Method for rapidly evaluating anti-seismic performance of bridge network based on capability spectrum analysis

Abstract

The invention discloses a bridge network anti-seismic performance rapid evaluation method based on capability spectrum analysis. The method comprises the following steps: firstly, carrying out finite element modeling on bridges in a regional bridge network needing to be analyzed by using OpenSees, extracting piers, and carrying out vulnerability analysis on the piers; a bridge vulnerability curve is obtained based on a capacity spectrum method, then the failure probability of the bridge in a certain damage state serves as a post-earthquake damage index, and the bridge failure probability is replaced by the post-earthquake failure probability of the corresponding road section; after the post-earthquake failure probability of each road section exists, all paths between a starting point and an ending point, namely, to-be-researched OD pairs in a network area are analyzed, the passing probability of each path after the earthquake is calculated based on the Bayesian theorem and an event independence calculation method, all the paths under the OD pairs are sorted according to the passing probability, and therefore the optimal passing path is obtained; and the path with small passing probability is avoided. According to the invention, a scientific basis is provided for regional bridge network anti-seismic planning and emergency management.

Description

Technical Field

[0001] The present invention relates to a rapid assessment method for the seismic performance of a bridge network based on capacity spectrum analysis, and involves the fields of disaster prevention and mitigation engineering, structural engineering, earthquake engineering, and transportation engineering. Background Art

[0002] In recent years, with the acceleration of urbanization, the scale of transportation infrastructure has continued to expand. As key nodes in the transportation network, the seismic performance of bridges directly impacts transportation connectivity and emergency rescue efficiency during earthquake disasters. However, traditional bridge seismic vulnerability analysis methods rely primarily on complex nonlinear dynamic time-history analysis, which is computationally expensive and inefficient, making them difficult to apply to the rapid assessment of large-scale regional bridge networks. Furthermore, existing research has focused on the seismic performance of individual bridges, while insufficient analysis of the impact of the overall connectivity of bridge networks has hindered effective prediction of the post-earthquake transportation network capacity, which in turn impacts the optimal selection of post-disaster rescue routes. The application of the capacity spectrum method and complex network theory offers new insights into this rapid assessment. The capacity spectrum method simplifies the analysis process, making it faster to analyze the vulnerability of individual bridges, while complex network theory offers a novel perspective on the interaction between bridges and their surrounding transportation networks. By combining these two approaches, it is possible to effectively assess the seismic capacity of the entire transportation network, taking into account bridge vulnerability, thereby enabling rapid formulation of rescue and recovery measures after a disaster.

[0003] Existing methods for analyzing the vulnerability of single bridges primarily include constructing vulnerability curves based on probabilistic seismic demand analysis (PSDA) and performance-based seismic assessments, such as the capacity spectrum method. The capacity spectrum method, by combining the results of a nonlinear static pushover analysis of a structure with the seismic demand spectrum, efficiently determines the performance points of a structure under earthquake action, thereby assessing its damage probability. However, extending this method to large-scale bridge networks and establishing a quantitative relationship between the vulnerability of a single bridge and network connectivity remain challenges and key areas of current research.

[0004] Complex network theory (such as tools like NetworkX) has been applied to the reliability analysis of infrastructure systems in the context of seismic performance of transportation bridge networks. Existing studies typically assume that the failure probabilities of network components are independently distributed. However, under actual earthquakes, bridge damage exhibits spatial correlation and uncertainty, making it difficult for traditional network connectivity analysis methods to accurately reflect the true impact of earthquakes on transportation networks. Furthermore, further research is needed to rapidly generate network-level vulnerability curves based on the vulnerability of individual bridges and identify critical vulnerable paths to guide emergency management.

[0005] Therefore, this paper proposes a rapid seismic performance assessment method for bridge networks that integrates the capacity spectrum method with complex network theory. By using OpenSees to build a parametric pier model and combining it with the capacity spectrum method to efficiently determine the vulnerability of individual bridges, NetworkX is then used to construct a transportation network model, quantifying the relationship between earthquake intensity and network connectivity. Ultimately, this method enables rapid seismic performance assessment and critical path optimization for regional bridge networks. This method can provide a scientific basis for prioritizing bridge reinforcement before an earthquake and for planning emergency routes after an earthquake. Summary of the Invention

[0006] In response to the above problems, the present invention proposes a rapid assessment method for the seismic performance of bridge networks based on capacity spectrum analysis. The regional seismic vulnerability analysis of bridge networks aims to evaluate the damage level of bridges in the region under earthquake action and its impact on the overall performance of the transportation network, and provide a decision-making basis for post-disaster emergency rescue and traffic recovery. The invention first establishes a parametric pier model based on OpenSees, obtains the base shear-displacement curve of the pier through Pushover static nonlinear analysis, and converts it into a capacity spectrum curve; then, it combines the Peer seismic motion database and the SeismoSignal program to generate a demand spectrum, and solves the performance points of the pier under different earthquake intensities through the capacity spectrum method, and then establishes a single bridge vulnerability curve. On this basis, NetworkX is used to construct a transportation network model, map the vulnerability probability of a single bridge to the network path, and quantify the impact of earthquakes on network connectivity. Ultimately, by calculating the travel probability of OD (origin-destination) paths under different earthquake intensities, the optimal rescue path and key vulnerable nodes were identified. Based on the multiplication principle of probability and traversal analysis of paths in the graph, the overall travel probability between ODs in the complex network was calculated, assessing the overall earthquake damage of the network and providing a scientific basis for pre-earthquake bridge reinforcement and post-earthquake emergency management. This method combines the efficiency of the capacity spectrum method with the spatial correlation of complex network theory to achieve rapid assessment of the seismic performance of regional bridge networks and improve the seismic resilience of transportation systems.

