A method for assessing the seismic toughness of rail transit networks based on weighted fractal dimension

Abstract

This invention provides a method for assessing the seismic resilience of rail transit networks based on weighted fractal dimension, comprising: (1) network data processing and topology model construction; (2) earthquake scenario construction and structural vulnerability analysis; (3) fractal weight construction and impact simulation method; (4) weighted fractal dimension resilience calculation; and (5) rail transit network resilience assessment. This invention is logically conceived. Through a series of data acquisition, model construction, simulation operation, and computational analysis, it can comprehensively consider multiple dimensions such as network structure, facility performance, and passenger flow value, thereby achieving accurate quantification of the seismic resilience of urban rail transit networks.

Description

Technical Field

[0001] This invention belongs to the field of urban infrastructure disaster prevention and mitigation and digital twin technology, specifically involving a method for assessing the seismic resilience of rail transit networks based on weighted fractal dimension. Background Technology

[0002] With the acceleration of global urbanization, urban rail transit networks, as the backbone of urban transportation, are directly related to the safety of the city's lifeline and its post-disaster recovery capabilities. Therefore, their safety and reliability are crucial for the sustainable development of cities. As urban rail transit systems shift from construction to network operation, the operating environment becomes increasingly complex, and the paralysis of urban rail transit networks often leads to more severe socio-economic impacts. Therefore, it is necessary to conduct a thorough and accurate quantitative assessment of the seismic resilience of urban rail transit networks.

[0003] Existing resilience assessment methods rely on the Euclidean space assumption in network topology model construction, neglecting the impact of actual network fractal characteristics and self-organized evolution on resilience. This leads to distorted characterization of passenger flow distribution and insufficient analysis of dynamic coupling mechanisms. Moreover, existing resilience assessment methods suffer from a "structure-function" disconnect in multi-scale coupling analysis, lacking a dynamic correlation between macro-network resilience assessment and micro-facilities' seismic performance, thus failing to comprehensively and accurately reflect the true resilience level of urban rail transit networks under seismic loading.

[0004] Fractal dimension methods possess advantages such as objectivity, globality, and dynamism, and have broad application prospects in the field of resilience quantification assessment. Fractal dimension methods objectively measure the topological complexity of a network using mathematical methods, capturing the ability of the structure to maintain services from a holistic network perspective, and transforming abstract structural features into computable indicators, including characteristic parameters such as self-similarity and connection density. However, this method still has many areas that require further research in terms of weight design, algorithm path, and dynamic representation.

[0005] Currently, there are almost no quantitative assessment methods and technologies for resilience based on fractal dimension, especially for the seismic resilience of urban rail transit networks. Summary of the Invention

[0006] To overcome the limitations of current methods for quantitatively assessing the seismic resilience of urban rail transit networks, this invention proposes a weighted fractal dimension-based method for assessing the seismic resilience of rail transit networks. This method is logically designed and, through a series of data collection, model building, simulation operation, and computational analysis, can comprehensively consider multiple dimensions such as network structure, facility performance, and passenger flow value, thereby achieving accurate quantification of the seismic resilience of urban rail transit networks.

[0007] To address the aforementioned technical problems, this invention provides a method for assessing the seismic toughness of rail transit networks based on weighted fractal dimension, which mainly includes the following steps:

[0008] (1) Network data processing and topology model construction;

[0009] (2) Earthquake scenario construction and structural vulnerability analysis;

[0010] (3) Fractal weight construction and impact simulation method;

[0011] (4) Calculation of weighted fractal dimension toughness;

[0012] (5) Resilience assessment of rail transit network.

[0013] The method for assessing the seismic toughness of rail transit networks based on weighted fractal dimension, wherein step (1) specifically includes the following steps:

[0014] First, obtain the route vector data and station spatial coordinates from the GIS platform, and then extract the node adjacency matrix A based on this data:

[0015] A = [a ij ] N×N ,

[0016] Matrix A represents the physical connection relationships between nodes, and a topology connection model of the urban rail transit network is constructed based on matrix A:

[0017] (G=(V,E));

[0018] Where, (V={v1,v2,...,v n}) represents the set of site nodes, (E={e ij |v i ,v j ∈V) represents the set of connecting edges between stations;

[0019] Then, based on the big data of transportation card swipe records, a travel matrix is ​​generated using a travel chain reconstruction algorithm.

[0020] The method for assessing the seismic resilience of rail transit networks based on weighted fractal dimension, wherein the implementation method of the travel chain reconstruction algorithm is as follows:

[0021] (1.1) In the data preprocessing stage, a site cleaning function is defined. This function takes the original site name as input and generates a standardized site name output by removing the starting number and redundant text. At the same time, file processing parameters are set, the column definitions of the CSV file are specified, and a memory-optimized data type dictionary is configured.

[0022] (1.2) In the file processing flow, the CSV encoding format is automatically detected and the data is loaded into a memory-optimized structured dataset. After filtering the valid records with the traffic type "subway", the station cleaning function is applied to generate a valid travel column. The single-sided record temporary storage queue and the OD counting structure with the origin and destination tuples as keys are initialized. When processing by passenger ID group, the timestamp of each group is sorted in ascending order and the cleaned station and cost list is extracted. For a single record, the entry and exit station type is determined based on the cost value and then it is attempted to match with the temporary storage queue to form a complete trip. The OD counting structure is updated or stored in the corresponding queue. For continuous records, the valid record pairs are traversed, the entry and exit records of the same station are skipped, and the valid origin and destination pairs are accumulated to the OD counting structure.

[0023] (1.3) Matrix Generation Control Process: Initialize the global OD counting structure and set the basic path; traverse the target date range to construct the complete file path; if the file exists, call the daily processing function to obtain the daily travel data and merge it into the global OD counting structure; finally, extract all unique origin and destination station lists to create an empty OD matrix; traverse all origin and destination keys in the global OD counting structure to calculate the OD to fill the daily average passenger flow matrix, and export the complete matrix to an Excel file. The matrix expression is as follows:

[0024]

[0025] In the above formula, t represents unit time, Z+ represents the set of non-negative integers, |V| is the total number of stations in the network, and the elements... This represents the travel demand from the starting point p∈V to the ending point q∈V within the time period t∈T.

[0026] The method for assessing the seismic toughness of rail transit networks based on weighted fractal dimension, wherein step (2) is specifically as follows:

[0027] First, a two-dimensional intensity field model integrating seismic motion parameter characteristics and spatial attenuation laws is introduced. Using the intensity attenuation formula, the integrated seismic vulnerability parameters of the random seismic intensity distribution are determined. The intensity attenuation formula is as follows:

[0028] I = a + b * Mc * ln(R + r0);

[0029] In the above formula, I is the earthquake intensity, M is the earthquake magnitude, R is the distance from the epicenter, and a, b, c, and r0 are all regression parameters.

[0030] Secondly, a mapping relationship between seismic intensity and peak ground acceleration (PGA) is established, and the PGA distribution is calculated. The linear relationship between the logarithm of the ground motion parameters and seismic intensity is shown in the following formula:

[0031] logPGA = a × I + b;

[0032] In the above formula, logPGA is the logarithm of the ground motion parameters, PGA is the peak ground acceleration, a and b are the fitting coefficients, and I is the earthquake intensity.

