Two-stage shock resistance toughness improvement decision-making method of subway system

Abstract

According to the two-stage anti-seismic toughness improvement decision-making method of the subway system, the pre-earthquake reinforcement optimization model is established, the pre-earthquake subway system information is collected, the optimal reinforcement strategy is obtained according to the pre-earthquake subway system information and the pre-earthquake reinforcement optimization model, and the influence of the earthquake on the subway assembly is reduced; the method comprises the following steps: establishing a post-earthquake recovery optimization model, collecting post-earthquake subway system information, obtaining a Pareto optimal solution set of a recovery strategy according to the post-earthquake subway system information and the post-earthquake recovery optimization model, selecting an optimal recovery strategy of a damaged subway assembly according to actual conditions, and accelerating the subway system function recovery speed; according to the two-stage anti-seismic toughness improvement decision-making method of the subway system, the anti-seismic toughness of the subway system is improved by improving the capability of maintaining the function of the subway system when the earthquake occurs and rapidly recovering the function after the earthquake occurs; and a method support is provided for the government and subway operation departments to make subway system shock resistance toughness improvement decisions.

Description

Technical Field

[0001] The present invention relates to the field of improving the seismic resilience of subway systems, and in particular to a two-stage seismic resilience improvement decision-making method for subway systems. Background Art

[0002] The subway system is a core component of the urban public transportation system, and its safety is crucial to the functional operation of the city. In recent years, with the acceleration of urbanization, the scale of the subway system has continued to expand, making its operation and management more complicated, which requires the subway system to have higher resilience to cope with various challenges. Earthquakes are one of the most far-reaching challenges to the subway system; in the past few decades, many earthquakes around the world have caused the function of the subway system to decline or even be interrupted, which not only caused huge economic losses, but also had a profound impact on the normal operation of the city; therefore, how to improve the seismic resilience of the subway system has become an important issue that needs to be solved urgently.

[0003] Before an earthquake occurs, seismic reinforcement of the subway system is one of the key measures to reduce earthquake damage. At present, the seismic reinforcement methods of the subway system are mainly focused on enhancing the seismic performance of a single subway structure, including the use of higher-strength building materials, improved structural design, and the addition of support and shock-absorbing devices. Although these seismic reinforcement measures can effectively improve the seismic performance of a single subway structure, they lack systematicity and integrity. After an earthquake, the rapid recovery of the subway system's functions is crucial to ensuring the normal operation of the city and the safe travel of residents. At present, the post-earthquake recovery methods of the subway system lack systematic planning, making it difficult to quickly and effectively restore the functions of the subway system. At the same time, the methods for improving the seismic resilience of the subway system are mostly concentrated in a single stage, lacking a comprehensive seismic resilience improvement strategy for the pre- and post-earthquake stages. Summary of the invention

[0004] In order to solve the problems in the prior art that the pre-earthquake seismic measures of the subway system lack systematicity and the efficiency of post-earthquake functional recovery of the subway is low, a two-stage seismic resilience improvement decision-making method for the subway system is provided; this method improves the ability of the subway system to maintain its function during an earthquake and quickly restore its function after an earthquake by formulating a reinforcement strategy in the pre-earthquake stage and a recovery strategy in the post-earthquake stage, thereby improving the seismic resilience of the subway system.

[0005] A two-stage seismic resilience improvement decision-making method for subway systems, comprising:

[0006] Step 1: Collect pre-earthquake subway system information and establish a pre-earthquake reinforcement optimization model;

[0007] Step 2: Obtain the optimal reinforcement strategy based on the pre-earthquake subway system information and the pre-earthquake reinforcement optimization model;

[0008] Step 3: Collect post-earthquake subway system information and establish a post-earthquake recovery optimization model;

[0009] Step 4: Obtain the Pareto optimal solution set of the optimal recovery strategy based on the post-earthquake subway system information and the post-earthquake recovery optimization model;

[0010] Step 5: Strengthen the subway system before the earthquake according to the optimal reinforcement strategy, and repair the subway system after the earthquake according to the Pareto optimal solution set of the optimal recovery strategy.