[0007] The above purpose is achieved through the following technical solutions:

[0008] A rapid assessment method for the seismic performance of a bridge network based on capacity spectrum analysis comprises the following steps:

[0009] S1. Finite element model establishment and analysis: Use OpenSees to perform finite element modeling on bridges in the regional bridge network to be analyzed, and study the vulnerability of individual bridges. In the bridge finite element modeling, extract the bridge piers and perform vulnerability analysis on them.

[0010] S2. Obtain the bridge vulnerability curve using the capacity spectrum method: After extracting the finite element modeled bridge piers, perform a static pushover analysis on the piers to obtain the capacity spectrum curve. Select the acceleration time history data of the earthquake motion to be studied, and use the seismic wave analysis program SeismoSignal to obtain the demand spectrum curve of the earthquake motion under different peak accelerations. After coordinate conversion with the obtained capacity spectrum curve, plot it in the same coordinate system to obtain the performance point of the pier under the selected earthquake. Convert the peak response displacement and other parameters obtained from the performance point into the corresponding damage standard to calculate the vulnerability of the pier. In bridge engineering, the pier top drift rate threshold corresponding to different damage states is specified: the damage state of the bridge structure can be divided into five levels, namely intact, normal use, use after repair, life safety and collapse prevention. Draw the bridge vulnerability curve under each damage state;

[0011] S3. After obtaining the bridge vulnerability curve in S2, the failure probability of the bridge in a certain damage state is used as the post-earthquake damage indicator. That is, the weight of the edge in NetworkX is substituted into the bridge network, and the bridge failure probability is replaced by the post-earthquake failure probability of the corresponding road section. In this way, the vulnerability of the bridge is linked to the vulnerability of the bridge network system.

[0012] S4. Seismic performance assessment of bridge networks: After obtaining the post-earthquake failure probability of each road section, analyze the OD pairs to be studied in the network area, that is, all paths between the starting point and the end point. Based on the Bayesian theorem and the event independence calculation method, calculate the pass probability of each path after the earthquake. Then, sort all the paths under the OD pairs according to the pass probability to obtain the optimal pass path and avoid paths with low pass probability.

[0013] Furthermore, the capacity spectrum method described in step S2 is used to obtain the fragility of the bridge pier, and the specific steps are as follows:

[0014] S211. Finite element modeling was used to perform pushover analysis on various bridge piers to obtain capacity curves of pier top displacement versus pier bottom shear force. A loading mode of uniformly distributed lateral loads and concentrated top loads was used to simulate the stress conditions of the piers and obtain the corresponding capacity curves. After coordinate transformation, the capacity spectrum curve was obtained. The transformation formula is as follows:

[0015]

[0016] Where S a is the pseudo-acceleration spectrum, S d is the pseudo-displacement spectrum, V b is the shear force at the pier bottom, u n represents the displacement of the pier top, Φ N1 is the amplitude of the fundamental vibration mode at the control node, is the effective mass of the corresponding basic vibration mode, that is, the modal mass, Γ1 *is the modal participation coefficient of the fundamental mode, m j is the concentrated mass at node j, Φ j1 is the amplitude of the fundamental mode at node j, N represents the number of nodes;

[0017] S212: Select the acceleration time history data for the earthquake motion to be studied, modulate the original acceleration peak value, and obtain the acceleration time history data from 0.1g to 1g. In SeismoSignal, derive the demand spectrum curve corresponding to each peak acceleration. Intersect the capacity spectrum curve and the demand spectrum curve coordinates to obtain the performance point of the structure. According to the spectrum displacement d s The cumulative probability of a structure experiencing a certain damage state is calculated using the formula:

[0018]

[0019] Where P[d s / S d ] is the probability of the bridge being damaged under a given position, Φ is the cumulative probability of the standard normal function, β ds is the standard deviation of the structural damage state ds, S d,ds is the mean value of the spectral displacement when the damage state is ds level;

[0020] With the peak ground acceleration (PGA) as the abscissa and the cumulative exceedance probability as the ordinate, the fragility curves of the bridge piers under various damage states were fitted.

[0021] Furthermore, step S3 specifically includes the following sub-steps:

[0022] S311. Graph definition and creation: Use the NetworkX library to create an undirected weighted graph consisting of nodes and edges. Nodes represent specific objects, and edges represent relationships between nodes, i.e., linking road segments. The code creates an empty undirected graph, then adds nodes and assigns location information to each node. It also adds edges and assigns weights. Attributes are set for nodes and edges. Node attributes specify the node's location on a two-dimensional plane for subsequent visualization. Edge weight attributes represent the edge's probability of passage, which is determined by calculating the bridge damage probability associated with the edge.

[0023] S3111. Specific classification and selection of graph types:

[0024] Undirected graph: The edges have no direction, and the edges only connect two nodes as bidirectional road segments;

[0025] Weighted Graph: The edges of the graph have weights, and the weights of the edges represent the failure probability of the bridge after the earthquake;

[0026] MultiGraph: allows multiple edges to connect the same pair of nodes, each edge has different attributes, used to simulate a variety of complex path conditions;

[0027] S312. All Simple Path Search: Find all simple paths from the start node to the target node. A simple path is a path that does not contain repeated nodes. This is achieved based on a graph traversal algorithm, exploring all simple paths in the graph using a depth-first search or breadth-first search strategy.