[0033] Then, the failure probability distribution of the main structure of the rail transit network under different peak ground accelerations (PGA) was quantitatively evaluated using a seismic vulnerability model. The vulnerability curve of the main structure of the rail transit network conforms to the intermediate critical value S of the seismic intensity index IM of the main structure of the rail transit network at a certain performance level. im and the total log-normal standard deviation β tot Based on the characteristics of a normal distribution, the formula for calculating the cumulative probability of damage to the main structure of a rail transit network is as follows:

[0034]

[0035] In the above formula, P f Let d be the probability that the seismic response of the main structure of the rail transit network exceeds a given performance level under a given seismic motion intensity. s To determine the seismic response of a structure under a given seismic intensity, Let S be the critical value of a given structural performance level, Φ be the standard normal cumulative probability function, and S be the critical value of the structural performance level. im β represents the intermediate critical value of the seismic intensity index IM for the main structure of the rail transit network at a certain performance level. tot The total log-normal standard deviation;

[0036] Finally, the seismic attenuation factor η is introduced to determine the intermediate critical value S of the seismic intensity index IM of the rail transit network structure at a certain performance level. im Make corrections to obtain the result applicable to the remaining service life T. rem equivalent ground motion intensity Its expression is:

[0037]

[0038] In the above formula, S im T represents the peak ground acceleration (PGA) corresponding to a cumulative damage probability of 0.5 during the design reference period. design For the structural design service life, T rem The remaining service life of the structure satisfies 0 <T rem ≤T design K is the shape parameter of the extreme value type II distribution; therefore, the formula for calculating the cumulative probability of damage to the main structure of the rail transit network is modified by the number of years.

[0039] The method for assessing the seismic toughness of rail transit networks based on weighted fractal dimension, wherein step (3) is specifically as follows:

[0040] Based on the matrix D obtained in step (1.3)(t) , combined with the rail transit network topology structure, a passenger flow dynamic distribution model is constructed:

[0041] First, use path finding and graph traversal algorithms to perform passenger flow distribution for each OD pair (o, d), and the path selection is determined by the minimization operator Ψ od :

[0042]

[0043] In the above formula, Π od : the set of all feasible paths from (o → d); w e : the path cost function of the section (e); h(n): the heuristic function used to estimate the minimum cost from node o to the end point d; where the path flow needs to satisfy the discrete dynamic conservation condition:

[0044]

[0045] In the above formula, refers to the passenger flow volume of the specific section k on the path π od among the passengers with the origin and destination (o, d) at time point t; is the path-section association indicator used to indicate whether the specific section k is included in the specific path π od ; d od (t) refers to the total passenger flow volume from the starting point o to the end point d at time point t;

[0046] The total flow volume x e (t) of the section e is the sum of the path flow volumes of all paths containing e:

[0047]

[0048] After aggregating the flow volumes of all sections, a passenger flow network at time point t is formed;

[0049] Within each discrete time step t, dynamically update the topology of the rail transit network sections according to external shocks and repairs. Based on the updated rail transit network, re-execute the path finding and graph traversal algorithms to re-perform passenger flow distribution; then, output the path flow distribution at different time points t and the passenger flow network formed after flow volume aggregation;

[0050] Secondly, based on the passenger flow network after the above distribution, introduce a time-varying intensity weight factor when the weight value of the edge between nodes in the network, and decompose the passenger flow distribution characteristics into the trend quality based on the gravity model, where the weight value W ij of the edge between nodes is calculated as follows:

[0051]

[0052] In the above formula, Pa ij Indicates OD (Original Demand) passenger flow. λ is used to describe the value differences of different origin-destination (OD) passenger flows. ij This is a correction factor for passenger flow value. Let represent the shortest generalized travel distance from node i to node j, where i, h, k, l, and j represent the node numbers;

[0053] Then, the functional importance of a site in the network is quantified based on node strength, where node strength Q... i The calculation formula is as follows:

[0054]

[0055] In the above formula, W ij V is the weight of the edges between nodes in the network. i It represents the set of all neighboring nodes of a node;

[0056] Finally, a random earthquake scenario is set within a specific spatial range. The parameters required for earthquake scenario simulation include the coordinates of the epicenter and the magnitude. Monte Carlo simulation is then performed in conjunction with the spatial distribution model of the ground motion field.

[0057] The Monte Carlo simulation requires the following operations during each simulation:

[0058] (3.1) Cataclysmic Impact Simulation

[0059] Based on the established random earthquake scenario, the intensity attenuation formula in step (2) and the formula relating the logarithm of the ground motion parameters to the intensity are used to calculate the v of each node in the network. i With each connecting edge e ij The PGA value of the region is used, and then the seismic vulnerability probability function of the corresponding component is used to randomly generate v for each node in the network. i With each connecting edge e ij The state of damage;

[0060] (3.2) Dynamic redistribution of passenger flow

[0061] Based on matrix D in step (1.3) (t) Based on the damage status obtained in step (3.1) above, the dynamic OD matrix and path flow distribution under the post-earthquake road network topology change conditions are calculated using the passenger flow dynamic allocation model.

[0062] (3.3) Node Strength Update

[0063] Based on the dynamic OD matrix and path traffic distribution obtained in step (3.2) above, the weight values ​​W of the edges between nodes are applied. ij The calculation formula recalculates the weight value of each node in the network, and then applies the node strength Q. i The calculation formula updates the strength value Q of each node. i .

[0064] The method for assessing the seismic toughness of rail transit networks based on weighted fractal dimension, wherein step (4) is to calculate the Hausdorff measure dimension based on the operable box dimension definition proposed by Mandelbrot; the specific process is as follows:

[0065] First, a specific station density value is selected as the screening threshold, and a greedy coloring method is used to achieve multi-scale box coverage of the network. The box side length value will be used as an important quantitative indicator of the spatial fractal characteristics of the rail transit network.

[0066] Secondly, based on the information dimension theory and the weighted network framework, the probability measure of the i-th covering cell is calculated using the following formula under a grid covering a box of size r:

[0067]

[0068] In the above formula, F refers to the node, and B... i (r) represents the i-th covering box of size r, and μ(·) is the node strength measure. For box B i (r) is the sum of the strengths of all nodes covered, i.e.:

[0069]

[0070] In the above formula, S total (r) represents the sum of node strengths within the study area, i.e.:

[0071]

[0072] In the above formula, Q k The strength of the k-th node is given by N(r), where N(r) is the total number of boxes in the coverage network of size r. Then, the uncertainty of passenger flow distribution is characterized using the Shannon entropy formula: The introduction of probability measures improves the ability of information dimension calculation to quantitatively reflect passenger flow clustering characteristics. The improved Shannon entropy calculation formula is as follows:

[0073]

[0074] Finally, the fractal dimension D i The improved box dimension calculation formula incorporating probability measures is as follows:

[0075]

[0076] The method for assessing the seismic toughness of rail transit networks based on weighted fractal dimension, wherein the greedy coloring method for achieving multi-scale box coverage of the network is specifically implemented using an optimal grid size algorithm, and the implementation method is as follows:

[0077] (4.1) For each target average number of stations in the target average number of stations list, first calculate the required grid density, which is the total number of operating stations divided by the target average number of stations, rounded up; then, find the optimal grid side length using a binary search method, specifically including initializing the minimum side length, maximum side length, and precision, and looping under the condition that the maximum side length minus the minimum side length is greater than the precision: calculate the middle side length as the average of the minimum side length and the maximum side length, call the effective grid calculation function to obtain the effective grid number, calculate the current average number of stations as the total number of operating stations divided by the effective grid number, if the current average number of stations is greater than or equal to the target average number of stations, update the maximum side length to the minimum side length and set the candidate side length to the middle side length, otherwise update the middle side length to the minimum side length; after the loop ends, the optimal side length will be output.