[0011] Beneficial Effects

[0012] The present application proposes a two-stage decision-making method for improving the seismic resilience of a subway system. Combined with the specific conditions of the subway system before an earthquake, a pre-earthquake reinforcement strategy for subway components in the subway system is formulated to reduce the impact of earthquakes on subway components; the damage conditions of subway components in the subway system after an earthquake are obtained, a repair strategy for damaged subway components is formulated, and the speed of functional recovery of the subway system is accelerated; the present application proposes a two-stage decision-making method for improving the seismic resilience of a subway system. By improving the ability of the subway system to maintain functions during an earthquake and to quickly restore functions after an earthquake, the seismic resilience of the subway system is improved, providing methodological support for the government and subway operating departments in making decisions on improving the seismic resilience of the subway system. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 A flowchart of a specific implementation method of this application;

[0014] Figure 2 A flowchart for obtaining the optimal reinforcement strategy for the specific implementation of this application;

[0015] Figure 3 A flowchart of a Pareto optimal solution set for a recovery strategy obtained for a specific implementation of the application;

[0016] Figure 4 The subway network topology diagram of the specific implementation method of this application and the spatial distribution of PGA under the action of earthquake;

[0017] Figure 5 A comparison of post-earthquake functional loss of the subway system before and after reinforcement according to a specific implementation method of this application;

[0018] Figure 6 A post-earthquake destruction scenario of a subway system according to a specific embodiment of the present application;

[0019] Figure 7 A Pareto optimal solution set of the recovery strategy of the specific implementation mode of this application;

[0020] Figure 8 Comparison of recovery curves between the optimal recovery strategy of the specific implementation of this application and the recovery strategy based on functional importance. DETAILED DESCRIPTION

[0021] The following will be combined Figures 1 to 8 , describing the present implementation mode, a two-stage seismic resilience improvement decision method for a subway system, comprising:

[0022] Step 1: Collect pre-earthquake subway system information and establish a pre-earthquake reinforcement optimization model;

[0023] Step 2: Obtain the optimal reinforcement strategy based on the pre-earthquake subway system information and the pre-earthquake reinforcement optimization model;

[0024] Step 3: Collect post-earthquake subway system information and establish a post-earthquake recovery optimization model;

[0025] Step 4: Obtain the Pareto optimal solution set of the recovery strategy based on the post-earthquake subway system information and the post-earthquake recovery optimization model;

[0026] Step 5: Strengthen the subway system before the earthquake according to the optimal reinforcement strategy, and repair the subway system after the earthquake according to the Pareto optimal solution set of the recovery strategy.

[0027] Specifically, the two-stage seismic resilience improvement decision-making method of the subway system of the present application is combined with the specific situation of the subway system before the earthquake, and a pre-earthquake reinforcement strategy for the subway components in the subway system is formulated. The optimal reinforcement strategy is obtained through a genetic algorithm to reduce the impact of the earthquake on the subway components; the damage situation of the subway components in the subway system after the earthquake is obtained, and a repair strategy for the damaged subway components is formulated. The Pareto optimal solution set of the recovery strategy is obtained through a non-dominated sorting genetic algorithm. The optimal recovery strategy is selected from the Pareto optimal solution set of the recovery strategy according to the actual situation, and the subway system is repaired after the earthquake according to the optimal recovery strategy to speed up the functional recovery of the subway system.

[0028] Furthermore, the pre-earthquake reinforcement optimization strategy is: RS = {rs1, rs2, L, rs N}, where rs k ∈{0,1},rs k =1 means subway component c k Reinforced, rs k =0 means subway component c k The set of all subway components in the subway system is denoted by C = {c1, c2, L, c N}.

[0029] Furthermore, the subway system includes multiple subway components, and the subway components are subway stations or station sections; the subway system information before the earthquake includes: the total number of subway components, the number of stations in the subway system, the number of reinforced subway components, the reinforcement improvement rate of each subway component, and the seismic vulnerability parameters of each subway component; the seismic vulnerability parameters include the median value and logarithmic standard deviation of the earthquake intensity parameters. Specifically, the specific situation of the subway system before the earthquake is obtained.

[0030] Specifically, an optimization strategy for pre-earthquake reinforcement is formulated based on the specific conditions of the subway before the earthquake.