[0028] S313, path probability calculation: For each simple path found, traverse the edges in the simple path, obtain the edge pass probabilities, and multiply them to obtain the path pass probability;

[0029] S314. Graph visualization: Use the matplotlib library and NetworkX drawing functions to visualize the graph. Draw nodes: set the node position, label, color, and size; draw edges: set the edge width and color; set the edge of the path with the maximum pass rate to green and the other edges to black to highlight the path with the maximum pass rate;

[0030] S315, Graph Connectivity and Reliability Analysis: The code defines bridges and their damage probabilities, as well as the correspondence between edges and bridges. Based on this correspondence, the pass probability of an edge is calculated. If an edge corresponds to multiple bridges, the pass probability of the edge is calculated based on the joint probability of the damage probabilities of these bridges.

[0031] S316. Bridge network selection: Use image recognition or simulated coordinates to establish data for each node in the corresponding bridge network system in NetworkX, clarify the distribution of each functional node and common path intersection, and mark the locations of rescue access nodes and nodes to be rescued;

[0032] S317. Use NetworkX to link the node sections in S316 to form a preliminary transportation network system.

[0033] S318. Based on the displacement threshold calculation formula (displacement threshold = pier height × displacement angle limit), the angular displacement limits for different damage states are as follows: intact: displacement angle limit 1 / 500; normal use: displacement angle limit 1 / 400; repaired use: displacement angle limit 1 / 175; life safety: displacement angle limit 1 / 100; collapse prevention: displacement angle limit 1 / 50. Extract the post-earthquake failure probability of the bridge under the damage state to be studied from the fragility curve obtained in S212.

[0034] S319, repeating the step of S318 to calculate the failure probability of each bridge in the bridge network after the earthquake under the required use state;

[0035] S320: Substitute the bridge failure probability of each road section as a weight into the traffic route network completed in S317. Since the impact of earthquakes on roads mainly depends on whether bridges are damaged, the bridge failure probability is used as the probability of interrupting traffic on the path where the bridge is located.

[0036] S321. The calculation of the pass probability of each road section and the pass probability of the entire path follows the series calculation formula. The specific steps for calculating the pass probability are as follows:

[0037] S3211. Let the bridge set corresponding to a path where edge e=(u, v) connects node u and node v be B. e , it is known that each bridge b i The damage probability is P bi , then the passing probability of edge e is p e The calculation formula is as follows:

[0038] Case 1: The edge corresponds to a bridge

[0039] When | B e |=1, that is, when edge e corresponds to only one bridge b1, the passing probability P of edge B1 e for:

[0040]

[0041] Case 2: The edge corresponds to two bridges

[0042] When | B e |=2, that is, when the edge corresponds to two bridges b1 and b2, since the two bridges are independent, the passing probability of edge e is P e is the probability that both bridges are open to traffic, that is:

[0043]

[0044] Case 3: The edge does not correspond to a bridge

[0045] When | B e When |=0, it is assumed that edge e passes normally, and the passing probability of edge e is:

[0046] P e =1

[0047] S3212, Single Path Passage Probability Calculation

[0048] Suppose there is a path P from node s to node t = {P1, P2, ..., P m}, where v1=s,v n =t, the set of edges on the path is E P ={(v1,v2),(v2,v3),…,(v n-1 ,vn )}, since the passage of each edge on the path is an independent event, the passage probability of the path is P P is the product of the pass probabilities of all edges on the path, that is:

[0049]

[0050] Furthermore, the specific steps of bridge network seismic performance assessment in step S4 are as follows:

[0051] S411. Under a certain OD pair in the bridge network system, analyze and obtain all the passable paths between the OD pair;

[0052] S412, based on the calculation of the traffic rate of each road section in S321, use NetworkX to sort all the traffic paths under the OD pair according to the traffic probability;

[0053] S413. The path with the highest probability of passage is selected, and NetworkX visually labels the path with the best probability of passage, and conversely labels the path with the lowest probability of passage. A network diagram of the best and worst paths of the simulated bridge and road network system after the earthquake is visualized in NetworkX.

[0054] S414. Use the most probable path obtained in S413 as a life-safety path, formulate a corresponding emergency rescue plan, analyze various factors of the worst-case path, and take preventive and evasive measures.

[0055] S415. Calculate the overall OD pass rate using the Bayesian principle:

[0056] Suppose the set of all simple paths from node s to node t is P = {P1, P2, ..., P m}, to calculate the overall passing rate p from node s to node t overall , we need to first calculate the probability P that all paths are blocked all_fail Then subtract this probability from 1;

[0057] Each path P i The probability of failure is Since the paths are independent of each other, the probability that all paths are blocked is:

[0058]

[0059] Then the overall passing rate from node s to node t is:

[0060]

[0061] Beneficial effects

[0062] The bridge network seismic vulnerability analysis and post-earthquake assessment method of the present invention has significant advantages in terms of scientificity, practicality, and innovation. The present invention uses a rapid bridge network seismic performance assessment method based on capacity spectrum analysis, enabling the method to efficiently and accurately complete the seismic performance assessment of regional bridge transportation network systems. By constructing a three-level assessment framework of "single bridge vulnerability-network connectivity-regional seismic resilience," a full-chain seismic performance analysis from structural components to transportation systems is achieved. This method breaks through the limitations of traditional research that only focuses on single structures. Through the NetworkX network topology algorithm, the bridge damage probability is converted into a path capacity indicator, providing a technical path for the seismic assessment of regional transportation systems.