[0078] (4.2) When dividing the grid based on the optimal side length, the number of columns is calculated as the east-west span divided by the optimal row side length and rounded up, and the number of rows is calculated as the north-south span divided by the optimal column side length and rounded up. All grid cells are traversed: the geographical boundary of the cell is calculated, a geographical region object Box is created, the site region detection function is called to obtain the list of sites in the region, if the site list is not empty, a fractal box proxy fBox is created, a bidirectional association between fBox and the site list is established, and the mapping from Box to fBox is registered to the dictionary; otherwise, empty regions are discarded.

[0079] The method for assessing the seismic toughness of rail transit networks based on weighted fractal dimension, wherein the implementation process of the effective grid calculation function is as follows: the number of columns is calculated by dividing the east-west span by the middle row side length and rounding up, and the number of rows is calculated by dividing the north-south span by the middle column side length and rounding up. The effective counter is initialized to 0. Each grid cell is traversed to create a temporary geographic region. If the station region detection function returns a non-empty list, the counter is incremented by 1. Finally, the counter is returned.

[0080] The implementation process of the site region detection function is as follows: initialize an empty site list, traverse all operating sites, add the site coordinates to the site list if they are within the region boundary, and return the site list.

[0081] The method for assessing the seismic toughness of rail transit networks based on weighted fractal dimension, wherein step (5) is specifically as follows:

[0082] First, using the impact simulation method described in step (3), at each time step t of the simulation... k Based on the weighted fractal dimension resilience calculation method in step (4), the time step t is calculated. k Dynamic weights W ij (t k ) and node strength Q i (t k Using the weighted fractal dimension resilience calculation method in step (4), the spatial fractal dimension D(t) of the network at that moment is solved. k );

[0083] Then, for the continuously acquired system toughness performance values ​​D based on fractal dimension i Construction process function D s (t):

[0084] D s (t)=D i for t∈[i,i+1),i=0,1,...,n-1;

[0085] Where i represents the i-th simulation time point; D i The fractal dimension toughness value is calculated at time i; the function value remains constant in the interval [i, i+1).

[0086] For process function D s The evaluation of (t) adopts a four-dimensional index system, namely redundancy R. d (t), robustness R b Efficiency quantity E f With toughness loss L r Describe and characterize the redundancy R of the rail transit network d (t), robustness R b Efficiency quantity E f With toughness loss L r These four indicators together reveal the functional state evolution and inherent resilience mechanism of the rail transit network throughout the entire disaster cycle;

[0087] The redundancy R d The formula for calculating (t) is as follows:

[0088] R d (t)=max(0,R(t-R) L );

[0089] Redundancy characterizes whether the instantaneous functional level R(t) of the rail transit network exceeds the minimum resilience threshold R for meeting basic needs at any time t before or after a disaster, in the pre-disaster steady state or at any time t after a disaster. L Resource reserve adequacy;

[0090] The robustness Rb The calculation formula is as follows:

[0091]

[0092] Robust quantities focus on the moment the disaster ends. The limiting state accurately characterizes the instantaneous functional retention level of the system after it has withstood an impact, and its range is R. b ∈[0,R0] inherently reflects the system's inherent resilience, that is, its core ability to withstand destruction without collapsing;

[0093] The efficiency quantity E f The calculation formula is as follows:

[0094]

[0095] Efficiency, as a time-function joint measure, comprehensively evaluates the system's recovery performance, where T... rec The critical recovery time to restore functionality to the original resilience level R0 is defined, R(t) ∞ The efficiency quantity E represents the final steady-state recovery value reached by the system. f The calculation formula is adjusted by the coefficient α, which is an exponential function that emphasizes the sensitivity of the recovery rate, and by the coefficient β, which is a power-law term that considers the saturation characteristics of the final recovery degree.

[0096] The toughness loss L r The calculation formula is as follows:

[0097]

[0098] The toughness loss is calculated from the perspective of cumulative damage, and the system function is calculated from the time of disaster t. d Until the system sets a final deadline t ∞ During this period, the actual functional level R(t) was lower than the basic demand threshold R. N The area of ​​the gap;

[0099] Based on the above four-dimensional indicator system, a multi-dimensional evaluation index Λ for system resilience is constructed. Its core lies in the decoupling analysis and synergistic integration of the multi-dimensional essence of resilience:

[0100]

[0101] In the above formula, T represents the total study duration, specifically the total simulation duration set in the simulation; the entropy weight method assigns weights w. i The entropy weight method is used to calculate the weights of the four-dimensional indicators w1, w2, w3, and w4 to ensure the objective quantification of the contribution of each dimension and to satisfy ∑w i The constraint condition is 1.

[0102] By adopting the above technical solution, the present invention has the following beneficial effects:

[0103] Compared with existing technologies, the advantages of this invention lie in its integration of complex network theory and fractal geometry principles at the theoretical modeling level. It establishes a network resilience assessment model based on spatial self-similarity characteristics, revealing intrinsic connections and evolutionary patterns at the macro-level, meso-level, and micro-level local scales, and identifying vulnerable substructures that are difficult to detect using traditional methods. By introducing dynamic weighting indicators for node strength, it addresses the problem that traditional static topology analysis (such as degree centrality and betweenness centrality) cannot reflect the actual load-bearing pressure of nodes, dynamically capturing the clustering effect and potential bottleneck risks of hub nodes under real operational conditions. Furthermore, it directly embeds the spatiotemporal heterogeneity of seismic performance into the resilience quantification system, simulating the spatiotemporal distribution patterns of physical structural damage under earthquake disasters and the resulting chain reaction of functional failures such as decreased network connectivity, extended travel time, and traffic redistribution, thus achieving a dynamic coupled assessment of physical damage and functional degradation.

[0104] This invention has broad portability. Based on the theoretical framework of complex networks and fractal geometry, it can be applied to the resilience assessment of different types of spatial infrastructure networks such as power grids, water supply networks, and communication networks. By simulating and evaluating strategies such as hardening key nodes, adding emergency channels, and optimizing scheduling strategies, it quantifies the improvement effect on the speed of network function recovery and the degree of service level maintenance, and provides a basis for cost-benefit analysis.

[0105] This invention provides a network resilience assessment method that is theoretically rigorous, comprehensive in dimensions, dynamically responsive, accurately quantified, and highly efficient and practical. It deeply reveals the inherent resilience mechanism of complex transportation networks, provides decision support for improving disaster resistance, ensuring functions, and rapid recovery capabilities, and has important theoretical value and practical significance for the construction of resilient cities. Attached Figure Description

[0106] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0107] Figure 1 A flowchart is constructed for the toughness quantification standard of fractal dimension;

[0108] Figure 2 A schematic diagram of the topology model of a city's rail transit network;

[0109] Figure 3 This is a schematic diagram of the two-dimensional seismic intensity attenuation distribution;

[0110] Figure 4 Schematic diagram of seismic vulnerability curves for different rail transit network components;

[0111] Figure 5 This is a schematic diagram illustrating the correction of the earthquake vulnerability curve based on its age.

[0112] Figure 6 A schematic diagram showing the coverage of a city's rail transit network.

[0113] Figure 7 This is a schematic diagram of the fractal dimension fitting of a city's rail transit network. Detailed Implementation

[0114] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0115] The present invention will be further explained below with reference to specific embodiments.