[0031] Furthermore, the method of obtaining the optimal reinforcement strategy through genetic algorithm is:

[0032] S1, input the number of subway components to be reinforced and the seismic vulnerability parameters of each subway component before reinforcement into the genetic algorithm, set the first generation population size, maximum evolutionary generations, crossover rate and mutation rate;

[0033] S2, randomly generate a first generation population, which includes multiple individuals; each individual represents a pre-earthquake reinforcement optimization strategy; set the evolutionary generation Gen = 0;

[0034] S3. Calculate the average post-earthquake functional loss of each individual in the current generation population

[0035] S4. The individuals of the current generation population are divided according to the average post-earthquake functional loss. Sort by size, select D individuals, D is a positive integer, divide the selected D individuals into multiple groups, each group contains two individuals, and the individuals in each group perform crossover operation according to the set crossover rate to generate new offspring individuals; among the new offspring individuals, randomly select some individuals according to the set mutation rate to perform mutation operation to obtain a new generation of population; let Gen = Gen + 1;

[0036] S5. Determine whether Gen has reached the maximum evolutionary generation. If so, calculate the average post-earthquake functional loss of multiple subway systems. By comparison, the average post-earthquake functional loss of the subway system The pre-earthquake reinforcement optimization strategy corresponding to the minimum value is output as the optimal reinforcement strategy; otherwise, the process returns to step S3 and ends when the evolutionary generation reaches the set maximum evolutionary generation.

[0037] Specifically, a pre-seismic reinforcement optimization model for the subway system is established to minimize the average post-seismic functional loss of the subway system under a given earthquake. In order to optimize the target, a genetic algorithm (GA) is used to solve the pre-seismic reinforcement optimization model of the subway system and obtain the optimal reinforcement strategy of the subway system, which is used to guide the pre-seismic reinforcement work of the subway system.

[0038] Furthermore, the average post-earthquake functional loss The calculation method is:

[0039] Set the earthquake intensity parameter value IM, the number of subway system destruction scenarios M s , the number of damage states of each subway component is N DS , the number of subway components to be reinforced is recorded as N RS , N is the total number of subway components; i∈{1,2,L,M s},l∈{1,2,L,N DS}

[0040] Calculate subway component c k The damage state DS under the i-th damage scenario k ;

[0041] Where r is a random number uniformly distributed on [0,1]; For subway components c k The probability of reaching the lth damage state;

[0042] Where Ф[·] represents the standard normal cumulative distribution function, S m,k,l and β k,l are the subway components c in the lth damage state respectively. k Median value and logarithmic standard deviation of seismic intensity parameters before reinforcement; subway component c k The median value of the earthquake intensity parameter before reinforcement is S m,k =(S m,k,1 ,S m,k,2 ,L,S m,k,NDS ), subway component c k The logarithmic standard deviation of the ground motion intensity parameter before reinforcement is β k =(β k,1 ,β k,2 ,L,β k,NDS );

[0043] Set subway component c k The reinforcement improvement rate corresponding to the lth damage state is w k,l , w k,l >1; Calculate the reinforced subway component c in the lth damage state k Median value of earthquake vulnerability function The logarithmic standard deviation β of the seismic vulnerability function of subway components before and after reinforcement remains unchanged. k The reinforcement improvement rate wk =(w k,1 ,w k,2 ,L,w k,NDS );

[0044] Calculate the post-earthquake residual function ratio (RFI) of the subway system under the i-th damage scenario i , Among them, FI pre The pre-seismic function of the subway system, FI post is the post-earthquake function of the subway system under the i-th damage scenario;

[0045]

[0046]

[0047] Where n is the number of stations in the subway system n≤N, ω s For subway components c s The weight is equal to the subway component c s Ratio to the number of passengers served by the subway system; For subway components c z The weight is equal to the subway component c z Ratio to the number of passengers served by the subway system; c s ∈C, c z ∈C, subway component c s and subway component c z For the station; For subway components c s The pre-seismic function For subway components c s The residual function after the earthquake, when the subway component c s When the damage state is DS0 or DS1 otherwise and They are the subway components c before and after the earthquake. s To subway component c z The probability of selecting the hth valid path; and The subway components c before and after the earthquake s To subway component c z The travel time of the hth effective path; H represents the travel time from subway component c s To subway component c z The number of valid paths;

[0048] According to the post-earthquake residual function ratio RFI of the subway system under the i-th damage scenario i Calculate the average post-earthquake functional loss of the subway system

[0049]

[0050] Furthermore, the post-earthquake recovery optimization strategy is: the repair sequence of damaged subway components is X, where X = {x1, x2, L, x m}, where x j ∈C,x a ∈C,x a ≠x j , a,j∈{1,2,L,m}, m≤N, and m is the number of damaged subway components.