[0063] By introducing the capacity spectrum method, the vulnerability of structures is efficiently determined, accelerating the subsequent regional bridge vulnerability assessment process and providing a solid foundation for the seismic performance evaluation of large bridge networks. Building on the rapid vulnerability assessment of individual bridges, the capacity spectrum method is innovatively combined with pushover analysis, reducing computational time compared to traditional time-history analysis methods. OpenSees modeling enables rapid parametric modeling of various typical bridge pier types, resulting in highly efficient single-model analysis, meeting the needs for rapid assessment during the 72-hour post-earthquake rescue period.

[0064] The overall network pass rate algorithm developed using NetworkX quantifies the road network's ability to withstand disruptions, supports the development of graded reinforcement strategies, and provides a theoretical basis for the optimal seismic design of new bridges. The assessment of path passability between different ODs and the identification of optimal and worst-case paths provide a scientific basis for post-disaster rescue strategy development. The proposed assessment framework is compatible with multiple types of transportation networks and can adapt to different seismic fortification requirements by adjusting damage index thresholds. The developed NetworkX-Python interface program supports integration with GIS platforms, enabling spatial visualization of assessment results.

[0065] In addition, this method is based on actual needs. Taking bridge parameters, regional traffic network status and seismic motion data as input, it quickly outputs relevant results of regional bridge network vulnerability assessment, which not only realizes the formulation of post-disaster rescue strategies, but also provides effective decision-making support for traffic restoration and bridge repair. The present invention greatly shortens the assessment time and ensures the accuracy and feasibility of the assessment results, providing an efficient and intelligent technical solution for the seismic performance assessment of bridge networks. It significantly improves the disaster prevention and control capabilities of major infrastructure. In the future, by accessing real-time monitoring data from the Internet of Things, a dynamic risk assessment system based on digital twins can be further developed to provide key technical guarantees for the construction of smart city disaster prevention systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1Flowchart of the rapid seismic performance assessment method for bridge networks based on capacity spectrum analysis;

[0067] Figure 2 This is the cross-sectional structural diagram of the bridge structure and piers. Figure 2 In the figure, (a) is the overall schematic diagram of the bridge model, (b) is the cross-sectional structural diagram of the pier, and (c) is the structural diagram of the pier;

[0068] Figure 3 Loading mode diagram for Pushover;

[0069] Figure 4 These are four bridge pier capacity curves according to the embodiments of the present invention;

[0070] Figure 5 The performance point diagram is obtained by intersecting the capability spectrum and the demand spectrum;

[0071] Figure 6 is the pier vulnerability curve;

[0072] Figure 7 Modeling graphs for NetworkX bridge networks;

[0073] Figure 8 Annotate the network graph for path probabilities;

[0074] Figure 9 Mark the map for the best travel path;

[0075] Figure 10 Label the graph for the worst-case travel path. DETAILED DESCRIPTION

[0076] The present invention will be further described in detail below with reference to the following examples and specific implementation methods. However, this should not be construed as limiting the scope of the present invention to the following examples, as all technologies implemented based on the present invention fall within the scope of the present invention.

[0077] Example

[0078] Take four different specifications of beam bridges and part of the urban traffic road network system as examples, such as Figure 1 As shown, the rapid assessment method of bridge network seismic performance based on capacity spectrum analysis of this embodiment includes the following steps:

[0079] S1. Finite Element Modeling and Analysis: Finite element modeling was performed using OpenSees on bridges in the regional bridge network to investigate the vulnerability of individual bridges. In bridge finite element modeling, the focus was on the nonlinear response of the entire bridge structure under earthquakes. Superstructures are highly rigid, and the probability of overall damage under earthquakes is relatively low. Generally, damage to the superstructure occurs after the lower piers buckle, deform, or collapse. Therefore, pier damage under earthquakes was the primary analysis target, and the piers were extracted for vulnerability analysis.

[0080] S2, the capacity spectrum method is used to obtain the bridge vulnerability curve: After extracting the finite element modeled bridge piers, a static pushover analysis is performed on the bridge piers to obtain the capacity spectrum curve. Appropriate earthquake acceleration time history data is selected, and the seismic wave analysis program SeismoSignal is used to obtain the demand spectrum curve of the earthquake motion under different peak accelerations. After coordinate conversion with the obtained capacity spectrum curve, it is plotted in the same coordinate system to obtain the performance point of the bridge pier under the selected earthquake. The peak response displacement and other parameters obtained from the performance point are converted into the corresponding damage standard, thereby calculating the vulnerability of the bridge pier. In bridge engineering, the pier top drift rate threshold corresponding to different damage states is stipulated: the damage state of the bridge structure can be divided into five levels, namely intact, normal use, use after repair, life safety and collapse prevention. Plot the vulnerability curve under each damage state;