[0116] like Figure 1 As shown in the figure, this embodiment provides a method for assessing the seismic toughness of rail transit networks based on weighted fractal dimension, which specifically includes the following steps:

[0117] (1) Network data processing and topology model construction

[0118] By utilizing the open geographic information processing interface of the TransBigData platform and calling the API of a city's rail transit data module, a vector dataset of a city's rail transit network, including lines 1 to 13 and 16 (14 backbone lines in total), was systematically obtained. This dataset contains information on line routes, station topology, and geographic coordinates. GIS tools were then used to perform WGS84 coordinate system transformation on the station coordinates, and the east-west span L of the network was calculated. x With north-south span L y As a basis for subsequent grid division. Figure 2 As shown, based on this dataset, the node adjacency matrix A is extracted, and a topological connection model G=(V,E) for a certain urban rail transit network is constructed, where V={v1,v2,...,v...} n} represents the set of site nodes, E = {e ij |v i ,v j Let ∈V} represent the set of connecting edges between stations. The topology of a certain urban rail transit network contains 339 nodes and 933 connecting edges.

[0119] Based on the original passenger flow records extracted from the smart card swipe records of a certain city's transportation system, a travel matrix is ​​generated using a travel chain reconstruction algorithm; the implementation method of the travel chain reconstruction algorithm is as follows:

[0120] (1.1) In the data preprocessing stage, a site cleaning function is defined. This function receives the original site name input and generates a standardized site name output by removing the starting number and redundant text. At the same time, file processing parameters are set, the CSV file column definitions are specified, and a memory-optimized data type dictionary is configured.

[0121] (1.2) In the file processing flow, the system (specifically, the data processing subsystem used to process the travel chain reconstruction algorithm in the complete simulation running system built using code) automatically detects the CSV encoding format and loads the data into a memory-optimized structured dataset. After filtering the valid records with the traffic type "subway", it applies the station cleaning function to generate valid travel columns; initializes the one-sided record temporary storage queue and the OD (origin and destination, referring to the amount of traffic from the origin to the destination) counting structure with (origin, destination) tuples as keys; when processing by passenger ID group, it sorts each group of timestamps in ascending order and extracts the cleaned station and cost list: for a single record, it determines the entry and exit station type based on the cost value and attempts to match it with the temporary storage queue to form a complete trip, updates the OD counting structure or stores it in the corresponding queue; for continuous records, it traverses the valid record pairs, skips the entry and exit records of the same station, and accumulates the valid (origin, destination) pairs into the OD counting structure.

[0122] (1.3) The matrix generation control process initializes the global OD counting structure and sets the basic path; iterates through the target date range to construct the complete file path. If the file exists, it calls the daily processing function to obtain the daily travel data and merges it into the global OD counting structure; finally, it extracts all unique origin and destination station lists to create an empty OD matrix, iterates through all (origin, destination) keys in the global OD counting structure to calculate the OD to fill the daily average passenger flow matrix, and exports the complete matrix to an Excel file.

[0123] Based on the above method, the basic OD matrix of a certain urban rail transit network is formed:

[0124]

[0125] Where t is the unit time, T is the total time; Z+ represents the set of non-negative integers (including 0 and positive integers), and |V| is the total number of stations in the network (i.e. the number of nodes in the topology model), thus indicating that the matrix is ​​a non-negative square matrix of the number of stations multiplied by the number of stations; This represents the passenger flow from the starting point (p) to the ending point (q). The final result is an OD matrix for a city's rail transit network containing 288 valid stations.

[0126] (2) Earthquake scenario construction and structural vulnerability analysis

[0127] First, a two-dimensional intensity field model integrating seismic motion parameter characteristics and spatial attenuation laws is introduced (the two-dimensional intensity field model mainly refers to "Research on Intensity Attenuation Relationship Model in Eastern China"). The two-dimensional intensity field model is a seismic destructive force assessment model that integrates spatial directional heterogeneity. Its core is to construct an elliptical seismic intensity distribution field through intensity attenuation formulas in two dimensions: the major axis and the minor axis, to more accurately quantify the spatial distribution of seismic destructive force. The major axis represents attenuation along geological faults or the dominant direction of seismic wave propagation (usually attenuating more slowly); the minor axis represents attenuation perpendicular to the fault direction (usually attenuating more rapidly). Physical meaning: Seismic energy propagation has directionality (e.g., energy attenuation is slower along the fault strike and faster perpendicular to it). Using the intensity attenuation formulas, the random seismic intensity distribution is determined, integrating seismic vulnerability parameters. Specifically, the minor axis intensity attenuation formula for eastern my country is used to determine the random seismic intensity distribution in a certain region, as shown in the figure. Figure 3 As shown. The formula for the attenuation of short-axis intensity in eastern my country is as follows:

[0128]

[0129] In the formula: I is the intensity, M is the magnitude, R is the epicentral distance (km), σ I The standard deviation is denoted as .

[0130] The above-mentioned two-dimensional intensity field model construction process:

[0131] ① Establish a coordinate system

[0132] geographic coordinates Convert to a local coordinate system (x, y) with the epicenter as the origin and the fault direction as the x-axis:

[0133]

[0134] Where θ is the fault strike angle, R e The radius of the Earth;

[0135] ② Calculate the reference axis attenuation

[0136] Intensity attenuation first along the major axis (x-axis):

[0137] I x =a1+b·M-c1 ln(R) x +r0);

[0138] Where R x The distance along the x-axis (i.e., |x|);

[0139] Intensity decreases further along the minor axis (y-axis):

[0140] I y=a² + b·M - c² ln(R) y +r0);

[0141] R y This is the distance along the y-axis (i.e., |y|);

[0142] ③ Determine the ellipse parameters

[0143] For any point P(x,y), its intensity I P satisfy:

[0144]

[0145] in, It is an intensity of I P The radius of the major axis at time is obtained by inversely solving the major axis attenuation formula:

[0146]

[0147] It is an intensity of I P The minor axis radius at time t is obtained by inversely solving the minor axis attenuation formula:

[0148]

[0149] ④ Solve for the intensity at any point

[0150] Solve the equation for point P(x,y):

[0151]

[0152] This is a nonlinear equation about I, which needs to be solved using numerical methods (such as Newton's iteration method).

[0153] Secondly, based on the weighted least squares regression equation in existing research, a mapping relationship between seismic intensity and peak ground acceleration (PGA) is established. By combining the analytic hierarchy process (AHP) with structural response spectrum characteristics, the simulated PGA distribution of a certain region is calculated. The fitting equation uses the most commonly used linear relationship between the logarithm of seismic ground motion parameters and intensity. The formula for the linear relationship between the logarithm of seismic ground motion parameters and seismic intensity in my country is as follows:

[0154]

[0155] In the formula, PGA is the peak ground acceleration, logPGA is the logarithm of the ground motion parameters, I is the seismic intensity, and σ p The standard deviation is denoted as .

[0156] Then, the failure probability distribution of the main structure of the rail transit network under different peak ground accelerations (PGA) was quantitatively evaluated using a seismic vulnerability model. The vulnerability curve of the main structure of the rail transit network conforms to a two-parameter log-normal distribution. Seismic vulnerability probability functions were established for different damage conditions (moderate damage, severe damage, and complete damage) of different types of structural components (such as shield tunnel tracks, above-ground tracks, underground stations, and elevated stations) in the main structure of the rail transit network. The cumulative probability calculation formula for the failure of components in the main structure of the rail transit network is as follows:

[0157]

[0158] In the formula, P f Let d be the probability that the seismic response of the main structure of the rail transit network exceeds a given performance level under a given seismic motion intensity. s To determine the seismic response of a structure under a given seismic intensity, Let S be the critical value of a given structural performance level, Φ be the standard normal cumulative probability function, and S be the critical value of the structural performance level. im β represents the intermediate critical value of the seismic intensity index IM for the main structure of the rail transit network at a certain performance level. tot The total log-normal standard deviation is given.