[0051] Furthermore, the post-earthquake subway system information includes: the number of damaged subway components, the post-earthquake damage status of each damaged subway component, the repair duration of each damaged subway component, and the maximum number of components allowed to be repaired simultaneously.

[0052] Furthermore, in step 4, the method for obtaining the Pareto optimal solution set of the recovery strategy based on the post-earthquake subway system information and the post-earthquake recovery optimization model is as follows:

[0053] S1. Input the damage state of each damaged subway component, the repair duration of each damaged subway component and the maximum number of components allowed to be repaired simultaneously into the non-dominated sorting genetic algorithm; set the first generation population size, the maximum number of evolution generations, the crossover rate and the mutation rate;

[0054] S2, randomly generate a first generation population, which includes multiple individuals, each of which represents a post-earthquake recovery optimization strategy; set the evolutionary generation Gen=0;

[0055] S3. Calculate the total recovery time TRT and resilience loss factor R of each individual in the current generation population L ;

[0056] S4, perform non-dominance calculation on each individual in the current generation population to obtain the non-dominance degree of each individual, sort each individual from large to small according to the obtained multiple non-dominance degrees, and select the first E1 individuals with large non-dominance degrees; calculate the crowding degrees of the selected E1 individuals respectively, and sort the E1 individuals from large to small according to the crowding degrees of each individual, and select the first E2 individuals with large crowding degrees; divide the selected E2 individuals into multiple groups, each group contains two individuals, and the individuals in each group are crossovered according to the set crossover rate, and some individuals are randomly selected from the crossover individuals according to the set mutation rate to perform mutation operations to obtain offspring individuals; merge the parent and offspring individuals into a new population, and generate the next generation population according to the non-dominance sorting and crowding degree distance, and the size of the next generation population is the same as that of the previous generation; let Gen = Gen + 1;

[0057] S5. Determine whether Gen has reached the maximum evolutionary generation. If so, calculate the multiple total recovery times TRT and multiple toughness loss factors R L The Pareto optimal solution set of the recovery strategy is obtained through the Pareto optimal allocation strategy, and the Pareto optimal solution set of the recovery strategy includes multiple post-earthquake recovery optimization strategies; if not, return to step S3 until the evolutionary generation reaches the set maximum evolutionary generation.

[0058] Furthermore, the total recovery time TRT is calculated as follows:

[0059] The post-earthquake damage state of the damaged subway components corresponding to the repair sequence X of the damaged subway components is recorded as The duration of repair of damaged subway components is recorded as The repair start time of the damaged subway components corresponding to the repair sequence X of the damaged subway components is recorded as

[0060] Among them, damaged subway components x j The repair start time is Damaged subway componentsx j The repair duration is t0 is the time when the earthquake starts;

[0061] The total recovery time TRT of the post-earthquake subway system is obtained according to the repair start time and repair duration corresponding to X;

[0062]

[0063] The toughness loss factor R L The calculation method is:

[0064] Where RFI(t) is the residual function ratio of the subway system at time t, RE When the repair is finished,

[0065] Among them, FI pre The pre-seismic function of the subway system, FI post (t) is the function of the subway system at time t;

[0066]

[0067]

[0068] n is the number of stations in the subway system n≤N, For damaged subway components x s The weight of For damaged subway components xz The weight of x s ∈C,x z ∈C, subway component x s and Metro Components x z For the station; and The damaged subway components are x s and x z The pre-seismic function Subway components damaged before the earthquake s To Metro Components x z The probability of selecting the g-th valid path; Subway components damaged before the earthquake s To damaged subway components x z The travel time of the g-th valid path; and The damaged subway components are x s and x z The residual capacity after the earthquake at time t is Damaged subway componentsx s of otherwise when Damaged subway componentsx z of otherwise is the damaged subway component x at time t s To Metro Components x z The probability of selecting the g-th valid path; is the damaged subway component x at time t s To damaged subway components x z The travel time of the g-th effective path; G represents the travel time from the damaged subway component x s To damaged subway components x z The number of valid paths.