[0081] S3, the modeling principle and analysis method of NetworkX in the present invention: The present invention uses the following methods and principles in graph theory to perform vulnerability analysis on the bridge network, and defines the nodes that need to be studied in the complex transportation network (for example, hospitals and communities are defined as corresponding starting points and end points). Girvan-Newman is used to perform community detection to obtain the specific areas that need to be analyzed in the transportation network. Breadth-first search (BFS) is used to perform path search and analysis on this basis. It accesses all nodes in the graph in breadth-first order. Generate a list of edges in the BFS traversal of the graph, and obtain a visualization result of the graph. Finally, the connectivity and reliability analysis of the graph is performed based on the iterative algorithm and Prim's algorithm. Starting from a starting node, each time select the edge with the smallest weight among the edges connected to the current spanning tree, and add its corresponding node to the spanning tree until all nodes are added to form an efficient network topology. In the network analysis example, the road and bridge network system of the study area is modeled to make the network conform to the actual traffic conditions in the area. The modeled bridges are arranged in the network. In the resulting bridge vulnerability curve in S2, the failure probability of the bridge in a certain state is used as the post-seismic damage indicator (the weight of the edge in NetworkX) and introduced into the bridge network. The bridge failure probability can be replaced by the failure probability of the corresponding road section, thus linking the bridge vulnerability with the seismic performance of the bridge network system.

[0082] S4, seismic performance assessment of bridge networks: After obtaining the post-earthquake failure probability of each road section, all paths between the O (starting point) and D (end point) pairs to be studied in the network area are analyzed. Based on Bayes' theorem and event independence calculation method, the pass probability of each path after the earthquake can be accurately and quickly calculated. All paths under the OD pairs are sorted according to the pass probability to obtain the optimal pass path, avoiding paths with low pass probability. In addition, this invention can also solve the earthquake damage status of the entire network and avoid the interruption and paralysis of the transportation network caused by the earthquake.

[0083] The bridge modeling and analysis described in step S1 includes the following information:

[0084] Numerical analysis models for four beam bridges were developed using the Kent-Scott-Park concrete constitutive model. Piers were the primary targets of study, with pier heights of 10m, 12m, 15m, and 22m, respectively. Column cross-sectional diameters were 1m, 1m, 1.4m, and 2m, respectively. The various combinations of pier heights and axial compression ratios reflect the diversity of bridges within the network. A fiber model was employed to improve the accuracy of the simulation of the nonlinear behavior of the piers under seismic loads. The peak stress of the cover concrete was 32.0 MPa with a thickness of 40mm, while the peak stress of the core concrete was 36.7 MPa. The steel bar yield strength was 400 MPa with a diameter of 32mm, and the longitudinal reinforcement was 1.9%-3.1%. The Steel02 model was used for the steel bar constitutive model, while the Concrete01 model was used for the concrete constitutive model. Fiber-Section was used to simulate cross-sectional properties. Column elements were 1m long and represented by fiber-type beam-column elements. Figure 2 Figures 1 and 2 show the bridge structure and pier cross-section structure diagrams. (a) is the overall schematic diagram of the bridge model, (b) is the pier cross-section structure diagram, and (c) is the pier structure diagram.

[0085] The capacity spectrum method described in step S2 is used to quickly calculate the fragility of the bridge pier. The specific steps are as follows:

[0086] S211: Pushover analysis is performed on the bridge piers in finite element modeling 4 to obtain the capacity curve of pier top displacement-pier bottom shear force. The loading mode is as follows: Figure 3 and capability curves such as Figure 4 , after the coordinate transformation, the capacity spectrum curve is obtained. The transformation formula is as follows:

[0087]

[0088] Where S a is the pseudo-acceleration spectrum, S d is the pseudo-displacement spectrum, V b is the shear force at the pier bottom, u n represents the displacement of the pier top, Φ N1is the amplitude of the fundamental vibration mode at the control node, is the effective mass of the corresponding basic vibration mode, that is, the modal mass, Γ1 * is the modal participation coefficient of the fundamental mode, m j is the concentrated mass at node j, Φ j1 is the amplitude of the fundamental mode at node j, and N represents the number of nodes.

[0089] S212: Select a seismic data with an original peak acceleration of 0.28g, modulate it to obtain acceleration time history data from 0.1g to 1g, derive the corresponding demand spectrum curve in SeismoSignal, and intersect the capacity spectrum curve with the demand spectrum curve to obtain the corresponding performance point, such as Figure 5 ;

[0090] According to the spectrum shift d s The formula can be used to calculate the cumulative probability of a structure experiencing a certain level of damage, thereby drawing the vulnerability curve of the bridge pier, such as Figure 6 :

[0091]

[0092] Where P[d s / S d ] is the probability of the bridge in a given position moving down to a related damage state, Φ is the cumulative probability of the standard normal function, β ds is the standard deviation of the structural damage state ds, S d,ds is the mean value of the spectral displacement when the damage state is ds level.

[0093] The modeling principle and analysis method of NetworkX in step S3 of the present invention are specifically as follows:

[0094] S311, Graph definition and creation: An undirected weighted graph is created using the NetworkX library, representing a traffic network with travel probabilities. The graph consists of nodes and edges. Nodes represent specific objects (hospitals, neighborhoods), and edges represent relationships between nodes (linked road sections). The code creates an empty undirected graph, then adds nodes, assigns location information to each node, adds edges, and assigns weights. Attributes are set for nodes and edges. Node attributes are used to specify the location of nodes on a two-dimensional plane for subsequent visualization. The weight attribute of an edge represents the travel probability of the edge, which is determined by calculating the probability of bridge damage associated with the edge.

[0095] S3111, Specific classification and selection of graph types:

[0096] Undirected graph: The edge has no direction, and the edge only connects two nodes as a bidirectional road segment.