[0159] Related studies provide specific values ​​for the intermediate critical values ​​of the seismic intensity index IM and the total log-normal standard deviation for different components under different damage conditions. The fitting parameters for the underground station are the seismic intensity index S under moderate damage levels. im Value 0.9, seismic intensity index S under severely damaged leveling im Value 1.34, ground motion intensity index S under completely destroyed level im Value 1.52 and total β tot The value is 0.5; the fitting parameter for the elevated station (side type) is the seismic intensity index S under moderate damage level. im Value 0.43, seismic intensity index S under severely damaged leveling im Value 0.86, ground motion intensity index S under completely destroyed level im Value 1.61 and total β tot The value is 0.75; the fitting parameter for the elevated station (island type) is the seismic intensity index S under moderate damage level. im Value 0.39, seismic intensity index S under severely damaged leveling im Value 0.73, ground motion intensity index S under completely destroyed level im Value 1.29 and total β tot The value is 0.71; the fitting parameter for the shield tunnel track is the seismic intensity index S under moderate damage level. im Value 0.8 and total β totValue 0.6, seismic intensity index S under severe and complete damage level im No data available; the fitting parameter for the ground track is the ground motion intensity index S under moderate damage level. im Value 0.7 and total β tot Value 0.6, seismic intensity index S under severe and complete damage level im No data is available. (e.g.) Figure 4 As shown, there are significant differences in the fragility curves of different components.

[0160] Finally, based on the seismic attenuation factor η, the intermediate critical value S of the seismic intensity index IM of the rail transit network structure at a certain performance level is determined. im Make corrections to obtain the result applicable to the remaining service life T. rem equivalent ground motion intensity Its expression is:

[0161]

[0162] In the above formula, S im T represents the peak ground acceleration (PGA) corresponding to a cumulative damage probability of 0.5 during the design reference period. design For the structural design service life, T rem The remaining service life of the structure satisfies 0 <T rem ≤T design K is the shape parameter of the extreme value type II distribution; therefore, the formula for calculating the cumulative probability of damage to the main structure of the rail transit network is modified by the number of years.

[0163] In this embodiment, the remaining service life T of the structure is considered. rem For the median value of fragility S im (i) The median value is obtained by making corrections. The formula for calculating the seismic vulnerability correction of rail transit network structures is as follows:

[0164]

[0165] In the formula, S im T represents the peak ground acceleration (PGA) corresponding to a cumulative damage probability of 0.5 over a 100-year design reference period. rem Given the remaining useful life of the structure (in years), it satisfies 0. <T rem ≤100; Correction diagram as shown Figure 5 As shown.

[0166] Based on the network topology and component spatial distribution obtained in step (1), for each node (v) in the network i ) and each connecting edge (e ij Associate the set of vulnerability parameters corresponding to its dominant structural type.

[0167] (3) Fractal Weight Construction and Impact Simulation Method

[0168] First, based on the OD matrix D obtained in step (1.3), (t) , combined with the rail transit network topology structure, construct the following passenger flow dynamic allocation model:

[0169] First, use the path finding and graph traversal algorithm (abbreviated as A Star, widely used in fields such as game development and robot navigation, which is an extension of the Dijkstra algorithm; this algorithm is a heuristic search algorithm that combines the advantages of breadth-first search (BFS) and depth-first search (DFS); it selects the optimal path by evaluating the cost of each node) to allocate passenger flow for each OD pair (o, d), and the path selection is determined by the minimization operator Ψ od :

[0170]

[0171] where, Π od : the set of all feasible paths from (o→d); w e : the path cost function of the section (e); h(n): heuristic function (such as Euclidean distance, etc.), used to estimate the minimum cost from node o to the end point d. Among them, the path flow needs to satisfy the discrete dynamic conservation condition:

[0172]

[0173] where, refers to the passenger flow volume of the specific section k on the path π od among the passengers with the origin and destination (o, d) (from the starting point o to the end point d) at time point t; is the path-section association indicator, used to indicate whether the specific section k is included in the specific path π od ; d od (t) refers to the total passenger flow volume (total travel demand) from the starting point o to the end point d at time point t;

[0174] Secondly, the total flow x e (t) of the section e is the sum of the path flows of all paths containing e:

[0175]

[0176] After aggregating the flows of all sections, a passenger flow network at time point t is formed;

[0177] Within each discrete time step t, the rail transit network topology is dynamically updated (retained, removed, or restored) based on external shocks (such as seismic disturbances) and repair progress:

[0178] Based on the updated rail transit network, the path finding and graph traversal algorithms are re-executed to redistribute passenger flow.

[0179] Finally, the path traffic distribution at different time points t is output. The passenger flow network formed after traffic aggregation provides dynamic passenger flow network data for the subsequent calculation of the weight values ​​of the edges between nodes.

[0180] Secondly, based on the aforementioned passenger flow network (a single passenger flow OD, after traffic flow allocation in the rail transit network, forms a single passenger flow line; while multiple passenger flow lines formed after traffic flow allocation by different passenger flow ODs intertwine to form a passenger flow network), a time-varying intensity weight factor is introduced into the weight values ​​of the edges between nodes in the network. This deconstructs the passenger flow distribution characteristics into a trend quality based on a gravity model, where the weight value W of the edges between nodes is... ij The calculation formula is as follows:

[0181]

[0182] Where: Pa ij Indicates OD (Original Demand) passenger flow. λ is used to describe the value differences of different origin-destination (OD) passenger flows. ij This is a correction factor for passenger flow value. Let represent the shortest generalized travel distance from node i to node j, where i, h, k, l, and j represent the node numbers.

[0183] Then, the functional importance of a site in the network is quantified based on node strength, where node strength Q... i The calculation formula is as follows:

[0184]

[0185] In the formula: W ij V is the weight of the edges between nodes in the network. i It represents the set of all neighboring nodes of a node.

[0186] Finally, a random earthquake scenario is set within a specific spatial range. The parameters required for the earthquake scenario simulation include the coordinates of the hypocenter and the magnitude. Monte Carlo simulation is then performed in conjunction with the spatial distribution model of the ground motion field. The following operations are required in each simulation:

[0187] (3.1) Catastrophic Impact Simulation: Based on the set random earthquake scenario, the intensity attenuation formula in step (2) and the linear relationship between the logarithm of the ground motion parameters and the intensity are used to calculate the v of each node in the network. i With each connecting edge e ij The PGA value of the region is used, and then the seismic vulnerability probability function of the corresponding component is used to randomly generate v for each node in the network. i With each connecting edge e ij The state of damage.

[0188] (3.2) Dynamic redistribution of passenger flow: based on matrix D in step (1.3). (t) Based on the damage status obtained in step (3.1), the dynamic OD matrix and path flow distribution under the post-earthquake road network topology change conditions are calculated using the passenger flow dynamic allocation model described in step (3).

[0189] (3.3) Node strength update: Based on the dynamic OD matrix and path traffic distribution obtained in step (3.2), apply the weight value W of the edges between nodes. ij The calculation formula recalculates the weight value W of each node in the network. ij Then apply node strength Q i The calculation formula updates the strength value Q of each node. i After the node strength update is completed, a real-time data foundation is provided for the weighted fractal dimension toughness calculation in the subsequent step (4).