[0069] Specifically, the function of the damaged subway component remains unchanged until the repair is completed. Once the subway component begins to be repaired, the repair work will continue until the subway component is restored to the pre-earthquake functional level; at time t, the subway component x j Functional status FS(x j ,t) is calculated as: in and They are subway components x j pre- and post-earthquake functional status;

[0070] The number of subway components N that are repaired simultaneously during the repair process t The calculation formula is: in The maximum number of components allowed to be repaired simultaneously; [] represents Iverson brackets. When Y is true, [Y] = 1, otherwise [Y] = 0.

[0071] The two-stage seismic resilience improvement decision-making method for a subway system of the present application can be used as a two-stage seismic resilience improvement decision-making method, or it can be split into two seismic resilience improvement decision-making methods according to the pre-earthquake and post-earthquake stages and used independently.

[0072] Specific embodiment: Taking a subway system as an example, the network topology diagram of the subway system is as follows: Figure 4 As shown in the figure, a deterministic method was used to determine the set earthquake used in the analysis based on historical earthquakes. The magnitude of the set earthquake was 6.5, which is one of the most destructive earthquakes in history that occurred in the area where the subway system is located. The epicenter is as follows: Figure 4 As shown in the figure, the spatial distribution of the peak acceleration PGA under earthquake action is assumed to be Figure 4 As shown;

[0073] Number of reinforced subway components N RS Set to 100, the reinforcement improvement rate w corresponding to each damage state of different subway components i are all set to 1.5; the seismic vulnerability parameters of subway components before reinforcement are shown in Table 3, where DS1, DS2, DS3 and DS4 represent slight damage, moderate damage, severe damage and complete damage, respectively. The damage states of subway stations are divided into slight damage (DS1), moderate damage (DS2), severe damage (DS3) and complete damage (DS4), that is, the number of damage states of subway stations N DS 4; minor damage refers to slight cracks and local deformations in the station structure, but the main functions of the station can still be maintained; moderate damage refers to obvious damage to the station structure, such as larger cracks, local buckling, partial failure of supporting components, etc.; severe damage refers to serious damage to the station structure, including significant failure, large-area buckling or deformation of the main load-bearing components (such as columns and beams, etc.); complete damage refers to complete failure of the station structure; basically intact (DS0) means that the station structure has not been significantly damaged or deformed, and all the functions of the station remain normal.

[0074] The damage status of the subway section is divided into slight damage (DS1), moderate damage (DS2), severe damage (DS3) and complete damage (DS4), that is, the number of damage status N of the subway section DS=4; slight damage means that the interval structure has slight cracks and local deformation, and the train operation will not be significantly affected; moderate damage means that the interval structure is obviously damaged, such as large cracks, local buckling, partial failure of supporting components, etc.; severe damage means that the interval structure is seriously damaged, including large-scale failure, obvious deformation, and serious leakage of major load-bearing components (such as lining, arch, side wall, bridge pier, etc.); complete damage means that the interval structure is completely failed; basically intact (DS0) means that the interval structure is not damaged or deformed, all functions of the interval remain normal, and train operation and passenger safety are not affected in any way; As shown in Table 1, the pre-seismic reinforcement optimization model of the subway system is established;

[0075] Table 1 Pre-seismic reinforcement optimization model for subway system

[0076]

[0077] The parameters of the GA genetic algorithm are set as follows: the population size, maximum evolutionary generations, crossover rate, and mutation rate are set to 500, 200, 0.9, and 0.8, respectively, and the number of subway system destruction scenarios under earthquake action is set to M. s =500, calculate the post-earthquake residual function ratio RFI of the subway system under the i-th damage scenario i , the subway system function loss FL corresponding to the destruction scenario i i =1-RFI i .

