: Step 3, Define the first The distances between each target node and the optimal and inferior solutions are expressed as follows: Step 4: Use the proximity formula The importance of all bridge nodes is ranked.

7. The pre-earthquake pre-strengthening analysis and optimization method for urban bridge networks based on a dynamic-static fusion model according to claim 6, characterized in that: In step six, reinforcement strategies are formulated based on the static evaluation results, the dynamic simulation of the collapse, and the dynamic correction results, and are implemented according to the formula. Calculate the toughness of the bridge network system after pre-strengthening.

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