[0190] (4) Calculation of weighted fractal dimension toughness

[0191] Based on Mandelbrot's operational definition of box dimension, the Hausdorff measure dimension is calculated: First, a specific station density value is selected as a screening threshold, and a greedy coloring method is used to achieve multi-scale box coverage of the network. The box side length will serve as an important quantitative indicator of the spatial fractal characteristics of the rail transit network. Specifically, the aforementioned use of the greedy coloring method to achieve multi-scale box coverage of the network employs an optimal grid size algorithm, and the specific implementation method is as follows:

[0192] (4.1) For each target average number of stations in the target average number of stations list, first calculate the required grid density, which is the total number of operating stations divided by the target average number of stations, rounded up; then, find the optimal grid side length using a binary search method, specifically including initializing the minimum side length, maximum side length, and precision, and looping under the condition that the maximum side length minus the minimum side length is greater than the precision: calculate the middle side length as the average of the minimum side length and the maximum side length, call the effective grid calculation function to obtain the effective grid number, calculate the current average number of stations as the total number of operating stations divided by the effective grid number, if the current average number of stations is greater than or equal to the target average number of stations, update the maximum side length to the minimum side length and set the candidate side length as the middle side length, otherwise update the middle side length to the minimum side length; after the loop ends, the optimal side length will be output.

[0193] (4.2) When dividing the grid based on the optimal side length, the number of columns is calculated as the east-west span divided by the optimal row side length and rounded up, and the number of rows is calculated as the north-south span divided by the optimal column side length and rounded up. All grid cells are traversed: the geographical boundary of the cell is calculated, a geographical region object Box is created, the site region detection function is called to obtain the list of sites in the region, if the site list is not empty, a fractal box proxy fBox is created, a bidirectional association between fBox and the site list is established, and the mapping from Box to fBox is registered to the dictionary; otherwise, empty regions are discarded.

[0194] The implementation of the aforementioned effective grid calculation function includes: calculating the number of columns as the east-west span divided by the middle row side length and rounded up, and the number of rows as the north-south span divided by the middle column side length and rounded up; initializing the effective counter to 0; traversing each grid cell to create a temporary geographic region; incrementing the counter by 1 if the site region detection function returns a non-empty list; and finally returning the counter. The implementation of the site region detection function includes: initializing an empty site list; traversing all operating sites; adding a site to the site list if its coordinates are within the region boundary; and returning the site list.

[0195] A schematic diagram of the coverage of a city's rail transit network box is shown below. Figure 6 As shown. Secondly, based on information dimension theory and the weighted network framework, under a grid coverage of box size r, the probability measure of the i-th covering unit is calculated using the following formula:

[0196]

[0197] In the formula: B i (r) represents the i-th covering box of size r, and μ(·) is the node strength measure. For box B i (r) is the sum of the strengths of all nodes covered, i.e.: S total(r) represents the sum of node strengths within the study area, i.e.: N(r) is the total number of boxes in the overlay network at size r.

[0198] Then, the Shannon entropy formula is used to characterize the uncertainty of passenger flow distribution: The introduction of probability measures improves the ability of information dimension calculation to quantitatively reflect passenger flow clustering characteristics. The improved Shannon entropy calculation formula is as follows:

[0199]

[0200] Fractal dimension D i The improved box dimension calculation formula incorporating probability measures is as follows:

[0201]

[0202] In practice, it is difficult to achieve r→0. A common approach is to fit ln N. r (F) ~ ln(r), if a linear relationship exists, the absolute approximation of the slope of the line can be considered as the box dimension. For example... Figure 7 As shown, a data point set of I(r) and lnr is established in a rectangular coordinate system. The least squares method is used to perform linear regression fitting on the experimental data. The coefficient of determination R in the regression analysis is... 2 =0.9723, indicating that the linear regression model has a good fit. This statistical result confirms that the urban rail transit network possesses significant fractal characteristics. Furthermore, the absolute value of the slope of the regression line represents the intensity information dimension of the system. The initial fractal dimension D of the urban rail transit network was calculated. i = 1.22101. Similarly, the fractal dimension of different network damage conditions can be obtained. After 20 Monte Carlo simulations, with the source center coordinates set to random points ranging from 30.7°N to 31.7°N and from 121.08°E to 121.88°E, the initial fractal dimension D of a certain urban rail transit network after a magnitude 4 earthquake is obtained. i The initial fractal dimension D of a city's rail transit network after a magnitude 5 earthquake is 1.19018 with a standard deviation of 0.02717. i The initial fractal dimension D of a city's rail transit network after a magnitude 6 earthquake is 1.12746 with a standard deviation of 0.04814. i The initial fractal dimension D of a city's rail transit network after a magnitude 7 earthquake is 0.96188 with a standard deviation of 0.09831. i The initial fractal dimension D of a city's rail transit network after an 8-magnitude earthquake is 0.65166 with a standard deviation of 0.12666. iThe value was 0.37866, and the standard deviation was 0.21326.

[0203] (5) Resilience assessment of rail transit networks

[0204] First, the impact simulation method in step (3) is used, and at each time step t of the simulation... k Based on the weighted fractal dimension resilience calculation method in step (4), the time step t is calculated. k Dynamic weights W ij (t k ) and node strength Q i (t k Applying the weighted fractal dimension resilience calculation method in step (4), the spatial fractal dimension D(t) of the network at that moment is solved. k );

[0205] Then, for the continuously acquired system toughness performance values ​​D based on fractal dimension i Construction process function D s (t):

[0206] D s (t)=D i for t∈[i,i+1),i=0,1,...,n-1;

[0207] Where i represents the i-th simulation time point; D i The fractal dimension toughness value is calculated at time i; the function value remains constant in the interval [i, i+1).

[0208] For process function D s The evaluation of (t) adopts a four-dimensional index system (i.e., redundancy R). d (t), robustness R b Efficiency quantity E f With toughness loss L r Describe and characterize the redundancy R of the rail transit network. d (t), robustness R b Efficiency quantity E f With toughness loss L r These four indicators together reveal the functional state evolution and inherent resilience mechanism of the rail transit network throughout the entire disaster cycle;

[0209] Redundancy R d The formula for calculating (t) is shown below:

[0210] R d (t)=max(0,R(t-R) L );

[0211] Redundancy characterizes whether the instantaneous functional level R(t) of the rail transit network exceeds the minimum resilience threshold R for meeting basic needs at any time t before or after a disaster, in the pre-disaster steady state or at any time t after a disaster. L Resource reserve adequacy;

[0212] The formula for calculating robustness is as follows:

[0213]

[0214] Robust quantities focus on the moment the disaster ends. The limiting state accurately characterizes the instantaneous functional retention level of the system after it has withstood an impact, and its range is R. b ∈[0,R0] inherently reflects the system's inherent resilience, that is, its core ability to withstand destruction without collapsing;

[0215] The formula for calculating efficiency is as follows:

[0216]

[0217] Efficiency, as a time-function joint measure, comprehensively evaluates the system's recovery performance, where T... rec The critical recovery time to restore functionality to the original resilience level R0 is defined, R(t) ∞ The efficiency quantity E represents the final steady-state recovery value reached by the system. f The calculation formula uses the coefficient α to adjust the exponential function that emphasizes the sensitivity of the recovery rate, and the coefficient β to adjust the power-law term that considers the saturation characteristics of the final recovery degree. Essentially, it quantifies the dynamic response performance of the system in achieving efficient and full recovery by utilizing redundant resources for self-organization or external intervention.