[0097] Weighted Graph: The edges of a graph have weights (e.g., distance, cost, etc.). In this invention, the edge weights represent the probability of failure of a bridge after an earthquake.

[0098] MultiGraph: Allows multiple edges to connect the same pair of nodes, each with different attributes. Used to simulate a variety of complex path conditions.

[0099] S312, All Simple Path Search: Find all simple paths from the start node to the target node. A simple path is one that does not contain repeated nodes. This is achieved using a graph traversal algorithm, exploring all possible paths in the graph using strategies such as depth-first search or breadth-first search.

[0100] S313, Path Probability Calculation: For each found path, traverse the edges in the path, obtain the edge pass probabilities, and multiply them together to obtain the path pass probability. This is based on the multiplication principle of probability, which states that the probability of multiple independent events occurring simultaneously is equal to the product of the probabilities of each event. Here, the pass events on each edge are independent.

[0101] S314, Graph Visualization: Use the matplotlib library and NetworkX's plotting capabilities to visualize the graph. Nodes are plotted, with their positions, labels, colors, and sizes set. Edges are plotted, with their widths and colors set. Edges along the path with the highest throughput rate are colored green, while other edges are colored black to highlight the path with the highest throughput rate.

[0102] S315, Graph Connectivity and Reliability Analysis: The code defines bridges and their damage probabilities, as well as the correspondence between edges and bridges. Using this correspondence, the edge traversability probability is calculated, taking into account the impact of bridge damage on edge traversability. If an edge corresponds to multiple bridges, the edge traversability probability is calculated based on the joint probability of the damage probabilities of these bridges. This involves concepts from reliability theory, which are used to analyze the connectivity and reliability of a graph in the presence of uncertainties (such as bridge damage).

[0103] The specific steps of modeling and analyzing the bridge network in NetworkX in step S4 of the present invention are as follows: the traffic conditions obtained by satellite photography are modeled in NetworkX, and the proposed framework is implemented in a hypothetical bridge network. Inspired by the Tangshan traffic network, a fictitious bridge network is modeled using Networkx. 45 path obstacles represent 45 bridges, and 17 nodes represent transportation hubs. Emergency response facilities (such as fire stations, medical centers, and the military) are located at node 1, the origin node. Multiple bridges are placed in a link, and connectivity is established through a series system. Residential areas are located at nodes 9 and 16. They represent target node 1 and target node 2, respectively. The vulnerability of different bridges has been obtained through S2, and the traffic probability obtained from the bridge vulnerability is arranged in the path as follows Figure 7 , we can get the traffic probability diagram of the road network, such as Figure 8 .

[0104] S411: Establish data for each node in the corresponding bridge network system in NetworkX through image recognition or simulated coordinates, clarify the distribution of each functional node and common path intersection, and mark the locations of rescue connection nodes and nodes to be rescued;

[0105] In S412, link the node sections in S411 in NetworkX to form a preliminary transportation network system;

[0106] S413, the damage state of the bridge structure mentioned in S2 can be divided into five levels. According to the displacement threshold calculation formula (displacement threshold = pier height × displacement angle limit), the displacement angle limit in normal use is about 1 / 400. From the fragility curve obtained in S212, the post-earthquake failure probability of the bridge in normal use can be extracted;

[0107] S414, repeating step S413 to calculate the failure probability of each bridge in the bridge network under normal use after the earthquake;

[0108] S415: Substitute the bridge failure probability of each road segment into the traffic route network completed in S312. Since the impact of earthquake on roads mainly depends on whether the bridge is damaged, the bridge failure probability is used as the probability of interruption of traffic on the path where the bridge is located.

[0109] S416: The calculation of the pass probability of each road segment and the pass probability of the entire path follows the series calculation formula. The specific steps for calculating the pass probability are:

[0110] S4161, let the bridge set corresponding to edge e = (u, v) be b e , it is known that each bridge b i The damage probability is P bi , then the passing probability P of edge ee The calculation formula is as follows:

[0111] Case 1: The edge corresponds to a bridge

[0112] When | B e |=1, that is, when edge e corresponds to only one bridge, the passing probability of edge B1 is:

[0113]

[0114] Case 2: The edge corresponds to two bridges

[0115] When | B e |=2, that is, when the edge corresponds to two bridges b1 and b2, since the two bridges are independent, the pass probability of edge e is the probability that both bridges are open to traffic, that is:

[0116]

[0117] Case 3: The edge does not correspond to a bridge

[0118] When | B e When |=0, it is assumed that edge e can pass normally, and the passing probability of edge e is:

[0119] P e =1

[0120] S4162, Single Path Passage Probability Calculation

[0121] Suppose there is a path P from node s to node t = {P1, P2, ..., P m}, where v1=s,v n =t, the set of edges on the path is E P ={(v1,v2),(v2,v3),…,(v n-1 ,v n )}. Since the passage of each edge on the path is an independent event, the passage probability of the path is P P is the product of the pass probabilities of all edges on the path, that is:

[0122]

[0123] S411, under a certain OD pair in the bridge network system, all traversable paths between the OD pair are analyzed and obtained;

[0124] S412: Based on the calculation of the traffic rate of each road section in S416, all traffic paths under the OD pair are sorted according to the traffic probability using NetworkX;

[0125] S413: The path with the highest probability of passage is selected. NetworkX can visually mark the path with the best probability of passage, and vice versa, conduct avoidance analysis on the path with the lowest probability of passage. The figure below shows the best and worst path visualization network diagram of a simulated bridge and road network system after an earthquake in NetworkX. Figure 9 and Figure 10 The path with the highest probability of passing between the disaster-stricken area and the rescue area OD (1-9) in the figure is marked with a dotted line. The path with the highest passing rate is 1 3 5 10 9, and the passing probability is 0.559. The path with the lowest passing rate is 1 3 5 4 2 6 7 8 17 15 14 10 11 12 13

[0126] 9. The probability of passing under normal use is only 0.084.