[0078] The optimal reinforcement strategy is obtained through GA genetic algorithm based on the pre-earthquake subway system information and pre-earthquake reinforcement optimization model; Figure 5 The post-earthquake functional losses of the subway system under the action of a 6.5-magnitude earthquake are given in three cases: before reinforcement, using a reinforcement strategy based on functional importance, and using an optimal reinforcement strategy. The reinforcement strategy based on functional importance is formulated according to the functional importance of subway components. The calculation formula for the functional importance CFI of subway components is:

[0079]

[0080] In the formula, CFI(c b ) is the subway component c b The functional importance coefficient of B represents a subway system in which all components function normally, and B' represents a subway component c b Loss of functionality, other subway components function normally, FI B For the function of subway system B, FI B' For the function of subway system B';

[0081] from Figure 5It can be obtained that the average post-earthquake functional loss of the subway system before reinforcement is 0.3671, and the average post-earthquake functional loss of the subway system after reinforcement using the reinforcement strategy based on functional importance and the optimal reinforcement strategy are 0.3159 and 0.2787 respectively. Compared with before reinforcement, the average post-earthquake functional loss decreased by 13.97% and 24.09% respectively. This shows that the optimal reinforcement strategy obtained based on the pre-earthquake reinforcement optimization model proposed in this invention can more effectively improve the post-earthquake function of the subway system.

[0082] Table 3 Seismic vulnerability parameters of subway components (PGA:g)

[0083]

[0084] After an earthquake, the number of damaged subway components and the damage status of each subway component are determined through subway component damage assessment, such as Figure 6 As shown; Figure 6 DS0, DS1, DS2, DS3 and DS4 represent basically intact, slightly damaged, moderately damaged, severely damaged and completely damaged respectively. A total of 281 subway components need to be repaired.

[0085] The repair duration of the damaged subway components is determined according to the damage state of the subway components and Table 4. After the evaluation of the available repair resources, the maximum number of components that can be repaired simultaneously is determined by the available resources of the subway system. It is set to 5, and the post-earthquake recovery optimization model of the subway system is established, as shown in Table 2;

[0086] Table 2 Post-earthquake recovery optimization model for subway system

[0087]

[0088]

[0089] The parameters of the non-dominated sorting genetic algorithm NSGA-II are set as follows: the population size is 500, the maximum evolutionary number is 200, the crossover rate is 0.9, and the mutation rate is 0.8. NSGA-II is used to solve the post-earthquake recovery optimization model of the subway system, and the Pareto optimal solution set of the post-earthquake recovery strategy of the subway system is obtained, which includes 83 optimal recovery strategies, such as Figure 7 As shown, three optimal recovery strategies are selected from the Pareto optimal solution set, such as Figure 7 The ORS1, ORS2 and ORS3 in the figure are compared with the restoration strategy based on functional importance (denoted as FIRS). The restoration order of components in the restoration strategy based on functional importance is determined according to the functional importance CFI of subway components. The restoration curves of the three ORS and FIRS are shown in Figure 2. Figure 8 shown; from Figure 8It can be seen that compared with the recovery curve of FIRS, the recovery curves of the three ORSs have maintained higher recovery efficiency in the early stage of the recovery process. The total recovery time TRT of ORS3 and FIRS is the same, but the toughness loss R of FIRS is L It is 38.3% higher than that of ORS3, which shows that the optimal recovery strategy obtained based on the post-earthquake recovery optimization model proposed in the present invention can more effectively reduce the resilience loss of the subway system.

Claims

1. A two-stage seismic resilience improvement decision-making method for subway systems. Features: include: Step 1: Collect pre-earthquake subway system information and establish a pre-earthquake reinforcement optimization model; Step 2: Obtain the optimal reinforcement strategy based on the pre-earthquake subway system information and the pre-earthquake reinforcement optimization model; Step 3: Collect post-earthquake subway system information and establish a post-earthquake recovery optimization model; Step 4: Obtain the Pareto optimal solution set of the recovery strategy based on the post-earthquake subway system information and the post-earthquake recovery optimization model; Step 5: Pre-earthquake reinforcement of the subway system is carried out according to the optimal reinforcement strategy, and post-earthquake repair of the subway system is carried out according to the Pareto optimal solution set of the recovery strategy.

2. A two-stage seismic resilience improvement decision-making method for a subway system according to claim 1, Features: The subway system includes multiple subway components, which are subway stations or station sections; the pre-earthquake subway system information includes: the number of stations in the subway system, the number of reinforced subway components, the reinforcement improvement rate of each subway component and the seismic vulnerability parameters of each subway component before reinforcement; the seismic vulnerability parameters include the median value and logarithmic standard deviation of the seismic motion intensity parameters.