[0218] The formula for calculating toughness loss is as follows:

[0219]

[0220] The toughness loss is calculated from the perspective of cumulative damage, and the system function is calculated from the time of disaster t. d Until the system sets a final deadline t ∞ During this period, the actual functional level R(t) was lower than the basic demand threshold R. N The area of ​​the gap;

[0221] Based on the above four-dimensional indicator system, a multi-dimensional evaluation index Λ for system resilience is constructed. Its core lies in the decoupling analysis and synergistic integration of the multi-dimensional essence of resilience:

[0222]

[0223] In the above formula, T represents the total study duration, specifically the total simulation duration set in the simulation; the entropy weight method assigns weights w. iThe entropy weight method is used to calculate the weights of the four-dimensional indicators w1, w2, w3, and w4 to ensure the objective quantification of the contribution of each dimension and to satisfy ∑w i The constraint condition is 1. This four-dimensional index system provides a methodological basis for evaluating the effectiveness of different repair strategies.

[0224] This invention is well-conceived. Through a series of data collection, model building, simulation operation, and computational analysis, it can comprehensively consider multiple dimensions such as network structure, facility performance, and passenger flow value, thereby achieving accurate quantification of the seismic resilience of urban rail transit networks.

[0225] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for evaluating the seismic resilience of a rail transit network based on a weighted fractal dimension, characterized in that, Mainly includes the following steps: (1) network data processing and topology model construction; (2) earthquake scenario construction and structure vulnerability analysis; (3) fractal weight construction and impact simulation method; the specific process is: An OD count structure with a pair of start and end points as a key is filled with a daily passenger flow matrix based on an effective travel column of a traffic type "subway" A passenger flow dynamic distribution model is constructed in combination with a rail transit network topology Firstly, the path search and graph traversal algorithm is used to assign passenger flow for each OD pair and the path selection is determined by the minimization operator : ； In the above formula, : all feasible path sets of : path cost function of link (e); : heuristic function for estimating the minimum cost from node to the terminal point ; where the path flow needs to satisfy the discrete dynamic conservation condition: ； In the above formula, denotes the passenger flow on a specific road segment at a time point ; , denotes the passenger flow on a specific road segment on a path among passengers with an origin-destination pair ; is a path-road segment association indicator, indicating whether a specific road segment is included in a specific path ; denotes the total passenger flow from the origin to the destination at a time point total flow of link e sum of all path flows containing e: ； After the flow aggregation of all road segments, the passenger flow network at the time point is formed. At each discrete time step Internally, the system dynamically updates the rail transit network topology and road segment information based on external impacts and repair progress. Based on the updated network, it re-executes pathfinding and graph traversal algorithms to redistribute passenger flow. Finally, it outputs the data at different time points. Path traffic distribution at time and the customer flow network formed after traffic aggregation; Secondly, based on the above-mentioned allocated passenger flow network, the time-varying strength weight factor is introduced to the weight value of the edge between the nodes in the network, and the passenger flow distribution characteristics are decomposed into the trend quality based on the gravity model, wherein the weight value of the edge between the nodes The calculation formula is as follows: ； In the above formula, OD passenger flow, to describe the value difference of different OD passenger flow, passenger flow value correction coefficient, represent the node The shortest generalized travel distance from node to node , , , , represent the node number; Then, the node strength is used to quantify the functional importance of a site in the network, where the node strength is calculated as follows: ； In the above formula, is the weight value of the edge between the nodes in the network, represents the set of all neighboring nodes of the node; Finally, set a random earthquake scenario in a specific spatial range, the parameters required for the simulation of the earthquake scenario simulation include the center coordinates and magnitude of the seismic source, and the Monte Carlo simulation is carried out combined with the spatial distribution model of ground motion field; The Monte Carlo simulation needs to perform the following operations in each simulation process: (3.1) disaster impact simulation Based on the set random earthquake scenario, the PGA value of each node and each connecting edge in the network is calculated by the intensity attenuation formula and the linear relationship formula between the logarithm of ground motion parameter and intensity , and then the damage state of each node and each connecting edge in the network is randomly generated according to the seismic vulnerability probability function of the corresponding component . , and then the damage state of each node and each connecting edge in the network is randomly generated according to the seismic vulnerability probability function of the corresponding component . (3.2) dynamic reassignment of passenger flow OD count structure based on a start point and end point tuple as a key filling matrix of daily passenger flow and the damage state obtained in the above step (3.1), using the passenger flow dynamic allocation model, calculate the dynamic OD matrix and path flow distribution under the condition of post-earthquake road network topology change; (3.3) node strength update Based on the dynamic OD matrix obtained in step (3.2) above and the path flow distribution, the weight values of the edges between nodes are applied The weight values of each node in the network are recalculated using the formula The strength values of each node are updated using the formula ; (4) weighted fractal dimension resilience calculation; (5) rail transit network resilience evaluation.

2. The method for evaluating the seismic resilience of a metro network based on a weighted fractal dimension according to claim 1, wherein, The step (1) specifically includes the following steps: First, the line vector data and station spatial coordinates are obtained from the GIS platform, and the node adjacency matrix is extracted based on the data : ； The matrix A represents the physical connection relationship between nodes, and a city rail transit network topology connection model is constructed based on the matrix A: ； wherein, represents a set of site nodes, represents a set of connection edges between sites; Then, based on the traffic card swiping record big data, the trip matrix is generated by using the trip chain reconstruction algorithm.

3. The method for evaluating the seismic resilience of a metro network based on a weighted fractal dimension according to claim 2, wherein, The implementation method of the trip chain reconstruction algorithm is: (1.1) In the data preprocessing stage, define a station cleaning function that receives the original station name input, generates a standardized station name output by removing the starting digits and redundant text, and sets file processing parameters to define CSV file column definitions and configure memory-optimized data type dictionaries; (1.2) In the file processing process, automatically detect the CSV encoding format to load data in a memory-optimized structured data set, filter valid records of traffic type "subway", and then apply the station cleaning function to generate valid trip columns; initialize a single-sided record temporary queue and an OD count structure with start and end point tuples as keys; when processing by passenger ID group, sort the time stamps in ascending order and extract the cleaned station and fee list for each group: for a single record, determine the entry and exit station type according to the fee value, then try to match with the temporary queue to form a complete trip, update the OD count structure or store it in the corresponding queue; For consecutive records, traverse the valid record pairs, skip the same station entry and exit records, and accumulate the valid start and end point pairs to the OD count structure; (1.3) The matrix generation total control process initializes the global OD count structure and sets the basic path; traverse the target date range to build the complete file path, if the file exists, call the daily processing function to obtain the daily trip data and merge it into the global OD count structure; finally, extract all unique start and end station lists to create an empty OD matrix, traverse all start and end keys of the global OD count structure to calculate the daily passenger flow of the OD pair and fill the matrix, and export the complete matrix to an Excel file, and the matrix expression is as follows: ； In the above equation, t is a unit of time, Z+ represents a set of non-negative integers, |V| is the total number of sites in the network, and element represents the amount of travel demand from the start point to the end point in the time period.