[0127] S414: Use the most probable path obtained in S413 as the life safety channel, formulate a corresponding emergency rescue plan, analyze various factors of the worst path, and take preventive and avoidance measures;

[0128] In S415, to evaluate the overall seismic performance of the bridge-road network system and prevent traffic paralysis and interruption between ODs, NetworkX was used to calculate the overall OD pass rate:

[0129] Suppose the set of all simple paths from node s to node t is P = {P1, P2, ..., P m To calculate the overall passing rate P from node s to node t overall , we can first calculate the probability P that all paths are blocked all_fail , and then subtract this probability from 1.

[0130] Each path P i The probability of failure is Since the paths are independent of each other, the probability that all paths are blocked is:

[0131]

[0132] Then the overall passing rate from node s to node t is:

Claims

1. A rapid assessment method for seismic performance of bridge networks based on capacity spectrum analysis is characterized by: The method comprises the following steps: S1. Finite element model establishment and analysis: Use OpenSees to perform finite element modeling on bridges in the regional bridge network to be analyzed, and study the vulnerability of individual bridges. In the bridge finite element modeling, extract the bridge piers and perform vulnerability analysis on them. S2. Obtain the bridge vulnerability curve using the capacity spectrum method: After extracting the finite element modeled bridge piers, perform a static pushover analysis on the piers to obtain the capacity spectrum curve. Select the acceleration time history data of the earthquake motion to be studied, and use the seismic wave analysis program SeismoSignal to obtain the demand spectrum curve of the earthquake motion under different peak accelerations. After coordinate conversion with the obtained capacity spectrum curve, plot it in the same coordinate system to obtain the performance point of the pier under the selected earthquake. Convert the peak response displacement and other parameters obtained from the performance point into the corresponding damage standard to calculate the vulnerability of the pier. In bridge engineering, the pier top drift rate threshold corresponding to different damage states is specified: the damage state of the bridge structure can be divided into five levels, namely intact, normal use, use after repair, life safety and collapse prevention. Draw the bridge vulnerability curve under each damage state; S3. After obtaining the bridge vulnerability curve in S2, the failure probability of the bridge in a certain damage state is used as the post-earthquake damage indicator. That is, the weight of the edge in NetworkX is substituted into the bridge network, and the bridge failure probability is replaced by the post-earthquake failure probability of the corresponding road section. In this way, the vulnerability of the bridge is linked to the vulnerability of the bridge network system. S4. Seismic performance assessment of bridge networks: After obtaining the post-earthquake failure probability of each road section, analyze the OD pairs to be studied in the network area, that is, all paths between the starting point and the end point. Based on the Bayesian theorem and the event independence calculation method, calculate the pass probability of each path after the earthquake. Then, sort all the paths under the OD pairs according to the pass probability to obtain the optimal pass path and avoid paths with low pass probability.

2. The rapid assessment method for seismic performance of bridge networks based on capacity spectrum analysis according to claim 1 is characterized in that: The capacity spectrum method described in step S2 is used to obtain the fragility of the bridge pier. The specific steps are as follows: S211. Finite element modeling was used to perform pushover analysis on various bridge piers to obtain capacity curves of pier top displacement versus pier bottom shear force. A loading mode of uniformly distributed lateral loads and concentrated top loads was used to simulate the stress conditions of the piers and obtain the corresponding capacity curves. After coordinate transformation, the capacity spectrum curve was obtained. The transformation formula is as follows: Where S a is the pseudo-acceleration spectrum, S d is the pseudo-displacement spectrum, V b is the shear force at the pier bottom, u n represents the displacement of the pier top, Φ N1 is the amplitude of the fundamental vibration mode at the control node, is the effective mass corresponding to the basic vibration mode, that is, the modal mass, is the modal participation coefficient of the fundamental mode, m j is the concentrated mass at node j, Φ j1 is the amplitude of the fundamental mode at node j, N represents the number of nodes; S212: Select the acceleration time history data for the earthquake motion to be studied, modulate the original acceleration peak value, and obtain the acceleration time history data from 0.1g to 1g. In SeismoSignal, derive the demand spectrum curve corresponding to each peak acceleration. Intersect the capacity spectrum curve and the demand spectrum curve coordinates to obtain the performance point of the structure. According to the spectrum displacement d s The cumulative probability of a structure experiencing a certain damage state is calculated using the formula: Where P[d s / S d ] is the probability of the bridge being damaged under a given position, Φ is the cumulative probability of the standard normal function, β ds is the standard deviation of the structural damage state ds, S d,ds is the mean value of the spectral displacement when the damage state is ds level; With the peak ground acceleration (PGA) as the abscissa and the cumulative exceedance probability as the ordinate, the fragility curves of the bridge piers under various damage states were fitted.