3. A two-stage seismic resilience improvement decision-making method for a subway system according to claim 2, Features: The pre-earthquake reinforcement optimization model is: RS = {rs 1 ,rs 2 ,…,rs N }, where rs k ∈{0,1}, rsk=1 represents the subway component c k Reinforced, rs k =0 means subway component c k Not reinforced, the set of all subway components in the subway system is denoted by C = {c 1 ,c 2 ,…,c N }, c k ∈C, N is the total number of subway components.

4. A two-stage seismic resilience improvement decision-making method for a subway system according to claim 3, Features: Step 2: The method for obtaining the optimal reinforcement strategy based on the pre-earthquake subway system information and the pre-earthquake reinforcement optimization model is as follows: S1, input the number of subway components to be reinforced and the seismic vulnerability parameters of each subway component before reinforcement into the genetic algorithm, set the first generation population size, maximum evolutionary generations, crossover rate and mutation rate; S2, randomly generate a first-generation population, which includes multiple individuals; each individual represents a pre-earthquake reinforcement optimization strategy; Set evolution generation Gen = 0; S3. Calculate the average post-earthquake functional loss of each individual in the current generation population S4. The individuals of the current generation population are divided according to the average post-earthquake functional loss. Sort by size, select D individuals, where D is a positive integer; divide the selected D individuals into multiple groups, each group contains two individuals, and the individuals in each group perform crossover operations according to the set crossover rate to generate new offspring individuals; among the new offspring individuals, randomly select some individuals according to the set mutation rate to perform mutation operations to obtain a new generation of population; let Gen = Gen + 1; S5. Determine whether Gen has reached the maximum evolutionary generation. If so, calculate the average post-earthquake functional loss of multiple subway systems. By comparison, the average post-earthquake functional loss of the subway system The pre-earthquake reinforcement optimization strategy corresponding to the minimum value is output as the optimal reinforcement strategy; otherwise, the process returns to step S3 and ends when the evolutionary generation reaches the set maximum evolutionary generation.

5. A two-stage seismic resilience improvement decision-making method for a subway system according to claim 4, Features: Average post-earthquake functional loss The calculation method is: Set the earthquake intensity parameter value IM, the number of subway system destruction scenarios M s and the number of damage states N of each subway component DS , the number of subway components to be reinforced is recorded as N RS , N is the total number of subway components; i∈{1,2,…,M s },l∈{1,2,…,N DS } Calculate subway component c k The damage state DS under the i-th damage scenario k ; Where r is a random number uniformly distributed on [0,1]; For subway components c k The probability of reaching the lth damage state; Where Ф[·] represents the standard normal cumulative distribution function, S m,k,l and β k,l are the subway components c in the lth damage state respectively. k The median value of the seismic intensity parameter before reinforcement and the logarithmic standard deviation of the seismic intensity parameter; the median value of the seismic intensity parameter of the subway component ck before reinforcement is S m,k =(S m,k,1 ,S m,k,2 ,…,S m,k,NDS ), subway component c k The logarithmic standard deviation of the ground motion intensity parameter before reinforcement is β k =(β k,1 ,β k,2 ,…,β k,NDS ); Calculate the post-earthquake residual function ratio (RFI) of the subway system under the i-th damage scenario i , Among them, FI pre The pre-seismic function of the subway system, FI post is the post-earthquake function of the subway system under the i-th damage scenario; Where n is the number of stations in the subway system n≤N, For subway components c s The weight of For subway components c z The weight of s ∈C,c z ∈C, subway component c s and subway component c z For the station; For subway components c s The pre-seismic function For subway components c s The residual function after the earthquake, when the subway component c s The post-earthquake damage state is DS 0 or DS 1 hour otherwise and The subway components c before and after the earthquake s To subway component c z The probability of selecting the hth valid path; and The subway components c before and after the earthquake s To subway component c z The travel time of the hth effective path; H represents the travel time from subway component c s To subway component c z The number of valid paths; According to the post-earthquake residual function ratio RFI of the subway system under the i-th damage scenario i Calculate the average post-earthquake functional loss of the subway system 6. A two-stage seismic resilience improvement decision-making method for a subway system according to claim 1, Features: Post-earthquake subway system information includes: the number of damaged subway components, the post-earthquake damage status of each damaged subway component, the repair duration of each damaged subway component, and the maximum number of components allowed to be repaired simultaneously.