4. The method for evaluating the seismic resilience of a metro network based on a weighted fractal dimension according to claim 3, wherein, The specific process of step (2) is: Firstly, a two-dimensional intensity field model integrating seismic motion parameter characteristics and spatial attenuation law is introduced, and the intensity attenuation formula is used to determine the random seismic intensity distribution integrated with seismic vulnerability parameters, wherein the intensity attenuation formula is as follows: ； In the above formula, is the seismic intensity, is the earthquake magnitude, is the distance from the epicenter, , , , are regression parameters; Secondly, the mapping relationship between seismic intensity and peak ground acceleration (PGA) is established, and the PGA distribution is calculated, wherein the linear relationship formula between the logarithm of seismic motion parameter and seismic intensity is as follows: ； In the above formula, is the logarithm of the ground motion parameter, is the peak ground acceleration, , is the fitting coefficient, is the seismic intensity; Then, the damage probability distribution of the rail transit network main structure under the action of different peak ground acceleration PGA is quantitatively evaluated by the seismic vulnerability model, and the vulnerability curve of the rail transit network main structure conforms to the intermediate critical value of the ground motion intensity index IM of the rail transit network main structure at a certain performance level and the total lognormal standard deviation The normal distribution characteristics, and the calculation formula of the cumulative probability of the damage of the rail transit network main structure is as follows: ； In the above formula, is the probability that the structural seismic response of the main structure of the rail transit network exceeds a given performance level under a given ground motion intensity, is the seismic response of the structure under a given ground motion intensity, is the critical value of a given structural performance level, is the standard normal cumulative probability function, is the median critical value of the ground motion intensity indicator IM for the main structure of the rail transit network at a certain performance level, is the total lognormal standard deviation; Finally, the attenuation factor against seismic deterioration is introduced The intermediate critical value S of the ground motion intensity index IM for the rail transit network structure at a certain performance level im is modified to obtain the equivalent ground motion intensity for the remaining service life , which is expressed as ； In the above formula, is the peak ground acceleration (PGA) corresponding to the cumulative damage probability of 0.5 in the design reference period, is the design service life of the structure, is the remaining service life of the structure, satisfying , is the shape parameter of the extreme value type II distribution; thus, the cumulative probability calculation formula for the destruction of the main structure of the rail transit network is corrected for the service life.

5. The weighted fractal dimension-based seismic resilience assessment method for a metro network according to claim 1, wherein, The step (4) is based on the operational box dimension definition proposed by Mandelbrot to calculate the Hausdorff measure dimension; the specific process is: First, a specific station density value is selected as a screening threshold, and a greedy coloring method is used to realize network multi-scale box covering, and the box side length value will be an important quantitative index of the spatial fractal characteristics of the rail transit network; Secondly, according to the information dimension theory and the weighted network framework, under the grid coverage with the box size of , the probability measure calculation formula of the first coverage unit is as follows: ； In the above formula, F denotes a node, denotes the i-th covering box of size r, is a node strength measure, is the sum of the strengths of all nodes covered by the box i.e. ； In the above formula, The sum of the strengths of the nodes in the study range is, i.e.: ； In the above formula, Q k denotes the strength of the kth node, is the size the total number of boxes of the underlying network; Then, the Shannon entropy formula is used to represent the uncertainty of passenger flow distribution: The probability measure is introduced to improve the information dimension calculation, which can quantitatively reflect the passenger flow aggregation characteristics. The improved Shannon entropy calculation formula is as follows: ； Finally, the fractal dimension The improved box dimension calculation formula introducing the probability measure is as follows: 。 6. The weighted fractal dimension-based seismic resilience assessment method for a rail transit network according to claim 5, wherein, The network multi-scale box covering is implemented by using the optimal grid size algorithm, and the implementation method is as follows: (4.1) for each target average station number in the target average station number list, first calculate the required grid density, which is the total number of operating stations divided by the target average station number and then rounded up; then, the optimal grid side length is found by bisection method, which includes initializing the minimum side length, the maximum side length and the precision, and under the condition that the maximum side length minus the minimum side length is greater than the precision, the loop is executed: the intermediate side length is calculated as the average of the minimum side length and the maximum side length, the effective grid calculation function is called to obtain the number of effective grids, the current average station number is calculated as the total number of operating stations divided by the number of effective grids, and if the current average station number is greater than or equal to the target average station number, the maximum side length is updated to the minimum side length and the candidate side length is set to the intermediate side length, otherwise the intermediate side length is updated to the minimum side length; after the loop ends, the optimal side length is output; (4.2) when dividing the grid based on the optimal side length, the number of columns is calculated as the east-west span divided by the optimal row side length rounded up, the number of rows is calculated as the north-south span divided by the optimal column side length rounded up, and all grid cells are traversed: the geographical boundary of the cell is calculated, a geographical region object Box is created, a station area detection function is called to obtain a station list in the region, if the station list is not empty, a fractal box agent fBox is created, a bidirectional association between fBox and the station list is established, and the mapping from Box to fBox is registered to the dictionary, otherwise the empty region is discarded.

7. The weighted fractal dimension-based seismic resilience assessment method for a rail transit network according to claim 6, wherein, The implementation process of the effective grid calculation function is as follows: the number of columns is calculated as the east-west span divided by the intermediate row side length rounded up, the number of rows is calculated as the north-south span divided by the intermediate column side length rounded up, the effective counter is initialized to 0, and each grid cell is traversed to create a temporary geographical region region; if the station area detection function returns a non-empty list, the counter is incremented by 1, and finally the counter is returned; The implementation process of the station area detection function is as follows: an empty station list is initialized, all operating stations are traversed, and if the station coordinates are within the region boundary, the station list is added, and the station list is returned.

8. The weighted fractal dimension-based seismic resilience assessment method for a rail transit network according to claim 1, wherein, The specific process of step (5) is: First, using the impact simulation method described in step (3), at each time step of the simulation... Based on the weighted fractal dimension resilience calculation method in step (4), the time step is calculated. Dynamic weights and node strength Using the weighted fractal dimension resilience calculation method in step (4), the spatial fractal dimension of the network at that moment is solved. ; Then, for the continuously collected values of the system robustness performance based on the fractal dimension , a process function is constructed : ； wherein is the simulation time point; is the fractal dimension value calculated at the time instant; the function value is kept constant in the interval . Evaluation of process function , a four-dimensional index system is adopted, namely redundancy , robustness , efficiency and resilience loss . The redundancy , robustness , efficiency and resilience loss of rail transit network are described and characterized, which together reveal the functional state evolution and inherent resilience mechanism of rail transit network in the whole cycle of disaster. the redundancy amount The calculation formula is as follows: ； The redundancy quantifies the rail transit network at any time before or after a disaster its instantaneous level of functionality resources reserve margin beyond the minimum resilience threshold to meet basic needs ​ The robust quantity The formula for the calculation is as follows: ； Robustness measures focus on the limit state of disaster termination time The exact characterization of the instantaneous function retention level after the system withstands the impact, the value range of which inherently reflects the inherent anti-destroying strength of the system, that is, the core ability to resist destruction without collapse; The efficiency quantity The formula for calculating the efficiency quantity is as follows: ； The efficiency measure, as a joint measure of time and performance, synthetically evaluates the recovery performance of the system, where the key recovery time-to-restore is defined as the time needed to restore the performance to the original level of resilience and the steady-state recovery value reached by the system is denoted by The efficiency measure is calculated as an exponential function regulated by the coefficient emphasizing the sensitivity to the recovery rate, and a power-law term regulated by the coefficient taking into account the saturation characteristic of the final recovery degree. the amount of toughness loss The formula for calculating the amount of toughness loss is as follows: ； The amount of loss of resilience is calculated from the perspective of the cumulative damage, and the system functionality is calculated from the time of the disaster until the system sets the final deadline During this period, the actual functional level is lower than the basic requirement threshold R N gap area; Based on the above four-dimensional index system, the multi-dimensional evaluation index of system resilience is constructed The core is the decoupling analysis and collaborative integration of the multi-dimensional nature of resilience: ； In the formula, T is the total research duration, specifically the total simulation duration set in the simulation; the entropy weight method is used to weight That is, the weights of the four-dimensional indexes 、 、 and are calculated by using the entropy weight method to ensure the objective quantification of the contribution of each dimension and meet the constraint condition of .

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