3. The rapid assessment method for seismic performance of bridge networks based on capacity spectrum analysis according to claim 1 is characterized in that: Step S3 specifically includes the following sub-steps: S311. Graph definition and creation: Use the NetworkX library to create an undirected weighted graph consisting of nodes and edges. Nodes represent specific objects, and edges represent relationships between nodes, i.e., linking road segments. The code creates an empty undirected graph, then adds nodes and assigns location information to each node. It also adds edges and assigns weights. Attributes are set for nodes and edges. Node attributes specify the node's location on a two-dimensional plane for subsequent visualization. Edge weight attributes represent the edge's probability of passage, which is determined by calculating the bridge damage probability associated with the edge. S3111. Specific classification and selection of graph types: Undirected graph: The edges have no direction, and the edges only connect two nodes as bidirectional road segments; Weighted Graph: The edges of the graph have weights, and the weights of the edges represent the failure probability of the bridge after the earthquake; MultiGraph: allows multiple edges to connect the same pair of nodes, each edge has different attributes, used to simulate a variety of complex path conditions; S312. All Simple Path Search: Find all simple paths from the start node to the target node. A simple path is a path that does not contain repeated nodes. This is achieved based on a graph traversal algorithm, exploring all simple paths in the graph using a depth-first search or breadth-first search strategy. S313, path probability calculation: For each simple path found, traverse the edges in the simple path, obtain the edge pass probabilities, and multiply them to obtain the path pass probability; S314. Graph visualization: Use the matplotlib library and NetworkX drawing functions to visualize the graph. Draw nodes: set the node position, label, color, and size; draw edges: set the edge width and color; set the edge of the path with the maximum pass rate to green and the other edges to black to highlight the path with the maximum pass rate; S315, Graph Connectivity and Reliability Analysis: The code defines bridges and their damage probabilities, as well as the correspondence between edges and bridges. Based on this correspondence, the pass probability of an edge is calculated. If an edge corresponds to multiple bridges, the pass probability of the edge is calculated based on the joint probability of the damage probabilities of these bridges. S316. Bridge network selection: Use image recognition or simulated coordinates to establish data for each node in the corresponding bridge network system in NetworkX, clarify the distribution of each functional node and common path intersection, and mark the locations of rescue access nodes and nodes to be rescued; S317. Use NetworkX to link the node sections in S316 to form a preliminary transportation network system. S318. Based on the displacement threshold calculation formula (displacement threshold = pier height × displacement angle limit), the angular displacement limits for different damage states are as follows: intact: displacement angle limit 1 / 500; normal use: displacement angle limit 1 / 400; repaired use: displacement angle limit 1 / 175; life safety: displacement angle limit 1 / 100; collapse prevention: displacement angle limit 1 / 50. Extract the post-earthquake failure probability of the bridge under the damage state to be studied from the fragility curve obtained in S212. S319, repeating the step of S318 to calculate the failure probability of each bridge in the bridge network after the earthquake under the required use state; S320: Substitute the bridge failure probability of each road section as a weight into the traffic route network completed in S317. Since the impact of earthquakes on roads mainly depends on whether bridges are damaged, the bridge failure probability is used as the probability of interrupting traffic on the path where the bridge is located. S321. The calculation of the pass probability of each road section and the pass probability of the entire path follows the series calculation formula. The specific steps for calculating the pass probability are as follows: S3211. Let the bridge set corresponding to a path where edge e=(u, v) connects node u and node v be B. e , it is known that each bridge b i The damage probability is P bi , then the passing probability P of edge e e The calculation formula is as follows: Case 1: The edge corresponds to a bridge When | B e |=1, that is, when edge e corresponds to only one bridge b1, the passing probability P of edge B1 e for: Case 2: The edge corresponds to two bridges When | B e |=2, that is, when the edge corresponds to two bridges b1 and b2, since the two bridges are independent, the passing probability of edge e is p e is the probability that both bridges are open to traffic, that is: Case 3: The edge does not correspond to a bridge When | B e When |=0, it is assumed that edge e passes normally, and the passing probability of edge e is: P e ＝1 S3212, Single Path Passage Probability Calculation Suppose there is a path p from node s to node t = {P1, P2, ..., P m }, where v1=s,v n =t, the set of edges on the path is E P ={(v1,v2),(v2,v3),…,(v n-1 ,v n )}, since the passage of each edge on the path is an independent event, the passage probability of the path is P P is the product of the pass probabilities of all edges on the path, that is:

4. The rapid assessment method for seismic performance of bridge networks based on capacity spectrum analysis according to claim 1 is characterized in that: The specific steps of bridge network seismic performance assessment in step S4 are as follows: S411. Under a certain OD pair in the bridge network system, analyze and obtain all the passable paths between the OD pair; S412, based on the calculation of the traffic rate of each road section in S321, use NetworkX to sort all the traffic paths under the OD pair according to the traffic probability; S413. The path with the highest probability of passage is selected, and NetworkX visually labels the path with the best probability of passage, and conversely labels the path with the lowest probability of passage. A network diagram of the best and worst paths of the simulated bridge and road network system after the earthquake is visualized in NetworkX. S414. Use the most probable path obtained in S413 as a life-safety path, formulate a corresponding emergency rescue plan, analyze various factors of the worst-case path, and take preventive and evasive measures. S415. Calculate the overall OD pass rate using the Bayesian principle: Suppose the set of all simple paths from node s to node t is P = {P1, P2, ..., P m }, to calculate the overall passing rate P from node s to node t overall , we need to first calculate the probability P that all paths are blocked all_fail Then subtract this probability from 1; Each path P i The probability of failure is Since the paths are independent of each other, the probability that all paths are blocked is: Then the overall passing rate from node s to node t is:

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