7. A two-stage seismic resilience improvement decision-making method for a subway system according to claim 6, Features: The post-earthquake recovery optimization model is: the repair sequence of damaged subway components is X, X = {x 1 ,x 2 ,…,x m }, where x j ∈C,x a ∈C,x a ≠x j , a,j∈{1,2,…,m}, m≤N, and m is the number of damaged subway components.

8. A two-stage seismic resilience improvement decision-making method for a subway system according to claim 7, Features: Step 4: The method for obtaining the Pareto optimal solution set of the recovery strategy based on the post-earthquake subway system information and the post-earthquake recovery optimization model is as follows: S1. Input the damage state of each damaged subway component, the repair duration of each damaged subway component and the maximum number of components allowed to be repaired simultaneously into the non-dominated sorting genetic algorithm; set the first generation population size, the maximum number of evolution generations, the crossover rate and the mutation rate; S2, randomly generate a first-generation population, which includes multiple individuals, each of which represents a post-earthquake recovery optimization strategy; Set evolution generation Gen = 0; S3. Calculate the total recovery time TRT and resilience loss factor R of each individual in the current generation population L ; S4, perform non-dominance calculation on each individual in the current generation population to obtain the non-dominance degree of each individual, sort the individuals from large to small according to the obtained multiple non-dominance degrees, and select the first E1 individuals with large non-dominance degrees; Calculate the crowding degree of the selected E1 individuals respectively, and sort the E1 individuals from large to small according to the crowding degree of each individual, and select the first E2 individuals with large crowding degree, where E1 and E2 are positive integers and E1>E2; divide the selected E2 individuals into multiple groups, each group contains two individuals, and the individuals in each group are crossovered according to the set crossover rate, and randomly select some individuals after the crossover according to the set mutation rate to perform mutation operation to obtain offspring individuals; merge the parent and offspring individuals into a new population, and generate the next generation population according to the non-dominated sorting and crowding distance, and the size of the next generation population is the same as that of the previous generation; let Gen=Gen+1; S5. Determine whether Gen has reached the maximum evolutionary generation. If so, calculate the multiple total recovery times TRT and multiple toughness loss factors R L The Pareto optimal solution set of the recovery strategy is obtained through the Pareto optimal allocation strategy, and the Pareto optimal solution set of the recovery strategy includes multiple post-earthquake recovery optimization strategies; if not, return to step S3 until the evolutionary generation reaches the set maximum evolutionary generation.

9. A two-stage seismic resilience improvement decision-making method for a subway system according to claim 8, Features: The total recovery time TRT is calculated as follows: The post-earthquake damage state of the damaged subway components corresponding to the repair sequence X of the damaged subway components is recorded as The duration of repair of damaged subway components is recorded as The repair start time of the damaged subway components corresponding to the repair sequence X of the damaged subway components is recorded as Among them, damaged subway components x j The repair start time is Damaged subway componentsx j The repair duration is t 0 The moment when the earthquake started; The total recovery time TRT of the post-earthquake subway system is obtained according to the repair start time and repair duration corresponding to X; The toughness loss factor R L The calculation method is: Where RFI(t) is the residual function ratio of the subway system at time t, RE When the repair is finished, Among them, FI pre The pre-seismic function of the subway system, FI post (t) is the function of the subway system at time t; n is the number of stations in the subway system n≤N, For damaged subway components x s The weight of For damaged subway components x z The weight of x s ∈C,x z ∈C, subway component x s and Metro Components x z For the station; and The damaged subway components are x s and x z The pre-seismic function Subway components damaged before the earthquake s To Metro Components x z The probability of selecting the g-th valid path; Subway components damaged before the earthquake s To damaged subway components x z The travel time of the g-th valid path; and The damaged subway components are x s and x z The residual capacity after the earthquake at time t is Damaged subway componentsx s of otherwise when Damaged subway componentsx z of otherwise is the damaged subway component x at time t s To Metro Components x z The probability of selecting the g-th valid path; is the damaged subway component x at time t s To damaged subway components x z The travel time of the g-th effective path; G represents the travel time from the damaged subway component x s To damaged subway components x z The number of valid paths.

10. A two-stage seismic resilience improvement decision-making method for a subway system according to claim 9, Features: Number of subway components repaired simultaneously during post-earthquake repair in The maximum number of components that can be repaired simultaneously; [] represents Iverson brackets. When Y is true, [Y] = 1, otherwise [Y] = 0.

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